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astro-ph0603249

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we performed a large number of axisymmetric mhd simulations and did extensive analysis of the interaction of a rapidly rotating magnetized star with an accretion disk in the propeller regime . the results can be divided to two classes , strong " propellers and weak " propellers . the strong " propeller is characterized by the intense , wide - angle , conical matter outflow in the vicinity of the neutral line of the poloidal magnetic field and formation of well collimated , magnetically dominated jets along the rotational axis . in the weak " propeller regime there are no appreciable matter outflows from the disk and the collimated flow along the axis is much weaker . in this work the four main parameters of the model were varied : the magnetic moment of the star , its angular velocity , and @xmath387 coefficients of the kinematic viscosity and magnetic diffusivity . we calculated time - averaged total fluxes of matter , energy , and angular momentum and investigated their dependences on the main parameters of the model . the average characteristics were calculated during @xmath388 periods of rotation of the inner disk . the derived dependences were approximated in most cases by power law functions . but some dependences showed a threshold character with the flux becoming negligible for a range of the parameters . in all cases the interaction of the magnetized star with the accretion disk showed strongly non - stationary , quasi - periodic character . for example , in the reference case described in the paper , the typical period " of oscillations is several tens of our time - units . all fluxes of matter , energy , and angular momentum to the wind , jet , and star oscillate strongly with time . our simulation results are applied to classical t tauri stars and to millisecond pulsars . we conclude that propeller mechanism may be responsible for fast spinning - down of cttss to presently observed slow rotation during the first @xmath389 years of their evolution . in the case of accreting , magnetized millisecond pulsars , the propeller mechanism may be responsible for relatively fast spin - down during periods of lower accretion . this work was supported in part by nasa grants nag5 - 13220 , nag5 - 13060 , nng05gg77 g , by nsf grants ast-0307817 , ast-0507760 and by the crdf grant kp2 - 2555-al-03 . avk and gvu were partially supported by the grant rfbr 06 - 02 - 16608 . romanova , m.m . , ustyugova , g.v . , koldoba , a.v . , & lovelace , r.v.e . 2004b , apj , 616 , l151 ( rukl04 ) romanova , m.m . , ustyugova , g.v . , koldoba , a.v . , & lovelace , r.v.e . 2005 , apj , 635 , l165 ( rukl05 ) shakura , n.i . , & sunyaev r.a . 1973 , a & a , 1973 , 24 , 337

we present results of axisymmetric magnetohydrodynamic simulations of the interaction of a rapidly rotating , magnetized star with an accretion disk . the strong propellers are characterized by a powerful disk wind and a collimated magnetically dominated outflow or jet from the star . . the propeller mechanism may be responsible for the fast spinning - down of the classical t tauri stars in the initial stages of their evolution , and for the spinning - down of accreting millisecond pulsars .

we present results of axisymmetric magnetohydrodynamic simulations of the interaction of a rapidly rotating , magnetized star with an accretion disk . the disk is considered to have a finite viscosity and magnetic diffusivity . the main parameters of the system are the star s angular velocity and magnetic moment , and the disk s viscosity and diffusivity . we focus on the propeller " regime where the inner radius of the disk is larger than the corotation radius . two types of magnetohydrodynamic flows have been found as a result of simulations : weak " and strong " propellers . the strong propellers are characterized by a powerful disk wind and a collimated magnetically dominated outflow or jet from the star . the weak propellers have only weak outflows . we investigated the time - averaged characteristics of the interaction between the main elements of the system , the star , the disk , the wind from the disk , and the jet . rates of exchange of mass and angular momentum between the elements of the system are derived as a function of the main parameters . the propeller mechanism may be responsible for the fast spinning - down of the classical t tauri stars in the initial stages of their evolution , and for the spinning - down of accreting millisecond pulsars . = cmmib10 at 10pt

1507.03017

i

star - forming galaxies show a relatively tight correlation between their star - formation rate ( sfr ) and stellar mass . this relation , commonly known as the star - forming _ `` main sequence '' _ @xcite , has been intensively studied over the past decade ( e.g. , at @xmath8 , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . the main sequence is generally assumed to be a linear relation between log(sfr ) and log(@xmath0 ) with an associated scatter due to observational uncertainties and intrinsic scatter . the slope of the relation tells us about star formation efficiency as a function of stellar mass @xcite . the intrinsic scatter of the log(sfr)-log(@xmath0 ) relation is predicted to be due to variations in the gas accretion histories of different galaxies @xcite and indicates the level of burstiness in star formation history . the common physical interpretation of the tightness of the sfr-@xmath0 relation is that the bulk of the stellar mass in star - forming galaxies is built in a relatively steady process , as opposed to a rapid starburst mode , as occurs in major mergers . the merger - driven starburst galaxies with high specific sfrs tend to lie above the main sequence relation @xcite and the quiescent galaxies that have little ongoing star formation , identified by their red near - infrared colors @xcite , populate a region below the sequence @xcite . it has been argued that the majority of galaxies spend most of their lifetime on the main sequence @xcite . therefore , studying the parameters of the main sequence and comparing them with the galaxy formation models can shed light on our understanding of processes that govern galaxy evolution , such as stellar and agn feedback @xcite , gas accretion rates @xcite , and gas inflows and outflows @xcite . the sfr-@xmath0 relation can be used as a test for galaxy evolution simulations to see how well the simulations can reproduce the observed universe ( e.g. , * ? ? ? determining the slope and intrinsic scatter of the log(sfr)-log(@xmath0 ) relation can be hindered by sample selection effects , the diagnostic used to infer the sfr , and the method used to correct observed sfr for dust attenuation ( for a summary see , * ? ? ? the uv - selected samples and the uv - inferred sfrs are biased against massive and dusty galaxies where the bulk of star formation is obscured and the uv slope is decoupled from extinction . moreover , as sed- and uv - based sfrs are dependent on the same stellar population models used to infer the stellar masses , the scatter in the log(sfr)-log(@xmath0 ) relation may be underestimated when using sed or uv based sfr tracers @xcite . in order to overcome this issue , and more robustly measure sfrs for dustier galaxies , some studies have used sfr(ir)+sfr(uv ) as a proxy for bolometric sfr ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? however , estimating the sfr(ir ) based solely on _ spitzer_/mips 24@xmath9 m imaging has its shortcomings and could artificially tighten the main sequence if the scatter in l(ir ) at a given l(@xmath10 m ) luminosity is not taken into account ( e.g. , * ? ? ? * ; * ? ? ? we improve upon previous high - redshift studies by utilizing a representative sample of galaxies with measurements of the h@xmath3 and h@xmath4 emission lines . these lines offer the advantage of probing star formation on shorter timescales than the uv and ir , they are largely independent of the stellar population , and thus can be used to more accurately assess the intrinsic scatter in the log(sfr)-log(@xmath0 ) relation . the star - formation activity was at its peak at @xmath8 @xcite , making that redshift a critical epoch to study the evolution of galaxies . obtaining rest - frame optical spectra of large samples of galaxies at @xmath8 has been challenging until recently due to the high terrestrial background in the near - ir and the lack of multi - object near - ir spectrographs on 10-meter - class telescopes . the newly - commissioned mosfire spectrograph @xcite on the 10 m keck i telescope has enabled us to build a large sample of galaxies at @xmath8 with coverage in both the h@xmath3 and h@xmath4 lines . in this study , we use a large sample of 261 rest - frame optically selected and spectroscopically confirmed galaxies at @xmath11 , which was obtained as part of the mosfire deep evolution field ( mosdef ) survey @xcite . to study the sfr-@xmath0 relation , we use sfrs based on the h@xmath3 luminosity that are robustly corrected for dust attenuation using the balmer decrement ( l(h@xmath3)/l(h@xmath4 ) ) . we demonstrate how different sfr diagnostics and dust correction recipes can alter the slope and scatter of the log(sfr)-log(@xmath0 ) relation , and thus potentially affect our conclusions regarding the way in which galaxies build up their stellar mass at high redshift . the outline of this paper is as follows . in section [ sec : sample ] , we present our sample properties and our measurements including sfrs and stellar masses . in section [ sec : ms_analysis ] , we describe the methodology we used to derive the log(sfr)-log(@xmath0 ) relation parameters . we compare the scatter of the log(sfr)-log(@xmath0 ) relation for different sfr indicators in section [ sec : scatter ] . in section [ sec : slope ] , we discuss the slope of the log(sfr)-log(@xmath0 ) relation and the potential biases arising from sample selection , dust correction , and balmer absorption correction . we compare our findings to previous studies in section [ sec : compare ] , and finally , the results are summarized in section [ sec : summary ] . throughout this paper , a @xcite initial mass function ( imf ) is assumed and a cosmology with h@xmath12 = 70 km s@xmath13 mpc@xmath13 , @xmath14 = 0.7 , and @xmath15 = 0.3 is adopted .

we present results on the star - formation rate ( sfr ) versus stellar mass ( ) relation ( i.e. , the `` main sequence '' ) among star - forming galaxies at 1.37.61 using the mosfire deep evolution field ( mosdef ) survey . based on a sample of 261 galaxies with h and h spectroscopy , we have estimated robust dust - corrected instantaneous sfrs over a large range in ( ) . our sample is immune from these biases as it is rest - frame optically selected , h and h are corrected for balmer absorption , and the h luminosity is dust - corrected using the nebular color - excess computed from the balmer decrement .

we present results on the star - formation rate ( sfr ) versus stellar mass ( ) relation ( i.e. , the `` main sequence '' ) among star - forming galaxies at 1.37.61 using the mosfire deep evolution field ( mosdef ) survey . based on a sample of 261 galaxies with h and h spectroscopy , we have estimated robust dust - corrected instantaneous sfrs over a large range in ( ) . we find a correlation between log(sfr(h ) ) and log( ) with a slope of 0.65.08 ( 0.58.10 ) at 1.4.6 ( 2.1.6 ) . we find that different assumptions for the dust correction , such as using the color - excess of the stellar continuum to correct the nebular lines , sample selection biases against red star - forming galaxies , and not accounting for balmer absorption can yield steeper slopes of the log(sfr)-log( ) relation . our sample is immune from these biases as it is rest - frame optically selected , h and h are corrected for balmer absorption , and the h luminosity is dust - corrected using the nebular color - excess computed from the balmer decrement . the scatter of the log(sfr(h))-log( ) relation , after accounting for the measurement uncertainties , is 0.31dex at 2.1.6 , which is 0.05dex larger than the scatter in log(sfr(uv))-log( ) . based on comparisons to a simulated sfr- relation with some intrinsic scatter , we argue that in the absence of direct measurements of galaxy - to - galaxy variations in the attenuation / extinction curves and the imf , one can not use the difference in the scatter of the sfr(h)- and sfr(uv)- relations to constrain the stochasticity of star formation in high - redshift galaxies .

1507.03017

c

as part of the mosdef survey , we used a sample of 185 star - forming galaxies with h@xmath3 and h@xmath4 spectroscopy at @xmath49 to study the star - forming main sequence relation at @xmath8 . the parent catalog is _ h_-band ( i.e. , rest - frame optically ) selected and is accompanied by ancillary multi - band photometry @xcite , from which the uv - based sfrs were measured . the stellar masses were derived by comparing the emission - line corrected photometric seds with stellar population models . after taking into account the measurement uncertainties in the sfr and stellar mass , we found a measurement - subtracted scatter of 0.31dex in the log(sfr(h@xmath3))-log(@xmath0 ) relation at @xmath137 , which is 0.06dex larger than what we found based on the uv sfrs ( see , table [ tab : param ] ) . although in theory the time - scale variations in sfr can be traced by using different sfr diagnostics , such as uv and h@xmath3 , in the sfr-@xmath0 relation @xcite , we argue that in the absence of direct measurements of galaxy - to - galaxy variations in the attenuation curves and the imf , the difference in the scatter of the log(sfr(h@xmath3))-log(@xmath0 ) relation and the scatter of the log(sfr(uv))-log(@xmath0 ) relation can not be used to constrain the stochasticity of star formation . given these variations , the sfr(uv ) scatter could be as large or greater than the sfr(h@xmath3 ) scatter . theorists trying to reproduce the observed scatter in the log(sfr)-log(@xmath0 ) relation should proceed with caution , based on the results shown in this paper . the scatter in the log(sfr)-log(@xmath0 ) relation is tighter when the sfr(uv ) is corrected for extinction by @xmath34 derived from the sed modeling or when the sed - inferred sfrs are used , because the uv slope regulates the color - excess in the sed fitting from which the stellar masses were derived . in addition to the variations in the dust attenuation , imf , and metallicity , the scatter in the log(sfr)-log(@xmath0 ) relation may be due to other variables such as geometry , size , sfr surface density , and age ( e.g. , * ? ? ? * ; * ? ? ? . the significance of the effect of these variables on the scatter will be investigated in future studies . although in agreement with some simulations @xcite , the measurement - subtracted scatter we found is larger than some of the other works ( e.g. , * ? ? ? * ; * ? ? ? the discrepancy may indicate that the galaxy accretion and feedback processes are not as smooth as predicted by the simulations . we found a constant slope of @xmath71 for the @xmath138 sample and @xmath52 when we used the whole sample at @xmath139 , for @xmath140 . galaxy evolution simulations generally find a close - to - unity slope for the log(sfr)-log(@xmath0 ) relation ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , which translates to a stellar mass - independent specific sfr ( i.e. , sfr/@xmath0 ) . our shallower slope indicates higher ( lower ) sfr at low ( high ) stellar masses . as the slope of the log(sfr)-log(@xmath0 ) represents the star - formation efficiency , one explanation for close - to - unity slope in the galaxy simulations is that star formation is too inefficient at the low stellar - mass end due to feedback processes . the steep slope in the simulations may also be caused by a lack of quenching feedback that causes a dearth of red star - forming galaxies at the high - mass end of the sfr-@xmath0 relation . the slope of the log(sfr)-log(@xmath0 ) is influenced by various observational and measurement effects that could explain discrepancies in the slopes reported in different observational studies . we demonstrated three of the main effects here : dust correction , sample biases , and stellar absorption correction ( the last one is specific to the emission line studies ) . correcting the h@xmath3 emission line with the sed inferred @xmath141 , with the assumption of the calzetti curve , leads to a log(sfr)-log(@xmath0 ) slope of close to unity . a bias against dusty galaxies with low specific sfrs , as might be the case for uv - selected samples , may also result in steeper slopes of the log(sfr)-log(@xmath0 ) relation . finally , we showed that the balmer absorption correction has a significant effect on the dust - corrected sfrs and not applying the correction to the balmer emission lines could lead to an overestimation of the log(sfr)-log(@xmath0 ) slope . the evolution of the slope , normalization , and the scatter of the log(sfr)-log(@xmath0 ) relation is essential to our understanding of the processes that govern galaxy growth during cosmic time . once the whole mosdef sample becomes available , we have access to a large sample of rest - frame optical spectra for galaxies at @xmath142 , which makes it possible to study the sfr-@xmath0 evolution in redshift , using instantaneous and accurately - measured sfrs in a representative sample . furthermore , incorporating ir data into our analysis will allow us for a more detailed comparison with the existing studies . + we thank the referee for the constructive comments . funding for the mosdef survey is provided by nsf aag grants ast-1312780 , 1312547 , 1312764 , and 1313171 and grant ar-13907 , provided by nasa through a grant from the space telescope science institute . the authors thank the mosfire instrument team for building this powerful instrument , and for taking data for us during their commissioning runs . we are grateful to marc kassis at the keck observatory for his many valuable contributions to the execution of this survey . we also acknowledge the 3d - hst collaboration , who provided us with spectroscopic and photometric catalogs used to select mosdef targets and derive stellar population parameters . is thanks shoubaneh hemmati and mostafa khezri for useful discussions and feedback on the manuscript . we thank david sobral for providing the hizels h@xmath3 catalog that was used as a comparison to our results , and james aird for his help in matching agn selection catalogs . support for is is provided through the national science foundation graduate research fellowship dge-1326120 . nar is supported by an alfred p. sloan research fellowship . mk acknowledges support from the hellman fellows fund . alc acknowledges funding from nsf career grant ast-1055081 . we wish to extend special thanks to those of hawaiian ancestry on whose sacred mountain we are privileged to be guests . without their generous hospitality , most of the observations presented herein would not have been possible . this work is also based on observations made with the nasa / esa hubble space telescope ( programs 12177 , 12328 , 1206012064 , 1244012445 , 13056 ) , which is operated by the association of the universities for research in astronomy , inc . , under nasa contract nas 5 - 26555 .

we find that different assumptions for the dust correction , such as using the color - excess of the stellar continuum to correct the nebular lines , sample selection biases against red star - forming galaxies , and not accounting for balmer absorption can yield steeper slopes of the log(sfr)-log( ) relation . based on comparisons to a simulated sfr- relation with some intrinsic scatter , we argue that in the absence of direct measurements of galaxy - to - galaxy variations in the attenuation / extinction curves and the imf , one can not use the difference in the scatter of the sfr(h)- and sfr(uv)- relations to constrain the stochasticity of star formation in high - redshift galaxies .

we present results on the star - formation rate ( sfr ) versus stellar mass ( ) relation ( i.e. , the `` main sequence '' ) among star - forming galaxies at 1.37.61 using the mosfire deep evolution field ( mosdef ) survey . based on a sample of 261 galaxies with h and h spectroscopy , we have estimated robust dust - corrected instantaneous sfrs over a large range in ( ) . we find a correlation between log(sfr(h ) ) and log( ) with a slope of 0.65.08 ( 0.58.10 ) at 1.4.6 ( 2.1.6 ) . we find that different assumptions for the dust correction , such as using the color - excess of the stellar continuum to correct the nebular lines , sample selection biases against red star - forming galaxies , and not accounting for balmer absorption can yield steeper slopes of the log(sfr)-log( ) relation . our sample is immune from these biases as it is rest - frame optically selected , h and h are corrected for balmer absorption , and the h luminosity is dust - corrected using the nebular color - excess computed from the balmer decrement . the scatter of the log(sfr(h))-log( ) relation , after accounting for the measurement uncertainties , is 0.31dex at 2.1.6 , which is 0.05dex larger than the scatter in log(sfr(uv))-log( ) . based on comparisons to a simulated sfr- relation with some intrinsic scatter , we argue that in the absence of direct measurements of galaxy - to - galaxy variations in the attenuation / extinction curves and the imf , one can not use the difference in the scatter of the sfr(h)- and sfr(uv)- relations to constrain the stochasticity of star formation in high - redshift galaxies .

0704.1245

r

this survey of single pointing observations towards 23 massive star forming regions is meant as an initial , uniform survey from which to base future observations . with these observations , we can only comment on the molecular gas component within our beams ; we can not discuss the larger scale molecular dynamics , or the ionized gas components of these regions . for our sources , the selection criteria of having an hii region confirms that these regions are forming massive stars . figures [ fig : sno_sio ] through [ fig : hdet_sio ] show the single pointing sio and hco@xmath0/h@xmath1co@xmath0 spectra towards all sources ; the spectra are ordered according to sio integrated intensity . for each panel in these figures , line brightnesses have been corrected for the jcmt main beam efficiency and centered on the @xmath14 of the source ( table [ tab : sources ] ) . figures [ fig : sno_sio ] and [ fig : hno_sio ] show sio and hco@xmath0/h@xmath1co@xmath0 spectra , respectively , towards the sources with no sio detections . figures [ fig : sdet_sio ] and [ fig : hdet_sio ] show the sio and hco@xmath0/h@xmath1co@xmath0 spectra , respectively , towards sources with sio detections . peak line strengths and integrated intensities are given for all three lines in table [ tab : fits ] . sio was only detected in 14 out of our 23 sources , where we define a detection as a minimum of 4 @xmath15 in integrated intensity . the rms noise limits in integrated intensity were calculated using @xmath16 where @xmath17 is the rms noise level in k , @xmath18 is the velocity resolution of the observations , and @xmath19 is the number of channels over which the integrated intensity is calculated . hco@xmath0 was detected in all sources and h@xmath1co@xmath0 was detected in all but two sources . along with hco@xmath0 , we serendipitously observed so@xmath2 ( j=10@xmath20 - 10@xmath21 at 356.755 ghz ) in 17 of our sources . the hco@xmath0 and so@xmath2 lines are only separated by 17 km s@xmath6 and thus the lines were blended in eight sources . for the sources with so@xmath2 detections , we have also plotted ( in gray ) the lower intensity hco@xmath0 observations in order to highlight the so@xmath2 emission ( figures [ fig : hno_sio ] and [ fig : hdet_sio ] ) . double peaked hco@xmath0 line profiles were observed towards 10 sources , with nine of them having stronger blue peaks than red . this blue line asymmetry in an optically thick tracer such as hco@xmath0 is often suggestive of infall ( i.e myers et al . 1996 ) . we discuss the possibility of our observations tracing large scale infall further in section [ sec : hcop ] . the distances to our sources , as taken from the literature , are shown in table [ tab : sources ] . the average distance is 5.7 @xmath22 3.8 kpc , where the error quoted reflects the 1 @xmath15 dispersion in the distances . since our observations were taken with a 15@xmath9 beam , this resolution corresponds an average linear size of 0.4 pc for our observations . sio is a well known outflow tracer , since in the general interstellar medium , si is frozen out onto dust grains . when the gas in a region is shocked ( i.e. the gas through which a protostellar outflow is passing ) the dust grains can sublimate and si is released into the gas phase . after the passage of a shock , the sio abundance ( [ sio]/[h@xmath2 ] ) can jump to almost 10@xmath24 , whereas the dark cloud abundance of sio is often closer to 10@xmath25 ( see for example schilke et al . 1997 , caselli et al . 1997 , or van dishoeck & blake , 1998 ) . while sio is easily identified as an outflow tracer , the emitting region for hco@xmath0 is much less certain . many authors suggest that hco@xmath0 can be used to trace the envelope material surrounding a protostellar region ( i.e. hogerheijde et al . 1997 , rawlings et al . 2004 ) , while others suggest that it traces disk material ( i.e. dutrey et al . one thing that is apparent , however , is that it becomes optically thick very quickly and readily self absorbs . we detected so@xmath2 in 17 of our sources , suggesting that our beam contains at least some molecular gas at temperatures greater than 100 k ( see for instance doty et al . 2002 , charnley 1997 ) . however , fontani et al . ( 2002 ) have determined the average temperature in twelve massive star forming regions to be 44 k , using observations with beam sizes comparable to those presented here . for seven of our sources , which were observed in the fontani et al ( 2002 ) sample , the average temperature is also 44 k. thus , in the following analysis , we adopt an ambient temperature of 44 k for all sources . table [ tab : results ] shows the column densities for each region derived for both sio and h@xmath1co@xmath0 . the column density was calculated assuming that each tracer is optically thin , in local thermodynamic equilibrium , and at an ambient temperature of 44 k. for optically thin lines , the column density of the observed transition scales directly with the integrated intensity of the line ( see for instance , tielens 2005 ) : @xmath26 where @xmath27 is the column density in the upper state of the transition , @xmath28 is the einstein a coefficient , @xmath29 is the frequency of the j=@xmath30-@xmath31 transition , and @xmath32 is the integrated intensity of the line . the column density of this one state can then be related to the total column density of that molecule through the partition function . it is the total column density for the molecule ( not the observed state ) that is presented in table [ tab : results ] . for each source we determined the column density , or upper limit to the column density , in sio ( table [ tab : results ] ) using the methods described above . these column densities can be compared to the column densities of other molecules ( i.e. cs ) for the same regions in order to determine the fractional abundance of sio , if the abundance of the other molecule is known . we were able to obtain the cs or c@xmath33s column densities for fifteen of our sources from the literature . column densities for fourteen sources were taken from plume et al . ( 1997 , hereafter p97 ) , with the column density for one additional source taken from wang et al . ( 1993 ) . for those sources with c@xmath33s column densities instead of cs column densities , we assumed an abundance ratio of [ cs]/[c@xmath33s ] = 22 ( wilson & rood , 1994 ) to determine a cs column density . the abundance of cs , relative to h@xmath2 , was calculated by s03 for 13 of these sources , and we assume a cs abundance of @xmath34 for the other two source for which the cs column density is known , since this was the average cs abundance as calculated by s03 . we then compare the column density and abundance of cs to our observed sio column density , or column density upper limit , to determine the abundance of sio relative to h@xmath2 in our sources ( table [ tab : results ] ) . despite our source selection criteria requiring previous evidence of outflows , we detected sio towards only 14 of our 23 sources . this raises a number of questions , such as : is the observed sio in fact tracing outflow if we do not detect it in all sources ? why do we not detect sio in all sources ? is the signal being beam diluted at large distances ? has the si evolved into other species ? below we first address whether the detected sio can be used as an outflow tracer , and then discuss reasons for our non - detections of sio in nine of our sources . si is liberated in shocks , and if these shocks are not due to the outflow , they must be due to the photo dissociation region ( pdr ) surrounding the uchii region . evidence for diffuse ( not collimated ) sio can be seen in w75n ( shepherd , kurtz & testi , 2004 ) suggesting that the sio may be due to the pdr and not an outflow . models and observations of sio in the pdrs around high mass star forming regions suggest moderate sio enhancement , and that the sio abundance is independent of the ambient radiation field ( i.e. schilke et al . 2001 ) . schilke et al . ( 2001 ) find sio column densities of @xmath35 @xmath36 in their observed pdrs . this is , admittedly , below our detection threshold ; however , we detect average sio column densities of @xmath37 @xmath36 . this suggests a possibly higher sio abundance than found in pdrs . the enhanced sio column density alone is not enough to discount the origin of the sio in our sources as the pdr and so we can consider how our sio abundance varies with the ambient radiation field . for the gas near an hii region , we can approximate the strength of the ambient radiation field using the far infrared ( fir ) luminosity of the region . for twelve of our sources with sio detections and abundance calculations , we obtained the fir luminosity from either wood & churchwell ( 1989 ) , kurtz et al . ( 1994 ) or evans et al . we then scaled their values for the different source distances used in this study ( see table [ tab : results ] ) . comparing the sio abundance to the source luminosity ( see figure [ fig : iras ] ) , we find that the sio abundance increases with source luminosity . there is a 10% chance that this relationship could arise from uncorrelated data . thus , it is possible that our result is contrary to the findings of schilke et al ( 2001 ) , and we suggest that the sio we observe does come primarily from outflow shocks . we can also compare our detection rate of sio to that of the sio survey towards maser sources of harju et al ( 1998 ) who observed sio ( j=2 - 1 ) and sio ( j=3 - 2 ) . for comparison to our results , we only consider the sources in harju et al . which are listed as uchii regions . our detection rate is 61% , compared to their rate of 29% . while our detection threshold is slightly lower ( our observations have rms noise levels generally below 0.05 k at 347 ghz , while their rms noise levels are generally below 0.08 k ) , we suggest that the different detection rates are due to differences in the source selection criteria . although both samples contain uchii regions , our sample contains sources with previous observations of outflows , while harju et al . have selected sources based on previous observations of masers . for the 12 sources which overlap between the two studies , we detect sio towards 9 sources , while they detect sio towards 10 . they detected sio ( j=2 - 1 ) in g31.41 while we did not detect it in sio ( j=8 - 7 ) . based on this comparison to sio observations of uchii regions _ not _ selected by outflows , which have a lower sio detection rate , and that our sio abundance increases with source luminosity , we suggest that the sio , in the 14 sources in which it is detected , is being generated in the outflow . previous , high resolution observations of sio also suggest that sio can be enhanced in the outflows from high mass stars ( i.e. beuther et al . 2004 , beuther , schilke & gueth 2004 ) just as it is in the outflows from low mass stars . the nine non - detections in our sample could be caused by beam dilution if these sources are on average further away . however , if we compare the distances for sources with and without sio detections , we find average distances of 6.3 @xmath22 4.4 and 4.4 @xmath22 2.5 kpc , respectively . thus , the non - detections can not be attributed to larger average source distances and so beam dilution can play only a minimal role in the non - detections of sio . if these sio non - detections are not due to distance effects , there must be some local phenomenon which can explain why sio is not being detected in regions known to contain protostellar outflows . it is possible that the si is evolving into different species and the sio abundance is dropping back down to dark cloud values . pineau des forts et al . ( 1997 ) suggest that a few@xmath38 yr after the si is liberated from dust grains and forms sio , it can either freeze out back onto dust grains or oxidize and form sio@xmath2 . thus , the lack of sio may be due to silicon moving into other species if it was liberated more than 10@xmath39 yr ago . this interpretation implies that we did not detect sio in some of our sources because the outflow generating mechanism shut off more than 10@xmath39 years ago , and the outflow observed in hco@xmath0 ( or in other molecules by other authors ) is a remnant of previous accretion . the kinematic ages of nine of our sources are listed in the wu et al ( 2004 ) catalog of high velocity outflows . of these nine sources , five were also included in the p97 and s03 studies . this results in five sources for which we have both the kinematic age of the outflow , and the abundance of sio . the relationship between outflow age and sio abundance is shown in figure [ fig : age_abund ] along with the model predictions of pineau des forts et al . ( 1997 ) . with only five points , it is difficult to draw conclusions about the relationship between outflow age and sio abundance , especially given the uncertain beam filling factor . at higher resolution , these points would likely move upwards to higher abundances . a larger beam filling factor would move the points for the two young outflows ( g5.89 and cep a ) towards the model predictions . as for the other three outflows , this would move them further from the model predictions . we suggest that the outflow generating mechanism is continuing to shock these regions , replenishing the sio . the oldest of these sources ( g192.58 ) shows an infall signature in hco@xmath0 , which also suggests that the outflow is still being powered . given the large average distance to our sources ( 5.7 kpc ) , our 15@xmath9 beam subtends an average linear distance of 0.4 pc . thus , it is quite likely that the hco@xmath0 emitting region does not entirely fill our single jcmt beam . in general we can determine the beam filling factor , @xmath40 , for each source using @xmath41 where @xmath42 is the line brightness temperature measured at the telescope ( corrected for telescope efficiencies ) and @xmath43 is an approximation to the ambient temperature ( 44 k ) which is valid at densities greater than @xmath44 @xmath45 ( rholfs & wilson , 1994 ) . in a number of our sources , the hco@xmath0 is asymmetric , and thus can not be consistently used to determine a beam filling factor . instead , we can use the optically thin h@xmath1co@xmath0 line , and we can simplify the above equation to @xmath46 . these values are shown in table [ tab : results ] . hco@xmath0 becomes optically thick quite quickly due to its relatively high abundance with respect to h@xmath2 ( [ hco@xmath0]/[h@xmath2 ] @xmath48 ) , and as such , can be used to roughly trace outflow and to trace infall ( i.e. myers et al . 1996 ) if the line profile shows a double peak . we determined the optical depth of hco@xmath0 towards each source using equation 1 of choi et al . ( 1993 ) , and found that in all but one case ( g139.9 ) , it is optically thick . in all cases , the optical depth of hco@xmath0 is less than 77 ( the abundance ratio between hco@xmath0 and h@xmath1co@xmath0 , wilson & rood , 1994 ) , resulting in optically thin h@xmath1co@xmath0 towards all sources . because hco@xmath0 is optically thick in its line center , the line wings can be used to detect outflows , and so , if there is an outflow , it should be detectable in hco@xmath0 even if it goes undetected in sio . gaussian profiles were fit to our hco@xmath0 spectra ( either single or double gaussians , depending on the observed line shape ) , and the fits were subsequently subtracted from the spectra to leave only the residual outflowing gas . when using two gaussians to fit the self absorbed spectra , we employed a method similar to the single gaussian fitting of purcell et al . ( 2006 ) because we used the sides of the detected lines to fit our profiles ( see their figure 3 ) . comparing the two gaussian fits to single gaussian fits showed no significant differences in distinguishing line wing intensity . because of the possibility of contamination from so@xmath2 emission in the blue shifted outflow wing ( at -17 km s@xmath6 ) , the peak brightness of the residual emission was determined using only the red shifted wing emission . in all cases ( except for g10.47 for which we could not find a linear baseline ) , we found a minimum of a 5@xmath15 peak brightness temperature in the residual line wing emission , with 19 of our sources having a minimum of a 10@xmath15 peak . this result suggests that we can detect outflow motions in all sources using our detections of hco@xmath0 , despite not detecting sio towards every source . our observations show that for ten of our sources , the spectral line profile of the hco@xmath0 emission has a double peak . this profile could either be due to self absorption of the optically thick hco@xmath0 line or from multiple velocity components within our 15@xmath9 beam . to break this degeneracy , we observed the optically thin h@xmath1co@xmath0 . if the h@xmath1co@xmath0 line has a single peak at the same velocity as the hco@xmath0 absorption feature , then it is likely that the hco@xmath0 line is self absorbed . if , however , the h@xmath1co@xmath0 also has two peaks , and they are at approximately the same velocities as the two hco@xmath0 peaks , it would suggest that there are multiple components within the beam . of our ten sources with double hco@xmath0 peaks , only one shows a double peak profile in h@xmath1co@xmath0 ( g20.08 ) . this results in nine sources with double peaked optically thick hco@xmath0 . in addition to the nine optically thick sources , similar line asymmetries appear in a number of other sources . however , in these sources , there is no clear emission gap producing a double peak profile , only an emission shoulder ( i.e. de vries & myers 2005 ) . if we take g75.78 as an example , the hco@xmath0 line peak is red shifted from the rest velocity of the source , with a blue shifted emission shoulder . there are a number of different kinds of source dynamics that can lead to the double peaked line profiles seen in our spectra , such as infall , outflow and even rotation . however , infall is the only one of these processes which would produce line asymmetries which are consistently blue ( i.e. the blue peak is higher than the red peak or shoulder ) . if these profiles were due to outflow or rotation , there would be no statistical reason to have more sources with higher blue peaks than red peaks . many previous studies have investigated the statistical significance of using this type of optically thick blue line asymmetry to trace infall as opposed to other dynamical motions ( i.e. mardones et al . 1997 and gregersen et al . 1997 for low mass star forming regions , and fuller et al . 2005 for high mass star forming regions ) . of the 10 sources in our survey which have double peaked hco@xmath0 profiles , we suggest eight may be indicative of infall . the other two sources are g20.08 and g45.47 . g20.08 has already been shown to have multiple components in the beam from the double peaked h@xmath1co@xmath0 profile , and g45.47 has a brighter red peak than blue . there are two additional sources ( g19.61 , and g240.3 ) in which hco@xmath0 has a strong red shifted shoulder , which we suggest may also be tracing infall . this analysis gives a total of ten infall candidates in our sample of 23 sources . a recent survey of hco@xmath0 ( j=1 - 0 ) towards sources with methanol masers shows an even distribution of sources with blue and red line asymmetries , and a higher percentage of self absorbed lines than in our study ( purcell et al . 2006 ) . of the six sources which overlap between our survey and that of purcell et al , all six are self absorbed in hco@xmath0 ( j=1 - 0 ) . five of them have blue line asymmetries consistent with infall , while only one ( g31.41 ) has its red peak brighter than its blue peak . we only find self - absorption in hco@xmath0 ( j=4 - 3 ) for three of these six sources . in two of the sources for which we do not see a clear self - absorption feature , we do see evidence for a red shifted shoulder which may be showing unresolved infall . the sources in purcell et al . ( 2006 ) have an even distribution of red and blue line asymmetries , while we have a clear bias towards detecting blue line asymmetries . this comparison could suggest that the higher energy j=4 - 3 transition of hco@xmath0 is a better tracer of infalling gas because it does not self absorb as readily as the j=1 - 0 transition . for each of the 8 sources with blue , double peaked hco@xmath0 profiles , we can determine an infall velocity ( @xmath49 ) using the two layer radiative transfer model of myers et al . ( 1996 ) . using their equation 9 , we find infall velocities for all eight double peaked infall sources ( table [ tab : infall_rates ] ) . the mass infall rate can then be determined using : @xmath50 where @xmath51 is the mean molecular weight ( @xmath52 ) , the geometric mean radius ( @xmath53 ) is the unresolved circular radius of the hco@xmath0 emitting region derived from the beam radius and the beam filling factor ( @xmath54 ) , and @xmath55 is the ambient source density . for seven of the sources in table [ tab : infall_rates ] , the ambient density was determined by either p97 , hofner et al . ( 2000 ) , or wang et al . we could not find the ambient density for the eighth source ( g192.58 ) . from this analysis , we determine mass infall rates ranging from 1@xmath3 to 2@xmath4 m@xmath5 yr@xmath6 . these values are slightly higher than those generally observed for low mass star forming regions , but are consistent with the accretion rates derived for high mass star forming regions by mckee & tan ( 2003 ) . since outflow rates are orders of magnitude higher in high mass star forming regions ( i.e. beuther et al . 2002 ) it is not unreasonable to suggest that infall rates are also much higher in these regions . the mass outflow rate for only one of these sources ( cep a ) can be determined from the wu et al . ( 2004 ) survey of high velocity outflows by dividing the mass in the outflow by the kinematic age of the outflow . we find the ratio of the mass outflow rate to the mass infall rate to be @xmath56 . this value is only slightly higher than values seen in other high mass star forming regions ( i.e. behrend & maeder 2001 ) . also , models suggest that a mass equivalent to 20 - 30% of the mass accreted onto a protostar is ejected as a wind ( i.e. pelletier & pudritz 1992 , shu et al . 1994 ) , and that this wind entrains 5 - 20 times its mass in the outflow ( matzner & mckee 1999 ) . at a distance of 9.7 kpc , g45.07 is one of our furthest sources . this source was known from previous observations to have multiple continuum sources ( de buizer et al . 2003 , 2005 ) . the three continuum sources were observed in the mid - infrared ( mir ) and all three fall within 6@xmath9 of our map center . a fairly young outflow has also been mapped at high resolution ( @xmath57 synthesized beam ) in co and cs towards this region ( hunter et al . they observed a bipolar outflow with a position angle of -30@xmath58 ( east of north ) , as well as a red shifted absorption feature in their cs observations which they take to be indicative of infall . due to the large distance to this source , we should be able to detect all of the emission associated with this source in a fairly small map . in the left panel of figure [ fig : g45_maps ] we present a map of the sio ( contours ) and h@xmath1co@xmath0 ( halftone ) emission in this region . the right panel of figure [ fig : g45_maps ] shows the hco@xmath0 emission . in both figures , the 5@xmath15 ( 2.1 k km s@xmath6 ) h@xmath1co@xmath0 emission contour is plotted as a dashed line to help guide the eye . the first contour for sio in the left panel and only contour of hco@xmath0 in the right panel are also 5@xmath15 ( 2.2 and 3.5 k km s@xmath6 respectively ) . the differences in the 5@xmath15 contour levels for each tracer come from the different single channel rms levels between the two tunings , and the width of each line as given in table [ tab : fits ] . also plotted in both figures are the three mir continuum sources observed by de buizer et al ( 2003 , 2005 ) . if we did not have the added information provided by this map , there would be two main conclusions we could draw from our single pointing observations towards this source . the first is that the enhanced blue emission in all three tracers suggests that our pointing is observing more of the blue shifted outflow lobe than the red . second , since we only have one peak in the spectrum of each tracer , there is only one source and we can not classify it as infalling . the left panel of figure [ fig : g45_maps ] shows contours of sio emission superimposed on the h@xmath1co@xmath0 halftone . with beam spacings of 5@xmath9 , these maps are oversampled ; however we note that much of the structure in the sio emission is on scales comparable to the size of the jcmt beam . for instance , the structure at @xmath59 , @xmath60 is offset from the map center by more than the radius of our beam and could be independent from the emission at the map center . there is also sio emission at @xmath61 , @xmath62 , which is more than a full beam away from the map center , and suggests that the sio emission is more extended that the primary beam of our observations . in fact , it appears as though there is a second sio emission peak towards the upper left of the left panel of figure [ fig : g45_maps ] . interestingly , there does not appear to be as much h@xmath1co@xmath0 emission at this northern position . this comparison shows that the sio and h@xmath1co@xmath0 lines are tracing different gas populations in this region . the excess sio emission is offset from the map center in the same direction as the co emission shown in hunter et al . ( 1997 ) at much higher resolution . the right panel of figure [ fig : g45_maps ] shows the hco@xmath0 emission for this region . it appears that the hco@xmath0 emission extends much further than the sio emission , suggesting it is tracing the larger scale envelope material . the line through the middle of this plot indicates the cut taken for the position - velocity ( pv ) diagram along the outflow axis as described by hunter et al . ( 1997 ) the two panels of figure [ fig : pv ] show the pv diagrams for sio and hco@xmath0 in our maps both perpendicular and parallel to the outflow axis defined by hunter et al . our single pointing hco@xmath0 spectrum ( figure [ fig : hdet_sio ] ) suggests we are observing more blue shifted outflow emission than red shifted emission ; however , from our pv diagrams , we see that there is excess blue emission at all positions in our map . this excess blue emission can not be due to outflow alone ; instead , it could be due to an inherent velocity shift between the three continuum sources in our beam . we can , in fact , fit three gaussian components to most of our hco@xmath0 spectra . these gaussians peak at velocities of 60 , 52 and 44 km s@xmath6 , with the peak temperature for each component decreasing with velocity . the third component ( at 44 km s@xmath6 ) could not be fit at all positions because it was intrinsically weaker than the other two peaks , and was lost in the noise towards the edges of the map . it appears as though this third component might be contamination from so@xmath2 , which should occur at an apparent velocity of 41 km s@xmath6 ( or -17 km s@xmath6 in figure [ fig : hdet_sio ] ) . perpendicular to the outflow axis , the mean velocity of the hco@xmath0 line peak appears to shift from @xmath11 58 km s@xmath6 at an offset of @xmath63 from the source center to @xmath64 km s@xmath6 at an offset of @xmath65 from the source ( figure [ fig : pv ] ) . given our velocity resolution ( 1.08 km s@xmath6 ) and spatial resolution ( @xmath66 ) , is unclear whether this velocity shift is real . if it is , it could indicate large scale ( @xmath11 1.4 pc ) rotation within the core , on a much larger scale than would be expected for a rotating accretion disk . previously , we discussed the reasons why we do not detect sio towards a number of our sources , and have calculated the mass infall rates for the sources with double peaks in their hco@xmath0 emission , but we have not yet discussed the correlations between the two species . in figure [ fig : abund ] we plot the logarithm of the abundance of h@xmath1co@xmath0 against the same quantity for sio ( open circles ) , as well as the column densities of both species ( filled circles ) . the abundance of h@xmath1co@xmath0 was calculated in the same manner as the abundance of sio described above ( using the cs column density from p97 and the cs abundance from s03 ) . the probability of obtaining these correlations if the data are , in fact , uncorrelated is 6@xmath67 for the abundances , and 2@xmath68 for the column densities . as stated earlier , sio is a well known shock tracer , and as such , an increased abundance of sio would suggest more shocked material within our 15@xmath9 beam . the ( generally ) infall tracing hco@xmath0 has been shown by some authors to be destroyed in strong shocks ( i.e. bergin et al . 1998 , jrgensen et al . 2004 ) . however , wolfire & knigl ( 1993 ) suggest that hco@xmath0 can be enhanced in regions with high energy shocks , where electron abundances are much greater . this enhancement in the electron abundance increases the formation rate of ions , and we suggest that this is responsible for the h@xmath1co@xmath0 abundance enhancement in our sources . this correlation between the abundances of h@xmath1co@xmath0 and sio suggests that hco@xmath0 and h@xmath1co@xmath0 are not only tracing infalling gas , but also the outflowing gas as well . this conclusion is supported by the strong , and broad , line wing emission detected in hco@xmath0 ( see section [ sec : hcop ] ) . hco@xmath0 over abundances have been seen in high mass star forming regions not included in this study like ngc 2071 ( girart et al . 1999 ) and orion irc2 ( vogel et al . 1984 ) . in these two papers , the over abundances of h@xmath1co@xmath0 are with respect to ambient cloud tracers such as co and h@xmath2 , rather than the high density or shock tracers like the cs and sio with which we are comparing our h@xmath1co@xmath0 abundances . however , viti & williams ( 1999a , b ) show that hco@xmath0 is indeed over abundant with respect to cs in the gas surrounding hh objects , and jimnez - serra et al . ( 2006 ) also show that the abundance of h@xmath1co@xmath0 can be enhanced with respect to sio by up to a factor of ten in the same regions ahead of hh objects .

we present single pointing observations of sio , hco and hco from the james clerk maxwell telescope towards 23 massive star forming regions previously known to contain molecular outflows and ultracompact hii regions . we serendipitously detected so towards 17 sources in the same tuning as hco . we also find that the abundance of hco tends to increase along with the abundance of sio in sources for which we could determine abundances .

we present single pointing observations of sio , hco and hco from the james clerk maxwell telescope towards 23 massive star forming regions previously known to contain molecular outflows and ultracompact hii regions . we detected sio towards 14 sources and suggest that the non - detections in the other nine sources could be due to those outflows being older and without ongoing shocks to replenish the sio . we serendipitously detected so towards 17 sources in the same tuning as hco . we detected hco towards all sources , and suggest that it is tracing infall in nine cases . for seven infall candidates , we estimate mass infall rates between 1 and 2 m yr . seven sources show both sio detections ( young outflows ) and hco infall signatures . we also find that the abundance of hco tends to increase along with the abundance of sio in sources for which we could determine abundances . we discuss these results with respect to current theories of massive star formation via accretion . from this survey , we suggest that perhaps both models of ionized accretion and halted accretion may be important in describing the evolution of a massive protostar ( or protostars ) beyond the formation of an hii region .

0704.1245

c

without maps of each region , it is impossible to tell how much of the hco@xmath0 emission in the line center and in the line wings is due directly to infall and outflow motions ; however , based on the arguments we have presented above , we suggest that ten sources show infall motions , and all 23 source show outflow motions based on the hco@xmath0 line profiles . we have found evidence for recent outflow activity ( sio emission ) in 14 out of our 23 sources . seven of these outflow and infall sources overlap . m17s , g192.6 and g240 appear to show only infall signatures and no sio outflow signatures . they do , however , appear to have hco@xmath0 outflow signatures of a minimum of 8@xmath15 . detection of line wing emission in hco@xmath0 and the relationship between h@xmath1co@xmath0 and sio abundances described in the previous section suggest that while sio is tracing outflow in most sources and hco@xmath0 is tracing infall in some sources , hco@xmath0 is also observable in the outflowing gas for all regions . we find that the non - detection of sio in nine of our sources is not due to beam dilution or larger average distances to the source , but possibly to older outflows for which the si has likely either frozen back onto dust grains or evolved into sio@xmath2 . for these sources , it appears that the accretion may have ceased , and the observed outflowing gas is a remnant of previous accretion . we have found seven sources with sio outflow signatures but no infall signatures in hco@xmath0 . this result could be due to a number of factors such as beam dilution of the infalling gas which masks the spectral line profile we would expect for large scale infall . it is possible that , as the outflow ages and widens , it may impinge on the region in which we could detect infalling gas . for outflow cones oriented along the line of sight , the younger , narrower outflows would have infalling gas with large line of sight velocities and be likely to produce an observable infall signature . however , for the older outflows which have widened , the largest infall velocities will be in the plane of the sky , and unobservable at the resolution of the jcmt . however , this effect would not be as pronounced for outflows in the plane of the sky ( such as g5.89 , for which we do not see an infall signature ) . it is difficult to assess the importance of this effect without detailed information on the outflow orientation in each source . thus , we suggest that some of these sources may have finished accreting , and what we observe are remnant outflows from a previous phase of accretion . this scenario was suggested by klaassen et al . ( 2006 ) to explain the large scale outflow in g5.89 , and this source is one of these seven sources with an sio outflow and no apparent infall signature . the seven sources which show recent outflow activity ( those with sio emission ) and which appear to be undergoing infall are suggestive of ongoing accretion beyond the onset of the hii region . if accretion is ongoing in the presence of an hii region , then it seems likely that this accretion flow may be ionized . this ionized accretion scenario could be similar to low angular momentum accretion with high ionization as suggested by keto ( 2006 ) . thus , from this survey , we suggest that both models of ionized accretion and halted accretion may be important in describing the evolution of a massive protostar ( or protostars ) beyond the formation of an hii region . we would like to acknowledge the support of the national science and engineering research council of canada ( nserc ) . we thanks the referee for helpful comments which improved the paper . p.d.k would also like to thank e. keto and d. johnstone for helpful discussions during the preparation of this manuscript . 99 andre , p. , ward - thompson , d. , & barsony , m. 1993 , , 406 , 122 arce , h. g. , shepherd , d. , gueth , f. , lee , c .- f . , bachiller , r. , rosen , a. , & beuther , h. 2006 , arxiv astrophysics e - prints , arxiv : astro - ph/0603071 behrend , r. , & maeder , a. 2001 , , 373 , 190 beltrn , m. t. , cesaroni , r. , neri , r. , codella , c. , furuya , r. s. , testi , l. , & olmi , l. 2004 , , 601 , l187 bergin , e. a. , neufeld , d. a. , & melnick , g. j. 1998 , , 499 , 777 beuther , h. , schilke , p. , sridharan , t. k. , menten , k. m. , walmsley , c. m. , & wyrowski , f. 2002 , , 383 , 892 beuther , h. , et al . 2004 , , 616 , l23 beuther , h. , schilke , p. , & gueth , f. 2004 , , 608 , 330 beuther , h. , churchwell , e. b. , mckee , c. f. , & tan , j. c. 2006 , arxiv astrophysics e - prints , arxiv : astro - ph/0602012 beuther , h. , & shepherd , d. 2005 , cores to clusters : star formation with next generation telescopes , 105 caselli , p. , hartquist , t. w. , & havnes , o. 1997 , , 322 , 296 cesaroni , r. , neri , r. , olmi , l. , testi , l. , walmsley , c. m. , & hofner , p. 2005 , , 434 , 1039 charnley , s. b. 1997 , , 481 , 396 chini , r. , hoffmeister , v. , kimeswenger , s. , nielbock , m. , nrnberger , d. , schmidtobreick , l. , & sterzik , m. 2004 , , 429 , 155 choi , m. , evans , n. j. , ii , & jaffe , d. t. 1993 , , 417 , 624 churchwell , e. , walmsley , c. m. , & cesaroni , r. 1990 , , 83 , 119 de buizer , j. m. , osorio , m. , & calvet , n. 2005 , , 635 , 452 de buizer , j. m. , radomski , j. t. , telesco , c. m. , & pia , r. k. 2003 , , 598 , 1127 de vries , c. h. , & myers , p. c. 2005 , , 620 , 800 di francesco , j. , myers , p. c. , wilner , d. j. , ohashi , n. , & mardones , d. 2001 , , 562 , 770 doty , s. d. , van dishoeck , e. f. , van der tak , f. f. s. , & boonman , a. m. s. 2002 , , 389 , 446 dutrey , a. , guilloteau , s. , & guelin , m. 1997 , , 317 , l55 evans , n. j. , ii , et al . 1981 , , 244 , 115 fontani , f. , cesaroni , r. , caselli , p. , & olmi , l. 2002 , , 389 , 603 fuller , g. a. , williams , s. j. , & sridharan , t. k. 2005 , , 442 , 949 garay , g. , & lizano , s. 1999 , , 111 , 1049 girart , j. m. , ho , p. t. p. , rudolph , a. l. , estalella , r. , wilner , d. j. , & chernin , l. m. 1999 , , 522 , 921 gregersen , e. m. , evans , n. j. , ii , zhou , s. , & choi , m. 1997 , , 484 , 256 hanson , m. m. , luhman , k. l. , & rieke , g. h. 2002 , , 138 , 35 harju , j. , lehtinen , k. , booth , r. s. , & zinchenko , i. 1998 , , 132 , 211 hofner , p. , wyrowski , f. , walmsley , c. m. , & churchwell , e. 2000 , , 536 , 393 hogerheijde , m. r. , van dishoeck , e. f. , blake , g. a. , & van langevelde , h. j. 1997 , , 489 , 293 hunter , t. r. 1997 , ph.d . thesis , hunter , t. r. , phillips , t. g. , & menten , k. m. 1997 , , 478 , 283 jimnez - serra , i. , martn - pintado , j. , viti , s. , martn , s. , rodrguez - franco , a. , faure , a. , & tennyson , j. 2006 , , 650 , l135 jrgensen , j. k. , schier , f. l. , & van dishoeck , e. f. 2004 , , 416 , 603 keto , e. , & wood , k. 2006 , , 637 , 850 keto , e. 2003 , , 599 , 1196 keto , e. 2006 , arxiv astrophysics e - prints , arxiv : astro - ph/0603856 klaassen , p. d. , plume , r. , ouyed , r. , von benda - beckmann , a. m. , & di francesco , j. 2006 , , 648 , 1079 krumholz , m. r. , mckee , c. f. , & klein , r. i. 2005 , , 438 , 332 kumar , m. s. n. , fernandes , a. j. l. , hunter , t. r. , davis , c. j. , & kurtz , s. 2003 , , 412 , 175 kurtz , s. , churchwell , e. , & wood , d. o. s. 1994 , , 91 , 659 mardones , d. , myers , p. c. , tafalla , m. , wilner , d. j. , bachiller , r. , & garay , g. 1997 , , 489 , 719 matzner , c. d. , & mckee , c. f. 1999 , star formation 1999 , proceedings of star formation 1999 , held in nagoya , japan , june 21 - 25 , 1999 , editor : t. nakamoto , nobeyama radio observatory , p. 353 - 357 , 353 mckee , c. f. , & tan , j. c. 2003 , , 585 , 850 muzerolle , j. , calvet , n. , hartmann , l. , & dalessio , p. 2003 , , 597 , l149 myers , p. c. , mardones , d. , tafalla , m. , williams , j. p. , & wilner , d. j. 1996 , , 465 , l133 nakamura , f. 2000 , , 543 , 291 pelletier , g. , & pudritz , r. e. 1992 , , 394 , 117 pineau des forets , g. , flower , d. r. , & chieze , j .- 1997 , iau symp . 182 : herbig - haro flows and the birth of stars , 182 , 199 plume , r. , jaffe , d. t. , evans , n. j. , ii , martin - pintado , j. , & gomez - gonzalez , j. 1997 , , 476 , 730 plume , r. , jaffe , d. t. , & evans , n. j. , ii 1992 , , 78 , 505 pudritz , r. e. , & norman , c. a. 1986 , , 301 , 571 purcell , c. r. , et al . 2006 , , 367 , 553 rawlings , j. m. c. , redman , m. p. , keto , e. , & williams , d. a. 2004 , , 351 , 1054 rholfs , k. , wilson , t. l. 2004 , tools of radio astronomy ( 4th ed ; berlin ; springer ) schilke , p. , walmsley , c. m. , pineau des forets , g. , & flower , d. r. 1997 , , 321 , 293 schilke , p. , pineau des forts , g. , walmsley , c. m. , & martn - pintado , j. 2001 , , 372 , 291 shepherd , d. s. , & churchwell , e. 1996 , , 472 , 225 shepherd , d. s. , kurtz , s. e. , & testi , l. 2004 , , 601 , 952 shirley , y. l. , evans , n. j. , ii , young , k. e. , knez , c. , & jaffe , d. t. 2003 , , 149 , 375 shu , f. , najita , j. , ostriker , e. , wilkin , f. , ruden , s. , & lizano , s. 1994 , , 429 , 781 sollins , p. k. , zhang , q. , keto , e. , & ho , p. t. p. 2005 , , 624 , l49 tielens , a. g. g. m. 2005 , the physics and chemistry of the interstellar medium ( cambridge university press ) , 537 , 283 van dishoeck , e. f. , & blake , g. a. 1998 , , 36 , 317 viti , s. , & williams , d. a. 1999 , , 310 , 517 viti , s. , & williams , d. a. 1999 , , 305 , 755 vogel , s. n. , wright , m. c. h. , plambeck , r. l. , & welch , w. j. 1984 , , 283 , 655 yorke , h. w. 2002 , asp conf . ser . 267 : hot star workshop iii : the earliest phases of massive star birth , 267 , 165 wang , y. , jaffe , d. t. , evans , n. j. , ii , hayashi , m. , tatematsu , k. , & zhou , s. 1993 , , 419 , 707 wilson , t. l. , & rood , r. 1994 , , 32 , 191 wolfire , m. g. , & koenigl , a. 1993 , , 415 , 204 wood , d. o. s. , & churchwell , e. 1989 , , 69 , 831 wu , y. , wei , y. , zhao , m. , shi , y. , yu , w. , qin , s. , & huang , m. 2004 , , 426 , 503 lllcccccc g5.89 & 18 00 30.3 & -24 03 58 & 0.060 & 0.111 & 9 & 2&1 & w28a2 ( 1 ) + g5.97 & 18 03 40.4 & -24 22 44 & 0.044 & 0.069 & 10 & 2.7&5 & + g8.67 & 18 06 19.0 & -21 37 32 & 0.068 & 0.074&36 & 8.5&2 & 8.67 - 0.36 + g10.47 & 18 08 38.4 & -19 51 52 & & 0.100&67 & 12&2 & w31 ( 1 ) + g12.21 & 18 12 39.7 & -18 24 21 & 0.042 & 0.076&24 & 16.3&2 & 12.21 - 0.1 + m17s & 18 20 24.8 & -16 11 35 & 0.044 & 0.077&20 & 2.3&5 & m17 ( 2 ) + g19.61 & 18 27 38.1 & -11 56 40 & 0.048 & 0.065&43 & 4.5&1 & 19.61 - 0.23 + g20.08 & 18 28 10.4 & -11 28 49 & 0.044 & 0.068 & 42 & 4.1&1 & 20.08 - 0.13 + g29.96 & 18 46 03.9 & -02 39 22 & 0.044 & 0.079 & 98 & 9&1 & w43s + g31.41 & 18 47 33.0 & -01 12 36 & 0.044 & 0.061 & 97 & 8.5&1 & 31.41 + 0.31 + g34.26 & 18 53 18.5 & 01 14 58 & 0.047 & 0.131 & 58 & 3.7&1 & w44 + g45.07 & 19 13 22.1 & 10 50 53 & 0.044 & 0.073 & 59 & 9.7&1 & 45.07 + 0.13 + g45.47 & 19 14 25.6 & 11 09 26 & 0.037 & 0.063 & 58 & 8.3&6 & + g61.48 & 19 46 49.2 & 25 12 48 & 0.037 & 0.048 & 12 & 2&1 & s88 b + k3 - 50a & 20 01 45.6 & 33 32 42 & 0.035 & 0.077 & -24 & 8.6&3 & k3 - 50 + g75.78 & 20 21 44.1 & 37 26 40 & 0.038 & 0.068 & 0 & 5.6&1 & on 2n + cep a & 22 56 17.9 & 62 01 49 & 0.031 & 0.076&-10 & 0.7&1 & cep a + w3(oh ) & 02 27 03.8 & 61 52 25 & 0.026 & 0.079 & -48 & 2.4&2 & w3 ( oh ) + g138.3 & 03 01 29.2 & 60 29 12 & 0.066 & 0.073&-38 & 3.8&1 & s201 + g139.9 & 03 07 23.9 & 58 30 53 & 0.058 & 0.071 & -39 & 4.2&1 & + g192.58 & 06 12 53.6 & 17 59 27 & 0.037 & 0.053&9 & 2.5&3 & s255/7 + g192.6 & 06 12 53.6 & 18 00 26 & 0.074 & 0.098&9 & 2.5&3 & s255/7 + g240.3 & 07 44 51.9 & -24 07 40 & 0.035 & 0.048&68 & 6.4&4 & + + [ tab : sources ] lcc@@xmath22cccc@@xmath22cccc@@xmath22cc g5.89 & 2.3 & 75.3 & 0.7 & 120 & 39.2 & 690.0 & 0.8 & 105 & 8.9 & 65.2 & 0.4 & 35 + g5.97 & @xmath690.1 & @xmath690.3&0.1 & 8 & 12.4 & 50.5 & 0.2 & 15 & 0.6 & 1.6 & 0.1 & 8 + g8.67 & 0.2 & 1.6 & 0.3 & 13 & 13.8 & 80.0 & 0.3 & 38 & 5.6 & 20.9 & 0.2 & 10 + g10.47 & 1.0 & 9.9&&22 & 7.7 & 79.3 & 0.4 & 35 & 1.2 & 9.2&&15 + g12.21 & 0.2 & 2.5 & 0.2 & 25 & 10.0 & 93.8 & 0.3 & 30 & 0.8 & 6.5 & 0.2 & 15 + m17s & @xmath690.1 & @xmath690.7&0.2 & 15 & 16.2 & 79.0 & 0.2 & 15 & 2.9 & 9.4 & 0.2 & 11 + g19.61 & 0.8 & 15.9 & 0.3 & 45 & 10.8 & 162.2 & 0.4 & 55 & 1.8 & 16.1 & 0.2 & 20 + g20.08 & 0.4 & 6.9 & 0.3 & 40 & 6.5 & 75.0 & 0.3 & 40 & 1.1 & 9.7 & 0.2 & 25 + g29.96 & 0.5 & 7.9 & 0.3 & 40 & 23.6 & 160.4 & 0.3 & 30 & 3.8 & 13.2 & 0.1 & 10 + g31.41 & @xmath690.1 & @xmath690.7&0.2 & 15 & 1.6 & 6.8 & 0.2 & 13 & @xmath690.1 & @xmath690.3 & 0.1 & 3 + g34.26 & 1.3 & 26.0 & 0.4 & 55 & 27.8 & 228.2 & 0.6 & 35 & 4.3 & 33.2 & 0.2 & 25 + g45.07 & 0.7 & 10.3 & 0.3 & 37 & 15.0 & 169.4 & 0.4 & 45 & 1.5 & 11.2 & 0.3 & 33 + g45.47 & @xmath690.1 & @xmath690.3 & 0.1 & 12 & 10.1 & 59.4 & 0.2 & 20 & 1.3 & 6.1 & 0.1 & 12 + g61.48 & @xmath690.1 & @xmath690.3 & 0.1 & 8 & 10.8 & 58.5 & 0.1 & 18 & 1.5 & 4.7 & 0.1 & 8 + k3 - 50a & 0.3 & 2.1 & 0.1 & 16 & 18.6 & 154.8 & 0.3 & 25 & 1.8 & 10.6 & 0.2 & 18 + g75.78 & 0.3 & 2.2 & 0.1 & 13 & 12.5 & 136.8 & 0.3 & 45 & 2.5 & 10.3 & 0.2 & 17 + cep a & 0.5 & 7.3 & 0.2 & 45 & 23.2 & 234.7 & 0.4 & 60 & 4.5 & 23.4 & 0.2 & 28 + w3(oh ) & 1.4 & 14.5 & 0.2 & 50 & 18.5 & 148.2 & 0.3 & 30 & 2.4 & 11.6 & 0.1 & 15 + g138.3 & @xmath690.2 & @xmath690.3 & 0.1 & 2 & 5.0 & 10.6 & 0.2 & 8 & 0.3 & 0.5 & 0.1 & 4 + g139.9 & @xmath690.2 & @xmath690.3&0.1 & 11 & 8.6 & 18.8 & 0.1 & 6 & @xmath690.2 & @xmath690.3 & 0.1 & 2 + g192.58 & 0.3 & 1.3 & 0.1 & 8 & 14.5 & 84.2 & 0.2 & 25 & 1.1 & 5.5 & 0.1 & 15 + g192.6 & @xmath690.2 & @xmath690.6&0.2 & 30 & 12.0 & 54.1 & 0.3 & 15 & 0.8 & 2.2 & 0.2 & 8 + g240.3 & @xmath690.1 & @xmath690.4&0.2 & 10 & 7.3 & 59.1 & 0.2 & 30 & 0.4 & 2.5 & 0.1 & 14 + [ tab : fits ] lccrccccc g5.89 & y & n & 0.79 & 39.7 & 421.0 & -8.90 & 5.25&0.2 + g5.97 & n & n & 0.28 & 1.0 & @xmath691.7 & & 5.23 & + g8.67 & y & y & 0.24 & 12.7 & 9.0 & & 5.70 & + g10.47 & y & y & 0.16 & 5.6 & 55.4 & -9.53 & 6.26 & + g12.21 & y & n & 0.22 & 4.0 & 14.0 & -10.15 & 6.17 & + m17s & n & y & 0.33 & 5.7 & @xmath693.9 & @xmath69 - 10.73 & 5.72 & + g19.61 & y & y & 0.22 & 9.8 & 89.0 & -9.72 & 5.42 & + g20.08 & y & n & 0.13 & 5.9 & 38.6 & -10.48 & 4.86 & + g29.96 & y & n & 0.49 & 8.0 & 44.2 & -9.12 & 6.30 & + g31.41 & n & n & & @xmath690.2&@xmath693.9 & @xmath69 - 11.89&5.45 & + g34.26 & y & y & 0.58 & 20.2 & 145.0 & -10.43 & 5.77 & + g45.07 & y & n & 0.32 & 6.8 & 57.6 & -9.54 & 6.15&4 + g45.47 & y & n & 0.21 & 3.7 & @xmath691.7 & & 6.04 & + g61.48 & n & n & 0.23 & 2.9 & @xmath691.7 & @xmath69 - 10.80 & 5.01&7 + k3 - 50a & y & n & 0.40 & 6.5 & 11.7 & -11.60 & 6.35 & + g75.78 & y & n & 0.25 & 6.3 & 12.3 & & 5.65&3.7 + cep a & y & y & 0.47 & 14.2 & 40.8 & -9.78 & 4.40&0.2 + w3(oh ) & y & y & 0.39 & 7.1 & 81.1 & -11.16 & 5.12 & + g138.3 & n & n & 0.11 & 0.3 & @xmath691.7 & & 4.57&17 + g139.9 & n & n & & @xmath690.2 & @xmath691.7 & & 4.82 & 6 + g192.58 & y & y & 0.32 & 3.4 & 7.3 & -10.94 & 4.79&50 + g192.6 & y & y & 0.26 & 1.3 & @xmath693.4 & & & + g240.3 & y & y & 0.16 & 1.5 & @xmath692.2 & & & 2.3 + [ tab : results ] lc@@xmath22ccc@@xmath22c g8.67 & 0.4 & 0.1 & 1.8 & 4&2 + g10.47 & 1.8 & 0.3 & 7.2 & 100&80 + m17s & 1.4 & 0.5 & 5.0 & 4 & 2 + cep a & 0.23&0.07 & 10.0 & 0.17&0.07 + w3(oh ) & 0.06 & 0.02 & 60.0 & 3&1 + g192.58 & 0.8 & 0.3 & & + g192.6 & 0.9 & 0.4 & 4.0 & 2&1 + g34.26 & 1.5 & 0.3 & 3.6 & 14&4 + [ tab : infall_rates ]

we detected sio towards 14 sources and suggest that the non - detections in the other nine sources could be due to those outflows being older and without ongoing shocks to replenish the sio . we detected hco towards all sources , and suggest that it is tracing infall in nine cases . for seven infall candidates , we estimate mass infall rates between 1 and 2 m yr . seven sources show both sio detections ( young outflows ) and hco infall signatures . , we suggest that perhaps both models of ionized accretion and halted accretion may be important in describing the evolution of a massive protostar ( or protostars ) beyond the formation of an hii region .

we present single pointing observations of sio , hco and hco from the james clerk maxwell telescope towards 23 massive star forming regions previously known to contain molecular outflows and ultracompact hii regions . we detected sio towards 14 sources and suggest that the non - detections in the other nine sources could be due to those outflows being older and without ongoing shocks to replenish the sio . we serendipitously detected so towards 17 sources in the same tuning as hco . we detected hco towards all sources , and suggest that it is tracing infall in nine cases . for seven infall candidates , we estimate mass infall rates between 1 and 2 m yr . seven sources show both sio detections ( young outflows ) and hco infall signatures . we also find that the abundance of hco tends to increase along with the abundance of sio in sources for which we could determine abundances . we discuss these results with respect to current theories of massive star formation via accretion . from this survey , we suggest that perhaps both models of ionized accretion and halted accretion may be important in describing the evolution of a massive protostar ( or protostars ) beyond the formation of an hii region .

0708.2578

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high - redshift quasars are among the most luminous objects known and provide direct probes of the distant universe when the first generation of galaxies and quasars formed . in recent years , over twenty @xmath0 quasars with @xmath20 have been discovered ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? these luminous quasars are essential for understanding the accretion history of black holes ( bhs ) , galaxy formation , and chemical evolution at very early epochs . they harbor supermassive bhs with masses higher than @xmath21 and emit near the eddington limit ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , revealing the rapid growth of central bhs at high redshift . their emission lines show solar or supersolar metallicity in the broad line regions , indicating that there was vigorous star formation and element enrichment in the first gigayear of cosmic time ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? their absorption spectra show that the intergalactic medium ( igm ) at @xmath0 is close to the reionization epoch ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the majority of the currently known @xmath0 quasars were discovered from @xmath22 deg@xmath1 of imaging data of the sloan digital sky survey ( sdss ; * ? ? ? they were selected as @xmath23-dropout objects using optical colors . several other high - redshift quasars were discovered based on their infrared or radio emission . for example , @xcite discovered one quasar at @xmath24 in the noao deep wide - field survey ( ndwfs ; * ? ? ? * ) bootes field using the agn and galaxy evolution survey ( ages ) spectroscopic observations . the quasar was selected from a @xmath25 mid - infrared quasar sample and has a @xmath26 magnitude of 20.68 and an optical luminosity of @xmath27 . by matching the flamingos extragalactic survey ir survey @xcite data to the faint images of the radio sky at twenty - cm ( first * ) data , @xcite discovered a radio - loud quasar at @xmath28 in 4 deg@xmath1 of the ndwfs region . this quasar is a broad absorption line ( bal ) quasar with an optical luminosity of @xmath29 , comparable to the luminous sdss quasars at @xmath0 . despite the high - redshift quasar surveys mentioned above , very little is known about faint quasars ( @xmath30 ) at @xmath0 . the sdss main survey only probes the most luminous quasars , and with a density of 1/470 deg@xmath1 @xcite . the @xcite quasar at @xmath24 was @xmath30 , but the sample contains a single object and is selected from an area of less than 10 deg@xmath1 . @xcite found a very faint quasar with @xmath31 at @xmath32 in a 2.5 deg@xmath1 field around the luminous quasar sdss j114816.64 + 525150.3ddmmss.s , and the positions are expressed in j2000.0 coordinates . we use sdss jhhmm@xmath33ddmm for brevity . ] at @xmath34 . @xcite imaged a 3.83 deg@xmath1 region down to @xmath35 in the first results of the canada - france high - redshift quasar survey ( cfhqs ) and did not find any quasars at @xmath36 . in these surveys both the quasar samples and the survey areas are very small , thus they do not provide a good statistical study of high - redshift quasars at @xmath30 . recently , @xcite discovered four quasars at @xmath37 from about 400 deg@xmath1 of the cfhqs , including the most distant known quasar at @xmath38 . three of these quasars have @xmath26 magnitudes fainter than 21 . since their follow - up observations are not yet complete , they did not determine the spatial density of these quasars . finding faint quasars at @xmath0 is important for studying the evolution of the quasar population and quasars impact on their environments . @xcite obtained the bright - end quasar luminosity function ( qlf ) at @xmath0 , but the slope , @xmath39 , was very uncertain due to the small luminosity range of the sample . @xcite put a broad constraint on the bright - end slope of @xmath40 ( @xmath41 ) from the absence of lenses in four quasars at @xmath0 . @xcite have considered the implications of all existing @xmath0 quasar observations , including deep x - ray surveys , for the faint end of the high - redshift qlf . based predominantly on the x - ray surveys , they argue that there is a flattening of the qlf at @xmath42 . with the discovery of faint high - redshift quasars , the qlf can be well determined . the qlf at @xmath0 is important to understand bh growth at early epochs ( e.g. * ? ? ? * ; * ? ? ? * ) . while bright quasars at high redshift have central bh masses between @xmath43 and @xmath44 , fainter quasars with @xmath30 are expected to harbor bhs with masses of a few times 10@xmath45 or below ( e.g. * * ) , which may be associated with galaxies of lower masses . the qlf also enables us to determine the quasar contribution to the uv background at @xmath0 . detection of complete gunn - peterson troughs @xcite among the highest - redshift quasars indicates a rapid increase of the igm neutral fraction at @xmath0 , and suggests that we have reached the end of the reionization epoch ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? it is unclear what individual contributions of galaxies and quasars to the reionization are . although there is evidence showing that quasars are probably not the main contributor to reionization ( e.g. * ? ? * ; * ? ? ? * ; * ? ? ? * ) , a proper determination of the qlf at @xmath0 is needed to constrain the the quasar contribution . in this paper we present the discovery of five @xmath0 quasars with @xmath2 selected from 260 deg@xmath1 of the sdss southern survey , a deep imaging survey obtained by repeatedly scanning a 300 deg@xmath1 area in the fall celestial equatorial stripe @xcite . one of the five quasars , sdss j020332.39 + 001229.3 ( hereafter sdss j0203 + 0012 ) , was independently discovered by matching the ukirt infrared deep sky survey ( ukidss ; * ? ? ? * ) data to the sdss data @xcite . these five quasars , together with another quasar , sdss j000552.34000655.8 ( hereafter sdss j00050006 ) previously discovered in this region @xcite , form a well - defined low - luminosity quasar sample at high redshift . we use this sample and the luminous sdss quasar sample to measure the qlf and constrain the quasar contribution to the reionization of the universe at @xmath0 . the structure of the paper is as follows . in @xmath46 2 we introduce the quasar selection criteria and photometric and spectroscopic observations of quasar candidates . in @xmath46 3 we describe the properties of the five new quasars . we derive the qlf at @xmath0 in @xmath46 4 , and discuss the contribution of quasars to the ionizing background in @xmath46 5 . we give a brief summary in @xmath46 6 . throughout the paper we use a @xmath47-dominated flat cosmology with h@xmath6 km s@xmath7 mpc@xmath7 , @xmath8 , and @xmath9 @xcite .

we present the discovery of five quasars at selected from 260 deg of the sloan digital sky survey ( sdss ) southern survey , a deep imaging survey obtained by repeatedly scanning a stripe along the celestial equator . one of them was independently discovered by the ukirt infrared deep sky survey . these quasars , combined with another quasar known in this region , make a complete flux - limited quasar sample at . we model the bright - end quasar luminosity function ( qlf ) at as a power law .

we present the discovery of five quasars at selected from 260 deg of the sloan digital sky survey ( sdss ) southern survey , a deep imaging survey obtained by repeatedly scanning a stripe along the celestial equator . the five quasars with are 12 magnitudes fainter than the luminous quasars discovered in the sdss main survey . one of them was independently discovered by the ukirt infrared deep sky survey . these quasars , combined with another quasar known in this region , make a complete flux - limited quasar sample at . the sample spans the redshift range and the luminosity range ( h km s mpc , , and ) . we use the method to determine that the comoving quasar spatial density at and is mpc mag . we model the bright - end quasar luminosity function ( qlf ) at as a power law . the slope calculated from a combination of our sample and the luminous sdss quasar sample is , significantly steeper than the slope of the qlf at . based on the derived qlf , we find that the quasar / agn population can not provide enough photons to ionize the intergalactic medium ( igm ) at unless the igm is very homogeneous and the luminosity ( ) at which the qlf power law breaks is very low .

0708.2578

i

we have discovered five quasars at @xmath129 in 260 deg@xmath1 of the sdss deep stripe , including one previously discovered by @xcite . the most distant one is at @xmath28 . these quasars were selected as @xmath23-dropout objects from the coadds of 10 sdss imaging runs , going @xmath132 magnitudes fainter than the sdss main survey . the five quasars , with @xmath2 , are 12 magnitudes fainter than the luminous @xmath0 quasars found in the sdss main survey . the ly@xmath61 emission lines in two quasars sdss j03030019 and sdss j23150023 are narrow ( @xmath187 and 2400 km s@xmath7 ) but strong ( @xmath188 and 127 ) , while the ly@xmath61 emission lines in another two quasars sdss j03030019 and sdss j23150023 are broad ( @xmath189 and 4900 km s@xmath7 ) but weak ( @xmath190 and 17 ) . the fifth one , sdss j0353 + 0104 , is a bal quasar . the new quasars , together with a previously discovered quasar , sdss j00050006 , comprise a flux - limited quasar sample with @xmath3 at @xmath0 over 260 deg@xmath1 . the sample covers the luminosity range @xmath5 . the spatial density of the quasars at @xmath11 and @xmath12 is @xmath13 mpc@xmath14 mag@xmath7 . we use a single power - law form to model the bright - end qlf at @xmath0 and find a slope of @xmath17 , which is significantly steeper than the slope of the qlf at @xmath18 . using the derived qlf , we find that the quasar / agn population can provide enough photons required to ionize the igm at @xmath0 only if the igm is very homogeneous and the characteristic luminosity of the qlf is very low . to put better constraints on the quasar contribution , much deeper surveys are needed . the quasars in this paper were selected from the sdss coadded images with 518 runs . currently the sdss deep stripe has been scanned between 40 and 50 times , reaching @xmath191 magnitudes deeper than the main survey when co - added . we are performing a deeper survey of @xmath0 quasars down to @xmath192 in this region . we expect to obtain a flux - limited sample with @xmath193 in the next few years . we acknowledge support from nsf grant ast-0307384 , a sloan research fellowship and a packard fellowship for science and engineering ( lj , xf ) . we thank the mmt staff , magellan staff , and keck staff for their expert help in preparing and carrying out the observations . funding for the sdss and sdss - ii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , the u.s . department of energy , the national aeronautics and space administration , the japanese monbukagakusho , the max planck society , and the higher education funding council for england . the sdss web site is http://www.sdss.org/. the sdss is managed by the astrophysical research consortium for the participating institutions . the participating institutions are the american museum of natural history , astrophysical institute potsdam , university of basel , cambridge university , case western reserve university , university of chicago , drexel university , fermilab , the institute for advanced study , the japan participation group , johns hopkins university , the joint institute for nuclear astrophysics , the kavli institute for particle astrophysics and cosmology , the korean scientist group , the chinese academy of sciences ( lamost ) , los alamos national laboratory , the max - planck - institute for astronomy ( mpia ) , the max - planck - institute for astrophysics ( mpa ) , new mexico state university , ohio state university , university of pittsburgh , university of portsmouth , princeton university , the united states naval observatory , and the university of washington . adelman - mccarthy , j. k. , et al . 2007a , , in press ( astro - ph/0707.3380 ) adelman - mccarthy , j. k. , et al . 2007b , , submitted ( astro - ph/0707.3413 ) avni , y. , & bahcall , j. n. 1980 , , 235 , 694 barth , a. j. , martini , p. , nelson , c. h. , & ho , l. c. 2003 , , 594 , l95 becker , r. h. , white , r. l. , & helfand , d. j. 1995 , , 450 , 559 becker , r. h. , et al . 2001 , , 122 , 2850 bertin , e. , mellier , y. , radovich , m. , missonnier , g. , didelon , p. , & morin , b. 2002 , astronomical data analysis software and systems xi , 281 , 228 bouwens , r. j. , illingworth , g. d. , blakeslee , j. p. , & franx , m. 2006 , , 653 , 53 boyle , b. j. , shanks , t. , croom , s. m. , smith , r. j. , miller , l. , loaring , n. , & heymans , c. 2000 , , 317 , 1014 bunker , a. j. , stanway , e. r. , ellis , r. s. , & mcmahon , r. g. 2004 , , 355 , 374 chiu , k. , fan , x. , leggett , s. k. , golimowski , d. a. , zheng , w. , geballe , t. r. , schneider , d. p. , & brinkmann , j. 2006 , , 131 , 2722 cool , r. j. , et al . 2006 , , 132 , 823 dijkstra , m. , haiman , z. , & loeb , a. 2004 , , 613 , 646 djorgovski , s. g. , castro , s. , stern , d. , & mahabal , a. a. 2001 , , 560 , l5 douglas , l. s. , bremer , m. n. , stanway , e. r. , & lehnert , m. d. 2007 , , 376 , 1393 elston , r. j. , et al . 2006 , , 639 , 816 fan , x. 1999 , , 117 , 2528 fan , x. , et al . 2000 , , 120 , 1167 fan , x. , et al . 2001a , , 122 , 2833 fan , x. , et al . 2001b , , 121 , 31 fan , x. , narayanan , v. k. , strauss , m. a. , white , r. l. , becker , r. h. , pentericci , l. , & rix , h .- w . 2002 , , 123 , 1247 fan , x. , et al . 2003 , , 125 , 1649 fan , x. , et al . 2004 , , 128 , 515 fan , x. , et al . 2006a , , 131 , 1203 fan , x. , et al . 2006b , , 132 , 117 fan , x. , carilli , c. l. , & keating , b. 2006c , , 44 , 415 fontanot , f. , et al . 2007 , , 461 , 39 fukugita , m. , ichikawa , t. , gunn , j. e. , doi , m. , shimasaku , k. , & schneider , d. p. 1996 , , 111,1748 gnedin , n. y. , & ostriker , j. p. 1997 , , 486 , 581 golimowski , d. a. , et al . 2004 , , 127 , 3516 goto , t. 2006 , , 371 , 769 gunn , j. e. , & peterson , b. a. 1965 , , 142 , 1633 gunn , j. e. , et al . 1998 , , 116 , 3040 gunn , j. e. , et al . 2006 , , 131 , 2332 hogg , d. w. , finkbeiner , d. p. , schlegel , d. j. , & gunn , j. e. 2001 , , 122 , 2129 hopkins , p. f. , hernquist , l. , cox , t. j. , di matteo , t. , martini , p. , robertson , b. , & springel , v. 2005 , , 630 , 705 hopkins , p. f. , richards , g. t. , & hernquist , l. 2007 , , 654 , 731 ivezi , . , et al . 2004 , an , 325 , 583 jannuzi , b. t. , & dey , a. 1999 , in asp conf . 191 , photometric redshifts and high - redshift galaxies , ed . r. j. weymann , l. j. storrie - lombardi , m. sawicki , & r. j. brunner ( san francisco : asp ) , 111 jiang , l. , et al . 2006a , , 132 , 2127 jiang , l. , et al . 2006b , , 131 , 2788 jiang , l. , et al . 2007 , , 134 , 1150 kashikawa , n. , et al . 2006 , , 648 , 7 knapp , g. r. , et al . 2004 , , 127 , 3553 kurk , j. d. et al . 2007 , , in press ( astro - ph/0707.1662 ) li , y. , et al . 2007 , , 665 , 187 lupton , r. h. , gunn , j. e. , & szalay , a. s. 1999 , , 118 , 1406 lupton , r. h. , gunn , j. e. , ivezi , . , knapp , g. r. , kent , s. , & yasuda , n. 2001 , in _ astronomical data analysis software and systems x _ , edited by f. r. harnden jr . , f. a. primini , and h. e. payne , asp conference proceedings , 238 , 269 madau , p. , haardt , f. , & rees , m. j. 1999 , , 514 , 648 mahabal , a. , stern , d. , bogosavljevi , m. , djorgovski , s. g. , & thompson , d. 2005 , , 634 , l9 maiolino , r. , juarez , y. , mujica , r. , nagar , n. m. , & oliva , e. 2003 , , 596 , l155 mcgreer , i. d. , becker , r. h. , helfand , d. j. , & white , r. l. 2006 , , 652 , 157 mcquinn , m. , hernquist , l. , zaldarriaga , m. , & dutta , s. 2007 , , in press ( astro - ph/0704.2239 ) meiksin , a. 2005 , , 356 , 596 miralda - escud , j. , haehnelt , m. , & rees , m. j. 2000 , , 530 , 1 oke , j. b. , & gunn , j. e. 1983 , , 266 , 713 page , m. j. , & carrera , f. j. 2000 , , 311 , 433 pier , j. r. , munn , j. a. , hindsley , r. b. , hennessy , g. s. , kent , s. m. , lupton , r. h. , & ivezic , z. 2003 , , 125 , 1559 richards , g. t. , et al . 2004 , , 127 , 1305 richards , g. t. , et al . 2005 , , 360 , 839 richards , g. t. , et al . 2006 , , 131 , 2766 salvaterra , r. , haardt , f. , & volonteri , m. 2007 , , 374 , 761 schneider , d. p. , schmidt , m. , & gunn , j. e. 1991 , , 101 , 2004 , f. , & mathur , s. 2007 , , 660 , 1051 sheinis , a. i. , bolte , m. , epps , h. w. , kibrick , r. i. , miller , j. s. , radovan , m. v. , bigelow , b. c. , & sutin , b. m. 2002 , , 114 , 851 shen , y. , et al . 2007 , , 133 , 2222 skrutskie , m. f. , et al . 2006 , , 131 , 1163 smith , j. a. , et al . 2002 , , 123 , 2121 spergel , d. n. , et al . 2007 , , 170 , 377 srbinovsky , j. a. , & wyithe , j. s. b. 2007 , , 374 , 627 stoughton , c. , et al . 2002 , , 123 , 485 trump , j. r. , et al . 2006 , , 165 , 1 tucker , d. , et al . 2006 , an , 327 , 821 vanden berk , d. e. , et al . 2001 , , 122 , 549 venemans , b. p. , mcmahon , r. g. , warren , s. j. , gonzalez - solares , e. a. , hewett , p. c. , mortlock , d. j. , dye , s. , & sharp , r. g. 2007 , , 376 , l76 vestergaard , m. 2004 , , 601 , 676 volonteri , m. , & rees , m. j. 2006 , , 650 , 669 warren , s. j. , et al . 2007 , , 375 , 213 willott , c. j. , delfosse , x. , forveille , t. , delorme , p. , & gwyn , s. d. j. 2005 , , 633 , 630 willott , c. j. , , submitted ( astro - ph/0706.0914 ) wyithe , j. s. b. , & loeb , a. 2003 , , 595 , 614 wyithe , j. s. b. , & padmanabhan , t. 2006 , , 372 , 1681 yan , h. , & windhorst , r. a. 2004 , , 612 , l93 york , d. g. , et al . 2000 , , 120 , 1579 zheng , w. , kriss , g. a. , telfer , r. c. , grimes , j. p. , & davidsen , a. f. 1997 , , 475 , 469

the five quasars with are 12 magnitudes fainter than the luminous quasars discovered in the sdss main survey . the slope calculated from a combination of our sample and the luminous sdss quasar sample is , significantly steeper than the slope of the qlf at . based on the derived qlf , we find that the quasar / agn population can not provide enough photons to ionize the intergalactic medium ( igm ) at unless the igm is very homogeneous and the luminosity ( ) at which the qlf power law breaks is very low .

we present the discovery of five quasars at selected from 260 deg of the sloan digital sky survey ( sdss ) southern survey , a deep imaging survey obtained by repeatedly scanning a stripe along the celestial equator . the five quasars with are 12 magnitudes fainter than the luminous quasars discovered in the sdss main survey . one of them was independently discovered by the ukirt infrared deep sky survey . these quasars , combined with another quasar known in this region , make a complete flux - limited quasar sample at . the sample spans the redshift range and the luminosity range ( h km s mpc , , and ) . we use the method to determine that the comoving quasar spatial density at and is mpc mag . we model the bright - end quasar luminosity function ( qlf ) at as a power law . the slope calculated from a combination of our sample and the luminous sdss quasar sample is , significantly steeper than the slope of the qlf at . based on the derived qlf , we find that the quasar / agn population can not provide enough photons to ionize the intergalactic medium ( igm ) at unless the igm is very homogeneous and the luminosity ( ) at which the qlf power law breaks is very low .

1205.5771

i

we present results of radio continuum observations of the edge - on galaxy , ngc 4631 , using the karl g. jansky very large array ( hereafter , the expanded very large array , or evla ) in its c configuration . these are the first results from a new survey , continuum halos in nearby galaxies an evla survey ( chang - es ) , whose motivation , science goals , galaxy sample criteria , and expectations for improvements over previous surveys are described in a companion paper ( * ? ? ? * hereafter , paper i ) . the sample consists of 35 nearby edge - on galaxies and observations are being carried out in two frequency bands ( 1.5 ghz and 6 ghz , i.e. in l - band and c - band , respectively ) in all polarization products . the survey includes observations in three evla array configurations ( b , c , and d ) but the test data presented here were obtained at both frequencies in the c configuration only . in this second paper , our goals are to outline the observations and data reduction procedures used for the test data ( sect . [ sec : n4631 ] ) and to present the initial scientific results for ngc 4631 ( sect . [ sec : results ] ) . we pay particular attention to the data reduction procedures , especially with respect to differences that are introduced by using the wide evla frequency bands that are now available . the galaxy , ngc 4631 , was chosen because of its extensive radio continuum halo which has been known for some time @xcite . for a recent summary of previous observations of this galaxy , see @xcite . in this paper , we refer to the region , @xmath3 kpc , as the disk - halo interface and use ` halo ' for emission on larger scales ( @xmath4 kpc ) . ` high - latitude ' or ` extraplanar ' are also used to describe either of these components . it is worth keeping in mind that halos are not necessarily smooth since substructure is generally observed , depending on the spatial scales that are probed .

chang - es is exploiting the new wide - band , multi - channel capabilities of the karl g. jansky very large array ( i.e. the expanded very large array , or evla ) with observations in two bands centered at 1.5 and 6 ghz in a variety of array configurations with full polarization . these first results are based on c - array test observations in both observing bands of the well - known radio halo galaxy , ngc 4631 . in this paper , we outline the observations and the data reduction steps that are required for wide - band calibration and mapping of evla data , including polarization . polarization results ( uncorrected for internal faraday rotation ) are consistent with previous observations and also reveal some new features . on broad scales ,

we present the first results from the chang - es survey , a new survey of 35 edge - on galaxies to search for both in - disk as well as extra - planar radio continuum emission . chang - es is exploiting the new wide - band , multi - channel capabilities of the karl g. jansky very large array ( i.e. the expanded very large array , or evla ) with observations in two bands centered at 1.5 and 6 ghz in a variety of array configurations with full polarization . the motivation and science case for the survey are presented in a companion paper ( paper i ) . these first results are based on c - array test observations in both observing bands of the well - known radio halo galaxy , ngc 4631 . in this paper , we outline the observations and the data reduction steps that are required for wide - band calibration and mapping of evla data , including polarization . with modest on - source observing times ( 30 minutes at 1.5 ghz and 75 minutes at 6 ghz for the test data ) we have achieved best rms noise levels of 22 and 3.5jy beam at 1.5 ghz and 6 ghz , respectively . new disk - halo features have been detected , among them two at 1.5 ghz that appear as loops in projection . we present the first 1.5 ghz spectral index map of ngc 4631 to be formed from a single wide - band observation in a single array configuration . this map represents tangent slopes to the intensities within the band centered at 1.5 ghz , rather than fits across widely separated frequencies as has been done in the past and is also the highest spatial resolution spectral index map yet presented for this galaxy . the average spectral index in the disk is indicating that the emission is largely non - thermal , but a small global thermal contribution is sufficient to explain a positive curvature term in the spectral index over the band . two specific star forming regions have spectral indices that are consistent with thermal emission . polarization results ( uncorrected for internal faraday rotation ) are consistent with previous observations and also reveal some new features . on broad scales , we find strong support for the notion that magnetic fields constrain the x - ray emitting hot gas .

1205.5771

r

these new evla observations , even though they were obtained during a limited test run in a single array configuration ( table [ table : obs - n4631 ] ) , have revealed a number of new features not before seen in ngc 4631 . in this section , our intention is not to make an exhaustive list of all features , but rather summarize the more obvious or new results and to place them in the context of previous knowledge of this galaxy . the total intensity images displayed in figs . [ fig : l - band ] and [ fig : c - band ] show numerous extensions away from the plane at both frequencies . at l - band , in particular , two of the more prominent features appear in projection as loops or partial loops ( although they could represent shells ) that have been outlined in red in fig . [ fig : l - band]b . although we have noted a few cleaning artifacts in this image to the east and west of the major axis of the galaxy ( sect . [ subsec : imaging ] ) , the loops do not fall within the affected regions and they are either of sufficient signal - to - noise and/or persistent over various uv weightings ( some not displayed here but formed during experimentation with uv weightings as described in sect . [ subsec : imaging ] ) that we consider them to be real features . the diameter of the larger northern loop , which is only partial in fig . [ fig : l - band]b , is 6.3 kpc . it is also visible in the lower resolution fig . [ fig : l - band]c where it appears to ` frame ' the companion dwarf elliptical galaxy , ngc4627 which is 2.6 arcmin to the nw of the galaxy s center . this is likely a coincidence , since we will show below that the loop is related to the hot x - ray gas . the diameter of the smaller more easterly loop is 2.6 kpc and this loop becomes ` filled in ' in the lower resolution fig . [ fig : l - band]c . the eastern side of this loop and the weaker emission that extends upwards from it corresponds to the hi ` worm ' observed by @xcite . the latter feature sits above a significant hi supershell found by those authors whose diameter ( 3 kpc ) is approximately the same as our eastern loop . it is likely that these features are related and are associated with star forming regions that are present in the underlying disk . the closest prominent star formation complex is located at ra @xmath56 12@xmath5 42@xmath6 22@xmath57 , dec @xmath56 32@xmath8 32@xmath9 42@xmath58 ; it is marked with a cross in the h@xmath24 map of fig . [ fig : c - band]c . a search of previous radio continuum images of ngc 4631 @xcite does not reveal these loops , although the continuum image in @xcite shows hints of the larger central loop . since we see extraplanar structure on all scales in this galaxy , detecting specific features requires appropriately weighted uv data over scales that match the feature of interest . the spatial scales highlighted by our new data have now revealed these loops and the other arcs and filaments that we see extending from the plane . it is possible that some of the other broad extensions ( for example , at ra @xmath56 12@xmath5 42@xmath6 12@xmath57 , dec @xmath56 32@xmath8 31@xmath9 30@xmath58 ) would resolve into loops if viewed at higher resolution and sensitivity . the close connection between x - ray emission and the radio halo , first pointed out for this galaxy by @xcite and @xcite , finds stronger support in these observations . in fig . [ fig : l - band_xray ] , we show the soft x - ray emission from fig . [ fig : l - band]a , enhanced to show extra - planar emission , together with the low resolution l - band image from fig . [ fig : l - band]c . in this figure , we see that the x - ray emission forms a loop interior to the northern radio continuum loop , suggesting that hot gas may be confined by magnetic pressure . it is interesting that there is even a smaller vertical x - ray protrusion ( ra @xmath56 12@xmath5 42@xmath6 07@xmath57 , dec @xmath56 32@xmath8 36@xmath59 ) above the gap on the north - eastern side of the radio continuum loop . a close relationship has been found between radio continuum and x - ray emission in the outflow of ngc 253 as well @xcite . we can determine whether such confinement is feasible , assuming a simple case of unity filling factors , by estimating the minimum energy magnetic field strength following @xcite . assuming a proton to electron number density ratio of 100 , a line of sight distance equal to the width of the radio loop as shown in fig . [ fig : l - band_xray ] , an isotropic field direction , and a spectral index equal to the global average disk value , we find b@xmath60 @xmath0 g . the magnetic pressure is then @xmath61 erg @xmath62 . by comparison , the thermal pressure from the hot , x - ray - emitting gas is @xmath63 @xcite , implying that magnetic pressure is indeed sufficient to confine the thermal gas . at c - band , where we have higher spatial resolution ( fig . [ fig : c - band ] ) , we continue to see many vertical extensions . again , we do not discuss every feature , but point out the brightest extension which is on the north of the disk at ra = 12@xmath5 42@xmath6 09@xmath57 , dec = 32@xmath8 33@xmath59 10@xmath58 , and best seen in fig . [ fig : c - band]b . this extension is directly below the west side of the large northern loop seen in fig . [ fig : l - band]b . this feature protrudes 1 kpc above the main emission below it , or about 1.6 kpc from mid - plane . the detail and numerous extensions observed on this map reveal the complexity of the disk - halo interface in this galaxy . the disconnected ` patches ' of emission visible in fig . [ fig : c - band]c above and below the plane appear to represent brighter parts of the broader scale halo emission which has not been detected in its entirety in our data due to missing short spacings at c - band ( sect . [ subsec : imaging ] ) . the feature at ra @xmath56 12@xmath5 42@xmath6 23@xmath57 , dec @xmath56 32@xmath8 34@xmath59 30@xmath58 for example , corresponds to the hi worm mentioned above . the well - known close relationship between radio continuum , h@xmath64 , and co emission is also evident from fig . [ fig : c - band ] , to the extent that ` kinks ' , widenings and narrowings along the major axis are correlated between these components . radio continuum and h@xmath24 peaks are nicely coincident in the wider ` bulge ' region @xcite about 3 arcmin to the east of the galaxy s center within which the bright star formation complex mentioned above is located . the linear polarization maps with observed magnetic field vectors are shown in fig . [ fig : pol_maps ] and the percentage polarization with observed magnetic field vectors for c - band is shown in fig . [ fig : percentpol ] . recall that the q and u images have lower rms than the total intensity images ( sect . [ sec : polarization ] ) and hence some polarized emission can be seen outside of regions of total intensity . all maps have been corrected for foreground ionospheric faraday rotation , where necessary ( sect . [ subsec : pol - cal ] ) , but no faraday rotation correction has been done for the galaxy itself ; therefore , especially in the disk at l - band , we expect significant faraday depolarization , as indicated in sect . [ sec : polarization ] . this is evident in fig . [ fig : pol_maps]a which shows little polarized intensity in the disk at l - band . previous l - band images ( see especially * ? ? ? * ; * ? ? ? * ) similarly show little or no polarization right in the disk . the halo , however , should not be as strongly affected . the effects of faraday rotation should also be lower at c - band ( fig . [ fig : pol_maps]b ) but will not be negligible in the disk . for example , rotation measures of up to @xmath65 300 rad / m@xmath66 have been found for ngc 4631 in a larger 85 arcsec beam @xcite , corresponding to 43 degrees of rotation at 6 ghz ; the value could be higher still in our data set , given our smaller beam . again , away from the plane , faraday rotation should be minor , as has been demonstrated previously for the halo region of the edge - on galaxy , ngc 5775 ( * ? ? ? * cf . figs . 3 and 5 of that paper ) nevertheless , we prefer to be cautious about our comments regarding the magnetic field orientation in the following discussion . at l - band , the most prominent halo feature is a highly linearly polarized spur located at ra @xmath56 12@xmath5 42@xmath6 20@xmath57 , dec @xmath56 32@xmath8 34@xmath9 30@xmath58 . this spur is visible in the linearly polarized map of @xcite and also in the lower resolution 5 ghz map of @xcite . the spur is directly above the eastern radio continuum loop and may be related to the disturbance that has caused that loop as well as the hi supershell below it ( sect . [ sec : results_total ] ) . however , the galaxy also displays an v - shaped field structure on the northern side ( or ` x - shaped ' globally , see above references ) and this spur may be associated with the eastern side of that larger feature . at 6 ghz ( fig . [ fig : pol_maps]b , fig . [ fig : percentpol ] ) , it is interesting that the observed magnetic field orientation within the disk is parallel to the disk . previously published maps have shown the magnetic fields near the center of ngc 4631 to be perpendicular to the disk ( for example , see the 8 ghz image of * ? ? ? * arcsec resolution ) , although at larger radii the fields are parallel to the disk again @xcite . our 12 arcsec observations and omission of the largest spatial scales are targetting different scales and may now be revealing a disk - parallel component near the galaxy s center , although faraday - corrected maps are still required to confirm this . away from the disk , the magnetic field tends to become perpendicular to the plane , in agreement with previous observations . extra - planar polarized emission both to the north - east and north - west of the galaxy s center agrees in general with the image of @xcite at 5 ghz . a final point of interest is the sharpness with which the _ apparent _ magnetic field orientation changes ( 90 degrees within a single beam ) at ra @xmath56 12@xmath5 42@xmath6 12@xmath57 , dec @xmath56 32@xmath8 32@xmath9 30@xmath58 ( see fig . [ fig : percentpol ] ) . this change occurs at the location of a bright hii region complex visible in fig . [ fig : c - band]c which has been labelled cm67 by @xcite . if such a change is still visible after having corrected for faraday rotation , then it lends support for the notion that the magnetic field is swept outwards with the outflow from specific star forming regions . note that there are radio continuum spurs above and below this location ( fig . [ fig : c - band]c ) . if the change is not intrinsic but is due to faraday rotation alone , then either the ordered magnetic field in the line of sight has changed sharply at this position or the electron density has changed abruptly , or both . in either case , cm67 is an important region for follow - up studies with applied rotation measure corrections . our l - band spectral index maps ( figs . [ fig : alpha ] and [ fig : alpha_lowres ] ) are the first that have been formed from _ within _ an observing band for an edge - on galaxy and represent a tangent to the spectrum at 1.5 ghz , rather than an average between broadly separated frequencies as has been done in the past . the average spectral index is @xmath67 = - 0.84 @xmath65 0.05 ( sect . [ sec : spectral_index ] ) and therefore the l - band maps are clearly dominated by non - thermal emission . this result is typical of the values found in other galaxies @xcite and the milky way @xcite . previous values for the disk of ngc 4631 cover a rather wide range ( see * ? ? ? * ) , for example , -0.68 ( from 610 mhz and 10.7 ghz measurements ) , -0.45 ( from 327 mhz and 1.49 ghz ) , -0.69 ( from 327 mhz , 610 mhz , 1412 mhz , and 10.7 ghz data ) , and -0.9 ( from 610 mhz and 1412 mhz ) . also , although the global spectral index of ngc 4631 has been studied extensively @xcite the only previous spectral index _ maps _ that have been published can be found in @xcite whose highest resolution was 58 arcsec . our maps are the highest resolution spectral index maps yet presented for this galaxy . the average , global spectral curvature is positive ( @xmath68 , sect . [ sec : spectral_index ] ) . the most likely explanation is the contribution of thermal emission from the disk . to see whether this is feasible , we use the thermal flux density estimate of @xcite of @xmath69 mjy who makes use of the h@xmath24 luminosity of ngc 4631 and adjusts upwards to account ( roughly ) for dust obscuration . extrapolated to 1.5 ghz with a @xmath70 frequency dependence gives @xmath71 mjy with a variation of 2 mjy across l - band . the curvature that we have found from eqn . [ eqn : spectralfit ] corresponds to an increase of 2% at the upper frequency band edge in comparison to a non - curving spectral index . with a total flux density of 935 mjy at the band center ( sect . [ sec : spectral_index ] ) , a curved spectral index results in an increase of 16 mjy at the high frequency end of the observing band , over the value that would be observed if the spectral index were constant . this increase is less than the estimated thermal flux density at the upper end of the band , so it is clear that a thermal contribution is capable of accounting for the observed curvature . however , thermal emission contributes , on average , less than 7% of the flux at l - band , assuming that the thermal estimate of @xcite can be applied . an interesting result is the detail with which we have mapped the spectral index distribution in a single observation in a single frequency band . as indicated in sect . [ sec : spectral_index ] , the uncertainty at any point is approximately @xmath720.4 , though it becomes lower depending on the size of the region over which averages are taken . for the average spectral index over all maps , the uncertainty is smaller , i.e. @xmath720.05 . consequently , in the following , we point out only values of @xmath24 that are significant in comparison to the uncertainties which have been appropriately averaged over the region of interest and for which there are similar trends for all maps shown in figs . [ fig : alpha ] and [ fig : alpha_lowres ] . for example , contrast in the spectral index is observed in the region of the eastern loop ( see dashed arc in fig . [ fig : l - band]b ) . the contrast is most clearly seen in figs . [ fig : alpha_lowres]a and b. the average spectral index along the sides of the loop itself ( all maps ) is @xmath73 and this value does not differ significantly from the underlying disk at the loop ` footprints ' . in the regions interior to the loop and just exterior to it , on the other hand , the values are much steeper ( darker regions in fig . [ fig : alpha_lowres]a and b ) . the average spectral index interior to the loop is @xmath74 . both values indicate that a thermal contribution will be negligible at these locations and , as we did in sect . [ sec : results_total ] , we estimate a minimum energy magnetic field strength using the same assumptions as in that section but with these measured spectral indices . the result is b@xmath75 @xmath0 g along the loop to @xmath76 hz , results in b@xmath77 @xmath0 g . ] . this is not the first time that spectral index contrasts or steep spectral indices have been observed in galaxies that experience outflows . for example , @xcite show that the spectral index of radio continuum features that are located along hi shells in ngc 5775 is flatter than in the interior and that this flattening can not be due to a thermal contribution . as in ngc 4631 , the spectral index along the loop itself is not significantly different from that of the underlying disk at its location . moreover , although such steep spectral indices are not generally seen in our own galaxy @xcite , @xcite also find regions of very steep spectral index in the galaxy , ngc 253 , i.e. @xmath78@xmath79 is seen within the outflow cone originating from the nuclear region of that galaxy . ngc 4631 is known to be experiencing widely distributed disk - related activity rather than a localized nuclear starburst ( e.g. see * ? ? ? * ) , but the physics may be similar . for ngc 253 , strong electron energy losses are implied , for example . we defer the point - by - point decomposition of the map into thermal and non - thermal components to a future paper ; nevertheless , it is possible to see evidence for the dominance of thermal emission in at least two specific star forming regions , best seen at the highest resolution spectral index maps ( fig . [ fig : alpha ] ) . one has been pointed out earlier ( sect . [ sec : results_total ] ) and is marked with a cross on the h@xmath24 map of fig . [ fig : c - band]c as well as the high resolution spectral index map of fig . [ fig : alpha]b . the spectral index at this position is @xmath24 = -0.16 @xmath65 0.09 ( averaged from fig . [ fig : alpha]b over the star forming region ) which is entirely consistent with a thermal spectrum , within uncertainties . another star forming region located 1 arcmin to the ssw of this location and visible as a discrete peak in fig . [ fig : c - band]c also shows a similarly flat index , consistent with thermal emission .

new disk - halo features have been detected , among them two at 1.5 ghz that appear as loops in projection . this map represents tangent slopes to the intensities within the band centered at 1.5 ghz , rather than fits across widely separated frequencies as has been done in the past and is also the highest spatial resolution spectral index map yet presented for this galaxy . two specific star forming regions have spectral indices that are consistent with thermal emission . we find strong support for the notion that magnetic fields constrain the x - ray emitting hot gas .

we present the first results from the chang - es survey , a new survey of 35 edge - on galaxies to search for both in - disk as well as extra - planar radio continuum emission . chang - es is exploiting the new wide - band , multi - channel capabilities of the karl g. jansky very large array ( i.e. the expanded very large array , or evla ) with observations in two bands centered at 1.5 and 6 ghz in a variety of array configurations with full polarization . the motivation and science case for the survey are presented in a companion paper ( paper i ) . these first results are based on c - array test observations in both observing bands of the well - known radio halo galaxy , ngc 4631 . in this paper , we outline the observations and the data reduction steps that are required for wide - band calibration and mapping of evla data , including polarization . with modest on - source observing times ( 30 minutes at 1.5 ghz and 75 minutes at 6 ghz for the test data ) we have achieved best rms noise levels of 22 and 3.5jy beam at 1.5 ghz and 6 ghz , respectively . new disk - halo features have been detected , among them two at 1.5 ghz that appear as loops in projection . we present the first 1.5 ghz spectral index map of ngc 4631 to be formed from a single wide - band observation in a single array configuration . this map represents tangent slopes to the intensities within the band centered at 1.5 ghz , rather than fits across widely separated frequencies as has been done in the past and is also the highest spatial resolution spectral index map yet presented for this galaxy . the average spectral index in the disk is indicating that the emission is largely non - thermal , but a small global thermal contribution is sufficient to explain a positive curvature term in the spectral index over the band . two specific star forming regions have spectral indices that are consistent with thermal emission . polarization results ( uncorrected for internal faraday rotation ) are consistent with previous observations and also reveal some new features . on broad scales , we find strong support for the notion that magnetic fields constrain the x - ray emitting hot gas .

1205.5771

c

in this paper , we have presented the first results from a new survey , called chang - es , to observe radio continuum halos in 35 edge - on , normal spiral galaxies . the galaxies are being observed in all polarization products in two different bands , 1.5 ghz ( l - band ) and 6 ghz ( c - band ) , and over 3 different evla array configurations . this is the first comprehensive radio continuum survey of halos to include all polarization products . the motivation and science goals for the survey have been presented in paper i. our initial chang - es test observations of ngc 4631 have been carried out at c array alone and therefore are sensitive to the disk , the disk - halo interface , and inner halo emission ; we do not detect the faint large scale halo emission because of the lack of large scale sensitivity in this array configuration . our new results demonstrate that , even with modest integration times , new details of the emission in this galaxy have emerged . one advantage of the wide - band , multi - channel evla capabilities is the ability to form spectral index maps at a common spatial resolution _ within _ a single observing band in a single array configuration . we have formed such maps at l - band . our l - band spectral index map has the highest resolution yet obtained for this galaxy and is the first in - band spectral index map published for an edge - on galaxy . in addition , with appropriate uv weighting , the evla wide bands have allowed us to match spatial resolution between l - band and c - band in a single array configuration . @xmath80 at 1.5 ghz , two extra - planar features appear to form loops in projection . the larger loop is 6.3 kpc in diameter and located on the north side of the disk slightly to the west of center . the smaller loop , 2.6 kpc in diameter , is also on the north side of the disk but towards the east ( see fig . [ fig : l - band]b ) . @xmath80 the larger loop is exterior to the soft x - ray feature observed by @xcite ( fig . [ fig : l - band_xray ] ) . the minimum energy magnetic field is 8 @xmath0 g and the magnetic pressure in this loop ( @xmath61 erg @xmath62 ) is sufficient to constrain the hot x - ray gas ( @xmath63 erg @xmath62 ) . @xmath80 the smaller loop is approximately at the location of the hi worm and supershell identified by @xcite . the spectral index within and adjacent to the loop is much steeper ( @xmath81 ) than along the loop itself ( @xmath82 ) . @xmath80 at 6 ghz , the polarization is higher and the average percentage polarization is 7% over regions within which the s / n was high enough to be measured , i.e. predominantly in the disk . the _ apparent _ magnetic field orientation in the plane of the disk ( uncorrected for faraday rotation ) appears to be parallel to the disk . @xmath80 there is one position in the disk , corresponding to the hii region complex , cm67 , at which the apparent field orientation changes sharply ( fig . [ fig : percentpol ] ) ; this is a target region for future in - depth analysis including faraday rotation . @xmath80 at 1.5 ghz , the average spectral index is @xmath55 , indicating that the emission is predominantly non - thermal , on average , throughout the disk . however , a small thermal contribution is sufficient to explain the observed positive spectral curvature in this band . @xmath80 at specific discrete locations in the disk , it is clear that the thermal contribution is not negligible . an example is the location of a specific star forming region identified with a cross in fig . [ fig : c - band]c whose flat 1.5 ghz spectral index is consistent with thermal emission . jai and djs would like to thank the staff at the evla for their warm welcome and assistance during their sojourn in socorro . research at ruhr - universitt , bochum , is supported by deutsche forschungsgemeinschaft through grants , for1048 and for1254 . the digitized sky surveys were produced at the space telescope science institute under u.s . government grant nag w-2166 . the second palomar observatory sky survey ( poss - ii ) was made by the california institute of technology with funds from the national science foundation , the national geographic society , the sloan foundation , the samuel oschin foundation , and the eastman kodak corporation . the national radio astronomy observatory is a facility of the national science foundation operated under cooperative agreement by associated universities , inc . beck , r. , & krause , m. 2005 , astron . 6 , 326 , 414 bhatnagar , s. , rau , u. , green , d. a. , & rupen , m. p. 2011 , , ( arxiv1106.2796b ) braun , r. , oosterloo , t. a. , morganti , r. , klein , u. , & beck , r. 2007 , , 461 , 455 briggs , d. s. 1995 , high fidelity deconvolution of moderately resolved sources , phd thesis , the new mexico institute of mining and technology , socorro , nm brisken , w. 2003 , evla memo 58 , using grasp8 to study the vla beam cenacchi , e. , dallacasa , d. , & orfei , a. 2006 , mem . suppl . , 10 , 77 clark , b. g. 1980 , , 89 , 377 condon , j. j. 1992 , , 30 , 575 condon , j. j. , cotton , w. d. , & broderick , j. j. 2002 , , 124 , 675 conway , j. e. , cornwell , t. j. , & wilkinson , p. n. 1990 , , 246 , 490 cornwell , t. j. 2008 , ieee j. of selected topics in signal proc . 2 , no . 5 , 793 cornwell , t. j. , golap , k. , & bhatnagar , s. 2008 , ieee j. of selected topics in signal proc . 2 , no . 5 , 647 dumke , m. , krause , m. , & wielebinski , r. , & klein , u. 1995 , , 302 , 691 ekers , r. d. , & sancisi , r. 1977 , , 54 , 973 ghosh , t. , et al . 2011 , arxiv:1112.0509v1 golla , g. 1999 , , 345 , 778 golla , g. , & hummel , e. 1994 , , 284 , 777 heald , g. h. , et al . 2009 , , 503 , 409 heesen , v. , beck , r. , krause , m. , & dettmar , r .- j . 2011 , , 535 , a79 hoopes , c. g. , walterbos , r. a. m. , & rand , r. j. 1999 , , 522 , 659 hummel , e. , & dettmar , r .- j . 1990 , , 236 , 33 hummel , e. , lesch , h. , wielebinski , r. , & schlickeiser , r. 1988 , , 197 , l29 hummel , e. , beck , r. , & dettmar , r .- j . 1991 , , 87 , 309 irwin , j. a. et al . 2011 , , 410 , 1423 irwin , j. a. et al . 2012 , , paper i klein , u. , wielebinski , r. , & beck , r. 1984 , , 133 , 19 krause , m. 2004 , in the magnetized interstellar medium , eds . b. uyaniker , w. reich , and r. wielebinski , copernicus gmbh , katlenburg - lindau . , 173 krause , m. 2009 , in magnetic fields in the universe ii : from laboratory and stars to the primordial universe , revista mexicana de astronoma y astrofsica ( serie de conferencias ) , eds . a. esquivel , j. franco , g. garcia - segura , e. m. de gouvela dal pino , a. lazarian , s. lizano , & a. raga , vol . 36 , 25 lee , s .- w . , irwin , j. a. , dettmar , r .- j . , cunningham , c. t. , golla , g. , & wang , q. d. 2001 , , 377 , 759 niklas , s. , klein , u. , & wielebinski , r. 1997 , , 322 , 19 pacholczyk , a. b. 1970 , radio astrophysics , freeman and co. , san francisco pohl , m. , & schlickeiser , r. 1990 , , 239 , 424 rand , r. j. , & van der hulst , j. m. 1993 , , 105 , 2098 rau , u. , & cornwell , t. j. 2011 , , 532 , a71 reich , p. , reich , w. , & testori , j. c. 2004 , in the magnetized insterstellar medium , ed . b. uyanikar , w. reich , & r. wielebinski , 63 - 68 . sault , r. j. , & wieringa , m. h. 1994 , , 108 , 585 , 448 , 123 simmons , j. f. l. , & stewart , b. g. , , 142 , 100 soida , m. , krause , m. , dettmar , r .- j . , & urbanik , m. 2011 , , 531 , 127 strong , a. w. , orlando , e. , & jaffe , t. r. 2011 , , 534 , a54 sukumar , s. , & velusamy , t. 1985 , , 212 , 367 vaillancourt , j. e. 2006 , , 118 , 1340 wang , q. d. , et al . 1995 , , 439 , 176 wang , q. d. , immler , s. , walterbos , r. , lauroesch , j. r. , & breitschwerdt , d. 2001 , , 555 , l99 werner , w. 1988 , , 201 , 1 array & c & c + no . antennas & 25 & 22 + ac central frequency ( ghz ) & 1.375 & 5.5 + bd central frequency ( ghz ) & 1.625 & 6.5 + spw bandwidth ( mhz ) & 32 & 128 + no . spws ( ac plus bd ) & 16 & 16 + total bandwidth ( ac plus bd)(ghz ) & 0.512 & 2.048 + no . channels / spw & 64 & 64 + total no . channels & 1024 & 1024 + channel separation ( mhz ) & 0.500 & 2.00 + integration time ( s ) & 10 & 10 + obs . time ( min ) & 30 & 75 + flux calibrator & 3c286 & 3c286 + zero - polarization calibrator & oq208 & oq208 + phase calibrator & j1221 + 2813 & j1221 + 2813 + lcccccc uv weighting & briggs rob = 0 & briggs rob = 2 & briggs rob = 2 & briggs rob = 0 & briggs rob = 2 & briggs rob = 0 + uv taper ( k@xmath83 ) & none & none & 5 & none & none & 10 + nterms & 3 & 3 & 3 & 3 & 3 & 3 + no . self - cals & 1 a&p & 1 a&p & 1 a&p & 1 a&p & 1 a&p & 1 a&p + & + figure label & fig . [ fig : l - band](a ) & fig . [ fig : l - band](b ) & fig . [ fig : l - band](c ) & fig . [ fig : c - band](a ) & fig . [ fig : c - band](b ) & fig . [ fig : c - band](c ) + synth . beam + ( @xmath58 , @xmath58 , @xmath8 ) & 11.16 , 10.28 , -175.0 & 16.69 , 14.77 , 34.5 & 29.90 , 26.08 , 48.9 & 2.71 , 2.63 , -50.9 & 4.07 , 3.80 , 27.5 & 8.60 , 8.52 , 41.5 + rms ( @xmath0jy beam@xmath1 ) & 28 & 45 & 100 & 4.8 & 5.5 & 8.0 + & + synth . beam + ( @xmath58 , @xmath58 , @xmath8 ) & 11.01 , 10.13 , -176.8 & 12.28 , 14.41 , 33.7 & 29.35 , 25.51 , at 48.3 & 2.71 , 2.63 , -50.8 & 4.07 x 3.80 at 27.5 & 13.15 , 11.45 , 27.2 + rms ( @xmath0jy beam@xmath1 ) & 27 & 22 & 23 & 4.7 & 3.5 & 7.0 +

we present the first results from the chang - es survey , a new survey of 35 edge - on galaxies to search for both in - disk as well as extra - planar radio continuum emission . the motivation and science case for the survey are presented in a companion paper ( paper i ) . we present the first 1.5 ghz spectral index map of ngc 4631 to be formed from a single wide - band observation in a single array configuration . the average spectral index in the disk is indicating that the emission is largely non - thermal , but a small global thermal contribution is sufficient to explain a positive curvature term in the spectral index over the band .

we present the first results from the chang - es survey , a new survey of 35 edge - on galaxies to search for both in - disk as well as extra - planar radio continuum emission . chang - es is exploiting the new wide - band , multi - channel capabilities of the karl g. jansky very large array ( i.e. the expanded very large array , or evla ) with observations in two bands centered at 1.5 and 6 ghz in a variety of array configurations with full polarization . the motivation and science case for the survey are presented in a companion paper ( paper i ) . these first results are based on c - array test observations in both observing bands of the well - known radio halo galaxy , ngc 4631 . in this paper , we outline the observations and the data reduction steps that are required for wide - band calibration and mapping of evla data , including polarization . with modest on - source observing times ( 30 minutes at 1.5 ghz and 75 minutes at 6 ghz for the test data ) we have achieved best rms noise levels of 22 and 3.5jy beam at 1.5 ghz and 6 ghz , respectively . new disk - halo features have been detected , among them two at 1.5 ghz that appear as loops in projection . we present the first 1.5 ghz spectral index map of ngc 4631 to be formed from a single wide - band observation in a single array configuration . this map represents tangent slopes to the intensities within the band centered at 1.5 ghz , rather than fits across widely separated frequencies as has been done in the past and is also the highest spatial resolution spectral index map yet presented for this galaxy . the average spectral index in the disk is indicating that the emission is largely non - thermal , but a small global thermal contribution is sufficient to explain a positive curvature term in the spectral index over the band . two specific star forming regions have spectral indices that are consistent with thermal emission . polarization results ( uncorrected for internal faraday rotation ) are consistent with previous observations and also reveal some new features . on broad scales , we find strong support for the notion that magnetic fields constrain the x - ray emitting hot gas .

1004.0239

i

long - term ( @xmath0 20 years ) optical light curves are still available only for a relatively small number of active galactic nuclei ( agn ) and blazars . pioneering work in this field was made by several authors ( pica et al . 1988 ; webb et al . 1988 ) on relatively large samples of sources over a time window of about 20 years . for some sources these curves show long - term trends occurring over time scales of decades , while others show only short - term variability . a few sources had dedicated papers to their long - term optical variability . among the best studied sources we recall : oq 530 , whose optical brightness faded at 0.035 mag / yr for about one century ( massaro et al . 2004 ) ; s5 0716 + 71 , showing a monotonic brightening trend of 0.11 mag / yr of its mean luminosity over the last 40 years ( nesci et al . 2005 ) ; on 231 , with a long term decreasing trend of 0.023 mag / yr followed by an increasing one of 0.07 mag / yr ( massaro et al . 2001 ) ; wga 0447.9 - 0322 , with a long monotonic trend of 0.11 mag / yr , similar to s5 0716 + 71 ( nesci et al . 2007 ) ; 5c 3.178 declining at 0.03 mag / yr over 30 years ( sharov 1995 ) . in some cases a periodicity of the outbursts has also been found , the best case by far being oj 287 ( sillampaa et al 1988 , valtonen et al . 2009 ) . other such sources are ao 0235 + 164 , with a possible 5 years period of strong outbursts ( raiteri et al . 2008 and references therein ) and s5 0716 + 71 ( raiteri et al . 2003 ) with recurrence of about 3 years . also in the radio band a few sources have shown periodic outbursts ( e.g. 3c 454.3 , ciaramella et al . 2004 , qian et al . 2009 ) . the origin of the fast variations in blazars is generally explained by the relativistic boosting of perturbations moving down a jet pointing close to the line of sight . the relevant quantity for the boosting is the beaming factor @xmath1 , where @xmath2 and @xmath3 are the lorentz factor and the velocity ( in units of the speed of light ) of the perturbations bulk motion and @xmath4 is the angle between the jet and the line of sight . on the other hand the nature of secular variations is unclear . a suggestive possibility is that they can be associated with changes in the structure and/or direction of the inner jet ( see e.g. kadler et al . it is difficult , however , to obtain a clear evidence of such changes because it requires long and accurate multifrequency campaigns with vlbi angular resolution on a sample of several sources : such a study has been done e.g. by nesci et al . ( 2005 ) in the case of s5 0716 + 71 , suggesting that precession of the jet may indeed explain its observed light curve behavior , or massaro et al . ( 2004 ) in the case of oq 530 . with the successful launch of the fermi satellite for gamma ray astronomy , an all - sky monitoring of the blazars emission has started , which will probably bring to the attention of astronomers a number of poorly known sources . lists of potential gamma ray blazars have been prepared in the framework of the glast project by massaro et al . ( 2009 ) , containing about 2800 objects , and sowards - emmerd et al . ( 2005 ) , listing about 770 northern sky sources . for most of these sources very few data exist , basically those allowing their detection and the classification as an agn . a better knowledge of the properties of these sources will be useful for the interpretation of the gamma - ray data now available from the fermi mission . to determine the historic light curve of agns , an effective way is to use survey plates taken with wide angle instruments , like the schmidt telescopes , in fields covered over a large time span for patrol of other targets , like supernovae or variable stars . a good mine of such material is the archive of the asiago observatory ( http://dipastro.pd.astro.it/asiago/ ) , with its two schmidt instruments , the 67/92 cm , operative between 1965 and 1998 , and the 40/50 cm , operative between 1958 and 1992 . we selected therefore , from the massaro et al . ( 2009 ) catalogue , those sources for which no historic optical light curve is still published , nominally bright enough to be well measurable on the plates of the 67/92 cm telescope ( [email protected] ) , without an obvious strong host galaxy around , and for which a large ( @xmath650 ) number of plates is available spread over a long ( @xmath610 years ) time interval , so that a meaningful historic light curve can be derived . unfortunately , a very small number of sources matched these conditions , mainly due to their optical faintness . in this paper we report the results of our photometric measurements of these plates and the first optical historic light curve for three sources , bzbj1058 + 5611 , bzqj1148 + 5254 and bzbj1209 + 4119 .

all objects show evident long - term variability , over which short - term variations are superposed . one source , bzb j1058 + 5628 , showed a marked quasi - periodic variability of 1 mag on time scale of about 6.3 years , making it one of the few bl lac objects with a quasi- periodic behavior .

we present the historic photographic light curves of three little known blazars ( two bl lacs and one fsrq ) , bzb j1058 + 5628 , bzq j1148 + 5254 and bzb j1209 + 4119 spanning a time interval of about 50 years , mostly built using the asiago plate archive . all objects show evident long - term variability , over which short - term variations are superposed . one source , bzb j1058 + 5628 , showed a marked quasi - periodic variability of 1 mag on time scale of about 6.3 years , making it one of the few bl lac objects with a quasi- periodic behavior .

1004.0239

c

pica et al . ( 1988 ) and webb et al . ( 1988 ) studied the long - term behavior of several tens of agns with photographic plates for 15 to 20 years . for 61 sources they had enough data to morphologically classify their light curve in four types : class i flickering without long term trend ; class ii long term trend with small flickering ; class iii long term and short term variability of comparable amplitude ; class iv rare outburst with stable flux level . in the blazar sample of 22 sources of webb et al . ( 1988 ) there is no significant difference in the frequency of the light curve classes between fsrq and bl lac objects , while a marked difference between blazars and qso exists in the pica et al . ( 1988 ) sample of 39 sources , which includes a good number of radio steep spectrum quasars and radio quiet qso . to have some physical insight of our sources we report in table 7 some basic data : column 1 is the name , column 2 the log(power ) at 1.4 ghz , column 3 the absolute r magnitude computed from the usno b1 catalogue magnitude and literature redshift , column 4 the radio / optical flux ratio , column 5 the nir spectral slope from the jhk magnitudes in the 2mass catalogue , column 6 the optical spectral slope from the sdss data . we remark that , at variance with the other two sources , the spectral slopes computed for bzqj1148 + 52 have a very poor @xmath19 and are therefore marked with `` : '' . actually the spectrum of this source can not be well fitted with a power law in neither of the two explored ranges , probably due to the strong emission lines ( e.g. c iv equivalent width is 77 ) and of the uv bump which falls in the optical due to the source redshift . it is apparent from this table that our three sources are flat - spectrum radio - loud objects ( radio / optical flux ratio @xmath610 ) but have different absolute luminosities and show substantially different behaviors in their optical light curve . the strong - lined object is the brightest both in the radio and optical bands . only bzbj1058 + 56 was detected in gamma - rays by fermi - lat ( abdo et al . 2009 ) and possibly also by egret ( bloom et al . 2000 ) . from the point of view of the overall spectral energy distribution , a much used tool for the classification of blazars is the @xmath20 diagram ( padovani and giommi 1995 ) . on this diagram the blazars mainly occupy two areas : a horizontal branch and a diagonal branch ; a diagonal line of negative slope -1 is a line of constant radio / x - ray flux ratio . the line at @xmath21=0.75 is the formal border between hbl and lbl sources ( padovani and giommi 1995 ) . extreme hbl sources are located at the left side of the horizontal branch , extreme lbl at the upper side of the diagonal branch . for a synchrotron self compton emission model , as the peak of the synchrotron emission of a blazar moves from lower ( @xmath22hz ) to higher ( @xmath23hz ) frequencies the location of the source on this diagram moves from the upper left corner to the lower right one along the diagonal line and then back to the left along the horizontal branch . we report in fig . 7 this diagram for the sources in the roma bzcat , with the positions of our three objects marked . bzbj1209 + 41 and bzqj1148 + 52 have @xmath21 larger than 0.75 , and are located in the diagonal branch , with bzbj1209 being the most radio loud . bzbj1058 + 56 is already on the horizontal branch and is an hbl , as discussed by donato et al . ( 2005 ) also on the basis of bepposax x - ray spectra . none of them is however an extreme case . bzbj1058 + 56 showed regular oscillations of about 1 mag amplitude , with timescale of @xmath152300 days , over a monotonic decreasing trend of 0.07 mag / year ; it can be classified as class iii and is the source with the larger variability . its historic light curve contains 5 outbursts sampled by the asiago plate archive ; this source seems therefore an interesting case of quasi - periodic bl lac . further multiwavelength monitoring of this source , should be performed . bzqj1148 + 52 showed a monotonic decreasing trend with a slope similar to 1058 + 56 but without the oscillating behavior : the detected short - term variability is comparable to our photometric uncertainty , so no firm conclusions can be derived on their time scale . it can be put into class ii . it showed a substantially smaller variability than the other two bl lacs , both on short and long time scales . bzbj1209 + 41 showed a slight increasing trend ( 0.04 mag / year ) with large dips in its light curve : it is therefore quite unusual ( the opposite of class i ) and deserves further monitoring . unfortunately it is not bright enough to be easily followed with small telescopes . when a time interval of about 50 years in considered , all the long term trends detected in the time window of 27 years sampled by the asiago plates do not seem to hold , so that they might be considered just as part of longer variability trends . which processes can be behind these secular trends ? both physical processes and geometrical effects can be at work : in the first case one can imagine a monotonic variation of the number of radiating electrons , or of the average ambient magnetic field ; in the second case , a change in the doppler boosting factor along our line of sight due to the jet precession . the latter possibility can be considered as an indicator of a massive black hole binary system in the nuclear region ( see e.g. romero et al . 2003 ) . if we interpret the long term trends of our three sources as due to a slow precession of the jet , as in was supposed to be in the case of s5 0716 + 71 ( nesci et al . 2005 ) , then the periodicity should be of several 10@xmath24 days and therefore comparable to ( or even larger than ) the human lifetime . this poses a strong challenge because observations must be accumulated for several tens of years before any firm conclusion can be reached . a further difficulty for the data interpretations , if the monitoring is not dense enough , could be the occurrence of fast and/or large occasional outbursts / dips , which can mask the long - term trends . a strong support to confirm the precession model could come from imaging at high radio frequencies with vlbi techniques , which could detect monotonic variations in the jet direction and/or at lower frequencies showing residuals of radio emission in regions involved by the crossing of the jet in the past ( see e.g. massaro et al . 2004 ) . finally , we remark that the detection of the quasi - periodicity of bzb j1058 + 56 from the asiago plates suggests that further discoveries could be made using other , still unexplored , photographic plate archives . we thank the asiago observatory and the department of astronomy of padova university for hospitality for the plate archive search , and alfredo segafredo for scanning part of the plates . the guide star catalogue - ii is a joint project of the space telescope science institute and the osservatorio astronomico di torino ( oato / inaf ) . this research made use of the cds ( strasbourg ) , ned ( nasa /ipac extragalactic database ) and sdss ( sloan digital sky survey ) databases . abdo , a. a. et al . 2009 , , 700 , 597 adelman - mccarthy et al . 2008 , , 175 , 297 . the sixth data release of the sloan digital sky survey bade , n. , beckmann , v. , douglas , n. g. , barthel , p. d. , engels , d. , cordis , l. , nass , p. , & voges , w. 1998 , , 334 , 459 bloom , s. d. , hallum , j. , terasranta , h. , & tornikoski , m. 2000 529 , 675 ciaramella , a. , bongardo , c. , aller , h.d . , aller , m.f . , de zotti , g. , et al . 2004 , 419 , 485 collinge m. j. ; strauss , m. a. ; hall , p.b . 2005 , , 129 , 2542 donato , d. , sambruna , r. m. , & gliozzi , m. 2005 , , 433 , 1163 giveon , u. , maoz , d. , kaspi , s. , netzer , h. , & smith , p.s . 1999 , , 306 , 637 kadler , m. , hughes , p.a . , ros , e. , aller , m.f . , & aller , h.d . 2006 , , 456 , l1 laurent - muehleisen , s. a. , kollgaard , r. i. , ciardullo , r. , feigelson , e. d. , brinkmann , w. , & seibert , j. 1998 , , 118 , 127 lenz , p. , breger , m. , 2005 , coast 146 , 53 marcha m. j. m. , browne , i. w. a.,impey , c. d. , & smith , p. s. 1996 , , 281 , 425 massaro , e. , mantovani , f. , fanti , r. , nesci , r. , tosti , g. , & venturi , t. 2001 , , 374 , 435 massaro , e. , mantovani , f. , fanti , r. et al . 2004 , , 423 , 935 massaro , e. , giommi , p. , leto , c. , et al . 2009 , , 495 , 691 nesci , r. , massaro , e. , rossi , c.,sclavi , s. , maesano , m. , & montagni , f. 2005 , , 130 , 1466 nesci , r. , mandalari , m , & gaudenzi , s. , 2007 , , 133 , 965 padovani , p. , & giommi , p. , 1995 , , 444 , 567 pica , a.j . , smith , a.g . , webb , j.r . , leacock , r.j . , clements , s. , & gombola , p.p . 1998 , , 96 , 1215 qian , s.j . , kudryavtseva , n.a . , britzen , s. , krichbaum , t.p . , witzel , a , et al . 2007 chjaa , 7 , 364 raiteri , c. m. , villata , m. , chen , w. p. , et al . 2008 , , 485 , l17 raiteri , c.m . , villata , m. , tosti , g. , nesci , r. , et al . 2003 , 402 , 151 romero , g. e. , fan , jun - hui , & nuza , s. e. 2003 , chjaa , 3 , 516 sharov , a. , s. , 1995 , astronomy letters 21 , 447 . sillanp , a. , haarala , s. , valtonen , m. j. , sundelius , b. , & byrd , g. g. 1988 , , 325 , 628 sowards - emmerd , d. , romani , r.w . , michelson , p.f . , healey , s.e . , & nolan , p.l . 2005 , , 626 , 95 trager , s. c. , worthey , g. , faber , s. m. , burstein , d. , & gonzalez , j. j. 1998 , , 116,1 valtonen , m. j. , nilsson , k. , villforth , c. , lehto , h. j. , takalo , l. o. , et al . 2009 , , 698 , 781 lindfors , e. ; sillanp , a. ; hentunen , v .- p . ; mikkola , s. ; zola , s. ; webb , j.r . , smith , a.g . , leacock , r.j . , fitzgibbons , g.l . , gombola , p.p . , & shepherd , d.w . 1998 , , 95 , 374 cccccc + 164.27350 & 56.53899 & b & 16.55 & 16.62 & 0.08 + 164.32579 & 56.43882 & c & 17.72 & 17.66 & 0.08 + 164.34494 & 56.44861 & e & 17.68 & 17.74 & 0.09 + 164.35300 & 56.38940 & d & 16.09 & 16.00 & 0.09 + 164.38134 & 56.46707 & f & 17.22 & 17.29 & 0.09 + 164.47731 & 56.45302 & i & 15.61 & 15.80 & 0.07 + 164.47977 & 56.58929 & j & 16.16 & 16.38 & 0.08 + 164.60784 & 56.44601 & k & 16.58 & 16.65 & 0.08 + 164.61842 & 56.54285 & l & 17.01 & 16.98&0.09 + 164.62266 & 56.43455 & m & 15.58 & 15.57 & 0.05 + 164.65048 & 56.34049 & n & 15.19 & 15.33 & 0.06 + 164.65070 & 56.53979 & o & 15.94 & 15.92 & 0.06 + 164.67445 & 56.50317 & p & 17.73 & 17.67 & 0.08 + 164.69448 & 56.39540 & q & 15.43 & 15.31 & 0.06 + 164.75473 & 56.33177 & r & 17.12 & 17.03 & 0.07 + 164.80188 & 56.49624 & s & 17.71 & 17.60 & 0.08 + 164.82489 & 56.33905 & t & 15.50 & 15.43 & 0.09 + 164.84320 & 56.37278 & u & 17.18 & 17.32 & 0.13 + 164.97340 & 56.44394 & y & 16.18 & 16.02 & 0.16 + 164.97473 & 56.48899 & w & 17.43 & 17.35 & 0.14 + cccccc + 177.21235 & 52.93091 & b & 16.14 & 16.20 & 0.09 + 177.28202 & 52.84490 & e & 17.34 & 17.27 & 0.12 + 177.43974 & 52.97246 & f & 17.87 & 17.77 & 0.14 + 177.43928 & 52.98250 & g & 17.77 & 17.78 & 0.14 + 177.49464 & 52.97587 & h & 16.29 & 16.22 & 0.11 + 177.50878 & 52.98667 & i & 17.40 & 17.48 & 0.15 + 177.44770 & 53.04665 & l & 16.67 & 16.90 & 0.12 + 177.02230 & 52.99680 & m & 17.80 & 17.83 & 0.13 + 177.09700 & 53.01454 & n & 17.81 & 17.70 & 0.13 + 177.10528 & 52.90447 & p & 15.66 & 15.48 & 0.05 + 177.13476 & 52.89412 & q & 15.92 & 16.05 & 0.13 + 177.19421 & 53.00136 & s & 15.98 & 15.95 & 0.09 + 177.25626 & 53.02330 & t & 17.35 & 17.27 & 0.14 + 176.96426 & 52.95703 & u & 15.29 & 15.43 & 0.08 + 177.15185 & 52.84147 & v & 16.94 & 16.92 & 0.12 + cccccc + 182.48757 & 41.35025 & b & 17.02 & 17.09 & 0.09 + 182.38187 & 41.43152 & d & 17.00 & 17.06 & 0.08 + 182.41075 & 41.24259 & e & 16.23 & 16.30 & 0.07 + 182.23561 & 41.42514 & f & 16.98 & 17.09 & 0.09 + 182.39451 & 41.35070 & g & 18.34 & 18.24 & 0.16 + 182.38566 & 41.35420 & h & 16.07 & 16.20 & 0.12 + 182.19538 & 41.40745 & i & 16.59 & 16.67 & 0.07 + 182.20402 & 41.23872 & j & 14.97 & 14.97 & 0.11 + 182.33838 & 41.27927 & m & 15.36 & 15.33 & 0.07 + 182.29515 & 41.21913 & o & 17.49 & 17.40 & 0.09 + 182.35833 & 41.18281 & p & 15.34 & 15.29 & 0.06 + 182.29730 & 41.24304 & q & 18.63 & 18.42 & 0.16 + 182.37593 & 41.18086 & r & 17.83 & 17.81 & 0.13 + 182.37925 & 41.37451 & s & 18.39 & 18.02 & 0.12 + 182.44092 & 41.37890 & t & 18.03 & 18.39 & 0.21 + 182.21330 & 41.44316 & w & 18.01 & 17.91 & 0.16 + 182.20821 & 41.44291 & z & 17.83 & 17.86 & 0.12 + lcccc osc o712 & none & 34454.7917 & 16.25 & 0.35 + s40 02499&panc & 37694.2986 & 14.92 & 0.06 + s40 02529&panc & 37696.4341 & 14.83 & 0.08 + s40 02552&panc & 37698.4230 & 15.55 & 0.10 + s40 02605&panc & 37702.3035 & 14.73 & 0.08 + s40 02615&panc & 37707.5452 & 14.84 & 0.09 + s40 02634&panc & 37719.3348 & 15.00 & 0.10 + s40 02659&panc & 37732.3153 & 14.88 & 0.08 + s40 02691&panc & 37753.4709 & 14.93 & 0.08 + s40 02708&panc & 37760.3709 & 14.92 & 0.07 + s40 02732&panc & 37763.3938 & 14.83 & 0.11 + s40 02755&panc & 37780.3271 & 15.06 & 0.09 + s40 02781&panc & 37786.3313 & 14.74 & 0.07 + s40 02831&panc & 37817.4757 & 14.67 & 0.05 + s40 02845&panc & 37821.4848 & 14.92 & 0.21 + s40 02861&panc & 37824.5278 & 15.10 & 0.12 + s40 02896&panc & 37843.4882 & 14.74 & 0.16 + s40 03291&panc & 37972.6174 & 15.43 & 0.09 + s40 03324&panc & 37992.5924 & 15.22 & 0.15 + s40 03360&panc & 37998.5827 & 15.54 & 0.12 + s40 03400&panc & 38001.6591 & 15.27 & 0.10 + s40 03435&panc & 38005.6243 & 15.35 & 0.08 + s40 03504&panc & 38020.5355 & 15.47 & 0.09 + s40 03600&panc & 38049.5528 & 15.41 & 0.09 + s40 03675&panc & 38055.5382 & 15.41 & 0.06 + s40 03741&panc & 38081.4813 & 15.34 & 0.08 + s40 03817&panc & 38089.6466 & 15.20 & 0.10 + s40 03864&panc & 38106.3757 & 15.20 & 0.08 + s40 03908&panc & 38139.3243 & 15.35 & 0.14 + s40 03946&panc & 38166.4146 & 15.51 & 0.10 + s40 04007&panc & 38193.3931 & 15.06 & 0.06 + s40 04055&panc & 38207.5049 & 15.40 & 0.08 + s40 04138&none & 38316.6216 & 15.62 & 0.12 + s40 04235&panc & 38346.6146 & 15.40 & 0.07 + s90 00060&none & 39093.6000 & 15.41 & 0.04 + s90 00182&none & 39168.5667 & 15.06 & 0.04 + s90 00228&none & 39199.4076 & 15.64 & 0.11 + s90 00473&none & 39475.6201 & 15.28 & 0.06 + s90 00573&none & 39506.6292 & 15.54 & 0.10 + s90 00635&none & 39587.3840 & 15.35 & 0.08 + s90 00651&none & 39609.3285 & 15.34 & 0.06 + s90 00690&none & 39622.4472 & 15.18 & 0.04 + s90 01295&none & 39864.5653 & 15.48 & 0.09 + s90 01466&gg13 & 39914.4542 & 15.71 & 0.14 + s90 01571&gg13 & 39942.4750 & 15.56 & 0.07 + s90 01587&gg13 & 39947.3979 & 15.68 & 0.09 + s90 01623&gg13 & 39972.3958 & 15.62 & 0.06 + s40 06837&panc & 40150.6035 & 15.34 & 0.11 + s40 06838&none & 40150.6146 & 15.14 & 0.34 + s90 02203&gg13 & 40260.4757 & 15.39 & 0.05 + s90 02225&gg13 & 40263.4660 & 15.30 & 0.12 + s90 02230&gg13 & 40267.5819 & 15.12 & 0.08 + s90 02246&gg13 & 40271.4701 & 15.31 & 0.04 + s90 02276&gg13 & 40290.3903 & 15.81 & 0.04 + s40 07158&panc & 40319.4063 & 15.20 & 0.13 + s90 02289&gg13 & 40319.4861 & 15.30 & 0.05 + s90 02301&gg13 & 40321.5708 & 15.33 & 0.03 + s90 02315&gg13 & 40322.4868 & 15.30 & 0.04 + s40 07220&panc & 40327.3757 & 15.46 & 0.13 + s90 02350&gg13 & 40329.5382 & 15.51 & 0.03 + s40 07301&panc & 40392.4237 & 15.49 & 0.11 + s40 07302&panc & 40392.4333 & 15.49 & 0.12 + s40 07321&panc & 40412.4341 & 15.60 & 0.12 + s40 07494&panc & 40505.6098 & 15.68 & 0.13 + s90 04272&none & 40979.4882 & 16.34 & 0.06 + s90 04212&none & 40999.5375 & 16.10 & 0.09 + s90 04213&none & 40999.5521 & 16.06 & 0.06 + s90 05376&none & 41446.3486 & 15.82 & 0.19 + s90 07799&gg13 & 42425.4889 & 15.53 & 0.05 + s90 07880&gg13 & 42459.5257 & 15.46 & 0.05 + s90 07895&gg13 & 42514.3826 & 15.59 & 0.06 + s90 08415&gg13 & 42833.4562 & 15.81 & 0.10 + s90 08453&gg13 & 42863.4681 & 15.84 & 0.03 + s90 08925&gg13 & 43187.3549 & 16.36 & 0.15 + s90 08949&gg13 & 43226.4403 & 16.19 & 0.10 + s90 09446&gg13 & 43540.3833 & 16.30 & 0.11 + s90 09479&gg13 & 43569.3611 & 16.49 & 0.09 + s90 09818&gg13 & 43843.5243 & 16.16 & 0.09 + s90 09991&gg13 & 43966.5528 & 16.45 & 0.05 + s90 10300&gg13 & 44203.5389 & 16.38 & 0.07 + s90 10318&gg13 & 44220.4896 & 16.57 & 0.04 + s90 10368&none & 44250.3910 & 16.67 & 0.13 + s90 10393&none & 44273.3826 & 16.35 & 0.11 + s90 10467&none & 44344.4153 & 16.18 & 0.07 + s90 10780&none & 44611.5354 & 15.73 & 0.06 + s90 10816&none & 44630.3521 & 15.97 & 0.07 + s90 10864&none & 44636.4799 & 15.88 & 0.08 + s90 11238&none & 44931.5403 & 15.62 & 0.09 + s90 11273&none & 44941.4799 & 15.61 & 0.11 + s90 11328&gg13 & 44988.4722 & 16.11 & 0.06 + s90 11416&gg13 & 45026.5333 & 15.85 & 0.05 + s90 11462&gg13 & 45053.4306 & 15.91 & 0.06 + s90 11535&gg13 & 45105.4257 & 15.68 & 0.07 + s90 11847&none & 45343.4743 & 16.01 & 0.06 + s90 11934&none & 45367.4444 & 16.16 & 0.06 + s90 11981&none & 45398.4174 & 16.12 & 0.08 + s90 12029&none & 45407.4458 & 16.06 & 0.05 + s90 12057&none & 45440.3674 & 16.24 & 0.09 + s90 12307&gg13 & 45647.5139 & 17.05 & 0.05 + s90 12453&gg13 & 45766.5125 & 16.88 & 0.05 + s90 12483&gg13 & 45814.3646 & 17.20 & 0.05 + s90 12669&gg13 & 46027.5111 & 16.67 & 0.04 + s90 12748&gg13 & 46062.4549 & 16.71 & 0.09 + s90 13784&gg13 & 46909.4167 & 16.77 & 0.05 + s90 13998&gg13 & 47184.5174 & 16.77 & 0.07 + s90 14019&gg13 & 47205.4882 & 16.56 & 0.04 + s90 14052&gg13 & 47212.5042 & 16.54 & 0.04 + s90 14066&gg13 & 47231.3722 & 16.62 & 0.03 + s90 14413&gg13 & 47556.4083 & 16.44 & 0.04 + s90 14427&gg13 & 47558.4354 & 16.40 & 0.05 + s90 14984&gg13 & 48275.5528 & 16.30 & 0.09 + osc sj03821 & gg395 & 48296.8333 & 16.19 & 0.07 + s90 15014&gg13 & 48301.4118 & 16.34 & 0.12 + s90 15031&gg13 & 48329.3840 & 16.46 & 0.05 + s90 15136&gg13 & 48628.5125 & 15.98 & 0.05 + sdss ccd & g & 52263.0000 & 16.20 & 0.05 + vallin ccd & b & 54995.3625 & 15.33 & 0.16 + rrrrr osc o59 & none & 33360.8611 & 16.18 & 0.10 + s90 00201&none & 39181.4630 & 16.32 & 0.06 + s90 00235&none & 39201.4450 & 16.34 & 0.08 + s90 00484&none & 39477.5120 & 16.45 & 0.07 + s90 00561&none & 39503.4980 & 16.29 & 0.06 + s90 00625&gg13 & 39565.6040 & 16.40 & 0.10 + s90 00654&none & 39610.3470 & 16.51 & 0.06 + s90 01482&gg13 & 39938.3600 & 16.43 & 0.05 + s90 02382&gg13 & 40362.5150 & 16.48 & 0.08 + s90 02389&gg13 & 40364.4920 & 16.38 & 0.10 + s90 02403&gg13 & 40375.3970 & 16.63 & 0.11 + s90 02404&gg13 & 40386.3900 & 16.53 & 0.09 + s90 02405&gg13 & 40387.3900 & 16.55 & 0.10 + s90 02420&gg13 & 40406.4180 & 16.88 & 0.10 + s90 04273&gg13 & 41040.4990 & 16.74 & 0.06 + s90 04301&gg13 & 41057.4030 & 16.79 & 0.04 + s90 05319&none & 41393.4840 & 16.91 & 0.12 + s90 07151&gg13 & 42134.3530 & 16.76 & 0.08 + s90 07155&gg13 & 42149.4560 & 16.82 & 0.07 + s90 07870&gg13 & 42453.5000 & 16.91 & 0.05 + s90 07893&gg13 & 42511.5220 & 16.82 & 0.04 + s90 07898&gg13 & 42514.4610 & 16.85 & 0.05 + s90 08416&gg13 & 42835.4810 & 16.96 & 0.03 + s90 08532&gg13 & 42889.4340 & 16.73 & 0.10 + s90 08854&gg13 & 43140.5700 & 16.99 & 0.04 + s90 08928&gg13 & 43191.5140 & 16.91 & 0.05 + s90 08951&gg13 & 43226.4930 & 16.89 & 0.05 + s90 09444&gg13 & 43311.3970 & 16.73 & 0.11 + s90 09472&gg13 & 43553.5480 & 16.78 & 0.09 + s90 09486&gg13 & 43631.3660 & 16.95 & 0.05 + s90 09838&gg13 & 43846.5620 & 16.75 & 0.09 + s90 09910&gg13 & 43905.5020 & 16.81 & 0.04 + s90 09918&gg13 & 43926.4350 & 17.04 & 0.08 + s90 09943&gg13 & 43936.4310 & 16.96 & 0.05 + s90 09961&gg13 & 43960.3160 & 16.83 & 0.06 + s90 09967&gg13 & 43962.3930 & 16.79 & 0.06 + s90 09969&gg13 & 43963.3750 & 16.85 & 0.05 + s90 09984&gg13 & 43966.4140 & 16.95 & 0.11 + s90 10000&gg13 & 43986.4000 & 16.89 & 0.07 + s90 10028&gg13 & 44013.4060 & 16.86 & 0.10 + s90 10061&gg13 & 44017.4480 & 16.76 & 0.09 + s90 10309&gg13 & 44219.4630 & 16.92 & 0.07 + s90 10372&none & 44252.3540 & 17.13 & 0.18 + s90 10391&none & 44275.3410 & 17.09 & 0.11 + s90 10817&none & 44630.3770 & 17.03 & 0.10 + s90 10887&none & 44640.4960 & 16.79 & 0.09 + s90 11240&none & 44931.6040 & 16.87 & 0.05 + s90 11305&gg13 & 44972.6130 & 16.88 & 0.06 + s90 11329&gg13 & 44988.4990 & 16.99 & 0.05 + s90 11452&gg13 & 45048.4390 & 17.02 & 0.10 + s90 11481&gg13 & 45055.4430 & 16.90 & 0.04 + s90 11502&gg13 & 45086.4250 & 17.00 & 0.06 + s90 11855&none & 45344.4910 & 17.05 & 0.07 + s90 11942&none & 45378.4680 & 16.92 & 0.05 + s90 12028&none & 45407.4260 & 17.07 & 0.06 + s90 12059&none & 45440.4140 & 16.97 & 0.09 + s90 12455&gg13 & 45766.5700 & 17.10 & 0.08 + s90 12482&gg13 & 45813.4320 & 16.87 & 0.11 + s90 12485&gg13 & 45814.4090 & 17.02 & 0.10 + s90 12700&none & 46035.5630 & 17.00 & 0.07 + s90 12711&gg13 & 46049.3910 & 16.77 & 0.12 + s90 12746&gg13 & 46061.4730 & 17.02 & 0.06 + s90 12829&gg13 & 46171.3960 & 17.09 & 0.10 + s90 13211&none & 46419.5460 & 17.12 & 0.09 + s90 13231&gg13 & 46442.5120 & 17.16 & 0.06 + s90 13292&gg13 & 46478.4550 & 17.40 & 0.07 + s90 13303&gg13 & 46495.4500 & 17.18 & 0.10 + s90 13335&none & 46563.3790 & 17.06 & 0.08 + s90 13602&gg13 & 46770.5420 & 17.09 & 0.04 + s90 13756&gg13 & 46879.4530 & 17.01 & 0.05 + s90 13779&gg13 & 46908.3580 & 17.07 & 0.04 + s90 13796&none & 46937.3680 & 17.23 & 0.12 + s90 14025&gg13 & 47208.3990 & 17.24 & 0.04 + s90 14069&gg13 & 47231.4520 & 17.02 & 0.03 + s90 14422&gg13 & 47560.5290 & 17.17 & 0.03 + s90 14487&gg13 & 47586.4520 & 17.05 & 0.05 + s90 14516&gg13 & 47593.3880 & 17.19 & 0.05 + s90 14535&gg13 & 47651.3990 & 17.11 & 0.07 + s90 15374&gg13 & 48987.4730 & 17.31 & 0.10 + osc sj05730 & gg395 & 49456.7896&17.20 & 0.05 + sdss ccd & b & 52288.0000&17.17 & 0.03 + vallin ccd & b & 54995.3500 & 16.61 & 0.09 + rrrrr osc o1367 & none & 35190.8611 & 17.50 & 0.10 + s90 00184 & none & 39171.5993 & 18.10 & 0.08 + s90 00237 & none & 39201.4681 & 18.15 & 0.13 + s90 00297 & none & 39287.4389 & 17.78 & 0.17 + s90 00631 & none & 39585.4861 & 18.00 & 0.09 + s90 00648 & none & 39593.3966 & 18.15 & 0.12 + s90 00692 & none & 39622.4952 & 17.76 & 0.13 + s90 01519 & gg13 & 39942.5063 & 17.54 & 0.08 + s90 05377 & none & 41449.3452 & 17.54 & 0.08 + s90 06896 & gg13 & 42016.6196 & 17.62 & 0.21 + s90 07667 & none & 42391.5167 & 17.73 & 0.05 + s90 07748 & gg13 & 42402.5980 & 17.77 & 0.10 + s90 07851 & gg13 & 42451.5091 & 18.10 & 0.06 + s90 07905 & gg13 & 42515.4299 & 18.02 & 0.07 + s90 07942 & gg13 & 42541.4966 & 17.66 & 0.07 + s90 07976 & gg13 & 42569.3959 & 17.80 & 0.07 + s90 08368 & gg13 & 42817.5660 & 17.87 & 0.04 + s90 08461 & gg13 & 42866.4771 & 17.70 & 0.08 + s90 08523 & gg13 & 42872.5396 & 17.49 & 0.08 + s90 08530 & gg13 & 42889.3917 & 17.61 & 0.13 + s90 08567 & gg13 & 42904.5466 & 17.81 & 0.12 + s90 08907 & gg13 & 43165.4924 & 17.65 & 0.13 + s90 08922 & gg13 & 43189.5119 & 17.34 & 0.05 + s90 08954 & gg13 & 43226.5675 & 17.68 & 0.07 + s90 09013 & gg13 & 43284.4786 & 17.41 & 0.08 + s90 09034 & gg13 & 43307.4015 & 17.60 & 0.15 + s90 09499 & gg13 & 43657.4376 & 18.00 & 0.11 + s90 09928 & gg13 & 43927.5189 & 18.21 & 0.04 + s90 10052 & gg13 & 44016.4473 & 17.86 & 0.12 + s90 10346 & none & 44226.5035 & 17.98 & 0.13 + s90 10906 & none & 44642.5404 & 17.54 & 0.09 + s90 10947 & none & 44691.4446 & 17.42 & 0.14 + s90 11337 & gg13 & 44989.4911 & 18.61 & 0.08 + s90 11453 & gg13 & 45048.4675 & 18.15 & 0.09 + s90 11482 & gg13 & 45055.4723 & 18.36 & 0.09 + s90 11518 & gg13 & 45088.5147 & 18.48 & 0.10 + s90 11877 & none & 45347.4869 & 18.69 & 0.08 + s90 11885 & none & 45350.4841 & 18.87 & 0.12 + s90 11989 & none & 45399.4445 & 17.98 & 0.05 + s90 12040 & none & 45412.4348 & 17.65 & 0.10 + s90 12055 & none & 45439.5035 & 17.56 & 0.09 + s90 12441 & gg13 & 45738.4689 & 17.34 & 0.11 + s90 12493 & gg13 & 45816.5279 & 17.93 & 0.10 + s90 14075 & gg13 & 47232.4258 & 17.14 & 0.07 + s90 14382 & gg13 & 47535.5251 & 17.05 & 0.09 + s90 14442 & gg13 & 47564.4377 & 17.34 & 0.14 + s90 14994 & gg13 & 48277.5331 & 17.14 & 0.15 + s90 15022 & gg13 & 48306.5585 & 16.88 & 0.09 + s90 15043 & gg13 & 48331.4518 & 17.27 & 0.11 + osc sj06694&gg395 & 50161.9111 & 17.50 & 0.10 + sdss ccd & b & 52731.0000 & 18.30 & 0.05 + vallin ccd & b & 55040.3560 & 18.30 & 0.20 + band of bzbj1058 + 56 . from march 1953 to june 2009 . filled circles are data from the asiago 67/92 cm schmidt plates ; crosses from the asiago 40/50 cm schmidt corrected for the zero point shift ; open squares other data . error bars are omitted for clarity . a sinusoidal line with a period of 2590 days and a monotonic decreasing trend is reported for comparison . [ lc1058 ] ] band of bzbj1148 + 52 . from march 1950 to june 2009 . filled circles are data from the asiago 67/92 cm schmidt plates with gg13 filter ; crosses are unfiltered data from the same telescope corrected for the zero point shift ; open squares are other data . error bars are omitted for clarity . [ lc1148 ] ] band of bzbj1209 + 41 . from march 1955 to july 2009 . filled circles are data from the asiago 67/92 cm schmidt plates with gg13 filter ; crosses are unfiltered data from the same telescope corrected for the zero point shift ; open squares are other data . error bars are omitted for clarity . [ lc1209 ] ]

we present the historic photographic light curves of three little known blazars ( two bl lacs and one fsrq ) , bzb j1058 + 5628 , bzq j1148 + 5254 and bzb j1209 + 4119 spanning a time interval of about 50 years , mostly built using the asiago plate archive .

we present the historic photographic light curves of three little known blazars ( two bl lacs and one fsrq ) , bzb j1058 + 5628 , bzq j1148 + 5254 and bzb j1209 + 4119 spanning a time interval of about 50 years , mostly built using the asiago plate archive . all objects show evident long - term variability , over which short - term variations are superposed . one source , bzb j1058 + 5628 , showed a marked quasi - periodic variability of 1 mag on time scale of about 6.3 years , making it one of the few bl lac objects with a quasi- periodic behavior .

1405.5658

c

we have presented the long - term photometric behavior of v404 lyr which demonstrates total eclipses and multiperiodic pulsations , based on all available data as well as the @xmath0 data . our analyses of 2,922 eclipse timings , spanning more than 18 yrs , reveal that the orbital period of the system has varied due to two periodic variations superimposed on an upward - opening parabola , with cycle lengths of @xmath1=649 d and @xmath2=2,154 d and semi - amplitudes of @xmath3=193 s and @xmath4=49 s , respectively . the upward parabola indicates a continuous period increase , which can be plausibly explained by a combination of mass transfer from the secondary to the primary star and angular momentum loss . the most reasonable explanation for both cycles is a pair of ltt effects driven by the presence of a third and fourth component with minimum masses of @xmath8=0.47 m@xmath9 and @xmath10=0.047 m@xmath9 . as long as the inclination of the orbital plane of the fourth component is higher than 43@xmath12 , the mass of this object is below the theoretical threshold of @xmath130.07 m@xmath9 for a hydrogen - burning star . in eclipse timing diagrams , it is possible that the periodic variations with small amplitudes may be produced by the sporadic asymmetries of eclipse light curves due to stellar activity such as starspots and pulsations ( cf . lee et al . 2014 ) . as in the process described by lee et al . ( 2013b ) , we combined the _ kepler _ data at intervals of 10 orbital periods ( @xmath13 7.3 d ) and calculated 174 minimum epochs for those datasets using the w - d code through adjusting only the ephemeris epoch ( @xmath111 ) in the spot model of table 3 . the results are illustrated with the ` x ' symbols in figure 2 . it can be seen that the light - curve timings calculated from the w - d code agree well with our analysis of the eclipse timing variation . thus , we conclude that the orbital period of v404 lyr has varied due to two periodic oscillations plus an upward parabola . the @xmath0 light curves of v404 lyr were satisfactorily modeled using a cool spot on the secondary component and third - body parameters . the results represent the eclipsing pair as a semi - detached binary with @xmath20=0.382 , @xmath21=83@xmath12 , and @xmath22=1,193 k , in which the primary component fills its limiting lobe by approximately 93% . the cool spot may be produced by magnetic dynamo - related activity because the system is rotating rapidly and the components have a deep convective envelope . the third - body parameters from the w - d code are consistent with those calculated from the eclipse timings themselves . from the absolute parameters given in section 3 , it is possible to estimate the evolutionary state of the binary system in the mass - radius , mass - luminosity , and hertzsprung - russell ( hr ) diagrams ( hilditch et al . 1988 ; . ibanolu et al . 2006 ) . in these diagrams , the primary star lies in the main - sequence band , while the secondary is clearly beyond the terminal - age main sequence and its radius is more than two times oversized compared with the main - sequence stars of the same mass . furthermore , the locations of the two component stars fall amid those of previously - known near - contact binaries ( shaw 1990 , 1994 ) . thus , the eclipsing pair is a semi - detached and fo vir - type near - contact binary consisting of a detached main - sequence primary star and an evolved lobe - filling secondary component . through analyzing the light residuals from our w - d binary model , we found intrinsic variations of 40 frequencies between 0.60 and 4.11 d@xmath7 with amplitudes from 0.49 to 5.72 mmag . among these , seven frequencies near 2.0 d@xmath7 with large amplitudes and high stability for about 4 years transpired to originate from the pulsation of the primary component . @xmath16 sct pulsators are stars pulsating in low - order pressure modes with short periods of [email protected] d ( breger 2000 ) , whereas @xmath14 dor pulsators are a - f stars of luminosity class iv - v pulsating in high - order gravity modes with typical periods in the range 0.4@xmath153 d ( kaye et al . 1999 , henry et al . the pulsation periods of v404 lyr indicate that the primary component is a candidate for @xmath14 dor type pulsating stars , rather than @xmath16 sct variables . handler & shobbrook ( 2002 ) argued the relationship between the @xmath16 sct and @xmath14 dor variables and showed that the two pulsators are clearly separated by their pulsation constants : the @xmath16 sct stars have @xmath112 0.04 d and the @xmath14 dor stars @xmath113 0.23 d. as listed in the third column of table 5 , the pulsation constants of v404 lyr are in the range of [email protected] d. a recent study by zhang et al . ( 2013 ) indicates that the ratio of pulsation and orbital periods could function as a criterion to distinguish them in ebs , where @xmath1140.09 is the upper limit for @xmath16 sct stars . all of these results reveal that the primary component is a @xmath14 dor pulsator . the eclipsing pair of v404 lyr is a short - period semi - detached binary and its pulsating component has the largest filling factor ( 93% ) of the 78 known ebs with @xmath16 sct or @xmath14 dor pulsators ( zhang et al . 2013 ; maceroni et al . 2014 ; yang et al . 2014 ) . based on this , the pulsating characteristics of the primary star may be partly influenced by tidal interaction and secondary to primary mass transfer . the properties of a convective core in the @xmath14 dor star can be demonstrated through studying tidally induced and gravity mode pulsations . because it has evolved with mass accretion between the binary components , the pulsating primary star may have a different evolutionary history than single @xmath14 dor pulsators . high - resolution spectroscopy will assist in determining the absolute parameters of the multiple system and in understanding its evolutionary status better than is possible with photometry alone . this research has made use of the _ kepler _ and superwasp public archives . _ kepler _ was selected as the 10th mission of the discovery program . funding for the _ kepler _ mission is provided by the nasa science mission directorate . the wasp consortium comprises of the university of cambridge , keele university , university of leicester , the open university , the queen s university belfast , st . andrews university and the isaac newton group . funding for wasp comes from the consortium universities and from the uk s science and technology facilities council . we have used the simbad database maintained at cds , strasbourg , france . this work was supported by the kasi ( korea astronomy and space science institute ) grant 2014 - 1 - 400 - 06 . applegate , j. h. 1992 , apj , 385 , 621 agerer , f. , & hbscher , j. 1996 , inf . variable stars , 4383 , 1 agerer , f. , & hbscher , j. 1997 , inf . bull . variable stars , 4472 , 1 agerer , f. , & hbscher , j. 1998 , inf . bull . variable stars , 4562 , 1 agerer , f. , & hbscher , j. 1999 , inf . bull . variable stars , 4711 , 1 agerer , f. , & hbscher , j. 2000 , inf . bull . variable stars , 4912 , 1 basu , s. , et al . 2011 , apj , 729 , l10 br , i. b. , et al . 2006 , inf . bull . variable stars , 5684 , 1 borkovits , t. , et al . 2003 , inf . bull . variable stars , 5434 , 1 borkovits , t. , csizmadia , s. , forgcs - dajka , e. , & hegeds , t. 2011 , a&a , 528 , a53 borkovits , t. , et al . 2013 , mnras , 428 , 1656 borucki , w. j. , et al . 2010 , sci , 327 , 977 brt , l. , zejda , m. , & svoboda . stars , 74 , 1 breger , m. 2000 , in asp conf . 210 , delta scuti and related stars , eds . m. breger and m. montgomery ( san francisco : asp ) , 3 breger , m. , et al . 1993 , a&a , 271 , 482 brown , t. m. , latham , d. w. , everett , m. e. , & esquerdo , g. a. 2011 , aj , 142 , 112 butters , o. w. , et al . 2010 , a&a , 520 , l10 chapellier , e. , & mathias , p. 2013 , a&a , 556 , a87 csizmadia , s. , & sndor , z. 2001 , inf . variable stars , 5045 , 1 conroy , k. e. , pra , a. , stassun , k. g. , orosz , j. a. , fabrycky , d. c. , & welsh , w. f. 2014 , aj , 147 , 45 diethelm , r. 2001 , inf . variable stars , 5027 , 1 eastman , j. , siverd , r. , & gaudi , b. s. 2010 , pasp , 122 , 935 hambleton , k. m. , et al . 2013 , mnras , 434 , 925 handler , g. , & shobbrook , r. r. 2002 , mnras , 333 , 251 harmanec , p. 1988 , bull . czechoslovakia , 39 , 329 henry , g. w. , fekel , f. c. , & henry , s. m. 2005 , aj , 129 , 2815 hilditch , r. w. , king , d. j. , & mcfarlane , t. m. 1988 , mnras , 231 , 341 hbscher , j. , paschke , a. , & walter , f. 2006 , inf . stars , 5731 , 1 . ibanolu , c. , soydugan , f. , soydugan , e. , & derviolu , a. 2006 , mnras , 373 , 435 irwin , j. b. 1952 , apj , 116 , 211 irwin , j. b. 1959 , aj , 64 , 149 kallinger , t. , reegen , p. , & weiss , w. w. 2008 , a&a , 481 , 571 kaye , a. b. , handler , g. , krisciunas , k. , poretti , e. , & zerbi , f. m. 1999 , pasp , 111 , 840 kim , s .- l . , lee , j. w. , kwon , s .- g . , youn , j .- h . , mkrtichian , d. e. , & kim , c. 2003 , a&a , 405 , 231 koch , d. g. , et al . 2010 , apj , 713 , l79 koo , j .- , et al . 2014 , aj , 147 , 104 kreiner , j. m. , kim , c .- h . , & nha , i .- s . 2001 , an atlas of @xmath34@xmath115 diagrams of eclipsing binary stars ( krakow : wydawn . pedagogicznej ) kwee , k. k. , & van woerden , h. 1956 , bull . netherlands , 12 , 327 lanza , a. f. 2006 , mnras , 369 , 1773 lanza , a. f. , rodono , m. , & rosner , r. 1998 , mnras , 296 , 893 lee , j. w. , kim s .- l . , kim c .- h . , koch r. h. , lee c .- u . , , & park j .- h . 2009a , aj , 137 , 3181 lee , j. w. , kim , s .- l . , lee , c .- u . , & youn , j .- h . 2009b , pasp , 121 , 1366 lee , j. w. , hinse , t. c. , & park j .- h . 2013a , aj , 145 , 100 lee , j. w. , kim , s .- l . , lee , c .- u . , lee , b .- c . , park , b .- , & hinse , t. c. 2013b , apj , 763 , 74 lee , j. w. , park , j .- h . , hong , k. , kim , s .- l . , & lee , c .- u . , 2014 , aj , 147 , 91 lenz , p. , & breger , m. 2005 , comm . asteroseismology , 146 , 53 locher , k. 2005 , open eur . j. var . stars , 3 , 1 maceroni , c. , & rucinski s. m. , 1997 , pasp , 109 , 782 maceroni , c. , montalbn , j. , gandolfi , d. , pavlovski , k. , & rainer , m. 2013 , a&a , 552 , 60 maceroni , c. , et al . 2014 , a&a , 563 , 59 mkrtichian , d. e. , et al . 2004 , a&a , 419 , 1015 moya , a. , et al . 2005 , a&a , 432 , 189 nelson , r. h. 2005 , inf . stars , 5602 , 1 nelson , r. h. 2007 , inf . bull . stars , 5760 , 1 popova , m. , & kraicheva , z. 1984 , astrofiz . issled . izv . spets . obs . , 18 , 64 press , w. h. , teukolsky , s. a. , vetterling , w. t. , & flannery , b. p. 1992 , numerical recipes ( cambridge : cambridge univ . press ) , chapter 15 pribulla , t. , & rucinski , s. m. 2006 , aj , 131 , 2986 pra , a. , et al . 2011 , aj , 141 , 83 rappaport , s. , et al . 2013 , apj , 768 , 33 reed , m. d. , brondel , b. j. , & kawaler , s. d. 2005 , apj , 634 , 602 rodriguez , e. , et al . 2006 , a&a , 450 , 715 safr , j. , & zejda , m. 2002 , inf . bull . variable stars , 5263 , 1 shaw , j. s. 1990 , in active close binaries , ed . c. ibanoglu ( dordrecht : kluwer ) , 241 shaw , j. s. 1994 , mem . soc . astron . italiana , 65 , 95 somosvri , b. m. , & csizmadia , s. 2006 , in asp conf . ser . 349 , astrophysics of variable stars , eds . sterken and c. aerts ( san francisco : asp ) , 331 southworth , j. 2009 , mnras , 394 , 272 southworth , j. , et al . 2011 , mnras , 414 , 2413 surez , j. c. , et al . 2005 , a&a , 443 , 271 tassoul , m. 1980 , apjs , 43 , 469 torres , g. 2010 , aj , 140 , 1158 van hamme , w. 1993 , aj , 106 , 209 van hamme , w. , & wilson , r. e. 2007 , apj , 661 , 1129 wilson , r. e. , & devinney , e. j. 1971 , apj , 166 , 605 yang , y .- g . , wei , j .- y . , & 2014 , aj , 147 , 35 zhang , x. b. , luo , c. q. , & fu , j. n. 2013 , apj , 777 , 77 @xmath115 diagram of v404 lyr . in the upper panel , constructed with the linear terms of equation ( 1 ) , the continuous curve represents the ltt orbit . the residuals from this ephemeris are plotted in the lower panel . ] @xmath115 diagram of v404 lyr with respect to the linear terms of the quadratic _ plus _ two - ltt ephemeris . the full ephemeris is drawn as a solid curve and the dashed parabola results from the quadratic term of equation ( 2 ) . the second and third panels display the short- and long - term ltt orbits , respectively . the bottom panel represents the residuals from the complete ephemeris . in all panels , the blue ` x ' symbols refer to the minimum times obtained by means of analyzing 174 _ kepler _ datasets with the w - d code . ] lcrccc 2,454,230.63111 & @xmath1010.00031 & @xmath15989.0 & @xmath150.00103 & @xmath150.00092 & i + 2,454,249.63673 & @xmath1010.00077 & @xmath15963.0 & @xmath50.00042 & @xmath50.00057 & i + 2,454,252.55891 & @xmath1010.00046 & @xmath15959.0 & @xmath150.00110 & @xmath150.00096 & i + 2,454,256.57899 & @xmath1010.00070 & @xmath15953.5 & @xmath150.00113 & @xmath150.00098 & ii + 2,454,257.67461 & @xmath1010.00038 & @xmath15952.0 & @xmath150.00190 & @xmath150.00176 & i + 2,454,278.50706 & @xmath1010.00077 & @xmath15923.5 & @xmath150.00087 & @xmath150.00072 & ii + 2,454,279.60470 & @xmath1010.00048 & @xmath15922.0 & @xmath50.00037 & @xmath50.00053 & i + 2,454,282.52827 & @xmath1010.00044 & @xmath15918.0 & @xmath50.00024 & @xmath50.00039 & i + 2,454,283.62463 & @xmath1010.00049 & @xmath15916.5 & @xmath50.00021 & @xmath50.00036 & ii + 2,454,286.54651 & @xmath1010.00044 & @xmath15912.5 & @xmath150.00161 & @xmath150.00146 & ii + 2,454,287.64502 & @xmath1010.00032 & @xmath15911.0 & @xmath50.00050 & @xmath50.00066 & i + 2,454,291.66576 & @xmath1010.00050 & @xmath15905.5 & @xmath50.00115 & @xmath50.00130 & ii + 2,454,953.89883 & @xmath1010.00030 & @xmath50.5 & @xmath150.00020 & @xmath50.00057 & ii + 2,454,954.26383 & @xmath1010.00022 & @xmath51.0 & @xmath150.00066 & @xmath50.00011 & i + 2,454,954.63106 & @xmath1010.00079 & @xmath51.5 & @xmath50.00109 & @xmath50.00187 & ii + 2,454,954.99363 & @xmath1010.00070 & @xmath52.0 & @xmath150.00179 & @xmath150.00102 & i + 2,454,955.36131 & @xmath1010.00042 & @xmath52.5 & @xmath50.00042 & @xmath50.00119 & ii + 2,454,955.72618 & @xmath1010.00029 & @xmath53.0 & @xmath150.00017 & @xmath50.00060 & i + 2,454,956.09245 & @xmath1010.00070 & @xmath53.5 & @xmath50.00063 & @xmath50.00140 & ii + 2,454,956.45536 & @xmath1010.00073 & @xmath54.0 & @xmath150.00191 & @xmath150.00115 & i + lccccc @xmath111 & 2,454,953.53370(24 ) & & & bjd + @xmath116 & 0.73094341(21 ) & & & d + @xmath117 & 0.395(57 ) & & 0.387(30 ) & 0.098(31 ) & au + @xmath30 & 153.1(8.7 ) & & 43.6(4.5 ) & 191(17 ) & deg + @xmath29 & 0.08(27 ) & & 0.05(11 ) & 0.00(54 ) & + @xmath31 & 0.5543(98 ) & & 0.5549(44 ) & 0.167(12 ) & deg d@xmath7 + @xmath32 & 2,454,903(15 ) & & 2,454,703(8 ) & 2,454,301(101 ) & bjd + @xmath118 & 649(11 ) & & 648.8(5.1 ) & 2154(160 ) & d + @xmath119 & 197(28 ) & & 193(15 ) & 49(16 ) & s + @xmath120 & 0.0195(28 ) & & 0.0184(14 ) & 0.0000272(89 ) & m@xmath9 + @xmath121 & 0.479(38 ) & & 0.469(20 ) & 0.0468(75 ) & m@xmath9 + @xmath122 & 1.541(62 ) & & 1.545(32 ) & 4.91(42 ) & au + @xmath47 & & & & d + @xmath123/@xmath124 & & & & d yr@xmath7 + reduced @xmath125 & 2.256 & & & + lccccc @xmath111 ( bjd ) & & & + @xmath116 ( d ) & & & + @xmath20 & & & + @xmath21 ( deg ) & & & + @xmath64 ( k ) & 6,554(69 ) & 5,363(47 ) & & 6,555(67 ) & 5,362(46 ) + @xmath65 & 2.8406(6 ) & 2.6277 & & 2.8549(6 ) & 2.6400 + @xmath58 , @xmath59 & 0.638 , 0.243 & 0.645 , 0.186 & & 0.638 , 0.243 & 0.645 , 0.185 + @xmath60 , @xmath61 & 0.613 , 0.285 & 0.693 , 0.219 & & 0.613 , 0.285 & 0.693 , 0.219 + @xmath68/(@xmath126+@xmath127 ) & 0.8094(2 ) & 0.1906 & & 0.8072(2 ) & 0.1928 + @xmath128 ( pole ) & 0.4013(1 ) & 0.2778(1 ) & & 0.3999(1 ) & 0.2789(1 ) + @xmath128 ( point ) & 0.4605(2 ) & 0.4009(1 ) & & 0.4588(2 ) & 0.4024(1 ) + @xmath128 ( side ) & 0.4215(1 ) & 0.2895(1 ) & & 0.4199(1 ) & 0.2907(1 ) + @xmath128 ( back ) & 0.4380(1 ) & 0.3222(1 ) & & 0.4364(1 ) & 0.3234(1 ) + @xmath128 ( volume ) & 0.4207 & 0.2976 & & 0.4192 & 0.2989 + [ 1.0 mm ] + @xmath50(@xmath129 ) & & & + @xmath51 ( deg ) & & & + @xmath52 & & & + @xmath53 ( deg ) & & & + @xmath54 ( d ) & & & + @xmath55 ( bjd ) & & & + + colatitude ( deg ) & & & & & 60.7(5 ) + longitude ( deg ) & & & & & 352.9(2 ) + radius ( deg ) & & & & & 22.9(7 ) + @xmath64@xmath130/@xmath64@xmath131 & & & & & 0.872(9 ) + @xmath67 & & & + [ 1.0 mm ] + @xmath132(@xmath110 ) & 1.35 & 0.51 & & 1.35 & 0.52 + @xmath133(@xmath129 ) & 1.76 & 1.25 & & 1.76 & 1.26 + @xmath109 @xmath62 ( cgs ) & 4.08 & 3.95 & & 4.08 & 3.95 + @xmath134 ( g @xmath135 & 0.35 & 0.37 & & 0.35 & 0.37 + @xmath68(@xmath136 ) & 5.14 & 1.15 & & 5.12 & 1.17 + @xmath69 ( mag ) & 2.95 & 4.57 & & 2.96 & 4.56 + bc ( mag ) & @xmath50.01 & @xmath150.18 & & @xmath50.01 & @xmath150.18 + @xmath71 ( mag ) & 2.94 & 4.75 & & 2.95 & 4.74 + distance ( pc ) & & & + lccccc @xmath137 & [email protected] & [email protected] & [email protected] & 49.69 & @xmath14 dor + @xmath138 & [email protected] & [email protected] & [email protected] & 38.00 & @xmath14 dor + @xmath139 & [email protected] & [email protected] & [email protected] & 33.78 & @xmath14 dor + @xmath140 & [email protected] & [email protected] & [email protected] & 28.96 & @xmath14 dor + @xmath141 & [email protected] & [email protected] & [email protected] & 29.45 & @xmath14 dor + @xmath142 & [email protected] & [email protected] & [email protected] & 24.79 & @xmath14 dor + @xmath143 & [email protected] & [email protected] & [email protected] & 13.22 & @xmath13@xmath144 + @xmath145 & [email protected] & [email protected] & [email protected] & 15.46 & + @xmath146 & [email protected] & [email protected] & [email protected] & 17.03 & + @xmath147 & [email protected] & [email protected] & [email protected] & 18.09 & + @xmath148 & [email protected] & [email protected] & [email protected] & 10.64 & + @xmath149 & [email protected] & [email protected] & [email protected] & 9.05 & + @xmath87 & [email protected] & [email protected] & [email protected] & 11.73 & @xmath14 dor + @xmath150 & [email protected] & [email protected] & [email protected] & 11.38 & + @xmath151 & [email protected] & [email protected] & [email protected] & 11.71 & + @xmath152 & [email protected] & [email protected] & [email protected] & 12.13 & + @xmath88 & [email protected] & [email protected] & [email protected] & 11.99 & 4@xmath153 + @xmath91 & [email protected] & [email protected] & [email protected] & 8.39 & + @xmath154 & [email protected] & [email protected] & [email protected] & 7.29 & @xmath155 + @xmath156 & [email protected] & [email protected] & [email protected] & 13.67 & + @xmath157 & [email protected] & [email protected] & [email protected] & 9.40 & 4@xmath158 + @xmath159 & [email protected] & [email protected] & [email protected] & 8.10 & + @xmath160 & [email protected] & [email protected] & [email protected] & 12.31 & + @xmath161 & [email protected] & [email protected] & [email protected] & 8.13 & 4@xmath162 + @xmath163 & [email protected] & [email protected] & [email protected] & 7.49 & 4@xmath164 + @xmath165 & [email protected] & [email protected] & [email protected] & 5.85 & 2@xmath166 + @xmath167 & [email protected] & [email protected] & [email protected] & 5.22 & + @xmath168 & [email protected] & [email protected] & [email protected] & 5.72 & @xmath169 + @xmath170 & [email protected] & [email protected] & [email protected] & 7.31 & 4@xmath171 + @xmath172 & [email protected] & [email protected] & [email protected] & 5.18 & + @xmath173 & [email protected] & [email protected] & [email protected] & 5.80 & + @xmath174 & [email protected] & [email protected] & [email protected] & 6.78 & 4@xmath175 + @xmath176 & [email protected] & [email protected] & [email protected] & 7.56 & + @xmath177 & [email protected] & [email protected] & [email protected] & 4.70 & + @xmath178 & [email protected] & [email protected] & [email protected] & 4.72 & + @xmath179 & [email protected] & [email protected] & [email protected] & 7.39 & @xmath133@xmath144 + @xmath180 & [email protected] & [email protected] & [email protected] & 4.72 & @xmath181 + @xmath182 & [email protected] & [email protected] & [email protected] & 4.67 & + @xmath183 & [email protected] & [email protected] & [email protected] & 7.22 & + @xmath184 & [email protected] & [email protected] & [email protected] & 4.22 & 3@xmath158 + lccccccc @xmath85 & 1.97460 & 0.25 & 0.9351 & ( 26 , 2 ) & 0.9245 & + 0.0106 & 776.75 + @xmath102 & 2.11165 & 0.24 & @xmath15 & ( 24 , 2 ) & @xmath15 & @xmath15 & 767.97 + @xmath105 & 2.08421 & 0.24 & 0.9870 & ( 14 , 1 ) & 0.9755 & + 0.0115 & 777.01 + @xmath104 & 1.89372 & 0.26 & 0.8968 & ( 27 , 2 ) & 0.8909 & + 0.0059 & 773.05 + @xmath103 & 2.03560 & 0.24 & 0.9640 & ( 25 , 2 ) & 0.9608 & + 0.0032 & 770.53 + @xmath86 & 1.92342 & 0.26 & 0.9109 & ( 15 , 1 ) & 0.9126 & @xmath150.0017 & 766.52 + @xmath87 & 1.85446 & 0.27 & 0.8782 & ( 39 , 3 ) & 0.8772 & + 0.0010 & 768.88 + & & & & & average & + [email protected] & [email protected] +

we present the physical properties of v404 lyr exhibiting eclipse timing variations and multiperiodic pulsations from all historical data including the and superwasp observations . detailed analyses of 2,922 minimum epochs showed that the orbital period has varied through a combination with an upward - opening parabola and two sinusoidal variations , with periods of=649 d and=2,154 d and semi - amplitudes of=193 s and=49 s , respectively . the secular period increase with a rate of.41 d yr could be interpreted as a combination of the secondary to primary mass transfer and angular momentum loss . the most reasonable explanation for both sinusoids is a pair of light - travel - time effects due to two circumbinary objects with projected masses of=0.47 m and=0.047 m . the third - body parameters are consistent with those calculated using the wilson - devinney binary code . for the orbital inclinations the results demonstrate that the close eclipsing pair is in a semi - detached , but near - contact , configuration ; the primary fills approximately 93% of its limiting lobe and is larger than the lobe - filling secondary . this revealed that the primary component of v404 lyr is a dor type pulsating star , exhibiting seven pulsation frequencies in the range of 1.85.11 d with amplitudes of 1.38.72 mmag and pulsation constants of 0.24.27 d. the seven frequencies were clearly identified as high - order low - degree gravity - mode oscillations which might be excited through tidal interaction .

we present the physical properties of v404 lyr exhibiting eclipse timing variations and multiperiodic pulsations from all historical data including the and superwasp observations . detailed analyses of 2,922 minimum epochs showed that the orbital period has varied through a combination with an upward - opening parabola and two sinusoidal variations , with periods of=649 d and=2,154 d and semi - amplitudes of=193 s and=49 s , respectively . the secular period increase with a rate of.41 d yr could be interpreted as a combination of the secondary to primary mass transfer and angular momentum loss . the most reasonable explanation for both sinusoids is a pair of light - travel - time effects due to two circumbinary objects with projected masses of=0.47 m and=0.047 m . the third - body parameters are consistent with those calculated using the wilson - devinney binary code . for the orbital inclinations 43 , the fourth component has a mass within the hydrogen - burning limit of.07 m , which implies that it is a brown dwarf . a satisfactory model for the _ kepler _ light curves was obtained through applying a cool spot to the secondary component . the results demonstrate that the close eclipsing pair is in a semi - detached , but near - contact , configuration ; the primary fills approximately 93% of its limiting lobe and is larger than the lobe - filling secondary . multiple frequency analyses were applied to the light residuals after subtracting the synthetic eclipsing curve from the _ kepler _ data . this revealed that the primary component of v404 lyr is a dor type pulsating star , exhibiting seven pulsation frequencies in the range of 1.85.11 d with amplitudes of 1.38.72 mmag and pulsation constants of 0.24.27 d. the seven frequencies were clearly identified as high - order low - degree gravity - mode oscillations which might be excited through tidal interaction . only eight eclipsing binaries have been known to contain dor pulsating components and , therefore , v404 lyr will be an important test - bed for investigating these rare and interesting objects .

astro-ph0604495

r

figures [ fig:08sep03 ] through [ fig : hbc684 ] present the high - resolution spectra that will be discussed further in 4 . absorption and emission lines were identified using atlases of the solar spectrum and sunspot umbral spectrum in the near - infrared @xcite . @xmath2-band line identifications are from table 4 of @xcite . individual objects are discussed in detail in 4.5 . almost 40 absorption lines ( some blended ) were identified in the order 49 spectra of the object with the lowest rotational velocity , hbc 683 , and therefore the sharpest lines . fewer individual lines are identified in spectra with higher rotational velocity because nearby lines become increasingly blended as @xmath15 increases . the vast majority of the lines are atomic : mainly neutral fe , some neutral ti , ni , and si , and possibly s and c are identified . intrinsic oh absorption appears in most spectra and a possible detection of cn emission in hbc 684 . significant @xmath1-band veiling in all of the absorption line object spectra is evident when these are compared to template spectra at similar @xmath15 . strong emission lines of very different nature were detected in order 49 for two objects : br16 in as 353a and multiple atomic , and possible molecular , lines in hbc 684 . in the @xmath2-band spectra for the sample , neutral atomic lines , such as na , he , al , and mg , are observed in orders 33 , 34 , 36 , and 37 ( e.g. , figure [ fig : as353a_k ] ) . br @xmath21 appears in order 35 . molecular lines of co ( orders 32 and 33 ) and h@xmath22 ( order 36 ) are also present . the equivalent widths ( ew ) of the br@xmath21 line ( n=7@xmath44 , @xmath19=2.1661 @xmath18 ) were calculated for all objects observed in the @xmath2-band . for as 353a , the br@xmath21 ew , @xmath231 , is consistent with the br@xmath21 ew of @xmath24 from @xcite , derived from low spectral resolution ( r@xmath0800 ) observations made in 1996 . ew was also calculated for the br16 ( n=16@xmath44 , @xmath19=1.5661 @xmath18 ) line observed in @xmath1-band order 49 of as 353a . line fluxes were calculated using the equivalent widths and @xmath2-band magnitude from _ 2mass_. the uncertainty of the ew calculations is approximately @xmath61 , corresponding to an uncertainty of @xmath25 0.5 w@xmath4m@xmath26 for the br@xmath21 line fluxes and @xmath00.3 w@xmath4m@xmath26 for the br16 line fluxes . brackett line ews and fluxes appear in table [ table : ews ] . the lines that were primarily used to determine spectral type were two fe lines at 1.56259 @xmath18 and 1.56362 @xmath18 and a stellar oh doublet between them at 1.56314 @xmath18 in order 49 . for a k1 star , the fe lines are prominent and the oh line is nearly absent . for later k spectral types , the fe lines monotonically weaken while the oh line strengthens ; all three lines are of approximately equal strength for spectral type m1 . @xcite convolved rotation profiles from @xcite with the spectra of observed spectral type standard stars , resulting in template spectra , for a range of spectral types , with @xmath15=0 , 2 , 4 , 6 , 8 , 10 , 12 , 15 , 20 , 25 , 30 , 40 , and 50 km s@xmath5 . examples of the template spectra with @xmath15=10 km s@xmath5 are presented in figure [ fig : templates ] ; these objects are listed in table [ table : templates ] . uncertainties in the radial velocities of the template spectra are on the order of 1 km s@xmath5 @xcite . the best fit spectral types were estimated by comparison with these standard star template spectra from @xcite and then confirmed with cross - correlation . the spectral types are accurate to at least two subclasses ; there are templates for about every second subclass , but the difference between the template spectra is generally well - defined , especially in the fe and oh lines mentioned above . because of veiling of the object spectra by continuum emission from reprocessing in circumstellar disks and accretion - induced excesses , cross - correlation yields an artificial best fit for high values of @xmath15 . therefore , the @xmath15 of each object was determined by visual inspection and comparison to rotated spectral templates alone . the spectral type and @xmath15 for each object in the sample appear in table [ table : results ] . radial velocities were measured by cross - correlating the target spectra with the best fit template spectrum from @xcite . spectra of hbc 684 were inverted because the typical absorption lines appear in emission for this object ( see 4.5.5 ) . before cross - correlation , spectra were converted to the heliocentric reference frame , interpolated onto the same wavelength basis as the matching template spectrum , and rebinned by a factor of ten . because of the strong br16 emission line in order 49 , a different approach was used to measure the radial velocity of as 353a . absorption lines are more reliable for the measurement of radial velocity of an object because emission lines are produced by accretion flows or stellar winds , which have their own characteristic radial velocities . therefore , we avoided the strong br16 emission line in the spectra of as 353a and used only the absorption lines shortward and longward of br16 in the cross - correlation . to estimate the uncertainties in the radial velocity measurements , the target spectra were cross - correlated with five template spectra of varying rotational velocity and spectral type , including the best - fit template . the standard deviation of the resulting radial velocity measurements was less than 2 km s@xmath5 for all targets other than hbc 682a and hbc 684 . for several targets the standard deviation of measurements was less than 1 km s@xmath5 . we therefore adopt an uncertainty in the measurement of 2 km s@xmath5 for all targets . this is consistent with the more formal uncertainties for the same method derived by @xcite and @xcite . we measured each object s radial velocity at every epoch observed . table [ table : radvels ] lists the objects in column ( 1 ) , the ut dates of observation in column ( 2 ) , and the radial velocities measured for each object at each epoch in column ( 3 ) . for each object , we averaged the radial velocities over all epochs . these average values are reported in column ( 4 ) of table [ table : results ] . the standard deviation and the number of epochs for each target appear in columns ( 5 ) and ( 6 ) of table [ table : results ] . no average radial velocity is reported for hbc 682a because of the large variations between epochs . standard deviations are not given for fg aql / g3 and hbc 685 because only one observation of each object was made . targets were initially examined for radial velocity variability by cross - correlating spectra taken at different epochs . for all objects except hbc 682a , radial velocity variations were less than @xmath04 km s@xmath5 , with typical values around 1@xmath42 km s@xmath5 . this is within the estimated uncertainty of the radial velocity measurements . radial velocity variations for hbc 682a were as large as 12 km s@xmath5 . velocity shifts between spectra from ao and non - ao observations were systematically higher than the typical velocity shifts between non - ao spectra from different epochs . this may be the result of the different approach to the dispersion solution necessary with ao observations . the oh night sky lines used for the non - ao dispersion are distributed regularly throughout order 49 , allowing for an excellent solution . the arc lamp lines required for the ao observations dispersion solution are only four and their distribution across order 49 is sparse .

high - resolution-band spectra were also obtained for most of the sample objects . spectral types and rotational velocities are determined for all objects in the sample . many of the spectra reveal hydrogen emission lines typical of strong accretion processes , indicating that most of these objects harbor circumstellar disks and are less than a few million years old . based on previous estimates ,

we present the properties of a group of young stars associated with the well - studied t tauri star system as 353 , located in the aquila star - forming region . the association is identified using radial velocity measurements of sample objects selected from the herbig and bell catalog based on their spatial proximity to as 353 . radial velocities of nine objects were measured from multi - epoch high - resolution ( r,000 )-band spectra obtained with nirspec on keck ii . high - resolution-band spectra were also obtained for most of the sample objects . spectral types and rotational velocities are determined for all objects in the sample . the multi - epoch-band spectra were examined for radial velocity variations in order to detect possible spectroscopic binaries . eight of the nine objects have radial velocities that are consistent within the 1- scatter of the sample . from their mean of km s these eight objects have a standard deviation of 2 km s , which suggests that the sample stars are related . the ninth object shows significant radial velocity variations between epochs , characteristic of a spectroscopic binary . the overall multiplicity of the sample is high ; we observed 13 stars in seven systems , identifying three new candidate binary components in this project . many of the spectra reveal hydrogen emission lines typical of strong accretion processes , indicating that most of these objects harbor circumstellar disks and are less than a few million years old . based on previous estimates , we adopt a distance of 200 pc to the young stars in aquila in order to calculate luminosities and place the stars on an h - r diagram . we discuss possible interpretations of the enigmatic pure emission line spectrum of hbc 684 . this work represents the highest spectral resolution infrared observations to date of these intriguing , nearby young stars .

astro-ph0604495

c

to determine the general circumstellar properties of the sample we plot @xmath27 versus @xmath28 colors from the _ 2mass _ photometry ( figure [ fig : ccd ] ) . five of the objects have infrared excess according to this analysis , consistent with the same five objects that have ew(h@xmath7 ) @xmath8 10 ( table [ table : coords ] ) . visual extinctions were estimated by dereddening the objects to the ctts locus @xcite using @xmath29 from @xcite . the _ 2mass _ colors and the derived extinctions appear in table [ table : colors ] . the average visual extinction of the sample is 1.6 magnitudes , not including as 353a , which falls below the ctts locus , possibly as the result of scattered light or a blue component to the color from continuum excess emission produced in accretion flows . to estimate the ages of the aquila stars , we place all of the sample objects on an h - r diagram with the pre@xmath4main - sequence evolutionary tracks of @xcite ( figure [ fig : hrd ] ) . luminosities were calculated using the method described in 3.3 of @xcite . _ 2mass _ photometry was used for all objects except hbc 294 , for which the angularly resolved photometry of @xcite was used . @xmath30-band bolometric corrections were from ( table 4 in * ? ? ? * ) . temperatures were taken from @xcite based on the spectral types listed in table [ table : results ] . our adopted distance , 200 pc , was selected based on previous distance estimates to stars in this region . @xcite used 150@xmath650 pc as the distance to as 353b , citing distance estimates to the aquila rift and gould s belt . @xcite estimated the distance to the dark cloud l694 to be 230@xmath630 pc based on star counts . we adopt a distance that is consistent with both of these estimates , 200@xmath630 pc . the bolometric luminosities for the components of hbc 682 have been corrected for binarity based on their near - infrared flux ratio of 2.25 and 2.15 , calculated from @xmath1- and @xmath2-band unpublished nirc2 images , respectively . for as 353b the flux ratio of the components is @xmath01 , and for hbc 682 the flux ratio was calculated in @xmath1- and @xmath2-band from unpublished nirc2 images . based on a distance of 150 pc , the age of as 353b was most recently determined to be 5@xmath1010@xmath11 years @xcite . however , this calculation assumed that as 353b was a single star ; @xcite has since identified the system as a close binary comprised of two m1.5 stars with a flux ratio of @xmath01 . in placing as 353b on the hr diagram , we adopt our spectral type of m0 ( table [ table : results ] and 4.5.1 ) , a distance of 200 pc , and one - half the luminosity determined from the unresolved system . our resulting improved age for each component of as 353b is @xmath01 myr . although the vertical error bars are large because of the uncertain distances to the objects , the location of the ensemble on the h - r diagram suggests that most of the objects are approximately 1 myr old . the large scatter in age could be attributed to the uncertainty in extinction down to the photospheres as well as uncertainty in the amount of infrared excess , both of which could lead to over- or under - estimation of bolometric luminosity for a particular object . disk signatures in the young set of objects are consistent with an age of less than a few myr . hbc 682a and b and especially fg aql / g3 appear older , @xmath06@xmath412 myr , consistent with their lack of emission lines and ir excesses , although the spectrum of fg aql / g3 appears heavily veiled ( figure [ fig:08sep03 ] ) . the standard deviation of the radial velocities of all the stars in the sample ( @xmath02 km s@xmath5 ) , combined with many of the objects signatures of youth and spatial proximity , are consistent with most if not all of the targets being members of a young stellar association . the average radial velocity for each object ranges from @xmath46.8 to @xmath411.4 km s@xmath5 ; all but two of the objects have radial velocities within one standard deviation of the mean of @xmath48.6 km s@xmath5 . the only object for which a relatively constant radial velocity was not measured is hbc 682a , indicating that it may be a spectroscopic binary higher sampling frequency observations are needed to determine its mass ratio and and center of mass velocity . however , we speculate that hbc 682a is a probable member of the aquila association because of its proximity to hbc 682b ( @xmath01 ) . thus , it is likely that all nine stars in the sample belong to a single association that is part of the aquila star - forming region . the multiplicity among the aquila association members is comparable to that of taurus , the well - studied star - forming region with the highest binary fraction ( e.g. * ? ? ? * ; * ? ? ? of seven systems that we observed , as many as thirteen components were found . systems hbc 681 and hbc 682 were identified as multiple candidates for the first time . two systems were known binaries ( hbc 294 and hbc 682 ) and at least one is triple ( as 353 ) . additionally , hbc 682a may be a spectroscopic binary ( 4.5.3 ) and hbc 681 may have a low - mass companion ( 4.5.2 ) . the order 49 spectra from the three observations of as 353a are presented in figure [ fig : as353a ] . as 353a is best fit by a k5 template spectrum with @xmath15=10 km s@xmath5 , somewhat later than the k2 spectral type previously reported in the literature @xcite . the order 49 spectrum from the observation of as 353b presented in figure [ fig:08sep03 ] is best fit by an m0 template spectrum with @xmath15=20 km s@xmath5 , which is similar to the m1.5 spectral types found for both components of this subarcsecond binary by @xcite using low resolution @xmath2-band spectra . strong br16 ( n=16@xmath44 ) emission dominates the spectrum of as 353a in order 49 . a rise at the short wavelength end of the 2004 july 22 ( ut ) spectrum also suggests the presence of br17 , although the majority of the line falls outside the spectral coverage of the order . these strong brackett lines are consistent with the strength of the h@xmath7 detected in the optical @xcite and confirmed by us in a visible light echelle spectrum ( not shown ) . however , it is unusual to see what are presumably photospheric absorption lines superimposed on the emission line . the emission line appears to shift relative to the absorption lines between epochs . the veiling also appears variable ; for example , the absorption lines are markedly deeper in the ut 2004 july 22 spectrum than in earlier spectra ( figure [ fig : as353a ] ) . selected orders of the @xmath2-band spectra of as 353a along with probable feature identifications are presented in figure [ fig : as353a_k ] . order 35 shows strong br@xmath21 emission , which is again consistent with the strong h@xmath7 emission . also apparent in the @xmath2-band spectra are atomic mg , al , and he , the co(2@xmath40 ) bandhead , and possibly h@xmath22 , all in emission . this rich emission spectrum is also apparent at low resolution ( r@xmath0760 ) @xcite and in the optical @xcite . both as 353a and b occupy unusual locations on the color - color diagram . the position of as 353a indicates significant ir excess , consistent with the origin of the strong hydrogen emission in a circumstellar disk . the detection of as 353 by the _ iras _ satellite ( _ iras _ 19181@xmath171056 ; the components are unresolved in the _ iras _ beam ) also points to the presence of warm dust in the system @xcite . however , as 353a lies _ below _ the ctts locus , which may be the result of abundant scattered light in the circumstellar environment or a blue component of excess continuum emission from accretion flows . as 353b does not show ir excess on the color - color diagram , which is consistent with its classification as a wtts based on the strength of its h@xmath7 emission . however , the extinction is larger than that of other cluster members if it is dereddened to the ctts locus . the prominent neutral hydrogen emission from as 353a is likely a combination of accretion and stellar winds . emission is the primary characteristic used to identify circumstellar accretion @xcite . however , a strong stellar wind is indicated by other characteristics of this system , namely , that it is the exciting source of hh 32 , a system of bright , compact emission line regions that are produced by a highly collimated bi - polar outflow @xcite . the h@xmath7 emission from as 353a also displays a p cygni profile with absorption in the blue wing of the emission line @xcite , which indicates outflow from the star . the similar radial velocity measurements of as 353a and b ( @xmath411.4 and @xmath410.7 km s@xmath5 , respectively ) and similar proper motions measured by @xcite make it likely that they are indeed a bound pair . therefore , as 353 is a mixed t tauri system in which the more massive component is a ctts while the secondary is a wtts , which is thought to be more evolved than a ctts . the slight infrared excess implied by the @xmath31 color of as 353ba by @xcite , 0.56 magnitudes , suggests the possible presence of circumstellar material around at least one of the as 353b components . however , if the @xmath2- and @xmath32-band magnitudes for as 353ba are dereddened by an a@xmath33 of 2 magnitudes @xcite , the resultant k@xmath4l color is 0.44 magnitudes . for an a@xmath33 of 3 magnitudes ( this paper ) , the dereddened k@xmath4l color is 0.37 magnitudes . therefore , if circumstellar material is present at all around as 353ba , it is likely to be found at an advanced stage of dispersion . possibly the binarity of as 353b has played a role in the relatively early dissolution of its circumstellar disks . it has been suggested that as 353a is also a close binary @xcite . if true , this would complicate the idea that binarity drives accelerated disk evolution , as as 353a harbors one of the most substantial and active circumstellar disks known . @xcite find no evidence for a companion object down to a separation of 0.1@xmath34 , corresponding to 20 au for a distance of 200 pc to the system . if we assign as 353a a mass of 1.2 m@xmath12 ( figure [ fig : hrd ] ) , the velocity signature induced by a companion object with a mass of 0.8 m@xmath12 in a circular orbit is about 7.5 km s@xmath5 . any higher mass companion would result in a larger amplitude of radial velocity variability in as 353a , whereas any inclination of the system s orbit out of the plane of our line of sight , a larger distance to the system than 200 pc , or a smaller mass companion , would result in smaller amplitude velocity variations . over an interval of two years , however , no radial velocity variation greater than 1 @xmath3 was measured between our three observations . our observations , however , may be insensitive to highly eccentric spectroscopic binary orbits ( e.g. * ? ? ? hbc 294 is best fit by a k7 template spectrum with @xmath15=25 km s@xmath5 . this agrees with the spectral type reported in the hbc . the radial velocity is well - determined , with a standard deviation of @xmath9 0.5 km s@xmath5 based on measurements from three different epochs . hbc 294 , also known as v536 aql , is a typical ctts , with br@xmath21 emission detected in our @xmath2-band observations and h@xmath7 , pa@xmath35 , and optical forbidden emission lines reported in the literature , indicative of accretion from a circumstellar disk . @xcite describe evidence for a bipolar outflow from the system as well . @xcite first discovered hbc 294 to be a binary with an 052 separation at a position angle of 17 . the unresolved near - ir excess observed in the system indicates warm dust surrounding at least one of the stars . the _ iras _ psc flux measurements of hbc 294 ( _ iras _ 19365 + 1023 ) reveal even greater mid- to far - ir fluxes than those of as 353a at all but 100 @xcite . it is unclear whether the circumstellar material is located around one or both components of this binary . the lower 100 @xmath36 m flux suggests that circumstellar material is truncated by the binary companion . the extinction required to deredden hbc 294 to the ctts locus is comparable to the average extinction of the sample . a k5 template with @xmath15=20 km s@xmath5 provided the best fit to the spectrum of hbc 681 . the h@xmath7 emission of hbc 681 , ew=35 , is relatively low for the ctts in this sample , but still well above the 10 ctts limit . a clear ir excess is indicated by the location of hbc 681 on the color - color diagram . we identified a faint potential companion to hbc 681 at separation @xmath012 and a position angle of @xmath0195@xmath37 . the @xmath28 color of this object is @[email protected] , typical of an unreddened m6 star , which , at the age of the aquila association , would be substellar . however , the proper motion of this object must be observed to determine if the two objects are indeed related as hbc 681 is located in the direction of the galactic plane , and hence the field is crowded with faint background objects . for the spectrum of hbc 683 , we found a best fit using a k7 template spectrum with @xmath15=15 km s@xmath5 . this is later than the spectral type of k1 reported in the hbc . the 2003 september 08 ( ut ) order 49 spectrum of hbc 683 is one of the best for line identification because of the high signal to noise ratio and low @xmath15 relative to the rest of the sample . hbc 683 is a typical ctts and has the strongest h@xmath7 and br@xmath21 emission in our sample after as 353a . hbc 683 also shows a clear ir excess in the color - color diagram ( figure [ fig : ccd ] ) . these properties are all consistent with its ctts classification and the presence of an actively accreting circumstellar disk . as a result of the observations presented in this paper , hbc 682 was discovered to be a visual binary with a separation of @xmath01 . hbc 682a is best fit by a k5 template spectrum with @xmath15=50 km s@xmath5 , and hbc 682b by a k7 template spectrum with @xmath15=30 km s@xmath5 . both of these spectral types are earlier than that of m0 reported in the hbc . although the spectra of both components of hbc 682 have similar @xmath1- and @xmath2-band features , there are striking rotational and radial velocity differences between the two . hbc 682a has the broadest absorption lines in our sample , while hbc 682b is more typical . a consistent radial velocity was not measured for hbc 682a because of the large variations between epochs ( table [ table : radvels ] ) . this may be in part because of the wide and shallow absorption lines that make precise measurement of radial velocity more difficult . however , the radial velocity variations measured in 5 different epochs , were significantly larger than the typical variation for other objects , e.g. , 1@xmath42 km s@xmath5 . hbc 682a is therefore a candidate spectroscopic binary . we speculate that hbc 682a and b are bound because of their close proximity . verification by component proper motion measurements and by determination of the center of mass velocity of the hbc 682a spectroscopic binary is needed , particularly in that this system is located in projection on to the galactic plane and hence confusion with background sources is possible . the angularly unresolved hbc 682 system shows no ir excess , consistent with its weak h@xmath7 and lack of br@xmath21 emission . however , the classification of hbc 682 is complicated by the fact that it has only recently been resolved into a visual binary , and may in fact be a hierarchical triple . the components lack separate h@xmath7 emission measurements and resolved near - ir photometry , both of which might provide additional information about their individual circumstellar environments . an m0 template with @xmath15=15 km s@xmath5 provided the best fit to the fg aql / g3 system . the only observations of this object since @xcite are from _ 2mass _ and _ denis _ ( deep near infrared survey ) , which combined provide @xmath38- , @xmath30- , @xmath1-and @xmath2-band photometry . no ir excess is detected . there are as yet no known signatures of youth associated with fg aql / g3 ; @xcite did not detect h@xmath7 emission from this star and we did not observe it in the @xmath2-band . the @xmath1-band spectrum , however , appears highly veiled . the location within 20 of three cluster members and fg aql / g3 s measured radial velocity are consistent with cluster membership . however , further evidence is needed to confirm the youth of this object . the spectra from the three observations of hbc 684 are presented in figure [ fig : hbc684 ] . the inverted order 49 spectrum of hbc 684 is best fit by a k5 template spectrum with @xmath15=40 km s@xmath5 . the source of the emission lines in the spectra of this star is enigmatic . an examination of the fits files revealed that the emission lines appeared in the raw data . furthermore , emission lines were apparent in all orders of the raw @xmath1- and @xmath2-band data . although emission lines associated with accretion are common for young stars , they are usually manifested in strong hydrogen lines and only occasionally in other species , such as co and neutral na @xcite . hbc 684 shows only modest h@xmath7 ( 11 in the hbc and @xmath013 in our unpublished visible light spectrum ) and br@xmath21 emission , while most of the atomic lines in order 49 , mainly fe but possibly ti , si , and ni as well , all appear in emission . we have tentatively identified lines of oh and cn also in emission ; see figure [ fig : hbc684 ] and table [ table : lines ] for line identifications . in addition to these molecular lines in order 49 , many emission lines probably arising from oh were identified in orders 46 , 47 , 48 , and 50 , and several emission lines from cn in orders 48 and 50 . all of the typical ctts is this sample ( hbc 294 , hbc 681 , and hbc 683 ) show stronger h@xmath7 emission , and all but hbc 294 show stronger br@xmath21 emission as well ( table [ table : ews ] ) . @xcite reported a rich near - ir emission line spectrum of the class i young stellar object _ iras _ 04239@xmath172436 in taurus . although the resolution was modest ( r@xmath0500 ) , over a dozen emission features were identified in the observed spectral range of 1.1 to 2.5 @xmath18 . probable features included several co bandheads , br@xmath21 , br10 , br11 , br13 , br14 , pa@xmath35 , h@xmath22 , and neutral he . only the neutral ca triplet at @xmath19=2.26 @xmath18 was observed in absorption . we know of no other spectra , however , with low - excitation atomic and possibly molecular species in emission as they appear in hbc 684 s @xmath1-band spectra . the palomar observatory sky survey and _ 2mass _ images show some nebulosity to the north and east of hbc 684 ; however , this diffuse emission was not evident in more recent @xmath1-band images ( in short , 0.1s exposures ) taken with the nirspec slit - viewing camera ( scam ) in 2004 november . hbc 684 is an _ iras _ source ( _ iras _ 19046@xmath170508 ) with psc fluxes at 12 , 25 , 60 and 100 @xmath18 even greater than those of as 353a , which indicates a considerable amount of warm dust around the star . the near - ir excess of hbc 684 is the strongest in our sample ( figure [ fig : ccd ] ) . we suggest four mechanisms that might produce spectra such as those observed in hbc 684 . first , accretion could be creating an oblique shock close to the photosphere of the star , which occurs when the accretion speed equals the escape velocity of the star . however , the lack of strong h@xmath7 emission limits the amount of circumstellar material that could be accreting from a circumstellar disk . furthermore , our h@xmath7 spectrum shows a clear p cygni profile , characteristic of outflow , but not infall . hbc 684 s emission lines could also be produced by an inversion layer resembling the chromosphere of the sun . if some blocking mechanism such as a circumstellar disk , similar to the function of the moon during total solar eclipse , could be construed , a phenomenon resembling a solar flash spectra might be produced ( see * ? ? ? stellar chromospheres are heated by stellar coronae ; the x - ray emission frequently observed in young stars is thought to originate in the corona ( * ? ? ? * e.g. ) . however , the nearest known x - ray source in the vicinity of hbc 684 , 1rxs j190722.4@xmath17051231 in the _ rosat _ all - sky survey faint source catalog , is 3.2 away and is therefore probably not associated with hbc 684 . a transient impact on the photosphere could provide sufficient energy to excite the atomic metals that are observed in emission . in 1994 july fragments of the comet shoemaker - levy 9 plunged into the atmosphere of jupiter . @xcite observed the plume of the most energetic impact and found atomic emission lines from neutral na , fe , ca , li in the optical spectrum . infrared spectra of another impact show molecular band / line emission , including ch@xmath39 and co(2@xmath40 ) @xcite . given the few million year age of this association and the evidence for circumstellar material around hbc 684 , it is plausible that planetessimals are forming around and may occasionally fall into the star . indeed , the planet plunging phenomenon proposed to account for the high metallicity observed in extra - solar planetary systems @xcite may be invoked in this case . the slow motion merger of a giant planet or brown dwarf could create the requisite energy for the fe i emission lines ( on the order of 6@xmath47 ev ) without exciting significant hydrogen emission . such a merger would require a substantial circumstellar disk in order to abet angular momentum transfer ; the presence of a disk is supported by the strong near- and mid - ir excesses observed in this system . the p cygni profile in the h@xmath7 emission line implies an outflow of 200 km s@xmath5 . a planet plunging event might stimulate the velocity of such a jet . the duration of the effects of a merger is not known ; we have observed consistent emission line spectra of hbc 684 on three separate occasions over a 14 month period . in 1981 , a broad , strong p cygni profile was already present ( notes in hbc ) . a final possibility we consider is the stimulation of line emission by fluorescence . we found that the upper energy level terms for the order 49 fe i lines represent too broad a range of states for the production of all the @xmath1-band lines to be consistent with fluorescence originating in one particular pumping line . furthermore , all the lines expected in a normal k5 star are present in the infrared spectra of hbc 684 , except in emission . compare this , for example , to hbc 682b , which has a similar spectral type and value of @xmath15 . hbc 684 s emission lines also display similar line ratios as the corresponding absorption lines in a template spectrum or in hbc 682b . some of the unusual features in the hbc 684 spectra may be the result of fluorescence , but we are skeptical that this is the explanation for the entire set of emission lines observed .

eight of the nine objects have radial velocities that are consistent within the 1- scatter of the sample . from their mean of km s these eight objects have a standard deviation of 2 km s , which suggests that the sample stars are related . the overall multiplicity of the sample is high ; we observed 13 stars in seven systems , identifying three new candidate binary components in this project . we discuss possible interpretations of the enigmatic pure emission line spectrum of hbc 684 .

we present the properties of a group of young stars associated with the well - studied t tauri star system as 353 , located in the aquila star - forming region . the association is identified using radial velocity measurements of sample objects selected from the herbig and bell catalog based on their spatial proximity to as 353 . radial velocities of nine objects were measured from multi - epoch high - resolution ( r,000 )-band spectra obtained with nirspec on keck ii . high - resolution-band spectra were also obtained for most of the sample objects . spectral types and rotational velocities are determined for all objects in the sample . the multi - epoch-band spectra were examined for radial velocity variations in order to detect possible spectroscopic binaries . eight of the nine objects have radial velocities that are consistent within the 1- scatter of the sample . from their mean of km s these eight objects have a standard deviation of 2 km s , which suggests that the sample stars are related . the ninth object shows significant radial velocity variations between epochs , characteristic of a spectroscopic binary . the overall multiplicity of the sample is high ; we observed 13 stars in seven systems , identifying three new candidate binary components in this project . many of the spectra reveal hydrogen emission lines typical of strong accretion processes , indicating that most of these objects harbor circumstellar disks and are less than a few million years old . based on previous estimates , we adopt a distance of 200 pc to the young stars in aquila in order to calculate luminosities and place the stars on an h - r diagram . we discuss possible interpretations of the enigmatic pure emission line spectrum of hbc 684 . this work represents the highest spectral resolution infrared observations to date of these intriguing , nearby young stars .

astro-ph0604495

c

this paper presents the results of multi - epoch observations of a sample of nine young , late - type stars in the aquila star - forming region . sample objects were selected from @xcite based on their proximity to as 353a and classification as a wtts or ctts . the high - resolution ( r@xmath030,000 ) @xmath1-and @xmath2-band observations were made between 2002 july and 2004 november with nirspec on keck ii . the initial goal of this project was to examine one @xmath1-band order of the multiple - epoch spectra for radial velocity variations in order to detect spectroscopic binaries . one radial velocity variable object was discovered and absolute radial velocities were measured for the remaining eight objects . circumstellar properties of the stars were also examined via high - resolution @xmath2-band spectra and _ 2mass _ photometry . eight of the nine sample objects appear to be members of the same association because of similar radial velocities . the spatial extent of the known members , using our adopted distance of 200@xmath630 pc , is 32@xmath65 pc by 58@xmath69 pc . the ages of the observed objects exhibit a large scatter , with the youngest , most active members all of age @xmath01@xmath42 myr . two systems appear to have ages between 6 and 12 myr , and the oldest of these ( fg aql / g3 ) has not been confirmed to show signatures of youth . therefore , the aquila association of stars is apparently one of the youngest nearby star - forming regions . the visual extinction to the association is estimated to be about 1@xmath42 magnitudes . the circumstellar environments of associations members are varied , ranging from extremely active ( as 353a , whose winds drive hh 32 ) to nearly devoid of circumstellar material ( as 353b , hbc 682 , and fg aql / g3 , which all lack ir excess and strong h@xmath7 emission ) , with several typical ctts in between ( hbc 294 , hbc 681 , and hbc 683 ) . the source of the atomic and molecular emission lines in the spectra of hbc 684 is as yet unknown , but may be caused by an inversion layer , increased accretion , fluorescence , or a transient impact . for the seven systems in this study , hbc 681 , hbc 682 , hbc 683 , hbc 684 , hbc 294 , fg aql / g3 , and as 353 , there is a high total number of stars , thirteen at least , yielding @xmath02 stars per system . this multiplicity is significantly higher than even that of the taurus region ( @xmath01.6 stars per system ; @xcite ) , although it applies to only a small sample and may be significantly impacted by observational biases . the extremely interesting stars identified to date in this association certainly warrant further investigation . much work remains to characterize this unusual star - forming region . the most pressing task is to confirm the existence of a larger association by searching for other young stars in the region and identifying radial velocities and proper motions of the new members . obtaining a more accurate distance determination to the association will also be critical to unraveling the age - distance discrepancy . for the non - thermal radio source as 353b , this could be accomplished with vlbi ( e.g. * ? ? ? once more complete membership is determined , the aquila star - forming region can be characterized in terms of mass function , multiplicity fraction , and other parameters . further observations in the millimeter , sub - millimeter , infrared , radio , and x - ray will also provide valuable information about the circumstellar environments of these objects , which will improve our understanding of key phases of pre - main - sequence stellar evolution .

we present the properties of a group of young stars associated with the well - studied t tauri star system as 353 , located in the aquila star - forming region . the multi - epoch-band spectra were examined for radial velocity variations in order to detect possible spectroscopic binaries . this work represents the highest spectral resolution infrared observations to date of these intriguing , nearby young stars .

we present the properties of a group of young stars associated with the well - studied t tauri star system as 353 , located in the aquila star - forming region . the association is identified using radial velocity measurements of sample objects selected from the herbig and bell catalog based on their spatial proximity to as 353 . radial velocities of nine objects were measured from multi - epoch high - resolution ( r,000 )-band spectra obtained with nirspec on keck ii . high - resolution-band spectra were also obtained for most of the sample objects . spectral types and rotational velocities are determined for all objects in the sample . the multi - epoch-band spectra were examined for radial velocity variations in order to detect possible spectroscopic binaries . eight of the nine objects have radial velocities that are consistent within the 1- scatter of the sample . from their mean of km s these eight objects have a standard deviation of 2 km s , which suggests that the sample stars are related . the ninth object shows significant radial velocity variations between epochs , characteristic of a spectroscopic binary . the overall multiplicity of the sample is high ; we observed 13 stars in seven systems , identifying three new candidate binary components in this project . many of the spectra reveal hydrogen emission lines typical of strong accretion processes , indicating that most of these objects harbor circumstellar disks and are less than a few million years old . based on previous estimates , we adopt a distance of 200 pc to the young stars in aquila in order to calculate luminosities and place the stars on an h - r diagram . we discuss possible interpretations of the enigmatic pure emission line spectrum of hbc 684 . this work represents the highest spectral resolution infrared observations to date of these intriguing , nearby young stars .

1408.5940

i

the accretion of matter onto a forming star is inextricably associated with mass outflow . this manifests itself as well - collimated jets typically observed in higher excitation shock - excited forbidden lines such as [ sii ] or [ feii ] , or lower excitation emission of shock - exited h@xmath1 . larger - scale and older outflows are typically detected in co emission of entrained ambient material . while the precise mechanism of jet launching is actively being debated , steady progress has been made in observational studies of the launch regions of jets . such studies require the highest possible spatial resolutions , since all theories postulate that jets are launched from the inner regions of the protostellar disks on spatial scales of a few au , or from the protostar s magnetosphere , on scales of a stellar diameter . at present , the highest spatial resolutions for studies of the jet launch regions are achieved at optical wavelengths with the hubble space telescope ( hst ) , and at near - infrared wavelengths with adaptive optics on large ground - based telescopes . the near - infrared techniques have the advantage of being able to better penetrate dust extinction , so that the jet launch regions of more deeply embedded , generally younger stars can be observed . however , near - infrared laser - guide - star adaptive optics observations today are still limited by the requirement to have a fairy bright , optically visible ( r @xmath5 16 ) tip - tilt reference star close to the object , or that the object itself can serve this purpose . as a consequence , even at near - infrared wavelengths , the best candidates for high spatial resolution studies are objects near the end of their class i phase or early in the classical t tauri star phase because in nearby molecular ( dark ) clouds , the only available optical tip - tilt reference star is often the young star itself . in this paper we present detailed adaptive - optics corrected integral field spectroscopy of ngc 1333 svs 13 , the driving source of the famous chain of herbig - haro objects hh 7 - 11 @xcite . other commonly used names for svs 13 are v512 per and 2mass j03290375 + 3116039 . the svs 13 outflow appears relatively poorly collimated and is comprised of a number of individual shock fronts , as can be seen in fig . 1 that presents a progression from seeing - limited to diffraction - limited images of the svs 13 outflow . there is an anti - parallel counter outflow visible , but it is displaced from the axis of the hh 7 - 11 outflow . for a general overview of ngc 1333 and a review of the literature on the svs 13 subcluster , the reader is referred to the review article by @xcite . the two micron all sky survey ( 2mass ) position of svs 13 is @xmath6 at epoch 1999 nov . 26 with an accuracy of @xmath7 @xcite . this position lies between the vla configuration a radio position of vla 4b at 3.6 cm reported by @xcite at @xmath8 with an effective epoch of 1997.9 and estimated errors of @xmath9 and the 7 mm vla configuration b position of the same radio source , which @xcite give as @xmath10 with an epoch of 2001 may 4 . the epoch of the 2mass observations is between the epochs of the vla observations , and the reported near - infrared coordinates lie between those vla coordinates . within the errors of @xmath9 for the vla data and of @xmath7 for 2mass , and a tentatively indicated small proper motion of vla 4b , these data show that the near - infrared source svs 13 is identical to the vla mm and cm - wavelength source vla 4b . it should be noted that @xcite and @xcite , on the basis of older optical astrometry , had originally identified svs 13 with a different cm - radio source : vla 4a . m ) image based on the same original data as those used by @xcite for their proper motion study . the image shows the full extent of the shocked molecular hydrogen emission . the second panel from the top is a small portion of a h@xmath1 s(1 ) 2.122 @xmath4 m image obtained in 1996 with the quirc camera at the uh 2.2 m telescope that shows the emission features closest to svs 13 . the third panel shows the integrated h@xmath1 s(1 ) line intensity observed with osiris on keck ii in 2011 with the 100 mas spaxel scale , while the fourth panel was taken with osiris on keck i in 2012 with the 20 mas spaxel scale . ] we use the distance to ngc 1333 svs 13 determined by @xcite from vlbi parallax measurements of masers associated with this object : 235 @xmath11 18 pc . the study of the dynamics of the ngc 1333 region by @xcite has determined the systemic velocity of the gas near svs 13 to be 8 km @xmath12 relative to the local standard of rest . throughout this paper , we will give velocities relative to this systemic velocity of the ngc 1333 molecular core that svs 13 is embedded in . young , still accreting stars often experience eruptive changes in brightness that traditionally get classified into either fu orionis ( fuor ) or ex lupi ( exor ) type outbursts , depending on the duration of the outburst and its spectrum . the first review of these phenomena has been given by @xcite . fuor outbursts exhibit time scales of decades to centuries and the spectral characteristics of an optically thick luminous disk with absorption line spectra , while the less substantive exor outbursts have timescales of years , have been observed to actually return to pre - outburst brightness , and show optically thin emission line spectra . jets emanating from young stars are often comprised of a series of individual shock fronts that have been postulated to arise from changes in the jet velocity as a result of repetitive eruptive events , as described in the review by @xcite and references therein . this gives , in principle , a way to study the history of such eruptive accretion instabilities from the `` fossil '' record in the jet shock fronts . our target object , svs 13 , is certainly in this class of multi - shock outflow sources and has been observed to undergo an outburst around 1990 , but the light curve does not match either the classical fuor or exor curves . the relationship of this last observed outburst to the structure of the svs 13 outflow will be studied here . the proper motions of the shock fronts of the hh 7 - 11 system associated with svs 13 have been studied at optical wavelengths by @xcite and later by @xcite , and in the infrared in the h@xmath1 10 s(1 ) line by @xcite using the near - infrared camera and multi - object spectrometer ( nicmos ) , by @xcite using the united kingdom infrared telescope ( ukirt ) , and with the spitzer space telescope by @xcite . these studies all gave proper motions of the shock fronts in the range of 33 mas yr@xmath13 that establish a kinematic expansion age of 2100 yrs for the most distant shock front studied there , the hh 7 bow shock . in general , the jets seen in optical and near - infrared forbidden lines , mostly in [ sii ] and [ feii ] , offer the most direct view of the material ejected from an accretion disk or from a protostar s magnetosphere . there are differences in the details of theoretical models of this process , e.g. , in @xcite , @xcite , @xcite , or @xcite , but they all agree on the main point : jets originating from the magnetosphere of a rotating star , or from a rotating disk , and detected in high - excitation shock - excited lines are expected to carry away excess angular momentum and thereby enable the mass accretion process . however , to date , the most convincing detection of a rotational signature of jets from very young and still deeply embedded objects in sed classes 0 and i have been obtained with radio interferometric observations of outflows in co and sio emission . these observations typically achieve spatial resolutions of a few arcseconds but make up for this disadvantage by exquisite velocity resolution . carbon - monoxide high - velocity emission is mostly associated with the entrainment of ambient molecular material into a jet originally emitted at even higher velocity . any signature of the original jet rotation is expected to be highly confused at this turbulent interface between the jet and the ambient material . nevertheless , @xcite detected the kinematic signature of rotation in the jet of cb 26 in the co(2 - 1 ) line , very close to the source of the jet . @xcite found some evidence for rotational components in the ori - s6 outflow using various higher transitions of co and so , while @xcite recently reported a rotational signature in the hh 797 outflow in ic 348 using co(2 - 1 ) . in these cases , the strongest rotational signatures were found at some distance ( @xmath14 ) from the driving source . even farther away from the driving source , using sio data from the vla , @xcite found a rotation signature of the ngc 1333 iras 4a2 protostellar jet , consistent with the disk rotation in that object . the jet could only be observed at distances of more than 5@xmath15 from its source , and the rotation signature appears most pronounced at distances of 20@xmath15 . these results are far from universal , however . in a series of papers on hh 211 culminating in @xcite they obtained only a tentative detection of rotation . @xcite studied the kinematics of sio emission in the hh 212 jet and did not detect a credible rotational signature . in this paper we have tried to detect the kinematic signature of jet rotation in our [ feii ] data and are presenting our velocity data , but in the end failed to detect this effect .

we present the results of keck telescope laser adaptive optics integral field spectroscopy with osiris of the innermost regions of the ngc 1333 svs 13 outflow that forms the system of herbig - haro objects 7 - 11 . we postulate that the creation of a series of bubbles and the changes in outflow direction are indicative of a precessing disk and accretion events triggered by a repetitive phenomenon possibly linked to the orbit of a close binary companion . we have tried , but failed to detect , the kinematic signature of rotation of the microjet in the [ feii ] emission line at 1.644 m .

we present the results of keck telescope laser adaptive optics integral field spectroscopy with osiris of the innermost regions of the ngc 1333 svs 13 outflow that forms the system of herbig - haro objects 7 - 11 . we find a bright 0 long microjet traced by the emission of shock - excited [ feii ] . beyond the extent of this jet , we find a series of bubbles and fragments of bubbles that are traced in the lower excitation h 10 s(1 ) line . while the most recent outflow activity is directed almost precisely ( pa 145 ) to the south - east of svs 13 , there is clear indication that prior bubble ejections were pointed in different directions . within these variations , a clear connection of the newly observed bubble ejection events to the well - known , poorly collimated hh 7 - 11 system of herbig - haro objects is established . astrometry of the youngest of the expanding shock fronts at 3 epochs covering a time span of over two years gives kinematic ages for two of these . the kinematic age of the youngest bubble is slightly older than the historically observed last photometric outburst of svs 13 in 1990 , consistent with that event launching the bubble and some deceleration of its expansion . a re - evaluation of historic infrared photometry and new data show that svs 13 has not yet returned to its brightness before that outburst and thus shows a behavior similar to fuor outbursts , albeit with a smaller amplitude . we postulate that the creation of a series of bubbles and the changes in outflow direction are indicative of a precessing disk and accretion events triggered by a repetitive phenomenon possibly linked to the orbit of a close binary companion . however , our high - resolution images in the h and k bands do not directly detect any companion object . we have tried , but failed to detect , the kinematic signature of rotation of the microjet in the [ feii ] emission line at 1.644 m .

1408.5940

r

figure 1 shows the h@xmath1 shock - excited line emission associated with svs 13 on four different spatial scales : the top image is an archival spitzer space telescope infrared array camera ( irac ) @xcite channel 2 ( 4.5 @xmath4 m ) image covering most of the outflow emission . the second panel is a small cutout from a ground - based , seeing limited image in the h@xmath1 10 s(1 ) line obtained at the uh 2.2 m telescope , showing just the emission in the immediate vicinity of svs 13 . the third panel from the top is the s(1 ) integrated line image obtained with the 100 mas scale of osiris in 2011 and the bottom panel shows the 20 mas scale s(1 ) image from osiris obtained in 2012 , without deconvolution . we show this figure to demonstrate the relationship between the bubbles in the svs 13 outflow very close to the source and the larger scale structure of the flow further downwind . this relationship is not entirely trivial , since not all the bubbles have propagated in the same direction from the svs 13 star . the seeing - limited ground - based image shows the brightest of these bubbles in the glare of the psf . the intermediate , 100 mas scale , osiris line image shows three distinct partial bubbles near the source of the outflow , the outer two of which were also observed , but not further discussed , by @xcite , on hst / nicmos images and had also been detected through ukirt narrow - band fabry - perot imaging by @xcite . the best prior detection of these bubbles was by @xcite who used adaptive - optics - assisted long - slit spectroscopy and detected all the bubbles as a series of emission maxima along the slit . the most recent emission , the 0@xmath02 long [ feii ] jet , its faint extension into the s(1 ) bubble , and that youngest s(1 ) bubble are oriented at p.a . 145@xmath3 , as seen in fig . the older two bubbles , visible in the 100 mas image of fig . 1 , are lying more to the south at p.a . 159@xmath3 than those aforementioned features , indicating some variations in the jet emission direction . in contrast the main chain of herbig - haro knots hh 7 - 11 lies at p.a . 123@xmath3 @xcite . while at optical wavelengths , the svs 13 outflow manifests itself only in the herbig - haro chain hh 7 - 11 @xcite , longer wavelengths increasingly reveal a counterflow that appears displaced from the hh 7 - 11 axis , and appears in general fainter and less organized ( fig . 1 , top panel ) . based on spitzer telescope images over a time span of 7 years , @xcite have obtained one proper motion data point for a relatively well defined knot in that counterflow , and this one point is consistent with the counterflow originating from svs 13 . also , no other embedded protostar has been detected by @xcite to the north of svs 13 that might explain this flow as being independent from svs 13 . the displacement in the outflow axis , in combination with the recent changes in outflow direction reported in this paper , suggest that the source of the svs 13 outflow is changing direction , probably due to some precessing motion , as will be discussed in more detail in section 4.2 . as an explanation for the differences between the hh 7 - 11 flow and the counterflow , @xcite have suggested that the northern counterflow enters into the central cavity of ngc 1333 , resulting in different ambient pressure and excitation conditions than the hh 7 - 11 flow . we have obtained astrometry of the bubble expansion on two different spatial scales . relatively wide field osiris data cubes with the 100 mas spaxel@xmath13 scale were obtained on keck ii on 2011 august 21 and keck i on 2013 november 23 . a difference image of the h@xmath1 s(1 ) emission at these two epochs is shown in fig . 4 and illustrates that all three of the closest shock fronts to svs 13 are showing noticeable motion . the farthest of these three shock fronts was defined enough to allow a cross - correlation measurement of its expansion age in the box indicated in the figure . astrometry of the smallest and youngest expanding bubble was done on the 2012 november 4 and 2013 november 22/23 data that were taken at the keck i telescope with the same adaptive optics system and the same spaxel scale ( 20 mas spaxel@xmath13 ) and are therefore suitable for a precise astrometric measurement . in this case , the individual planes of the data cube were deconvolved using the lucy - richardson algorithm , to improve the definition of the bubble edge . figure 3 illustrates the expansion and motion of the youngest , smallest bubble between the three epochs by superposing fiducial marks that outline features in the middle ( 2012 ) image . for fine registration of the images , the iraf task xregister was used to measure the relative alignment of all the frames at the position of the svs 13 stellar object and a magnified and optimally registered version of the images was produced . to measure the expansion of the bubble , we worked under the assumption that its motion relative to the star can be described as a simple constant velocity expansion with the origin at the position of the star . we computed magnified versions of the individual 2012 november 4 images with magnification factors in the range from 0.95 to 1.10 and the center of the magnification on the svs 13 star . we then computed the product of these magnified images and each of the individual 2013 november 22 images . the average of this product in a box centered on the s(1 ) bubble feature image varies smoothly with expansion factor for each of these pairs and the maximum of this one - dimensional correlation function was simply read from the table of cross - correlation values . we show the cross - correlation functions of the 2012 and 2013 high resolution images in fig . 5 to illustrate the variations due to noise and deconvolution noise amplification , and to document how the errors of this measurement were obtained . error of the mean scaling factor . the mean value corresponds to a kinematic start of the expansion in 1980 , an early limit to the true starting date since the expanding bubble will realistically be decelerated . ] the expansion factor so determined was then converted to a kinematic expansion age of 32 yrs ( prior to 2012 ) , i.e. , kinematic starting time of the expansion in 1980 , which gives the upper limit to the true age of the bubble assuming that the bubble has been expanding at constant velocity . since , realistically , the bubble is expanding into the dense environment of a molecular core , the true age of this youngest bubble will be smaller than the kinematic expansion age and is therefore consistent with this expanding bubble having been generated in the 1990 photometric outburst of svs 13 that will be discussed in secion 4.4 . in 2012 , the apex of the bubble was located 654 mas from the star . the front end of the bubble therefore has moved with an average projected angular velocity of 20 mas yr@xmath13 ( 4.7 au yr@xmath13 = 22.3 km s@xmath13 at 235 pc distance ) away from the star . similarly , in 2012 , the bubble had a radius of 212 mas and an average radial proper motion of 6.6 mas yr@xmath13 ( 1.55 au yr@xmath13 = 7.35 km s@xmath13 ) . the proper motion of the bubble center is therefore the proper motion of the leading shock front minus the radial expansion : 13.4 mas yr@xmath13 @xmath2 15 km s@xmath13 . in order to also obtain an estimate of the kinematic age of the next two more distant bubbles , we used data cubes obtained in 2011 august 21 on keck ii with the 100 mas scale , and similar measurements obtained on 2013 november 22 on keck i. the difference of these two images is shown in fig . 4 . the only shock front where a clear maximum of this correlation function was detected in these 100 mas data was the most distant of the three , indicated by a box in fig . 4 , separated from the star by 2.87@xmath26 in 2011 . for this bow shock front , we derive a kinematic formation time of 1919 @xmath11 7 and a linear projected proper motion of 31 mas yr@xmath13 . we have not obtained a reliable kinematic age for the middle shock - excited feature at @xmath2 1@xmath05 from the star , between those two features discussed above ( fig . the fact that this rather poorly defined system of shock fronts lies pretty precisely in the middle of the 1980 and 1919 ( kinematic formation time ) features suggests that this feature must have formed , again in the kinematic sense without accounting for deceleration , around 1950 . if there is a regular pattern to the formation of these bubbles , which with only three examples can not be convincingly established yet , the next outburst could be expected within the next decade . it should be noted , as was already pointed out by @xcite that the proper motion of the major shock fronts in the older parts of the svs 13 outflow indicate a much longer time interval between shock front generating events : about 500 yrs . it is not clear whether svs 13 exhibits multiple periods , or whether the frequency of ejection events has recently increased . an argument for the latter point of view may be that the outflow direction has apparently changed in the past century , as we will discuss now . as demonstrated by fig . 1 , the two previous bubbles are located more toward the se of svs 13 and , for example , @xcite chose p.a . 159@xmath3 as the best slit orientation to cover them . the larger chain of hh objects 7 to 11 is oriented along a position angle of 123@xmath3 @xcite . the larger scale proper motion study by @xcite based on spitzer 4.5 @xmath4 m images shows some emission knots to the se of svs 13 with a proper motion vector generally to the se , in particular the herbig - haro knots 7 , 8 , and 10 . north of svs 13 , in the counter - flow , they find an emission knot with a generally northern proper motion vector ( p.a . -10@xmath3 ) that they ascribe to a chance superposition of another outflow far to the south of svs 13 and with generally northern outflow direction . the [ feii ] jet originating from svs 13 ( fig . 3 ) is oriented along p.a . 145@xmath3 and the h@xmath1 bubble center is displaced from svs 13 along the same angle . with the exception of this most recent h@xmath1 bubble , the other recent mass ejection events from svs 13 have therefore ejected material initially in a more southerly direction ( p.a . @xmath2 155@xmath3 - 159@xmath3 ) , as seen in figs . 1 , and 4 . with outflows generally being bipolar , there must also be mass ejected into a northerly direction . we therefore believe that , contrary to the assertion by @xcite , the 4.5 @xmath4 m emission knot north of svs 13 and with northerly proper motion is part of the counter jet to the bubbles reported here . the more distant parts of the s(1 ) emission nw of svs 13 are anti - parallel , but laterally displaced , from the hh 7 - 11 system of emission knots . we suggest that the hh 7 - 11 chain , the system of bubbles immediately south of svs 13 , the emission knots north of svs 13 , and the more distant emission knots further to the nw ( fig . 1 ) are all part of the same bipolar outflow originating in svs 13 . this outflow has the s - shaped morphology indicative of a precessing or otherwise unstable jet source . corroborating this , radio interferometry mapping of molecular emission near svs 13 by @xcite has similarly found an orientation of high - velocity material south of svs 13 different than the hh 7 - 11 herbig - haro chain . they had already concluded that the differences in the alignment of features of different age indicate a precessing source of the outflow . a prominent other example of such s - shaped morphology of a molecular hydrogen jet , iras 03256 + 3055 , is located just south of svs 13 in ngc 1333 and has been studied in detail by @xcite . the relatively low proper motion and spatial velocity measured for the h@xmath1 bubble studied here is consistent with proper motion measurements of the more distant hh 7 - 11 chain of shock fronts by @xcite , @xcite , and @xcite , but is inconsistent with the much higher proper motions reported by @xcite in the first near - infrared proper motion study of hh 7 - 11 . while a precessing accretion disk provides an explanation for the rapid changes in the outflow direction observed in svs 13 , our data do not show any indication for the presence of a companion object that would be close enough to cause the disk precession on the timescales discussed here . from the size and location of the h@xmath1 bubbles , we can conclude that bubble ejection events happen with a period of several decades . in the model where such events are triggered by periastron passages of a companion object , the orbital semimajor axis must be of order of tens of au , or several of the original 20 mas spaxels of our data . the fact that we do nt see a companion object implies that such an object , if it existed , is intrinsically too faint and/or too deeply embedded to be visible in the h and k atmospheric windows . the only other case of a young stellar object with a pronounced bubble structure of its outflow is xz tau that was studied in detail by @xcite on the basis of optical multi - epoch hst imaging . very similar to the case of svs 13 discussed here , their images show a series of bubbles with a collimated jet propagating inside of the bubbles . @xcite reported initial results of numerical simulations of a very young pulsed jet in close proximity to its driving source . their simulations were specifically tuned to reproduce the observations of the xz tau a chain of bubbles and therefore modeled a faster , more rapidly pulsing jet resulting in more rapidly expanding , overlapping bubbles . the general scenario underlying their model is however applicable to our case of svs 13 : the fuor - like photometric outburst in 1990 created a short - lived pulse of jet activity . this newly created , relatively fast jet ran into slower moving material ejected prior to the outburst event , and this internal shock created an expanding `` fireball '' that subsequently expanded ballistically into a bubble carried away from the star by the outflow . some time after the formation of the bubble , a fast continuous jet then emerges to catch up with the bubble , pierce it , and partially destroy it . in svs 13 this process currently repeats itself about every 30 years , creating the series of bubble fragments that forms the string of herbig - haro objects . in distinction from xl tau , the case of svs 13 also involves a significant change in the direction of the jet and bubble ejection leading to the s - shaped overall morphology of the herbig - haro chain . the individual velocity channels of the h@xmath1 s(1 ) line emission are shown in fig . 6 . in the blue - shifted wing of the velocity distribution , emission projected on the center of the bubble is visible , which is the expected characteristic of an expanding 3-dimensional bubble rather than a 2-dimensional ring . in fig . 7 , a color - coded velocity map of the h@xmath1 10 s(1 ) line emission is presented . the s(1 ) emission shows three distinguishable velocity features . emission near the intersection with the jet ( traced in [ feii ] ) shows the smallest blueshifted velocities and is coded red . the rim of the s(1 ) bubble where the line of sight is tangential to the bubble shows intermediate velocities , coded yellow in the figure . the highest velocities towards the observer are measured in the filamentary features projected against the center of the bubble and are coded in blue . in the brightly visible rim , the velocity centroid varies between -40 and -55 km s@xmath13 relative to the systemic velocity of the molecular material around svs 13 , while in the simple model of an expanding shell , those velocities should be constant and representative of the center motion of the bubble . we take -47 @xmath11 7 km s@xmath13 as the typical radial velocity of the bubble center . 10 s(1 ) line images of the svs 13 jet . the velocities indicated in each panel are relative to the systemic velocity of the svs 13 core . the bubble feature is blueshifted relative to the systemic velocity . ] s(1 ) line at 2.122 @xmath4 m . three distinct velocity features can be distinguished : the emission at the intersection of the jet with the bubble has the lowest ( blueshifted ) radial velocity , the rim of the bubble has intermediate velocities , and the features projected against the center of the bubble have the highest blueshifted velocities . overlayed on the velocity map are contours of the high - dynamic range lucy - richardson deconvolved flux maps that indicate the position of svs 13 itself . a color version of this figure is available in the electronic version of this paper . ] with the proper motion of the bubble center of 15 @xmath11 2 km s@xmath13 , this suggests an inclination angle of 18@xmath3 @xmath11 3@xmath3 against the line of sight . @xcite had given an inclination angle of 20@xmath3 to 40@xmath3 for emission close to svs 13 while @xcite has given 40@xmath3 for more distant emission knots . all the measurements of the inclination angle were done on different shock features . their spread is therefore a combination of measurement uncertainties and the true variations in the motion of these shock fronts . irrespective of which of the shock fronts are measures , all data indicate that the outflow emerging from svs 13 is pointed strongly towards the observer . this explains why the counterjet , which moves away from the observer and into the molecular core around svs 13 , is not detectable at optical wavelengths . shock fronts of this velocity running into stationary ambient molecular hydrogen are certainly capable of exciting v=10 s(1 ) line emission and are not in danger of dissociating the h@xmath1 , see , for example , @xcite . the infrared source svs 13 was discovered by @xcite at a k - band magnitude of 9.08 in a 36@xmath26 aperture . soon after the discovery , @xcite reported k = 8.48 in a 30@xmath26 aperture observed in 1978 . @xcite reported an observation by g. olofsson from 1980 at k=8.7 in a 14@xmath26 aperture as a private communication . @xcite measured a pre - outburst brightness on k=9.34 in a 6 - 8@xmath26 aperture at the irtf on 1981 , oct . 11 - 13 and @xcite measured k=9.30 in a 16@xmath26 aperture on 1981 , dec . the object experienced a sudden increase in brightness around 1990 , as first reported by @xcite and further studied by @xcite , @xcite , and @xcite . in the k band , where the best pre - outburst data are available , as listed above , the pre - outburst magnitude showed some variation between 9.0 and 9.5 mag . post - outburst , @xcite documented brightness variation between 8.0 and 8.6 mag . based on the small amplitude of the brightness increase , the post - outburst brightness fluctuation , and the emission lines in its spectrum , both @xcite and @xcite have concluded that svs 13 underwent an exor or similar outburst , but both papers left the possibility open that the outburst may be of a different nature . @xcite has studied the photometric behavior of svs 13 again and concluded that the object had not returned to its pre - outburst brightness at that time . motivated by the uncertain classification of this event , we have re - examined the historical photometry and are discussing new measurements . we have tried to gather the available photometric data on svs 13 from the literature and data archives . while many images of the svs 13 region exist , the star svs 13 is saturated on most of these , and useful data can only be obtained from shallow surveys , usually with small telescopes . in fig . 8 , we show all the available photometric data as a light curve . the 2mass survey list svs 13 as k@xmath27=8.169 and these data had been obtained on nov . 26 , 1999 . recent k@xmath27 data from the iris telescope @xcite show svs 13 varying in the range of k@xmath27=8.46 to 8.70 between 2012 august and 2014 january . the photometric color transformations between the ukirt system and the 2mass system for the k vs. k@xmath27 filters are insignificant @xcite , so a direct comparison can be made between the measurements by @xcite and the most recent data . there is extended emission around svs 13 , so very large photometric apertures tend to overestimate the brightness . the @xcite , @xcite , @xcite and @xcite data were corrected to the aperture diameter of 6@xmath26 used for the iris photometry , while all other photometric data shown here were originally obtained with apertures in the range of 5@xmath15 - 8@xmath26 , close enough to the iris aperture to not require a correction . figure 8 shows these aperture - corrected photometric values and clearly demonstrates that svs 13 has not declined back to its pre - outburst ( @xmath28 1990 ) brightness , but remains at or near its peak post - outburst brightness with some indication that brightness fluctuations have diminished over the course of the past 24 years . similar to the case of the low - luminosity , deeply embedded , cometary nebula oo ser @xcite and @xcite , svs 13 defies a clear classification as either fuor or exor . while fuors generally show late - type low gravity absorption spectra in the infrared @xcite indicative of a luminous , optically dense disk , the prototypical exor ex lupi shows the co bandheads and many other optical lines in emission during extreme exor outbursts @xcite . during minor outbursts , optical emission lines are observed , but co may be in photospheric absorption @xcite . svs 13 shows the co bandheads in emission @xcite . in the context of this paper , the important conclusion is that the elevated post - outburst level of accretion and therefore jet activity in svs 13 has persisted for the past 2 decades to the present , so that the light curve of svs 13 shares the long duration maximum with fuors , while spectroscopically , it resembles an exor , and the small outburst amplitude resembles neither . this suggests that at least for the younger , more deeply embedded accretion instability events , the traditional two classes may not be appropriate , and that a continous range of outburst characteristics may be a better way to understand this phenomenon . the light curve also implies that the next outburst of svs 13 , if indeed these outbursts occur repetitively about every 30 years , will start from a brighter state of svs 13 than the previous one . this would mean that in addition to the repetitive outbursts , we are also observing cumulative changes in svs 13 . the seeing - limited integral field spectroscopy of @xcite had only marginally resolved the [ feii ] emission around svs 13 . our adaptive - optics corrected osiris data show that [ feii ] traces a high - velocity microjet that extends from the source svs 13 into the area of the most recent molecular hydrogen bubble . the results are summarized in the false - color images ( fig . 3 ) . here , the wavelength - integrated continuum - subtracted flux of the h@xmath1 10 s(1 ) line was lucy - richardson deconvolved and is displayed in the red channel . to show the location of the stellar central object in svs 13 without introducing the artifacts from imperfect deconvolution of a dominant bright source , we have added 10% of the deconvolved flux of two continuum wavelength channels to the continuum - subtracted image . this produces , in effect , a high - dynamic - range version of the svs 13 image for the purpose of showing the relationship of features at different wavelengths . note that the wavelength channels used here were different from those used as the psf . the resulting deconvolved continuum image is therefore not the trivial solution of deconvolving the psf with itself . the green channel of fig . 3 shows the deconvolved integral over the [ feii ] line at 1.644 @xmath4 m . in the same way as described above , a fraction of the continuum wavelengths immediately adjacent to the line was added to the data to mark the location of the stellar source . finally , to adjust the color balance of the stellar object to white , the same fraction of the continuum wavelength channels on either side of the [ feii ] line was assigned to the blue channel . our lucy - richardson deconvolved images of the high - excitation [ feii ] shocks associated with the jets show that the jet is very narrow , about 20 - 40 mas wide . the velocity diagram in fig . 9 shows that the [ feii ] emission of the jet is blueshifted by -140 to -150 km s@xmath13 relative to the systemic velocity of the molecular material around svs 13 @xcite . a comparison of figs . 7 and 9 demonstrates that the [ feii ] emission is more blueshifted than the h@xmath1 s(1 ) emission . the direct superposition of the h@xmath1 and [ feii ] emission line images shows that the bright portions of the microjet [ feii ] emission extend up to the rim of the h@xmath1 bubble , and that faint traces of [ feii ] emission can be detected up to about the center of the bubble . the jet [ feii ] intensity drops by a factor of @xmath2 20 at the bubble surface . in fact , the brightest [ feii ] along the jet axis is seen directly upwind from the h@xmath1 bubble surface . the total 1.644 @xmath4 m [ feii ] flux is dominated by the emission outside of the expanding h@xmath1 bubble . since the front edge of the bright jet component near the bubble rim is not sharply defined , and subject to the degree of lucy - richardson deconvolution and the different quality of the adaptive optics correction achieved at the two epochs , we could not directly measure the proper motion of the jet front edge . from fig . 3 it seems clear that the [ feii ] shock emission from the jet is surrounded by an envelope of entrained ambient material radiating in the low - excitation shocked h@xmath1 lines , and that at least the bright portions of the jet [ feii ] emission terminate at the bubble rim . from the proper motion of the bubble front side , and the rate of bubble expansion ( section 4.2 ) , the expected , but not directly measured , proper motion of the side of the bubble facing svs 13 ( the back side in the direction of motion ) is 6.6 mas yr@xmath13 , which we also take as the proper motion of the front end of the bright jet . the length of the [ feii ] jet is therefore changing only very slowly , at a rate of @xmath2 7 mas year@xmath13 , and the centroid of the [ feii ] flux therefore moves at less than half this speed . this is responsible for the impression noted already by @xcite that the [ feii ] emission looked stationary . what we see from the jet in the [ feii ] emission line are either internal shocks or the shocks resulting from interaction with ambient molecular material that then gets entrained by the jet . the bulk of the jet material propagates into the area of the h@xmath1 bubble , but the excitation conditions are , apparently , less favorable to the formation of such shocks radiating in [ feii ] . 1.644 @xmath4 m wavelength data cubes of the svs 13 jet , deconvolved using the lucy - richardson algorithm , for the 2012 and 2013 data , respectively . the bottom panels show the corresponding velocity sigma maps . the white contours outline the line integrated [ feii ] flux distribution . it clearly shows that all the line emission from the jet is blue - shifted relative to the systemic velocity of svs 13 . a color version of this figure is available in the electronic version of this paper . ] we have tried , both on the 2012 and 2013 data , to detect the signature of jet rotation . initially , using only the 2012 data , such rotation appeared to be indicated @xcite . however , the 2013 data , and the re - reduced 2012 data with the new calibrations , did not confirm this ( fig . the velocity pattern measured in 2013 was more confused and , if anything , a faint indication of the opposite rotation direction was found . in fig . 9 ( lower panels ) we show the rms variations of the velocity measurements on the individual data cubes that were coadded to form the velocity maps in the top panels . these indicate that the errors of the velocity maps are below 10 km s@xmath13 in most parts of the [ feii ] jet . we conclude that the excellent spatial resolution and moderate spectral resolution of osiris are not sufficient to resolve the kinematic signature of jet rotation in svs 13 . the permitted atomic hydrogen line emission from svs 13 was found to be broad with line widths of @xmath2 180 @xmath11 10 km s@xmath13 for br@xmath29 by @xcite and for br-12 by @xcite . the emission is centered on the position of the continuum source , but spatially unresolved . our data cube in the hn3 filter contains the br-12 and br-13 hydrogen recombination lines that trace the same hot hydrogen recombination regions as the more frequently used br-@xmath29 does . in fig . 10 , we show the deconvolved images of svs 13 across the br-13 emission line after subtraction of the continuum emission . this figure confirms that emission in the atomic hydrogen recombination lines is spatially centered on the young star , and has the same flux profile as the continuum , i.e. we see no indication that the br-13 emission is extended . figure 10 has 10 mas pixels ( 2.35 au ) , and any systematic differences between the line and continuum psf are well below that angular scale . we conclude that the zone of atomic hydrogen emission , presumably the accretion disk itself , is less that 2 au in extent . it is actually expected to be only of order of the dimensions of the star itself , i.e. , about 2 orders of magnitude smaller than this limit . our velocity data are consistent with the higher spectral resolution data of @xcite who found that the br@xmath29 line is centered at -25 ( @xmath30 ) km s@xmath13 relative to the systemic velocity of the svs 13 core , essentially at the same velocity as the star . 2 au ) .

there is clear indication that prior bubble ejections were pointed in different directions . within these variations , a clear connection of the newly observed bubble ejection events to the well - known , poorly collimated hh 7 - 11 system of herbig - haro objects is established . astrometry of the youngest of the expanding shock fronts at 3 epochs covering a time span of over two years gives kinematic ages for two of these . the kinematic age of the youngest bubble is slightly older than the historically observed last photometric outburst of svs 13 in 1990 , consistent with that event launching the bubble and some deceleration of its expansion . a re - evaluation of historic infrared photometry and new data show that svs 13 has not yet returned to its brightness before that outburst and thus shows a behavior similar to fuor outbursts , albeit with a smaller amplitude .

we present the results of keck telescope laser adaptive optics integral field spectroscopy with osiris of the innermost regions of the ngc 1333 svs 13 outflow that forms the system of herbig - haro objects 7 - 11 . we find a bright 0 long microjet traced by the emission of shock - excited [ feii ] . beyond the extent of this jet , we find a series of bubbles and fragments of bubbles that are traced in the lower excitation h 10 s(1 ) line . while the most recent outflow activity is directed almost precisely ( pa 145 ) to the south - east of svs 13 , there is clear indication that prior bubble ejections were pointed in different directions . within these variations , a clear connection of the newly observed bubble ejection events to the well - known , poorly collimated hh 7 - 11 system of herbig - haro objects is established . astrometry of the youngest of the expanding shock fronts at 3 epochs covering a time span of over two years gives kinematic ages for two of these . the kinematic age of the youngest bubble is slightly older than the historically observed last photometric outburst of svs 13 in 1990 , consistent with that event launching the bubble and some deceleration of its expansion . a re - evaluation of historic infrared photometry and new data show that svs 13 has not yet returned to its brightness before that outburst and thus shows a behavior similar to fuor outbursts , albeit with a smaller amplitude . we postulate that the creation of a series of bubbles and the changes in outflow direction are indicative of a precessing disk and accretion events triggered by a repetitive phenomenon possibly linked to the orbit of a close binary companion . however , our high - resolution images in the h and k bands do not directly detect any companion object . we have tried , but failed to detect , the kinematic signature of rotation of the microjet in the [ feii ] emission line at 1.644 m .

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we have presented adaptive optics corrected integral field spectroscopy of the young outflow source svs 13 in ngc 1333 . the h@xmath1 10 s(1 ) line at 2.122 @xmath4 m , indicating low - velocity shocks , the higher excitation [ feii ] line of the micro - jet at 1.644 @xmath4 m , and atomic hydrogen emission in the hi12 - 4 and hi13 - 4 lines were analyzed and lead us to the following main conclusions : 1 . the hh 7 - 11 outflow originates in svs 13 , which is identical to vla 4b . 2 . the outflow , at present , originates as a micro - jet of @xmath2 0@xmath02 length , detectable in [ feii ] and oriented at p.a . the formation of the youngest partly formed bubble visible in h@xmath1 emission can be traced back to the @xmath2 1990 outburst . 4 . the bright parts of the [ feii ] microjet reach up to the boundary of the h@xmath1 s(1 ) bubble , but fainter [ feii ] emission can be traced another @xmath2 0@xmath02 to near the center of the bubble . 5 . beyond that , h@xmath1 s(1 ) emission outlines a curved path of the jet . 6 . the orientation of the next two bubbles at p.a . @xmath2 159@xmath3 is roughly point - symmetric to the orientation of outflowing material in the counter - jet found by @xcite in co and @xcite at 4.5 @xmath4 m . the chain of bubble fragments and their proper motions suggest that bubble - generating events are occurring repetitively , roughly every 30 years , at the present time . the formation of a series of expanding bubbles within the outflow by a series of eruptive events provides an explanation for the widening of the outflow cavity . atomic hydrogen emission in the hi12 - 4 and hi13 - 4 ( brackett series ) lines is detected around the continuum position of svs 13 , indicating ongoing accretion onto the star . the outflow source svs 13 remains at or near the peak brightness reached during the 1990 outburst . the light curve therefore resembles that of fuor type objects , while the emission line spectrum matches the characteristics of exors . svs 13 therefore represents an object somewhere between those classical classes . most of the data presented herein were obtained at the w.m . keck observatory , which is operated as a scientific partnership among the california institute of technology , the university of california and nasa . the observatory was made possible by the generous financial support of the w.m . keck foundation . some photometric data on svs 13 were obtained at the iris telescope on cerro armazones , which is operated under a cooperative agreement between the `` astronomisches institut , ruhr universitt bochum '' , germany , the `` universidad catolica del norte '' in antofagasta , chile , and the institute for astronomy , university of hawaii , usa . construction of the iris infrared camera was supported by the national science foundation under grant ast07 - 04954 . the operation of the iris telescope is supported by the `` nordrhein - westflische akademie der wissenschaften und der knste '' in the framework of the academy program by the federal republic of germany and the state of nordrhein - westfalen . we wish to thank angie barr dominguez , thomas dembsky , holger drass , lena kaderhandt , michael ramolla and christian westhues for operating the iris telescope for the acquisition of the data used in this paper , ramon watermann for writing the data reduction pipeline , and roland lemke for technical support . we thank tuan do and jessica lu for kindly providing the information about the osiris spaxel scales on the keck i and keck ii telescopes . this publication makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center/ california institute of technology , funded by the national aeronautics and space administration and the national science foundation . this publication also uses archival data obtained with the spitzer space telescope , which is operated by the jet propulsion laboratory , california institute of technology under a contract with nasa . skrutskie , m. f. , cutri , r. m. , stiening , r. , weinberg , m. d. , schneider , s. , carpenter , j. m. , beichman , c. , capps , r. , chester , t. , elias , j. , huchra , j. , liebert , j. , lonsdale , c. , monet , d. g. , price , s. , seitzer , p. , jarrett , t. , kirkpatrick , j. d. , gizis , j. , howard , e. , evans , t. , fowler , j. , fullmer , l. , hurt , r. , light , r. , kopan , e. l. , marsh , k. a. , mccallon , h. l. , tam , r. , van dyk , s. , & wheelock , s. 2006 , , 131 , 1163

, we find a series of bubbles and fragments of bubbles that are traced in the lower excitation h 10 s(1 ) line . while the most recent outflow activity is directed almost precisely ( pa 145 ) to the south - east of svs 13 ,

we present the results of keck telescope laser adaptive optics integral field spectroscopy with osiris of the innermost regions of the ngc 1333 svs 13 outflow that forms the system of herbig - haro objects 7 - 11 . we find a bright 0 long microjet traced by the emission of shock - excited [ feii ] . beyond the extent of this jet , we find a series of bubbles and fragments of bubbles that are traced in the lower excitation h 10 s(1 ) line . while the most recent outflow activity is directed almost precisely ( pa 145 ) to the south - east of svs 13 , there is clear indication that prior bubble ejections were pointed in different directions . within these variations , a clear connection of the newly observed bubble ejection events to the well - known , poorly collimated hh 7 - 11 system of herbig - haro objects is established . astrometry of the youngest of the expanding shock fronts at 3 epochs covering a time span of over two years gives kinematic ages for two of these . the kinematic age of the youngest bubble is slightly older than the historically observed last photometric outburst of svs 13 in 1990 , consistent with that event launching the bubble and some deceleration of its expansion . a re - evaluation of historic infrared photometry and new data show that svs 13 has not yet returned to its brightness before that outburst and thus shows a behavior similar to fuor outbursts , albeit with a smaller amplitude . we postulate that the creation of a series of bubbles and the changes in outflow direction are indicative of a precessing disk and accretion events triggered by a repetitive phenomenon possibly linked to the orbit of a close binary companion . however , our high - resolution images in the h and k bands do not directly detect any companion object . we have tried , but failed to detect , the kinematic signature of rotation of the microjet in the [ feii ] emission line at 1.644 m .

astro-ph9809366

i

recent analyses of extended rotation curves ( rcs ) of late - type spiral galaxies ( persic , salucci & stel 1996 ) have confirmed that in spirals of all luminosities a substantial dark matter ( dm ) component is detectable already in the optical region . the effect is stronger at lower luminosities : the dark - to - visible mass ratio at the optical radius @xmath0 is the radius encompassing the @xmath10 of the total integrated light . @xmath11 is the scale - length of the exponential surface brightness distribution @xmath12 . for a freeman ( 1970 ) disk , @xmath0 corresponds to the de vaucouleurs 25 @xmath13- photometric radius . ] scales with luminosity @xmath14 . for early - type spirals the status of our knowledge is different . the rcs presently available for these objects are fragmentary ( in particular in the nuclear regions ) , and only extend to @xmath15 ( see rubin et al . consequently , detailed mass decomposition have so far not been possible for these systems . in particular , it is not known whether dark halos are unambiguously present also in early - type spirals . it may be conjectured that for a given @xmath16 the dm fraction within the optical size is smaller in early than in late - type spirals : this , because in an early spiral the conspicuous stellar bulge , with @xmath17 , can supply a mass compact enough to make the rotation velocity higher than ( see rubin et al . 1985 ) , and the velocity profile different from , that of a late spiral of similar luminosity . in this case , the derivation of the halo parameters would be more uncertain for early than for late types : in fact , at small radii not two mass components ( disk + halo , like in sc - sd galaxies ) , but three mass components ( bulge + disk + halo ) will have locally similar ( solid - body like ) behaviors . so for non - extended rc data the mass solution of an sa galaxy would be degenerate even within the maximum - disk solution . in this paper we present the velocity and velocity - dispersion profiles of the stars and the ionized gas , measured along the major axis , for six early - type spirals . the six selected galaxies ( table 1 ) were already known to show emission lines and their photometric properties were known . of these , 5 had already been observed spectroscopically by rubin et al . ( 1985 ) , who obtained the rcs of the ionized gas , and photometrically by kent ( 1988 ) . ngc 2179 was the only galaxy in our sample still lacking spectroscopical and photometrical observations . to the originally observed sample belonged the early - type spiral too . its stellar and the gaseous kinematics , found to exhibit a star vs. star counterrotation , is presented and discussed by bertola et al . three - component models ( bulge + disk + halo ) based on observed photometry and kinematics are obtained for two galaxies of the sample : ngc 2179 and ngc 2775 .

we present the stellar and ionized - gas velocity curves and velocity - dispersion profiles along the major axis for six early - type spiral galaxies . lllllllllllllc & & & & & & & & & & & & + & & & & & & & & & & & & & + & & & & & & & & & & & & & + ngc 2179&sa & .sas0 .. col.(6 ) : inclination from rubin et al . ( 1985 ) except for ngc 2179 ( tully 1988 ) .

we present the stellar and ionized - gas velocity curves and velocity - dispersion profiles along the major axis for six early - type spiral galaxies . two of these galaxies , namely ngc 2179 and ngc 2775 , are particularly suited for the study of dark matter halos . using their luminosity profiles and modeling their stellar and gaseous kinematics , we derive the mass contributions of the luminous and the dark matter to the total potential . in ngc 2179 we find that the data ( measured out to about the optical radius ) unambiguously require the presence of a massive dark halo . for the brighter and bigger object ngc 2775 , we can rule out a significant halo contribution at radii . although preliminary , these results agree with the familiar mass distribution trend known for late - type spirals of comparable mass . lllllllllllllc & & & & & & & & & & & & + & & & & & & & & & & & & & + & & & & & & & & & & & & & + ngc 2179&sa & .sas0 .. &13.22&170&51&2885&2673&35.6&172.6 & 51 & 41 & 54 & 8.5 + ngc 2775&sa(r)&.sar2 .. &11.03&163&44&1350&1180&15.7 & 76.1&128&100 & 77 & 6.5 + ngc 3281&sa & .sas2p*&12.70&138&69&3380&3098&41.3&200.2 & 99 & 86 & 50 & 6.5 + ic 724&sa & .s .. 1 .. &13.4 & 60&55&5974&5853&78.0&378.2 & 70 & 62 & 56 & 2.0 + ngc 4698&sa & .sas2 .. &11.46&170&70 & 992 & 909&12.1 & 58.7&119 & 76&113 & 4.7 + ngc 4845&sa & .sas2./&12.10 & 75&72&1084 & 980&13.1 & 63.5&150 & 87&100 & 4.0 + notes col.(2 ) : classification from rsa ( sandage & tamman 1981 ) . col.(3 ) : classification from rc3 ( de vaucouleurs et al . 1991 ) . col.(4 ) : total observed blue magnitude from rc3 except for ic 724 ( rsa ) . col.(5 ) : observed position angle . col.(6 ) : inclination from rubin et al . ( 1985 ) except for ngc 2179 ( tully 1988 ) . col.(7 ) : heliocentric velocity of the galaxy derived as center of symmetry of the gas rc . col.(8 ) : systemic velocity derived from corrected for the motion of the sun with respect of the local group by . col.(9 ) : distance obtained as with mpc . col.(11 ) : radius of the 25mag arcsec isophote from rc3 . col.(12 ) : radius of the farthest measured stellar velocity . col.(13 ) : radius of the farthest measured gas velocity . col.(14 ) : total integration time of the spectroscopic observation .

astro-ph9809366

c

we have presented the ionized - gas and stellar kinematics , measured along the major axis , for a sample of six early - type spiral galaxies . ( due to the high values of @xmath32 in their inner regions , the gas rcs can not be used as circular - velocity curves . ) for ngc 2179 and ngc 2775 , we have modeled both the stellar and the gaseous kinematics to derive the mass contribution of the luminous and dark matter to the total potential , improving on the efforts by kent ( 1988 ) from gas kinematics alone . we have found that the innermost kinematics ( @xmath311 ) is very well and uniquely reproduced by taking into account the two luminous components . in the ( very luminous ) early - type spirals considered here , there is a large inner region in which ( essentially ) light traces the mass and the dm is a minor mass component . this is agreement with the ` weak ' maximum disk paradigm proposed by persic & salucci ( 1990 ) , but in disagreement with the claim by courteau & rix ( 1998 ) according to which in the most luminous spirals dm is a protagonist at essentially any radii . more in detail we have found that in ngc 2179 the combined stellar and gaseous rotation data ( measured out to about @xmath0 ) require the presence of a massive dark halo . in ngc 2775 , more luminous and massive than ngc 2179 , we can rule out a significant halo contribution out to @xmath312 . this result complies with the general trend of mass distribution known for later spirals ( persic et al . 1996 ) . salucci & persic ( 1997 ) , considering a large number of galaxies of mixed morphologies ( ellipticals , late spirals , dwarfs , and lsbs ) , have suggested that the halo structural parameters and the connection between the dark and the luminous matter show a strong continuity when passing from one hubble type to another . ellipticals , considered as luminous spheroids , and spirals , considered as luminous disks , are evidently very different systems , markedly discontinuous in terms of the distribution and global properties of the luminous matter . however , in the structural parameter space , ellipticals and spirals are contiguous , the main difference being that the former are more concentrated in both the dark and luminous components , probably due to the baryons dissipational infall being deeper in ellipticals than in spirals ( e.g. , bertola et al . 1993 ) . if so , it is hardly surprising that sa galaxies , being in some sense intermediate systems consisting of a luminous spheroid embedded in a luminous disk , fit in the regularity pattern of the dark - to - visible mass connection shared by ellipticals and spirals . in fig . [ fig : dm ] we plot our derived dark - to - visible mass ratios at the farthest measured radii for ngc 2179 and ngc 2775 ( filled circles ) onto the distribution , derived by salucci & persic ( 1997 ) for galaxies with the same visible mass . the agreement is good . even if the present result on early - type spirals is preliminary and without pretending to draw general conclusions from one particular case , it nevertheless seems to agree with the idea that , for galaxies of all morphological types , the dark - to - luminous mass ratio at any given radius depends only on the ( luminous ) mass of the galaxy . we are indebted to r.p . van der marel for providing his @xmath313 modeling software which became the basis of our modeling package . we also thank r. falomo for providing some photometric data reduction tools . we are most grateful to the vatican observatory research group for allocating the observing time . particular thanks go to r. boyle , s.j . for his help during the observing run at the vatt . the research of ap was partially supported by an _ acciaierie beltrame _ grant . jcvb acknowledges a grant from telescopio nazionale galileo and osservatorio astronomico di padova . this research has made use of the nasa / ipac extragalactic database ( ned ) which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . bernacca , p.l . , perinotto , m. 1970 , contr . asiago , 239 , 1 bertola , f. , rubin , v.c . , zeilinger , w.w . 1989 , apj , 345 , l29 bertola , f. , bettoni , d. , rusconi , l. , sedmak , g. 1984 , aj , 89 , 356 bertola , f. , pizzella , a. , persic , m. , salucci , p. 1993 , apj , 416 , l45 bertola , f. , cinzano , p. , corsini , e.m . , rix , h .- w . , zeilinger , w.w . 1995 , apj , 448 , l13 bertola , f. , cinzano , p. , corsini , e.m . , pizzella , a. , persic , m. , salucci , p. 1996 , apj , 458 , l67 bertola , f. , cappellari , m. , funes s.j . , j.g . , corsini , e.m . , pizzella , a. , vega beltrn , j.c . 1998a , apj , submitted bertola , f. , corsini , e.m . , vega beltrn , j.c . , sarzi , m. , pizzella , a. , funes , j.g . 1998b , in preparation binney , j. , davies , r.l . , illingworth , g.d . 1990 , apj , 361 , 78 binney , j. , tremaine , s. 1987 , galactic dynamics . princeton university press , princeton bregman , j.n , hogg , d.e . , roberts , m.s . 1992 , apj , 387 , 484 cinzano , p. 1995 thesis , universit di padova cinzano , p. , van der marel , r.p . 1994 , mnras , 270 , 325 courteau , s. , rix , h .- w . 1998 , apj , in press [ astro - ph/9707290 ] de vaucouleurs , g. , de vaucouleurs , a. , corwin , h.g . , buta , r.j . , paturel , g. , fouqu , p. 1991 , third reference catalogue of bright galaxies . springer - verlag , new york ( rc3 ) fasano , g. 1990 , internal report of the padova astronomical observatory fillmore , j.a . , boroson , t.a . , dressler , a. 1986 , apj , 302 , 208 freeman , k.c . 1970 , apj , 160 , 811 gerhard , o.e . 1993 , mnras , 265 , 213 gerhard , o.e . , vietri , m. , kent , s.m . 1989 , apj , 345 , l33 hernquist , l. 1990 , apj , 356 , 359 hoffleit , d. , jaschek , c. 1982 , the bright star catalogue . yale university observatory , new haven ( bsc ) keel , w.c . 1996 , apjs , 106 , 27 kent , s.m . 1985 , apjs , 59 , 115 kent , s.m . 1988 , aj , 96 , 514 kormendy , j. , westpfahl , d.j . 1989 , apj , 338 , 752 jaffe , w. 1983 , mnras , 202 , 995 lauberts , a. , valentijn , e.a . 1989 , the surface photometry catalogue of the eso - uppsala galaxies . eso , garching bei mnchen osterbrock , d.e . , fulbright , j.p . , martel , a.r . , keane , m.j . , trager , s.c . 1996 , pasp , 108 , 277 peletier , r.f . , davies , r.l . , illingworth , g.d . , davis , l.e . , cawson , m. 1990 , aj , 100 , 1091 persic , m. , salucci , p. 1990 , mnras , 247 , 349 persic , m. , salucci , p. , stel , f. 1996 , mnras , 281 , 27 roberts , m.s . , hogg , d.e . , bregman , j.n . , forman , w.r . , jones , c. 1991 , apjs , 75 , 751 rood , h.j . , page , t.l . , kintner , e.c . , king , i.r . 1972 , apj , 175 , 627 rubin , v.c . , burstein , d. , ford , w.k . , jr . , thonnard , n. 1985 , apj , 289 , 81 salucci , p. , persic , m. 1997 , in : m. persic , p. salucci ( eds . ) asp conf . 117 , dark and visible matter in galaxies and cosmological implications , asp , san francisco , p. 1 sandage , a. , bedke , j. 1994 , the carnegie atlas of galaxies . carnegie institution , flintridge foundation , washington ( cag ) sandage , a. , tammann , g.a . 1981 , a revised shapley - ames catalog of bright galaxies . carnagie institution , washington ( rsa ) sargent , w.l.w . , schechter , p.l . , boksenberg , a. , shortridge , k. 1977 , apj , 212 , 326 satoh , c. 1980 , pasj , 32 , 41 tully , r.b . 1988 , nearby galaxies catalog . cambridge university press , cambridge van der marel , r.p . 1991 , mnras , 253 , 710 van der marel , r.p . , binney , j. , davies , r.l . 1990 , mnras , 245 , 582 van der marel , r.p . , franx , m. 1993 , apj , 407 , 525 wilson , r.e . 1953 , general catalogue of stellar radial velocities . carnagie institution , washington

two of these galaxies , namely ngc 2179 and ngc 2775 , are particularly suited for the study of dark matter halos . using their luminosity profiles and modeling their stellar and gaseous kinematics , we derive the mass contributions of the luminous and the dark matter to the total potential . in ngc 2179 we find that the data ( measured out to about the optical radius ) unambiguously require the presence of a massive dark halo . for the brighter and bigger object ngc 2775 , we can rule out a significant halo contribution at radii . although preliminary , these results agree with the familiar mass distribution trend known for late - type spirals of comparable mass .

we present the stellar and ionized - gas velocity curves and velocity - dispersion profiles along the major axis for six early - type spiral galaxies . two of these galaxies , namely ngc 2179 and ngc 2775 , are particularly suited for the study of dark matter halos . using their luminosity profiles and modeling their stellar and gaseous kinematics , we derive the mass contributions of the luminous and the dark matter to the total potential . in ngc 2179 we find that the data ( measured out to about the optical radius ) unambiguously require the presence of a massive dark halo . for the brighter and bigger object ngc 2775 , we can rule out a significant halo contribution at radii . although preliminary , these results agree with the familiar mass distribution trend known for late - type spirals of comparable mass . lllllllllllllc & & & & & & & & & & & & + & & & & & & & & & & & & & + & & & & & & & & & & & & & + ngc 2179&sa & .sas0 .. &13.22&170&51&2885&2673&35.6&172.6 & 51 & 41 & 54 & 8.5 + ngc 2775&sa(r)&.sar2 .. &11.03&163&44&1350&1180&15.7 & 76.1&128&100 & 77 & 6.5 + ngc 3281&sa & .sas2p*&12.70&138&69&3380&3098&41.3&200.2 & 99 & 86 & 50 & 6.5 + ic 724&sa & .s .. 1 .. &13.4 & 60&55&5974&5853&78.0&378.2 & 70 & 62 & 56 & 2.0 + ngc 4698&sa & .sas2 .. &11.46&170&70 & 992 & 909&12.1 & 58.7&119 & 76&113 & 4.7 + ngc 4845&sa & .sas2./&12.10 & 75&72&1084 & 980&13.1 & 63.5&150 & 87&100 & 4.0 + notes col.(2 ) : classification from rsa ( sandage & tamman 1981 ) . col.(3 ) : classification from rc3 ( de vaucouleurs et al . 1991 ) . col.(4 ) : total observed blue magnitude from rc3 except for ic 724 ( rsa ) . col.(5 ) : observed position angle . col.(6 ) : inclination from rubin et al . ( 1985 ) except for ngc 2179 ( tully 1988 ) . col.(7 ) : heliocentric velocity of the galaxy derived as center of symmetry of the gas rc . col.(8 ) : systemic velocity derived from corrected for the motion of the sun with respect of the local group by . col.(9 ) : distance obtained as with mpc . col.(11 ) : radius of the 25mag arcsec isophote from rc3 . col.(12 ) : radius of the farthest measured stellar velocity . col.(13 ) : radius of the farthest measured gas velocity . col.(14 ) : total integration time of the spectroscopic observation .

0910.3001

i

the issue of accretion as the power source behind active galactic nuclei ( agns ) was decided as early as 1969 @xcite . since then , a 40-year effort to unravel the physics underlying this process has produced a great body of observational and theoretical work covering a host of the agn properties and phenomena . however , due to the small angular size of a black hole horizon , whether at the galactic or extragalactic setting , these studies were effectively performed mainly in the spectral ( but also the time ) domain ; the spatial structure of accretion flows , but those of scale of many parsecs , was then inevitably delegated to models , whose validity was determined by their ability to reproduce the spectral and timing observations with sufficient accuracy . at the risk of oversimplifying the issue , the spectral properties of agns were basically outlined ( among other works ) in @xcite who showed that the spectral energy distribution ( sed ) of agns includes three broad components in the ir , optical - uv and x - ray bands , with roughly equal energy per decade , with the radio comprising only a small fraction of their bolometric luminosity , of order @xmath12 in the radio - quiet ( rq ) agns and @xmath13 in radio - loud ( rl ) agns . considering that accretion produces most of its power in the last 10 or so schwarzschild radii , @xmath14 , outside the black hole horizon , barring an inherently non - thermal emission process ( as it turns out to be the case with blazars ) , it is strange that the observed seds exhibit roughly constant luminosity per decade . interestingly , the simplest of assumptions , namely radiation of the agn bolometric luminosity in black body form by an object ( most likely in the form of a cold disk of @xmath15 k ) of size a few @xmath14 of a supermassive black hole ( @xmath16 where @xmath17 is the solar mass ) , implies peak emission at uv frequencies , consistent with the observationally identified uv feature referred to above , known as the big blue bump ( bbb ) ; as such , this feature was modeled with emission by a geometrically - thin , optically - thick accretion disk extending usually to the innermost stable circular orbit ( isco ) of the black hole . of the other two distinct components the x - rays are generally attributed to emission by an optically - thin , hot ( @xmath18 k ) corona overlying this disk and heated by the action of magnetic fields that thread the geometrically - thin disk , in close analogy to the solar corona ( e.g. * ? ? ? * ; * ? ? ? finally , the ir emission was accounted for as the result of reprocessing the o - uv radiation by a geometrically thick ( scale height @xmath19 roughly equal to the local radius @xmath1 , i.e. @xmath20 ) , cool , molecular torus at large distances ( @xmath21 pc ) from the central engine [ an arrangement that presents a bit of a problem , since the temperature of this torus ( @xmath22 k ) is much less than the virial temperature of the gas at that distance and would lead to a configuration with @xmath23 ; see krolik & begelman ( 1988 ) . the region between the torus and the accretion disk was thought to be occupied by clouds with velocity widths ranging from tens of thousands to several hundreds of kilometers per second , producing the observed line radiation , with the ensemble of these components encapsulated in the well known cartoon of @xcite . while in most models these components are generally thought of as independent , principal component analysis ( pca ) of multiwavelength agn features by @xcite and @xcite indicated that most of the variance in the measured optical emission line properties and a broad range of continuum features ( radio , optical , x - ray ) of agns was contained in two sets of correlations , eigenvectors of the correlation matrix . this analysis suggested that the properties of these features are not independent ( despite their diverse locations and emission processes ) but are well correlated by two single underlying physical parameters through the physics of accretion and the conversion of its power to radiation and outflows . on the other hand , general theoretical arguments suggesting , e.g. a tight correlation between variations in the x - ray and o - uv components , given their implied proximity , were not confirmed by observations @xcite . the advent of x - ray instrumentation and in particular x - ray spectroscopy , established the presence of spectral components apparently present across the entire range of compact object masses from galactic black hole candidates ( gbhcs ) to luminous agns , namely outflowing x - ray absorbing matter in our line of sight ( los ) manifested as complex ( blueshifted ) absorption features of hydrogen equivalent column density @xmath24 @xmath25 . the presence of this absorbing material , often referred to as warm absorber , was first established in _ asca _ observations of many agns ( e.g. * ? ? ? * ) and gbhcs ( e.g. * ? ? ? * ) which provided clear evidence of highly ionized oxygen ( 0.739 kev ) and/or ( 0.871 kev ) along the los . more recently , grating spectra of high - resolving power obtained by _ chandra _ and _ xmm - newton _ have enabled the study of these absorption features in greater detail leading to the conclusion that they are present in a large fraction of agns and span a wide range ( @xmath26 ) in ionization parameter ( e.g. * ? ? ? * hereafter hbk07 ) . some sources appear to contain low and/or high velocity outflows ( e.g. hbk07 ; * ? ? ? * ) while a handful of objects exhibit a trans - relativistic outflow ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? in addition in both agns and gbhcs the observed outflows from at least a number of sources have been suggested to be accelerated magnetically ( rather than by another process ) off an accretion disk ( e.g. , see miller et al . 2006 , 2008 for gro j1655 - 40 ; kraemer et al . 2005 and crenshaw & kraemer 2007 for ngc 4151 ) . a brief review of luminous agn winds is found in @xcite . these facts imply the presence of gas covering a large fraction of the solid angle and distributed over a large range of radii , perhaps the entire range between the x - ray source and the torus , indicating agns to be multiscale and multiwavelength objects rather than a class with properties determined only by the power released by accretion in the black hole vicinity . this last point has gained further support with the discovery of the correlation between the accreting black hole mass and the velocity dispersion of the surrounding stellar population @xcite . from the theoretical point of view , most early agn treatments were focused on the structure of the innermost regions of the accretion flow and as such they limited themselves to the study of the conditions in a rather narrow range of radii . nonetheless , several treatments of magnetohydrodynamic ( mhd ) accretion disk winds , aiming to account for the observed agn outflows , employed self - similar solutions , which naturally span a large range in radius ( e.g. blandford & payne 1982 , hereafter bp82 ; contopoulos & lovelace 1994 , hereafter cl94 ) . using the structure of these solutions , ( * ? ? ? * hereafter kk94 ) proposed that the so - called molecular torus of the agn unification scheme is a dynamical rather than a static object , namely an mhd wind of the type suggested in the above works . kk94 also contented that agreement between model and observation demanded a rather specific type of wind , a particular case of those discussed in cl94 , one that we also concentrate on in the present work . at the same time , they noted that the 2d geometry of these winds ( with low column at inclination angles @xmath27 , i.e. along the wind axis , and high column at @xmath28 ) provided , in addition , a natural framework for the unification scheme of type i and ii seyfert galaxies proposed by antonucci & miller ( 1985 ) , thereby linking the large scale agn spectral classification to the dynamics of agn accretion / outflows . self - similar solutions of the accretion flow equations were also provided by @xcite , who considered the structure of hot accretion flows in the regime of low accretion rate , i.e. for accretion rates less than the eddington value , @xmath29 . because for these low rates the accretion time scale @xmath30 is shorter than the gas cooling time @xmath31 , in fact @xmath32 , only a fraction @xmath11 of the energy released in the dissipation of the plasma kinetic energy is radiated away with the remainder advected into the black hole ( hence the term advection dominated accretion flows or adafs ) ; as a result , the accretion luminosity is then proportional to @xmath33 ( rather than @xmath34 ) . the high temperature of the inner adafs , provides naturally for the hot component required to produce the observed x - ray emission , which , rather than being an independent component , within adafs is incorporated in the dynamics of accretion itself ( see * ? ? ? * for recent review ) . more recently , @xcite , elaborated further on adafs elucidating , among others , the reason for which the bernoulli integral of adafs is positive ( a point that had been noted by * ? ? ? * ; * ? ? ? * ) , that being that the viscous stresses transfer outward , in addition to angular momentum , also mechanical energy . they then proposed that this excess energy can be carried away in the form of wind over a large range of radii , thereby leading to configurations similar to those obtained in the more detailed studies of bp82 and cl94 , while at the same time maintaining some of the general properties of adafs . the combination of radiatively inefficient flows with the simultaneous presence of winds led to the nomenclature advection dominated inflow - outflow solutions ( adios ) . following these pioneering works , many attempts have been made in recent years to reproduce and explain the kinematics and x - ray spectra of the observed outflows in agns ( see , among others , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? motivated by these considerations we are taking a closer look at the issue of warm absorbers ( x - ray absorbing medium ) in terms of specific disk - wind models , namely those of cl94 . as it will be discussed in more detail later on , these solutions are characterized by a parameter @xmath35 , which determines the distribution of axial current in the wind as a function of the radius ; this parameter , in conjunction with the mhd conservation laws and the radial force balance , determines both the radial dependence of the matter density in the wind and the radial dependence of the toroidal magnetic field component @xmath36 . taking our lead from the works of @xcite and hbk07 , in the present work we restrict our attention to wind models with @xmath37 , i.e. the value used also by kk94 . this is in a sense a critical value of this parameter because , as discussed in cl94 , it leads to winds with toroidal magnetic field @xmath38 and therefore magnetic field energy on the disk that diverges only logarithmically at small and large @xmath1 and as such it can be considered as a minimum magnetic energy " configuration ( kk94 ) ; values of @xmath39 lead to configurations with power - law divergence either at small or large @xmath40 . in addition , the choice @xmath37 leads to a wind with radial density profile @xmath41 , i.e. a profile with equal column per logarithmic radial interval ( and normalization that depends on the polar angle @xmath3 and the mass - accretion rate @xmath11 ) , a fact that is in general agreement with the profiles implied by the ionized absorbers data analysis to date ( hbk07 ) . it is worth noting that a similar density profile was invoked by @xcite and @xcite to explain the fourier frequency dependence of the soft - hard x - ray lags observed in gbhcs and in agns ( papadakis et al . 2002 ) . with the wind 2d ( @xmath1 and @xmath3 ) density field as a function of radius and angle provided by the models of cl94 ( i.e. ignoring at present effects that can be attributed to other agents that could affect the wind structure ) and the assumption of a point x - ray source of a given spectrum at the origin , one can compute their 2d ionization structure and in particular the local column density of specific ionic species as a function of radius and angle . one can also compute the integrated column of each such ion , quantities that can be directly compared to observation ( hbk07 ) . this we do in the present work . while a number of issues remain open or are sidestepped in the present self - similar wind models , this is the price to pay in order to limit the number of free parameters to just two ( the wind mass flux and the observer inclination angle ) , a fact that allows the study of the properties of warm absorbers within the global perspective of agn unification . our paper is structured as follows : in 2 we review the mhd wind equations and structure as given in cl94 and make a connection of these winds with flows of the adaf / adios type by relating the wind density normalization to the ionizing luminosity produced by the idealized point source at the coordinate origin . in 3 we provide the general 2d ionization structure , the local column of specific ions as a function of radius as well as the total ionic column of a given charge state and for each element , as well as the absorption line profiles of selected transitions . in 4 the results are compared to observation , the properties and limitation of the present treatment are discussed and a course for future work is charted .

based on earlier observational clues and theoretical arguments , we focus our attention on a subset of these winds , namely those with radial density dependence ( is the spherical radial coordinate ) . we employ the photoionization code ` xstar ` to compute the ionic abundances of a large number of ions of different elements and then compile their line - of - sight ( los ) absorption columns . the amd is found to be independent of , in good agreement with its behavior inferred from the x - ray spectra of several active galactic nuclei ( agns ) . our models describe the x - ray absorption properties of these winds with only _ two parameters _ , namely the mass - accretion rate and los angle . as such , we concur with previous authors that these wind configurations , viewed globally , incorporate all the requisite properties of the parsec scale torii " invoked in agn unification schemes . we indicate that a combination of the amd and absorption line profile observations can uniquely determine these model parameters and their bearing on agn population demographics .

we present the two - dimensional ( 2d ) ionization structure of self - similar magnetohydrodynamic ( mhd ) winds off accretion disks around irradiated by a central x - ray point source . based on earlier observational clues and theoretical arguments , we focus our attention on a subset of these winds , namely those with radial density dependence ( is the spherical radial coordinate ) . we employ the photoionization code ` xstar ` to compute the ionic abundances of a large number of ions of different elements and then compile their line - of - sight ( los ) absorption columns . we focus our attention on the distribution of the column density of the various ions as a function of the ionization parameter ( or equivalently ) and the angle . particular attention is paid to the absorption measure distribution ( amd ) , namely their hydrogen - equivalent column per logarithmic interval , , which provides a measure of the winds radial density profiles . for the chosen density profile the amd is found to be independent of , in good agreement with its behavior inferred from the x - ray spectra of several active galactic nuclei ( agns ) . for the specific wind structure and x - ray spectrum we also compute detailed absorption line profiles for a number of ions to obtain their los velocities , km s ( at ) for and km s ( at ) for , in good agreement with the observation . our models describe the x - ray absorption properties of these winds with only _ two parameters _ , namely the mass - accretion rate and los angle . the probability of obscuration of the x - ray ionizing source in these winds decreases with increasing and increases steeply with the los inclination angle . as such , we concur with previous authors that these wind configurations , viewed globally , incorporate all the requisite properties of the parsec scale torii " invoked in agn unification schemes . we indicate that a combination of the amd and absorption line profile observations can uniquely determine these model parameters and their bearing on agn population demographics .

0910.3001

i

in this work we have presented a detailed study of the ionization structure of model mhd winds off accretion disks ; this is our first attempt to model within this context the recent observations of absorption features in the _ asca , xmm _ and _ chandra _ x - ray spectra , the so - called warm absorbers . to this end we have employed the self - similar 2d hydromagnetic wind models developed by cl94 that provide the fluid 2d density and velocity fields , which we coupled to photoionization calculations using ` xstar ` . our consideration of magnetocentrifugal ( mhd ) winds / outflows in this work has been motivated and supported in part by recent observational implications that at least in a number of agns and gbhcs the inferred driving mechanism of the observed x - ray ionized wind medium is magnetic rather than thermal or radiative ( e.g. , see miller et al . 2006 , 2008 for gro j1655 - 40 ; kraemer et al . 2005 and crenshaw & kraemer 2007 for ngc 4151 ) . given the scope of our paper , our model wind is necessarily overly simple . it ignores a host of issues that affect the structure of winds off accretion disks and replaces them with the self - similar models of cl94 . the interested reader can get a feeling of the multitude and complexity of the issues not addressed in the present treatment by looking at the works of , e.g. , @xcite and @xcite ( and references therein ) and also ( * ? ? ? * for disks with several distinct values of the accretion rate @xmath290 ) . these include , among others , the radiative transfer in the wind , the ensuing effects of radiation pressure and also the influence of the vertical gradient of @xmath291 in the launching of the wind . as shown in these references the winds can be radiation driven in the inner part of the disk ( due to the increased flux at this spatial domain ) while being magnetically launched at larger radii . in this respect our model winds are quite different in structure and variability from the more realistic winds of @xcite at small radii , while they should be more similar to those of his at larger radii where radiation pressure is smaller and the wind is magnetically launched . realistic models must by necessity consider the transition of the underlying disk from radiation pressure , at small @xmath1 , to gas pressure dominance at larger radii ; this fact would likely force a different choice of our boundary condition @xmath292 and therefore yield a field geometry that breaks the self - similarity of our solutions . wind models very similar to those used herein but with the inclusion of the effects of the radiation pressure that break the self - similarity were discussed by kk94 and @xcite . one should therefore view our models with the above caveats in mind . the significance and assumptions of the models we propose is basically justified _ a posteriori _ by their ability to interpret the observations . self - similarity is one of the fundamental assumptions of our model winds . however , whether exactly self - similar or not , any model that would attempt to account the entire range of ionic species shown e.g. in @xcite must by necessity cover a very broad range in the photoionization parameter @xmath2 . then , the column of each such ion provides a measure of the corresponding hydrogen equivalent column @xmath158 as a function of @xmath2 , i.e. the amd . these two quantities ( @xmath293 ) can then be employed to provide a measure of the gas density @xmath294 as a function of the distance @xmath1 from the x - ray source . barring the possibility of several independent regions at different distances but similar columns as indicated by the functional form of the amd ( one could consider this is possibility at the risk of introducing an inordinate number of free parameters ) , models with radial density profiles as those considered here are a natural consequence of the amd obtained by the _ chandra _ observations . the wind ionization structure was followed in 1d as described in 2.2 , namely along the observer s los , assuming the ionizing source to be point - like . clearly , a more comprehensive treatment of this problem should take into account also the backward emitted radiation which will reach the observer from the regions of the disk on the other side of the black hole , as well as the scattered radiation , whose effects could be significant . we plan to return to these issues in a future publication . the 2d structure of the winds considered in our analysis implies , at a minimum , a two - parameter description of the absorption features . however , the self - similarity of the problem simplifies further the treatment by allowing the separation of the @xmath1 and @xmath3 variables with the wind density obtaining the form @xmath295 . the parameter @xmath35 is a most important parameter of these models because it determines both the radial dependence of the ionization parameter @xmath2 and the wind column density per decade of radius along a given direction ( los ) . in the models examined in the present work we restricted our study to the value @xmath37 , which leads to a radial density profile @xmath296 this is an interesting profile in that it provides for an ionization parameter @xmath2 with a similar dependence , i.e. @xmath297 , and most importantly , with equal column per decade in radius , across the entire range in radius and the corresponding range in @xmath2 ; as a result , ionic species of very different ionization properties , existing over a wide range of ionization parameter ( and radius ) , have roughly comparable column densities , independent of the distance and are therefore possible to detect . as noted in cl94 , the value of @xmath35 determines also the axial current distribution in radius within the wind , with the corresponding magnetic energy per unit length at the wind base being also constant per ( cylindrical ) decade in radius . it is worth comparing our work with that of kk94 , who used the same type of mhd wind with the value of @xmath35 as we do herein : while these authors focused their study on the effects of dust on radiation transfer , we focus our attention on the effects of the ionizing radiation on the x - ray spectra of agns , in particular on the ionized absorbers . kk94 also noted in passing the relevance of their models to the x - ray agn spectra well ahead of the detailed outflow observations made with _ chandra_. while the structure of the wind in @xmath1 and @xmath3 is provided by the models of cl94 , for the remaining parameters of our models , namely the normalization of the wind density and the x - ray luminosity of the ionizing source we have chosen to use the scalings of adafs , or better adios ; as a result the x - ray luminosity is proportional to the square of the ( normalized ) accretion rate at the inner edge of the disk @xmath33 rather than simply @xmath11 , assumed in standard accretion disks . therefore , restricting ourselves to models with @xmath37 , the global ionization structure of a given wind , including the normalization of the column density , depends only on _ two parameters _ , namely @xmath11 and the observer s inclination angle @xmath3 . this parametrization provides an extremely economical set of assumptions concerning not only the outflows , i.e. the wind ionization structure seen in absorption in detailed x - ray spectra , but also for the entire ( radio - quiet ) agn unification picture : figure [ fig : density ] which exhibits the normalization of the wind density as a function of @xmath3 along the magnetic field line of @xmath298 , makes apparent the difference in column between face - on and edge - on views , implying that the wind , if extending to sufficiently large radii , can in fact serve as the proposed molecular torus associated with agn unification , a point originally made by kk94 , also for winds with @xmath37 ; it is of interest to note that the few objects for which sufficiently detailed observations exit are consistent values @xmath299 ( hbk07 ; * ? ? ? within this same context and ionizing luminosity considerations , one should note the dependence of source obscuration on the x - ray luminosity , namely its reduced value for objects accreting at a higher fraction of their eddington rate @xmath11 , which apparently is in general agreement with observations . it remains to be seen whether these notions can withstand the scrutiny of more consistent and encompassing observational tests . at this point we would like to stress the importance of the amd in the study of agn outflows / winds , a quantity enunciated by hbk07 and modeled in detail in the preceding sections . analyses similar to those of hbk07 and @xcite are indispensable because they produce a consistent analysis of the entire set of absorption features in the agn x - ray absorption spectra . at the same time they underscore the unique value of x - ray spectroscopy which , in a wavelength band of @xmath300 decades , can encapsulate the properties of ions that span @xmath301 orders of magnitude in ionization parameter and , for models with @xmath299 , a similar range in radius ; at the same time , measurement of their absorption columns yields the equivalent hydrogen column of the flow , @xmath158 , over a similar range in radius , thereby going a long way toward the determination of the physics underlying the outflow dynamics . the fact that the amd analyses to date are roughly independent of @xmath2 provide support to our use of the @xmath37 or @xmath302 models , reiterating that a similar density profile was invoked on the basis of agn and gbhc timing properties @xcite . we have thus presented a concrete example of the amd dependence on @xmath2 for our @xmath37 models with @xmath303 and two different values of the observer s inclination angle ( see table [ tab : tbl-1 ] for details ) . as expected we found the amd to be constant , i.e. independent of @xmath2 , over many decades in this parameter ( i.e. the local column density @xmath280 is independent of ionization states @xmath2 of ions ) . with @xmath304 , equation ( [ eq : column1 ] ) implies @xmath305 @xmath25 ( yielding a total column of @xmath306 @xmath25 ) for @xmath253 and @xmath307 @xmath25 ( total of @xmath308 @xmath25 ) for @xmath254 over @xmath309 erg cm s@xmath7 , in good agreement with the observed amd of iras 13349 + 2438 ( hbk07 ; * ? ? ? * ) and also some other agns detailed below . one should note that these values depend primarily on @xmath11 and @xmath3 and are independent of the black hole mass . the mass of the object gets involved only as a measure of its total luminosity , which does not appear in the expression for @xmath158 , implying that these models could in principle be applicable also in gbhcs . high quality x - ray absorption data are in fact available for the gbhc gro j1655 - 40 and were used to argue for magnetic driving of the wind in this system too @xcite . these spectra are distinguished from those of agns by the prominent absence of low ionization state ions . this is to be expected given that the presence of the companion star limits the extent of the disk to roughly half the distance between the two objects or @xmath310 cm . given that the schwarzschild radius of the compact object is @xmath311 cm the entire disk size covers only a range of @xmath312 in radius ; considering ( based on fig . [ fig : amd ] ) that in the inner region of the wind ( @xmath313 cm ) major elements ( even heavier species ) are almost fully ionized , one would expect the presence of ions over only a factor of 1000 in @xmath2 , in rough agreement with the observation . given that our models provide also the complete velocity field of the mhd wind we have also produced a sequence of synthetic absorption profiles as described in 2.2 and shown in 3.2 . we have done so for two charge levels of fe , namely and . with our fiducial model predicting the column to be maximum at @xmath314 erg cm s@xmath7 , we then infer the corresponding los velocity ( see fig . [ fig : fe ] ) to be @xmath315 km s@xmath7 in excellent agreement with the observed values of iras 13349 + 2438 . it is important to note that the model produces not only the correct velocity @xmath153 at the maximum value of @xmath316 but also the observed @xmath317 normalization _ for the same inclination angle_. it is therefore possible with measurements of the combined line widths and column densities to reproduce within the present models both @xmath35 , @xmath3 and @xmath11 , thereby providing a complete specification of these winds . in addition to iras 13349 + 2438 , the nearby bright seyfert mcg 6 - 30 - 15 has been observed to show , as one of the multiple ionization zones , an x - ray ionized absorber with an outflow velocity of @xmath318 km s@xmath7 at @xmath319 and @xmath320@xmath25 ( e.g. * ? ? ? * ; * ? ? ? * ) also in good agreement with our model results for @xmath321 ( see fig . [ fig : fe ] ) . clearly , a different choice of a set of conserved quantities ( wind variables ) in the model would produce a slightly different field line geometry in which the resulting mhd outflow could in principle obtain higher los velocities ( perhaps by factors of magnitudes ) , and this will be studied in detail in a future work . as noted above our model is quite successful in reproducing the observed amd of iras 13349 + 2438 . more recently , @xcite presented a compilation of the amd of a number of agn with @xmath4 which are slightly different from constant but with @xmath322values of @xmath323 which are still very close to unity ; e.g. ngc 3783 ( @xmath324 ) , ngc 5548 ( @xmath325 ) , ngc 7469 ( @xmath326 ) and mcg-6 - 30 - 15 @xmath327 . we believe some of these amds are sufficiently close to those of our fiducial model to be virtually indistinguishable . by comparison , the mhd wind models of bp82 have @xmath328 and @xmath329 . their ionization parameter decreases more slowly with @xmath1 ( @xmath330 ) and hence a range of 5 - 6 decades in @xmath2 implies a range of 10 - 12 decades in radius with the corresponding distances being unrealistic . most importantly , the wind columns would decrease with radius ( @xmath331 ) and the amd dependence on @xmath2 would be @xmath332 , in clear disagreement with these observations , and thus their model is essentially ruled out @xcite . despite the apparent success of this first model , one should bear in mind that several aspects have been treated in a rather simplified fashion . here we discuss some of them and their influence on the results presented so far : \1 . the shape of the ionizing spectrum used so far ( @xmath333 between 13.6 ev and 13.6 kev with @xmath214 ) is quite simplistic , however , such spectra are often used in similar type calculations ( e.g. * ? ? ? this is a crude approximation to the observed spectra characterized by complex spectral shapes . spectral features like the bbb and the uv to x - ray luminosity ratio @xmath334 @xcite play a role in our results ( a recent review of the broad band agn seds can be found , e.g. , in * ? ? ? more recently , @xcite sampled 110 bright soft - xray selected agns for a simultaneous study of optical / uv and x - ray data and reported strong correlations between the x - ray spectral slope and the optical / uv slope which should be included in a more comprehensive treatment . multi - components of the broad - band agn spectra , as those discussed by @xcite and @xcite , should play an important role in characterizing the observed x - ray spectral features . adding softer photons ( responsible for the optical / uv components ) could impact the radiative transfer between those more complex photon distributions and the ionized matter ( see , e.g. , * ? ? ? * ; * ? ? ? * for multi - component injected spectra ) . in fact , we have mimicked the presence of such softer photons by choosing larger values of the spectral index of our models ( @xmath335 ) . for the same total luminosity ( implemented in the definition of @xmath2 ) , it was found in this trial run that the radial position of the peak column density of a given ion ( e.g. ) decreases , because the presence of a given ion requires a certain flux of _ ionizing _ photons per atom ; in a steep spectrum the proper ratio is found at larger values of the parameter @xmath2 or correspondingly smaller values of the distance @xmath336 . as a result , the widths of the corresponding transitions should be larger and therefore the proper ionizing spectrum is necessary for the correct interpretation of the relations between ionic column densities and wind kinematics ( see * ? ? ? * ; * ? ? ? * for a similar approach ) . the ionizing source has been considered , for simplicity , to be point - like . a source of finite size will provide for more complex illumination , especially for parts of the wind at which the source angular extent is significant . most importantly an extended source would impact the absorption line profiles , since a line of sight may pass through matter other than that used in section 3.2 . finally , to treat the radiative transfer correctly at all energies , one should eventually need to resort to a 2d approach rather than the 1d model ( radial only ) presently used , which would modify the global ionization structure ( fig . [ fig:2d]b ) . the wind equations , as presently implemented include only mhd forces , while it is apparent that in the presence of the ionic species we produce one should also include the effects of radiation pressure . because the latter depends on the ionization state of the plasma which in turn depends on its kinematics , implemented correctly , this should be done iteratively in a way similar to @xcite . based on the rather small effect that the radiation force seems to have on the structure of these winds , we believe that our present results are generally valid . in summary , we have presented above a first attempt at interfacing theoretical models of mhd winds with agn observations , in particular the absorption features in their x - ray spectra of ionized outflows . we have placed most of our emphasis on modeling the corresponding amds , which , based on the existing observations seems to favor a specific value of the model parameter @xmath35 which determines the radial density dependence of our models , namely @xmath299 . with the value of this parameter set by observation , our models present a _ two - parameter _ family of agn wind structure , namely @xmath11 and @xmath3 . we have found that , based on the limited number of objects discussed above , our models fare rather well in accommodating the observations and the possibility of incorporating agn unification within the same models , as discussed in kk94 . there is still a multitude of issues related to x - ray absorption that remain open , e.g. whether the model can accommodate the high velocity ( @xmath337 ) outflows associated with x - ray absorption features ( see , e.g. , * ? ? ? * ; * ? ? ? * for some attempts with monte carlo simulations ) in the spectra of some bright quasars such as apm 08279 + 5255 , pg 1211 + 143 and pds 456 ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in the context of our model this point may be well explained with an optimized magnetic field geometry [ i.e. @xmath58 distribution determined by gs - equation ( [ eq : gs ] ) ] that provides a favorable los velocity component . important as they are , these go beyond the scope of the present work and we expect to return to them in future publications . we are grateful to our anonymous referee for his / her constructive comments that improved the manuscript . we would like to thank tim kallman for his help with ` xstar ` incisive comments . we express our gratitude to george chartas for his comments on the model , takanori sakamoto and javier garcia for their assistance with scripting and running ` xstar ` as well as helpful comments . this work was supported in part by nasa adp grant .

we present the two - dimensional ( 2d ) ionization structure of self - similar magnetohydrodynamic ( mhd ) winds off accretion disks around irradiated by a central x - ray point source . we focus our attention on the distribution of the column density of the various ions as a function of the ionization parameter ( or equivalently ) and the angle .

we present the two - dimensional ( 2d ) ionization structure of self - similar magnetohydrodynamic ( mhd ) winds off accretion disks around irradiated by a central x - ray point source . based on earlier observational clues and theoretical arguments , we focus our attention on a subset of these winds , namely those with radial density dependence ( is the spherical radial coordinate ) . we employ the photoionization code ` xstar ` to compute the ionic abundances of a large number of ions of different elements and then compile their line - of - sight ( los ) absorption columns . we focus our attention on the distribution of the column density of the various ions as a function of the ionization parameter ( or equivalently ) and the angle . particular attention is paid to the absorption measure distribution ( amd ) , namely their hydrogen - equivalent column per logarithmic interval , , which provides a measure of the winds radial density profiles . for the chosen density profile the amd is found to be independent of , in good agreement with its behavior inferred from the x - ray spectra of several active galactic nuclei ( agns ) . for the specific wind structure and x - ray spectrum we also compute detailed absorption line profiles for a number of ions to obtain their los velocities , km s ( at ) for and km s ( at ) for , in good agreement with the observation . our models describe the x - ray absorption properties of these winds with only _ two parameters _ , namely the mass - accretion rate and los angle . the probability of obscuration of the x - ray ionizing source in these winds decreases with increasing and increases steeply with the los inclination angle . as such , we concur with previous authors that these wind configurations , viewed globally , incorporate all the requisite properties of the parsec scale torii " invoked in agn unification schemes . we indicate that a combination of the amd and absorption line profile observations can uniquely determine these model parameters and their bearing on agn population demographics .

1602.06030

i

consider a non - linear , non - gaussian state space model for an observed sequence @xmath0 . this model , with parameters @xmath1 , assumes that the @xmath2 are drawn from an observation density @xmath3 , where @xmath4 is an unobserved markov process with initial density @xmath5 and transition density @xmath6 . here , the @xmath7 might be either continuous or discrete . we may be interested in inferring both the realized values of the markov process @xmath8 and the model parameters @xmath1 . in a bayesian approach to this problem , this can be done by drawing a sample of values for @xmath9 and @xmath1 using a markov chain that alternately samples from the conditional posterior distributions @xmath10 and @xmath11 . in this paper , we will only consider inference for @xmath9 by sampling from @xmath10 , taking the parameters @xmath1 to be known . as a result , we will omit @xmath1 in model densities for the rest of the paper . except for linear gaussian models and models with a finite state space , this sampling problem has no exact solution and hence approximate methods such as mcmc must be used . one method for sampling state sequences in non - linear , non - gaussian state space models is the embedded hmm method ( neal , 2003 ; neal , beal and roweis , 2004 ) . an embedded hmm update proceeds as follows . first , at each time @xmath12 , a set of @xmath13 `` pool states '' in the latent space is constructed . in this set , @xmath14 of the pool states are drawn from a chosen pool state density and one is the current value of @xmath7 . this step can be thought of as temporarily reducing the state space model to an hmm with a finite set of @xmath13 states , hence the name of the method . then , using efficient forward - backward computations , which take time proportional to @xmath15 , a new sequence @xmath16 is selected from the `` ensemble '' of @xmath17 sequences passing through the set of pool states , with the probability of choosing each sequence proportional to its posterior density divided by the probability of the sequence under the pool state density . at the next iteration of the sampler , a new set of pool states is constructed , so that the chain can sample all possible @xmath7 , even when the set of possible values is infinite . another method is the particle gibbs with backward sampling ( pgbs ) method . the particle gibbs ( pg ) method was first introduced in andrieu , doucet and holenstein ( 2010 ) ; whiteley suggested the backward sampling modification in the discussion following this paper . lindsten and schon ( 2012 ) implemented backward sampling and showed that it improves the efficiency of pg . starting with a current sequence @xmath9 , pgbs first uses conditional sequential monte carlo ( smc ) to construct a set of candidate sequences and then uses backward sampling to select a new sequence from the set of candidate ones . here , conditional smc works in the same way as ordinary smc when generating a set of particles , except that one of the particles at time @xmath12 is always set to the current @xmath7 , similar to what is done in the embedded hmm method , which allows the sampler to remain at @xmath7 if @xmath7 lies in a high - density region . while this method works well for problems with low - dimensional state spaces , the reliance of the smc procedure on choosing an appropriate importance density can make it challenging to make the method work in high dimensions . an important advantage of particle gibbs , however , is that each iteration takes time that is only linear in the number of particles . both the pgbs and embedded hmm methods can facilitate sampling of a latent state sequence , @xmath9 , when there are strong temporal dependencies amongst the @xmath7 . in this case , using a method that samples @xmath7 conditional on fixed values of @xmath18 and @xmath19 can be an inefficient way of producing a sample from @xmath20 , because the conditional density of @xmath7 given @xmath18 and @xmath19 can be highly concentrated relative to the marginal density of @xmath7 . in contrast , with the embedded hmm and pgbs methods it is possible to make changes to blocks of @xmath7 s at once . this allows larger changes to the state in each iteration of the sampler , making updates more efficient . however , good performance of the embedded hmm and pgbs methods relies on appropriately choosing the set of pool states or particles at each time @xmath12 . in this paper , our focus will be on techniques for choosing pool states for the embedded hmm method . when the latent state space is one - dimensional , embedded hmms work well when choosing pool states in a variety of ways . for example , in shestopaloff and neal ( 2013 ) , we choose pool states at each time @xmath12 by constructing a `` pseudo - posterior '' for each latent variable by taking the product of a `` pseudo - prior '' and the observation density , the latter treated as a `` pseudo - likelihood '' for the latent variable . in shestopaloff and neal ( 2014 ) , we choose pool states at each time @xmath12 by sampling from the marginal prior density of the latent process . ways of choosing pool states that work well in one dimension begin to exhibit problems when applied to models with higher - dimensional state spaces . this is true even for dimensions as small as three . since these schemes are global , designed to produce sets of pool states without reference to the current point , as the dimension of the latent space grows , a higher proportion of the sequences in the ensemble ends up having low posterior density . ensuring that performance does nt degrade in higher dimensions thus requires a significant increase in the number of pool states . as a result , computation time may grow so large that any advantage that comes from using embedded hmms is eliminated . one advantage of the embedded hmm method over pgbs is that the embedded hmm construction allows placing pool states locally near the current value of @xmath7 , potentially allowing the method to scale better with the dimensionality of the state space . switching to such a local scheme fixes the problem to some extent . however , local pool state schemes come with their own problems , such as making it difficult to handle models with multiple posterior modes that are well - separated the pool states might end up being placed near only some of the modes . in this paper , we propose an embedded hmm sampler suitable for models where the state space is high dimensional . this sampler uses a sequential approximation to the density @xmath21 or to the density @xmath22 as the pool state density . we show that by using this pool state density , together with an efficient mcmc scheme for sampling from it , we can reduce the cost per iteration of the embedded hmm sampler to be proportional to @xmath23 , as with pgbs . at the same time , we retain the ability to generate pool states locally , allowing better scaling for high - dimensional state spaces . our proposed scheme can thus be thought of as combining the best features of the pgbs and the embedded hmm methods , while overcoming the deficiencies of both . we use two sample state space models as examples . both have gaussian latent processes and poisson observations , with one model having a unimodal posterior and the second a multimodal one . for the multimodal example , we introduce a `` mirroring '' technique that allows efficient movement between the different posterior modes . for these models , we show how our proposed embedded hmm method compares to a simple metropolis sampler , a pgbs sampler , as well as a sampler that combines pgbs and simple metropolis updates . further details on ensemble methods are available in the phd thesis of shestopaloff ( 2016 ) .

this new scheme allows the embedded hmm method to be used for efficient sampling in state space models where the state can be high - dimensional . previously , embedded hmm methods were only applied to models with a one - dimensional state space . we demonstrate that using our proposed pool state selection scheme , an embedded hmm sampler can have similar performance to a well - tuned sampler that uses a combination of particle gibbs with backward sampling ( pgbs ) and metropolis updates . the scaling to higher dimensions is made possible by selecting pool states locally near the current value of the state sequence .

we propose a new scheme for selecting pool states for the embedded hidden markov model ( hmm ) markov chain monte carlo ( mcmc ) method . this new scheme allows the embedded hmm method to be used for efficient sampling in state space models where the state can be high - dimensional . previously , embedded hmm methods were only applied to models with a one - dimensional state space . we demonstrate that using our proposed pool state selection scheme , an embedded hmm sampler can have similar performance to a well - tuned sampler that uses a combination of particle gibbs with backward sampling ( pgbs ) and metropolis updates . the scaling to higher dimensions is made possible by selecting pool states locally near the current value of the state sequence . the proposed pool state selection scheme also allows each iteration of the embedded hmm sampler to take time linear in the number of the pool states , as opposed to quadratic as in the original embedded hmm sampler . we also consider a model with a multimodal posterior , and show how a technique we term `` mirroring '' can be used to efficiently move between the modes .

1407.7679

i

traditionally , thermodynamics is a theory that describes systems exchanging energy and entropy with idealized heat reservoirs and work sources . it provides two fundamental laws every system must obey : the first law ( energy balance ) and the second law ( entropy increase ) . reconciling these macroscopic laws with a microscopic picture of atoms and molecules in motion raises subtle issues . as far back as the nineteenth century , maxwell speculated that an external agent , using microscopic information to control the state of a system , might be able to circumvent the second law @xcite . this agent is now known as ` maxwell s demon ' . accepting the possibility of ` intelligent interventions ' ( due to idealized measurement and information processing devices such as computers ) , it is widely accepted that the correct application of landauer s principle @xcite will save the second law , as noted by bennett @xcite in his analysis of szilard s famous engine @xcite . note however that maxwell s demon can also be ` exorcized ' without reference to intelligent interventions , by showing that any device designed to exploit molecular scale fluctuations to violate the second law , must fail or must produce a large dissipation somewhere else as analysed for specific models by smulochowski @xcite and feynman @xcite . see also ref . @xcite for opposing arguments and refs . @xcite for other illustrative models . besides the possibility of actively measuring and controlling the system , bennett noted that a tape of bits in a low entropy state might act as a thermodynamic resource while the tape randomizes itself @xcite , which can be regarded as another form of a maxwell demon in which the low entropy state of the tape allows for the rectification of thermal fluctuations , for instance to lift a mass or cool a cold reservoir . a particular mathematical model was proposed and analyzed by mandal and jarzynski @xcite and has been followed by further models exploring the possibility of maxwell s demon devices incorporating an information reservoir in the thermodynamic description @xcite . however , the models proposed above are rather abstract and it would be desirable to find a _ physical _ model able to reproduce the same results . by ` physical ' model we mean that we start with a well - defined and well - motivated hamiltonian describing an explicit , physically realizable system , and , following standard procedures ( e.g. as used to derive master equations ) , we end up with a mathematical description equivalent to those above . in this paper we will indeed show that a quantum dot spin valve with perfectly polarized leads allowing only for one sort of spins to tunnel through , which interacts with a tape of electrons causing spin flips , provides a physical implementation of the device proposed in ref . @xcite in the sense that it has identical dynamics and thermodynamics ( though a quite different physical interpretation ) . a similar model was already put forward by datta in ref . @xcite where the ` impurities ' in his model correspond to the electrons on the tape in our model . for another physical realization also see ref . @xcite . the models discussed above all rely on measurements or interactions with a bit at predetermined discrete times or intervals . the resulting dynamics can in general not be formulated as a differential equation anymore . an alternative approach to feedback control relies on a continuous measurement scheme and the fact that a master equation ( me ) can be unraveled in terms of trajectories representing the actual state of the system . this approach yields an effective differential equation for the system dynamics and has been extensively used in the field of open quantum systems and quantum information @xcite . furthermore , it was successfully applied to construct maxwell demon like feedbacks and to study the thermodynamics of such systems @xcite . it was shown that such feedback schemes can also be formulated within an inclusive approach not relying on any phenomenological measurements or feedback actions @xcite . in addition to the me picture , the thermodynamic implications of continuous feedback schemes were studied for langevin dynamics as well @xcite . aside from the quest to design illustrative devices , which are able to rectify thermal fluctuations by some sort of information processing , the question naturally arises as to whether it is possible to treat the different approaches above in a unified framework @xcite . to address this question with our model following the three cases investigated by barato and seifert @xcite we will design a measurement - based feedback scheme , which has identical system dynamics as the tape model , and we will derive an effective me for poisson distributed bits on the tape or measurement times respectively . we will compare the different forms of the second laws and we will show that the second law for discrete feedback control can provide a smaller , equal or larger bound on the amount of extractable work as compared to the second law involving the tape of bits . for the effective me we will show that its associated entropy production represents the same physical statement as the second law involving the tape of bits . _ outline : _ we start with the description of the model including the system , the tape of bits and the system - bit interaction in sec . [ sec physical implementation of the model ] and we show that it is equivalent to a brownian ratchet demon . sec . [ sec thermodynamics ] is then devoted to a thorough study of its thermodynamics . in sec . [ sec measurement based feedback scheme ] we will study a measurement based feedback scheme , which yields identical system dynamics but different thermodynamics and we will compare the two different second laws . finally , we derive an effective me for a poisson distributed tape in sec . [ sec effective master equation ] and discuss its thermodynamic behaviour in relation to the other approaches . in sec . [ sec conclusions ] we discuss our results .

the model is exactly solvable and we show that it can be equivalently interpreted as a brownian ratchet demon . we then consider a measurement based discrete feedback scheme , which produces identical system dynamics , but possesses a different second law inequality . we show that the second law for discrete feedback control can provide a smaller , equal or larger bound on the maximum extractable work as compared to the second law involving the tape of bits . finally , we derive an effective master equation governing the system evolution for poisson distributed bits on the tape ( or measurement times respectively ) and we show that its associated entropy production rate contains the same physical statement as the second law involving the tape of bits .

we propose a physically realizable maxwell s demon device using a spin valve interacting unitarily for a short time with electrons placed on a tape of quantum dots , which is thermodynamically equivalent to the device introduced by mandal and jarzynski [ pnas * 109 * , 11641 ( 2012 ) ] . the model is exactly solvable and we show that it can be equivalently interpreted as a brownian ratchet demon . we then consider a measurement based discrete feedback scheme , which produces identical system dynamics , but possesses a different second law inequality . we show that the second law for discrete feedback control can provide a smaller , equal or larger bound on the maximum extractable work as compared to the second law involving the tape of bits . finally , we derive an effective master equation governing the system evolution for poisson distributed bits on the tape ( or measurement times respectively ) and we show that its associated entropy production rate contains the same physical statement as the second law involving the tape of bits .

0912.1072

i

the classical de finetti theorem states that an exchangeable sequence of real random variables is a mixture of independent and identically distributed ( i.i.d . ) sequences of random variables . moreover , there is an ( almost surely unique ) measure - valued random variable , called the _ directing random measure _ , conditioned on which the random sequence is i.i.d . the distribution of the directing random measure is called the _ de finetti measure _ or the _ mixing measure_. this paper examines the _ computable _ probability theory of exchangeable sequences of real - valued random variables . we prove a uniformly computable version of de finetti s theorem , which implies that _ computable _ exchangeable sequences of real random variables have _ computable _ de finetti measures . the classical _ proofs _ do not readily effectivize ; instead , we show how to directly compute the de finetti measure ( as characterized by the classical theorem ) in terms of a computable representation of the distribution of the exchangeable sequence . along the way , we prove that a distribution on @xmath0^\omega$ ] is computable if and only if its moments are uniformly computable , which may be of independent interest . a key step in the proof is to describe the de finetti measure in terms of the moments of a set of random variables derived from the exchangeable sequence . when the directing random measure is ( almost surely ) continuous , we can show that these moments are computable , which suffices to complete the proof of the main theorem in this case . in the general case , we give a proof inspired by a randomized algorithm which succeeds with probability one . these results are formulated in the turing - machine - based bit - model for computation over the reals ( for a general survey , see braverman and cook @xcite ) . this computational model has been explored both via the type-2 theory of effectivity ( tte ) framework for computable analysis , and via effective domain - theoretic representations of measures . computable analysis has its origins in in the study of recursive real functions , and can be seen as a way to provide `` automated numerical analysis '' ( for a tutorial , see brattka , hertling , and weihrauch @xcite ) . effective domain theory has its origins in the semantics of programming languages , where it continues to have many applications ( for a survey , see edalat @xcite ) . here we use methods from these approaches to transfer a representational result from probability theory to a setting where it can directly transform statistical objects as represented on a computer . the computable probability measures in the bit - model coincide with those distributions from which we can generate exact samples to arbitrary precision on a computer . as such , our results have direct implications for programming languages which manipulate probability measures on real numbers via exact interfaces . in many areas of statistics and computer science , especially machine learning , one is often concerned with distributions on data structures that are higher - order or are defined using recursion . probabilistic functional programming languages provide a convenient setting for describing and manipulating such distributions . exchangeable sequences play a fundamental role in both statistical models and their implementation on computers . description of an exchangeable process , in which one uses previous samples or sufficient statistics to sample the next element in the sequence , a direct implementation in these languages would need to use non - local communication ( to record new samples or update sufficient statistics ) . this is often implemented by modifying the program s internal state directly ( i.e. , using _ mutation _ ) , or via some indirect method such as a state monad . the classical de finetti theorem implies that ( for such sequences over the reals ) there is an alternative description in which samples are conditionally independent ( and so could be implemented without non - local communication ) , thereby allowing parallel implementations . but the classical result does not imply that there is a _ program _ which computes the sequence according to this description . even when there is such a program , the classical theorem does not provide a method for finding it . the computable de finetti theorem states that such a program _ does _ exist . moreover , the proof itself provides the _ method _ for constructing the desired program . in section [ funcpure ] we describe how an implementation of the computable de finetti theorem uniformly transforms procedures which induce exchangeable stochastic processes into equivalent procedures which do not modify non - local state . this transformation is of interest beyond its implications for programming language semantics . in statistics and machine learning , it is often desirable to know the representation of an exchangeable stochastic process in terms of its de finetti measure ( for several examples , see section [ partialexch ] ) . many such processes in machine learning have very complicated ( though computable ) distributions , and it is not always feasible to find the de finetti representation by hand . the computable de finetti theorem provides a method for automatically obtaining such representations .

we prove a uniformly computable version of de finetti s theorem on exchangeable sequences of real random variables . as a consequence , exchangeable stochastic processes in probabilistic functional programming languages can be automatically rewritten as procedures that do not modify non - local state . along the way , we prove that a distribution on the unit interval is computable if and only if its moments are uniformly computable .

we prove a uniformly computable version of de finetti s theorem on exchangeable sequences of real random variables . as a consequence , exchangeable stochastic processes in probabilistic functional programming languages can be automatically rewritten as procedures that do not modify non - local state . along the way , we prove that a distribution on the unit interval is computable if and only if its moments are uniformly computable . de finetti s theorem , exchangeability , computable probability theory , probabilistic programming languages , mutation 03d78 , 60g09 , 68q10 , 03f60 , 68n18

math0403376

i

the present paper is concerned with the floer homology groups @xmath0 of a compact symplectic manifold @xmath1 with contact type boundary , as well as with their cohomological dual analogues @xmath2 . the latter were defined by viterbo in @xcite and are invariants that take into account the topology of the underlying manifold _ and _ , through an algebraic limit process , all closed characteristics on @xmath3 . their definition is closely related to the symplectic homology groups of floer , hofer , cieliebak and wysocki @xcite . throughout this paper we will assume that @xmath4 is exact , and in particular @xmath5 . this last condition will be referred to as _ symplectic asphericity_. the groups @xmath0 are invariant with respect to deformations of the symplectic form @xmath4 that preserve the contact type character of the boundary and the condition @xmath6 . the groups @xmath0 actually depend only on the _ symplectic completion _ @xmath7 of @xmath8 . the manifold @xmath7 is obtained by gluing a positive cone along the boundary @xmath3 and carries a symplectic form @xmath9 which is canonically determined by @xmath4 and the conformal vector field on @xmath8 . we shall often write @xmath10 instead of @xmath0 . the grading on @xmath10 is given by minus the conley - zehnder index modulo @xmath11 , with @xmath12 the minimal chern number of @xmath8 . there exist canonical maps @xmath13 @xmath14 which shift the grading by @xmath15 . * theorem a ( knneth formula ) . * _ let @xmath16 and @xmath17 be compact symplectic manifolds with restricted contact type boundary . denote the minimal chern numbers of @xmath8 , @xmath18 and @xmath19 by @xmath20 , @xmath21 and @xmath22 respectively . _ 1 . for any ring @xmath23 of coefficients there exists a short exact sequence which splits noncanonically @xmath24 & fh_k(m \times n , \ , \omega \oplus \sigma ) \ar@{->>}[d ] \\ & { \bigoplus_{\widehat r+\widehat s = k-1 } } { \text{\rm tor}}_1^a \big ( fh_{\widehat r}(m , \ , \omega ) , \ fh_{\widehat s}(n , \ , \sigma ) \big ) } } \ ] ] + the morphism @xmath25 induces a morphism of exact sequences whose source is the knneth exact sequence of the product @xmath26 and whose target is ( [ suite exacte kunneth floer ] ) . 2 . for any field @xmath27 of coefficients there is an isomorphism @xmath28^{\qquad \sim } & fh^k(m \times n , \ , \omega \oplus \sigma ) \ , } } \ ] ] + the morphism @xmath29 induces a commutative diagram with respect to the knneth isomorphism in cohomology for @xmath30 . in the above notation we have @xmath31 , @xmath32 , @xmath33 and the @xmath34 symbol associates to an integer its class in the corresponding @xmath35 ring . the reader can consult ( * ? ? ? * vi.12.16 ) for a construction of the knneth exact sequence in singular homology . the algebraic properties of the map @xmath29 strongly influence the symplectic topology of the underlying manifold . our applications are based on the following theorem , which summarizes part of the results in @xcite . * theorem ( viterbo @xcite ) . * _ let @xmath36 be a manifold with contact type boundary such that @xmath37 . assume the map @xmath38 is not surjective . then the following hold . _ 1 . the same is true for any hypersurface of restricted contact type @xmath39 bounding a compact region ; 2 . any hypersurface of contact type @xmath39 bounding a compact region carries a closed characteristic ( weinstein conjecture ) ; 3 . there is no exact lagrangian embedding @xmath40 ( here @xmath8 is assumed to be exact by definition ) ; 4 . for any lagrangian embedding @xmath40 there is a loop on @xmath41 which is contractible in @xmath8 , has strictly positive area and whose maslov number is at most equal to @xmath42 ; 5 . for any lagrangian embedding @xmath40 and any compatible almost complex structure @xmath43 there is a nonconstant @xmath43-holomorphic curve @xmath44 ( of unknown genus ) with non - empty boundary @xmath45 . viterbo @xcite introduces the following definition , whose interest is obvious in the light of the above theorem . a symplectic manifold @xmath16 which verifies@xmath46 is said to satisfy the strong algebraic weinstein conjecture ( sawc ) if the composed morphism below is not surjective @xmath47 we shall still denote the composed morphism by @xmath29 . theorem a now implies that the property of satisfying the sawc is stable under products , with all the geometric consequences listed above . * theorem b. * _ let @xmath1 be a symplectic manifold with restricted contact type boundary satisfying the sawc . let @xmath48 be an arbitrary symplectic manifold with restricted contact type boundary . the product @xmath49 satisfies the sawc and assertions ( a ) to ( e ) in the above theorem of viterbo hold . in particular , the weinstein conjecture holds and there is no exact lagrangian embedding in @xmath50 . _ the previous result can be applied for subcritical stein manifolds of finite type . these are complex manifolds @xmath51 which admit proper and bounded from below plurisubharmonic morse functions with only a finite number of critical points , all of index strictly less than @xmath52 @xcite . they satisfy the sawc as proved by viterbo @xcite . cieliebak @xcite has proved that their floer homology actually vanishes . we can recover this through theorem a by using another of his results @xcite , namely that every such manifold is stein deformation equivalent to a split one @xmath53 . this can be seen as an extension of the classical vanishing result @xmath54 , @xmath55 @xcite . * theorem c ( cieliebak @xcite ) . * _ let @xmath7 be a subcritical stein manifold of finite type . its floer homology vanishes _ @xmath56 the paper is organized as follows . in section [ constructions ] we state the relevant definitions and explain the main properties of the invariant @xmath57 . section [ la preuve de kunneth ] contains the proof of theorem a. the proofs of theorems b and c , together with other applications , are gathered in section [ appli ] . let us point out where the difficulty lies in the proof of theorem a. floer homology is defined on closed manifolds for any hamiltonian satisfying some generic nondegeneracy condition , and this condition is _ stable _ under sums @xmath58 on products @xmath59 . this trivially implies ( with field coefficients ) a knneth formula of the type @xmath60 . on the other hand , floer homology for manifolds with contact type boundary is defined using hamiltonians with a rigid behaviour at infinity and involves an algebraic limit construction . this class of hamiltonians is _ not stable _ under the sum operation @xmath58 on @xmath61 . one may still define floer homology groups @xmath62 , but the resulting homology might well be different , in the limit , from @xmath63 . the whole point of the proof is to show that this is not the case . this paper is the first of a series studying the floer homology of symplectic fibrations with contact type boundary . it treats trivial fibrations with open fiber and base . a spectral sequence of leray - serre type for symplectic fibrations with closed base and open fiber is constructed in @xcite . _ acknowledgements . _ this work is part of my ph.d . thesis , which i completed under the guidance of claude viterbo . without his inspired support this could not have come to being . i am grateful to yasha eliashberg , dietmar salamon , paul seidel , jean - claude sikorav and ivan smith for their help and suggestions . i also thank the referee for pointing out errors in the initial proofs of theorem c and proposition [ prop : symplectic capacities ] . during the various stages of preparation of this work i was supported by the following institutions : laboratoire de mathmatiques , universit paris sud ; centre de mathmatiques de lcole polytechnique ; cole normale suprieure de lyon ; departement mathematik , eth .

we prove the knneth formula in floer ( co)homology for manifolds with restricted contact type boundary . we use viterbo s definition of floer homology , involving the symplectic completion by adding a positive cone over the boundary . the knneth formula implies the vanishing of floer ( co)homology for subcritical stein manifolds . other applications include the weinstein conjecture in certain product manifolds , obstructions to exact lagrangian embeddings , existence of holomorphic curves with lagrangian boundary condition , as well as symplectic capacities . department of mathematics , ethz , rmistrasse 101 , 8092 zrich ( ch ) . email : [email protected]

we prove the knneth formula in floer ( co)homology for manifolds with restricted contact type boundary . we use viterbo s definition of floer homology , involving the symplectic completion by adding a positive cone over the boundary . the knneth formula implies the vanishing of floer ( co)homology for subcritical stein manifolds . other applications include the weinstein conjecture in certain product manifolds , obstructions to exact lagrangian embeddings , existence of holomorphic curves with lagrangian boundary condition , as well as symplectic capacities . department of mathematics , ethz , rmistrasse 101 , 8092 zrich ( ch ) . email : [email protected]

math0009179

r

assume that all intervals under consideration are closed . a multimodal map @xmath2 is renormalizable with respect to a critical point @xmath3 if there exist @xmath24 and an interval @xmath25 such that @xmath26 have disjoint interiors and @xmath27 . the smallest @xmath28 with this property is the period of the renormalization . if there is not an interval containing properly @xmath29 with the same property , then @xmath30 . the map @xmath31 restricted to @xmath29 is again a multimodal map . this map is called a @xmath32 of @xmath2 . such renormalization could be renormalizable with respect to @xmath3 again and so on . if this process never finish we say that @xmath2 is * infinitely renormalizable * with respect to @xmath3 . hence we can construct the intervals @xmath4 as in the introduction . let @xmath33 @xmath34 . since @xmath35 , @xmath36 is constant for large @xmath14 . denote @xmath37 , where @xmath14 is large , the set of critical points * involved * in the renormalizations with respect to @xmath3 . assume that there are no wandering intervals for @xmath2 ( for example , if the critical points are non - flat and @xmath2 is @xmath38 : see pg . 267 in @xcite ) . it is well - known that @xmath39 goes to zero . in particular for large @xmath14 , there is at most one critical point in each @xmath9 . we say that an interval @xmath40 is symmetric with respect to a critical point @xmath41 if @xmath2 is monotone in each connect component @xmath42 of @xmath43 and @xmath44 . let @xmath42 be an small interval which contains only one critical point @xmath41 . the symmetrization of @xmath42 is an interval @xmath45 which is a symmetric interval with respect to @xmath41 and @xmath46 . for large @xmath14 , @xmath4 is symmetric with respect to @xmath3 . for large @xmath14 , if @xmath47 and @xmath48 , where @xmath49 is the smallest number such that @xmath50 , we say that @xmath51 is the * successor * of @xmath52 at level @xmath14 and @xmath52 is the * predecessor * of @xmath51 at level @xmath14 . denote by @xmath53 the successor of @xmath52 at level @xmath14 . for @xmath54 denote by the corresponding capital letter @xmath55 the symmetrization of @xmath10 . let @xmath56 , with @xmath57 and @xmath58 , where @xmath52 is the predecessor of @xmath51 at level @xmath14 . then @xmath59 is a family of intervals with disjoint interior . note that , for large @xmath14 , the boundary of @xmath4 contains a periodic point and its symmetric with respect to @xmath3 . moreover , the orbit of this periodic point does not contain critical points . this implies that @xmath60 , where @xmath51 is the successor of @xmath52 at level @xmath14 , and that the boundary of @xmath61 contains a point of this periodic orbit . note that to prove the complex bounds ( see the precise statement in theorem [ cb ] ) for @xmath2 with respect to @xmath3 , it is sufficient prove the complex bounds for a renormalization with respect to @xmath3 . replacing @xmath2 for a deep renormalization with respect to @xmath3 , we can assume , without loss of generality , that @xmath2 satisfies the * standard conditions * : * @xmath2 is a composition of unimodal maps with non - flat critical points and @xmath62 . * the interval @xmath61 is symmetric with respect to @xmath52 . * for large @xmath14 and for all @xmath63 , @xmath55 contains exactly one critical point . * for large @xmath14 , there exists a periodic orbit such that @xmath61 contains in its boundary a point of this orbit , for all @xmath63 . * for every @xmath52 , @xmath60 , where @xmath51 is the successor of @xmath52 at level @xmath14 . moreover @xmath64 . * the intervals in @xmath59 have disjoint interior . [ ] [ ] [ .8]@xmath2 [ ] [ ] [ .8]@xmath2 [ ] [ ] [ .8]@xmath65 [ ] [ ] [ .8]@xmath66 [ ] [ ] [ .8]@xmath67 [ ] [ ] [ .8]@xmath55 [ ] [ ] [ .8]@xmath52 [ ] [ ] [ .8]@xmath3 [ ] [ ] [ .8]@xmath68 [ ] [ ] [ .8]@xmath69 [ ] [ ] [ .8]@xmath70 [ ] [ ] [ .8]@xmath71 [ ] [ ] [ .8]@xmath72 [ ] [ ] [ .8]@xmath51 [ ] [ ] [ .8]@xmath73 [ ] [ ] [ .8]@xmath74 [ ] [ ] [ .8]@xmath75 -th renormalization , with 3 critical points involved.,title="fig:",scaledwidth=60.0% ] we say that a set @xmath76 is a * nice set * if it is an union of closed intervals , each interval contains a unique critical point , the critical points of @xmath2 are contained in the interior of @xmath76 and @xmath77 , for all @xmath78 . let @xmath76 be a nice set and @xmath79 be the set of points not in @xmath76 but whose positive orbit intersects the interior of @xmath76 . the entry map associates to each @xmath80 the point @xmath81 in the interior of @xmath76 with smallest @xmath28 . it is easy to see that for each connect component @xmath42 of @xmath79 , @xmath28 is constant and the image of @xmath42 by the first entry map is a connect component of @xmath76 . moreover @xmath82 are disjoint connect components of @xmath79 . [ nice ] let @xmath41 be a critical point . then there exists @xmath83 such that @xmath84 and the connect component @xmath42 of @xmath85 which contains c is a symmetric interval @xmath42 with respect to @xmath41 and @xmath86 . in particular , the union of connect components of @xmath87 which contains a critical point is a nice set . if the lemmas does not holds then there exists critical points in @xmath88 . let @xmath89 be the closest one of @xmath41 . @xmath90 , otherwise there will be another critical point between @xmath89 and @xmath41 . but this implies @xmath91 , where @xmath92 , which is absurd . [ rnice ] denote by @xmath93 the nice set defined in the previous lemma . let @xmath94 . it is easy to see that @xmath95 . hence @xmath96 , @xmath97 , where @xmath51 is the successor of @xmath52 at level @xmath14 and @xmath98 is a domain of the first entry map to @xmath93 . clearly @xmath99 . when we write @xmath98 , assume that @xmath100 . we say that an interval @xmath42 has the property @xmath101 if there is at most one interval in @xmath102 in the interior of @xmath42 . note that the closure of @xmath42 contains at most 3 intervals in @xmath103 . for @xmath104 the intersection number of @xmath105 with a family of intervals is the number of intervals in the family which contains @xmath105 . the intersection number of a family of intervals is the maximal number of intersection with a point in @xmath1 . let @xmath42 be an interval such that @xmath31 is monotone in @xmath42 and @xmath106 is a family of intervals with disjoint interior such that @xmath107 intersects an unique interval in the family @xmath102 which is contained in @xmath107 . let @xmath45 be such that @xmath31 is monotone in @xmath40 and @xmath108 satisfies @xmath101 . then the intersection number of the family of intervals @xmath109 is at most three . if the intersection number is at least 4 , the interior of @xmath110 will contain at least two intervals @xmath111 and @xmath112 in the family @xmath102 , for some @xmath113 . since @xmath114 , for all @xmath63 , the intervals @xmath115 belong to @xmath102 , which is absurd , since @xmath108 satisfies @xmath101 . the previous lemma will allows us to use the real koebe lemma ( theorem 3.1 and 3.3 in chapter iv in @xcite ) without do considerations about the number of intersections of the families of intervals involved . [ pul ] let @xmath116 be an interval satisfying @xmath101 such that @xmath117 , with @xmath118 . then there exists an interval @xmath119 which contains @xmath120 such that the map @xmath2 is monotone in @xmath119 and @xmath121 . furthermore , @xmath119 satisfies @xmath101 . let @xmath119 be the maximal interval such that @xmath122 , @xmath123 and @xmath2 is monotone in @xmath119 . we claim that @xmath124 . otherwise there exists a critical point @xmath41 to @xmath2 in the boundary of @xmath119 such that @xmath125 is in the interior of @xmath116 . then , by lemma [ nice ] , the interior of @xmath126 contains @xmath127 , @xmath128 , in the left or right side of @xmath129 . this proves the first statement . the second statement is obvious , since @xmath2 restricted to @xmath119 is monotone and @xmath130 , for all @xmath128 . [ pulq ] let @xmath116 be an interval satisfying @xmath101 which contains @xmath66 , where @xmath52 is the predecessor of @xmath51 at level @xmath14 . then there exists @xmath119 such that @xmath131 and each connect component of @xmath132 is mapped monotonically to the connect component of @xmath133 which contains @xmath134 . furthermore , @xmath119 satisfies @xmath101 . similar to previous lemma . [ pak ] let @xmath116 be an interval such that @xmath135 . the * pullback of @xmath116 along the @xmath14-cycle of renormalization * exists if there are intervals @xmath136 , @xmath137 , @xmath138 for each @xmath128 , such that : * @xmath139 . for @xmath128 , @xmath140 and @xmath141 . furthermore , the map @xmath73 is monotone in @xmath138 . * the interval @xmath137 is the symmetric interval with respect to @xmath51 which contains @xmath142 and each connect component of @xmath143 , is mapped monotonically in a connect component of @xmath144 . here @xmath41 is the successor of @xmath51 at level @xmath14 . * the interval @xmath136 is the symmetric interval with respect to @xmath52 which contains @xmath61 such that each connect component of @xmath145 is mapped monotonically in a connect component of @xmath144 . here @xmath41 is the successor of @xmath52 at level @xmath14 . let @xmath146 be the maximal interval which contains @xmath55 satisfying the property @xmath101 . [ pula ] if @xmath116 is an interval satisfying @xmath147 , then the pullback of @xmath116 along the @xmath14-cycle of renormalization exists . furthermore , @xmath148 , where @xmath136 is as in the previous definition . immediate consequence of the previous lemmas . the @xmath149-neighborhood of an interval @xmath42 is @xmath149-@xmath42 @xmath150 . here the mirror image of interval @xmath42 near a critical point @xmath52 , which is not in @xmath42 , is the other interval @xmath152 near @xmath52 such that @xmath153 . [ rema ] in the previous lemma , suppose @xmath17-@xmath135 . then , by the real koebe lemma and the quasi symmetry in the critical points , one gets @xmath154 . furthermore @xmath155 , since the critical points to @xmath156 in @xmath136 are inside @xmath55 and @xmath157 contains in both connect components intervals in the form @xmath158 , @xmath128 , or mirror images of these intervals . each one of these intervals contains at least one critical point for @xmath156 . let @xmath159 s.t . @xmath160 . then @xmath161 tends to 0 . this follows of the non existence of wandering intervals .

we proved the so called complex bounds for multimodal , infinitely renormalizable analytic maps with bounded combinatorics : deep renormalizations have polynomial - like extensions with definite modulus . the complex bounds is the first step to extend the renormalization theory of unimodal maps to multimodal maps .

we proved the so called complex bounds for multimodal , infinitely renormalizable analytic maps with bounded combinatorics : deep renormalizations have polynomial - like extensions with definite modulus . the complex bounds is the first step to extend the renormalization theory of unimodal maps to multimodal maps . [ section ] [ section ] [ section ] [ section ]

0909.0005

i

the ads / cft correspondence @xcite provides a unique window into the dynamics of a class of strongly coupled gauge field theories . for large @xmath0 gauge theories , the dynamics in the planar limit is expected to be effectively classical , with @xmath1 controlling the quantum corrections . for a class of superconformal field theories arising as world - volume theories on d - branes or m - branes , the ads / cft correspondence identifies this classical dynamics of the single trace sector with that of classical string theory in a higher dimensional spacetime . furthermore , if the field theory is strongly coupled then one can truncate to the zero mode sector of the string theory , viz . , classical gravity in this higher dimensional spacetime . the correspondence therefore provides an avenue to explore the strong coupling dynamics of field theories by reformulating the physics in terms of an effective classical gravity theory . in this paper we continue our investigation of strongly coupled field theories on black hole backgrounds using the ads / cft correspondence , generalizing the results of @xcite . field theories in curved spacetime are known to exhibit a rich array of physical phenomena ranging from vacuum polarization and particle production to hawking radiation and its associated puzzles with information loss . however , much of the investigation in the past has focussed on perturbative field theory due to the lack of access to the full non - perturbative quantum state , even in the context where gravity is non - dynamical . our current interest lies in understanding relevant quantum states beyond perturbation theory ; this is where ads / cft comes into play . consider a field theory on a non - dynamical curved spacetime ( which we denote as @xmath2 ) with metric @xmath3 . we would like to know the behavior of interesting quantum states and in particular the expectation values of gauge invariant local operators at the non - perturbative level . if we restrict attention to strongly coupled conformal fields which arise in low - energy limits of d - brane world - volume theories , then we can exploit the ads / cft correspondence to answer these questions . this is achieved by identifying higher - dimensional asymptotically ads gravitational solutions dual to the desired field theory states on @xmath2 ; we will refer to these gravitational saddle points as @xmath4 . such bulk spacetimes are found by solving the gravitational equations of motion subject to the boundary condition that @xmath4 has as its timelike boundary @xmath2 . of the bulk spacetime @xmath4 be in the same conformal class as @xmath2 . we will however demand that @xmath5 in fact is isometric to @xmath2 . ] in particular , smooth static spacetimes are candidate duals for the field theory hartle - hawking states . of course , it might turn out that the field theory in question has a non - trivial phase structure , which implies that there are multiple such static saddle points for the bulk gravity description @xcite . in @xcite we examined in some detail the holographic duals of field theories on black hole backgrounds @xmath2 . in particular , we have argued that there are new classes of black hole geometries in asymptotically ads spacetimes : i ) single connected horizon solutions which we called black funnels and ii ) solutions with two disconnected horizons ; see . in the latter case , we called the component connected to the boundary horizon a black droplet . on the boundary ( we will refer to this as @xmath6-compact " ) . in contrast , when the boundary spacetime has a good asymptotic region describing physics far from the boundary black hole , a black funnel should asymptote to the bulk solution describing a deconfined plasma in this distant region of spacetime . for example , in the case of asymptotically flat boundaries , it should asymptote to the planar ads black hole . as we discuss below , the distinction between droplets and funnels is more subtle for spatially compact boundary metrics . ] the funnel solutions are dual to black holes coupling strongly to the field theory plasma . in contrast , the droplet solutions describe black holes coupling only weakly . in particular , the second outer horizon present in these solutions is interpreted as the field theory plasma , while the droplet itself describes field theory vacuum polarization near the horizon . the lack of connection between these two ads horizons is evidence of the weak coupling . note that while the gravitational dynamics may allow solutions where the two horizons have different temperatures , only the equal temperature solutions can be dual to field theory hartle - hawking states . as evidence for this picture , ref . @xcite exhibited funnel and droplet solutions dual to @xmath7 and @xmath8 dimensional conformal fields living on black hole backgrounds . in the @xmath7 case , we constructed black funnel solutions in whose boundary is the two dimensional black hole @xcite . while black droplets do not arise for @xmath7 boundary black holes , by exploiting the known ads c - metric solutions we were also able to construct both black funnels and black droplets in four bulk spacetime dimensions . however , the droplet solutions found in this way do not generically describe hartle - hawking states as they were accompanied by a second horizon of a different temperature , so that the solutions did not describe equilibria . due to the properties of the c - metric , the relevant 2 + 1 boundary metrics described black holes which asymptote to @xmath9 . a natural question to ask is whether further interesting solutions are hidden among the ads c - metrics . in the present work , we analyze this issue within the family of uncharged , non - rotating ads c - metric solutions . recall that the ads c - metric solutions have been useful in the past to construct localized black holes on a uv brane in the brane - world context @xcite and also more recently to construct plasma ball solutions on an ir brane @xcite ( see also @xcite ) our interest is to remove the uv brane and work with some prescribed boundary metric . since we are not a - priori fussed about what metrics we have on the boundary ( apart from the fact that they be black hole like ) , it seems plausible that new interesting solutions will emerge . as we shall see in the following , there is indeed a rich class of boundary black holes contained within the c - metric family . with this motivation , we undertake an exhaustive search of the ads c - metric family of solutions and find an interesting class of black funnel and black droplet solutions . in all cases , by using standard holographic methods we are able to compute the boundary stress tensor which includes the contribution from the quantum dynamics of the field theory in curved spacetime . we find that the stress tensor does indeed capture the thermal aspect of hawking radiation and is furthermore regular on the black hole horizon in the boundary . on the boundary we generally find black holes living in spatially compact universes ; i.e. , there are no spatial asymptopia . this class of solutions is therefore somewhat different from those which arise for the special choice of parameters examined in @xcite , where the boundary metric was asymptotically a hyperbolic cylinder @xmath9 . due to the absence of an asymptotic region , the precise definitions of funnel and droplet given in @xcite do not apply . we therefore extend these definitions in below . our new definitions are sufficient for spacetimes such as the c - metric which have an appropriate rotational killing field , even if they lack a useful asymptotic region . the organization of this paper is as follows : we begin in with a brief overview of the ads c - metric solutions . while these geometries have been studied in the literature before , we find it useful to review and generalize some of the results , especially those pertaining to the precise coordinate domains . we then analyze the c - metric family in detail in section , where we show that , apart from trivial cases that are exactly ads or a quotient , any uncharged , non - rotating asymptotically ads c - metric with vanishing nut charge can be interpreted in terms of funnels , droplets , and planar black holes . the discussion can clearly be generalized to include additional charges , but we refrain from doing so here in order to keep the discussion simple . we extract the boundary stress tensor for these solutions in which allows us to see the advertised thermal behavior of the field theories in black hole backgrounds . we end with a discussion in and describe some subtle limits in appendix [ s : lambn1 ] .

we recently argued that the dynamics of strongly coupled field theories in black hole backgrounds is related via the ads / cft correspondence to two new classes of ads black hole solutions : black funnels , and black droplets suspended above a second disconnected horizon . we continue our investigation of these solutions and construct a wide variety of examples from the ads c - metric in four bulk spacetime dimensions . the solutions we find are dual to field theories on spatially compact universes with killing horizons .

we recently argued that the dynamics of strongly coupled field theories in black hole backgrounds is related via the ads / cft correspondence to two new classes of ads black hole solutions : black funnels , and black droplets suspended above a second disconnected horizon . the funnel solutions are dual to black holes coupling strongly to a field theory plasma . in contrast , the droplet solutions describe black holes coupling only weakly . we continue our investigation of these solutions and construct a wide variety of examples from the ads c - metric in four bulk spacetime dimensions . the solutions we find are dual to field theories on spatially compact universes with killing horizons . ( 0,0)(0,0 ) ( 350 , 320)dcpt-09/59 ( 350,305)nsf - kitp-09 - 165

astro-ph9606106

r

as mentioned earlier we have carried out simulations with two initial magnetic field geometries ; namely a field transverse to the motion of the bullet ( henceforth identified as `` t '' models ) and parallel or aligned with the bullet motion ( henceforth identified as `` a '' models ) . table [ tbl-1 ] characterizes six mhd simulation pairs with a range of field strengths for each geometry . models t1t5 and a1a5 include 50 zones across a radius ( thus , termed @xmath45 runs ) while t6 and a6 use 100 zones ( @xmath48 runs ) . three additional , control models , n1n3 , have set the magnetic field to zero . they vary @xmath5 , but are otherwise identical to the t1t5 and a1a5 models . these purely gasdynamical cases are intended to assist in identifying mhd effects on the flows that might develop even when the field is initially weak . in addition we have explored the degree to which flow behaviors depend on the density contrast , @xmath5 , enabling us to compare the current simulations with our previous ones . all of the mhd models have assumed @xmath66 , while the gasdynamical models , n1,n2 and n3 have used @xmath66 , @xmath67 and @xmath68 , respectively . the duration of each run is indicated in table [ tbl-1 ] as @xmath69 . the appendix evaluates `` convergence '' issues associated with the grid . to summarize quickly the appended discussion , we conclude that the @xmath45 simulations are well converged by such global measures as the quantities defined in eqs . [ mbull][yav ] . the magnetic energy enhancement ( eq . [ emag ] ) is reasonably well converged in the transverse field cases and in the aligned field cases at early times . however , the topology of the aligned field makes it more sensitive to the details of eddy structures that form around the bullet as it is destroyed , and those details depend on numerical resolution . so , at late times the magnetic energy enhancement is not converged in our aligned - field simulations . in association with this , it is clear that structural details of the bullets at late times , @xmath70 , do depend on resolution , especially since the perturbations in the bullet structure that eventually lead to its destruction come out of the mismatch between the bullet geometry and the grid geometry in our simulations . those aspects should serve as reminders that calculations such as these are idealized efforts to understand the physics of clouds interacting with their environments and not intended to be used as predictors of detailed structures . that point is also made stronger by the recognition that bullet evolution , particularly after @xmath71 , depends physically on the initial bullet structure , including the bullet geometry ( see @xcite ) and the density contrast ( see discussion below ) . 1 , 2 and 3 contain images that provide a summary spanning pretty well the behaviors of the mhd models we have computed before significant mass stripped from the bullets begins to leave the grid . panels ( a ) and ( b ) in each of those figures represent transverse field cases , with t2 ( @xmath72 ) in ( a ) and t5 ( @xmath73 ) in ( b ) . panels ( c ) and ( d ) represent the analogous aligned field cases , with a2 in ( c ) and a5 in ( d ) . for each model two times are shown : @xmath74 and @xmath75 . 1 illustrates evolutionary aspects of the log gas density , fig . 2 shows the magnetic field lines and fig . 3 the vorticity . in the appendix , figs . a1 and a2 show log density and field lines at @xmath76 and @xmath77 for models t5 and a5 as well as their higher resolution representations , t6 and a6 . for comparison , 4 illustrates the log density distributions for the gasdynamical models n1n3 at @xmath71 and @xmath78 . it is convenient to begin our discussion with an outline of the evolution of bullet structures and associated magnetic fields in the cases with fields aligned to the direction of the bullet motion . those show less dramatic dynamical differences from the gasdynamical bullets discussed in @xcite , and closely resemble in some ways the aligned field simulations of shocked mhd clouds described in @xcite . several key points are clear from the figures listed above . first , in all the aligned - field cases the bullet shows signs of penetration by one or more large r - t bubbles by @xmath74 . there is little effect from the magnetic field on the bullet structure by this time . that impression extends to the strongest field cases we considered ; namely , a2 @xmath79 and a1 @xmath80 . indeed , the density distributions for a2 and a5 at this time are very similar and also hardly distinguishable from the analogous run with @xmath81 , model n1 ( see figs . 1 and 4 ) . this comparison is more quantitatively apparent in fig . 5 , which includes plots of density , @xmath82 , velocity as measured in the initial rest frame of the bullet , @xmath83 , gas pressure , @xmath84 , and magnetic pressure , @xmath85 , along a cut just above the @xmath41-axis for the same situations as in figs . 1 , 2 , and 3 . the solid lines correspond to @xmath74 , while dotted lines illustrate quantities at @xmath86 . furthermore , the vorticity structure around the bullet is practically the same for both a2 and a5 ( fig . 3 ) providing a very good indicator that the dynamics in the two models are very similar at this time ( see , , @xcite ) . qualitatively this vorticity structure is also the same as that found in three - dimensional gasdynamical simulations of shocked clouds at comparable dynamical times ( @xcite ) . the vorticity associated with flow over the bullet is negative ( clockwise ) . we see in fig . 3 that in the stronger field case , a2 , some vorticity of the opposite sign has been generated in the bullet wake in response to magnetic tension there , however . comparing at @xmath74 model a5 in fig . 1 with model n1 shown in fig . 4 , we see no detectable difference in density distributions . the field has not had any appreciable influence on the development of r - t and k - h instabilities , since it is not strong enough anywhere along the bullet boundary to suppress them directly . k - h instabilities will be suppressed by the field along the boundary according to linear theory , if the local alfvn speed exceeds roughly the velocity difference across the boundary ( @xcite ) . since the local mach number of the flow along the bullet boundary is generally less than or about unity , the criterion for the magnetic field removing k - h instabilities is roughly @xmath87 along the bullet boundary . similarly if the alfvn wave crossing time through a bubble perturbation on the bullet edge is less than the `` buoyancy rise time '' , @xmath88 where @xmath14 is the acceleration and @xmath89 is the length scale , the magnetic field will inhibit r - t instabilities . using eq . [ ub ] ( see below ) to estimate the acceleration of the bullet , we obtain a rough criterion for the magnetic field to stabilize r - t instabilities ; namely , @xmath90 . that leads in the present context again to @xmath87 , since @xmath91 . even in the case a1 with @xmath25 , the local @xmath27 along the bullet face and sides is everywhere greater than unity . in fact , we do not find at any time in aligned field models a1a6 that the magnetic field adjacent to the bullet is ever strong enough that @xmath92 ( there is one region with @xmath93 in the wake , as we will discuss below ) . however , even a relatively weak magnetic field can play a significant role in small scale flow dynamics , as pointed out by others ( , @xcite ; @xcite ) and as we shall explain further on . by @xmath74 the states of k - h and r - t instabilities are , on the other hand , rather strongly influenced by the density contrast choice , @xmath66 . the other panels in fig . 4 illustrate how , as the density contrast is increased , the penetration of the r - t bubbles into the bullet is enhanced for fixed @xmath20 . while , in the limit of large @xmath5 , the linear growth times on a given length for both k - h and r - t instabilities scale directly with @xmath22 , both growth rates include an additional term that increases with @xmath5 when it is finite . that tendency is consistent with the behaviors illustrated in fig . 4 . as a further test , we can compare run n3 ( @xmath94 ) with very similar gasdynamic simulations reported in @xcite . those earlier simulations were carried out using a ppm gasdynamic code and were designed to study dynamical feedback on bullets from cosmic - rays accelerated in shocks associated with the bullet . however , model number 1 in that paper omitted cosmic - rays . their fig . 4 illustrates density structure at @xmath74 , showing a good correspondence between the cloud structures in the two simulations , except that our current calculations show less evidence of small scale k - h structures along the bullet boundary . even when @xmath95 the mhd tvd code does suppress the smallest scale k - h instabilities in comparison with the ppm code , because it spreads the very strong contact shear layer of the bullet edge over several more zones . k - h instabilities are suppressed on scales less than the thickness of the shear layer . as a direct consequence of the penetration of the r - t bubbles , the bullet begins appreciably to expand laterally by @xmath96 . for all the aligned field cases , the mass weighted bullet height , @xmath97 , has expanded to roughly five times or more its initial value by @xmath86 ( see fig . this characteristic behavior was also noted by others with regard to gasdynamic simulations . as illustrated in fig . a1 , before @xmath98 , our bullets develop a roughly `` c''-shaped morphology on the computed half - plane in all of the aligned field cases , a1-a5 . ( including the reflected portion below the computed space , the cloud shape would be an `` e '' . ) that `` c '' continues to open up and thin itself even until the bullet moves off the grid . as the figures show bullet mass is stripped and carried into the wake , eroding the bullet body . in response to drag forces the bullet is accelerated towards a terminal velocity , @xmath8 , as measured in the original reference frame ; that is , the bullet or its fragments should come to rest in the surrounding flow . @xcite derived a simple theoretical model for the acceleration of a cloud based on ram pressure , taking into account the lateral expansion . the drag force actually comes from the difference in the total pressure across the bullet . assuming highly supersonic motion , we can estimate in the gasdynamic case from bernoulli s equation the pressure difference on the symmetry axis to be @xmath99 , where @xmath100 is the instantaneous speed of the bullet with respect to its initial reference frame and we have set @xmath21 . applied across the full bullet this leads to the usual expression for its acceleration , @xmath101 where @xmath102 is a drag coefficient that absorbs our ignorance of details of the pressure distribution and @xmath103 is the effective bullet radius as a function of time . borrowing the notion in @xcite that the bullet expansion begins only after @xmath71 , we write @xmath104 $ ] where we can term @xmath105 an expansion coefficient ( see also @xcite , @xcite ) . if @xmath106 , drag on the bullet increases with time , enhancing its acceleration . in an mhd flow we have to account for magnetic pressure in eq . [ accel ] . for aligned cases , however , the magnetic pressure does not enter into the bernoulli equation on axis and the magnetic pressure is not significant anyway . thus we expect the bullet motion to behave pretty much as in the gasdynamic case . we will comment later on modifications to eq . [ accel ] appropriate to transverse field cases . [ accel ] can be integrated to give @xmath107}}\right ) . \label{ub}\ ] ] all the aligned field cases can be fit well with a drag coefficient , @xmath108 , and an expansion coefficient , @xmath109 . there is a weak trend visible in fig . 6 for the acceleration of the bullets to be faster when the field is smaller , corresponding to a value of @xmath105 that depends inversely on @xmath110 . that just reflects the fact that stronger aligned fields do resist lateral expansion , keeping the bullet cross section somewhat smaller . we expect the magnetic fields themselves to respond differently to the motion of the bullet for the two field geometries we have used . that is apparent even by @xmath71 as shown in fig . the evolution of the aligned field is similar to that found by @xcite for shocked clouds with aligned fields . to the front of the bullet , field lines that initially pass through the bullet are swept and then `` folded '' over the top of the bullet in a configuration that is unstable to the resistive tearing mode . that instability leads to `` magnetic islands '' within and behind the bullet as seen at @xmath71 in fig . a2 c and d or at @xmath74 in fig . 2 c and d. the compact magnetic island closest to the axis coincides with the strong vortex at the rear of the bullet ( fig . magnetic flux initially formed into these islands is mostly annihilated by about @xmath98 ( or more properly `` expelled '' , since the total magnetic flux through the computational box does not change over time for the aligned field configuration ) . magnetic reconnection also takes place inside the bullet in consequence of the circulation developing after the bullet shock has exited ( see figs . 2 , 3 , and a2 ) . that significantly reduces the field strength within the bullet over time . through these reconnection events , magnetic flux is separated into two elements : that which passes around the bullet without reversal and that which passes through the bullet . the latter flux element continues to be involved with vortices around the bullet and subjected to reversals and reconnection . before the magnetic flux separation , there is a thin region of strongly concentrated field formed along the axis behind the bullet , analogous to the `` flux rope '' discussed for shocked clouds in some detail by @xcite . in our situation , as in theirs , this feature forms as a consequence of compression of field into the low pressure wake behind the bullet , followed by field - line stretching . in our case those field lines are temporarily anchored in the bullet on one end and drawn out to the rear by the expanding rarefaction wave ( see figs . a1 and a2 ) . just as for the shocked cloud case considered by @xcite , the magnetic field in this region can become locally dominant with @xmath111 . however , as fig . 2 shows clearly , the field configuration on the edge of the flux rope is susceptible to tearing mode instabilities , so that the rear flux rope disappears as part of the flux separation event . we do _ not _ see in any of our aligned field simulations that @xmath24 , nor that this flux rope plays a significant dynamical role in the evolution of the bullet . however , this feature is the dominant source of enhanced magnetic field energy before its flux is expelled ( see fig . 6 ) . the normalized magnetic energy enhancement , @xmath112 , ( eq . [ emag ] ) peaks at values between @xmath113 and @xmath68 near @xmath114 ( see fig . 6 ) . the peak value in model a1 ( @xmath25 , @xmath115 ) is about half that reported by @xcite for their shocked cloud during this phase for the same numerical resolution across the cloud and the same @xmath110 . since our post - bullet flux rope is significantly thinner than theirs , the comparison seems very good . our higher resolution , @xmath48 , weak field run , a6 , differs in @xmath112 by @xmath116% from the analogous low resolution , @xmath45 , a5 run for @xmath117 . so , through this stage the magnetic energy behavior seems well converged . for the aligned field geometry there is very little compression of the field , so from the start we should expect that field line stretching would be the primary contributor to magnetic field enhancement . along the boundary of the bullet the field remains weak before about @xmath98 , even in the @xmath25 case , because it is subject to reconnection that shortens the field lines . however , that reconnection leads directly to the flux separation mentioned , and through that the field topology above the bullet returns to something resembling its initial form ; namely , field lines pass directly around the bullet from front to back without folding . as the bullet body expands laterally , lines above it are stretched significantly ( see fig . 2 ) , but are no longer subject to reconnection . a relatively thin flux tube especially on the rear perimeter of the bullet envelops the now - distended cloud , extending into the wake . almost independently of the initial @xmath110 or the numerical resolution , the minimum local @xmath118 in this structure . after the flux separation event these field lines do not penetrate the strong vortex at the rear of the bullet . on the other hand , the flux that now passes through the bullet is drawn into the big r - t bubble and an associated vortex pair . through reconnection , however , those field lines divide into magnetic islands ( for the weaker initial field cases ) that are annihilated and flux that penetrates directly through the bullet . some flux passing through the bullet is drawn into the strong vortex at the rear and base of the bullet , leading to another region of strong magnetic flux on its perimeter . even though the magnetic pressure in these flux tubes is never dominant , the field can still play a major role in reducing the vorticity and leading the flow to become more nearly laminar and less disruptive . that dynamical behavior was shown recently in high resolution simulations of the mhd k - h instability ( @xcite ) . there it was found in k - h unstable mhd flows that even when @xmath119 the magnetic field , acting as catalyst , realigns the flow into a stable , broad and laminar shear layer . the field acts as a catalyst in the sense that kinetic energy is temporarily stored in the field so that locally the magnetic tension is at least significant if not dominant . that stored energy is released again during reconnection , but one result of the reconnection is that the velocity and magnetic fields are more closely aligned ; that is , the magnitude of the cross helicity is increased . the smoothing and spreading of the flow should significantly reduce stripping from the bullet . this conclusion is consistent with that reached by @xcite , that the magnetic field reduces the intensity of vortices around their clouds and , thus , increases the cloud survivability . the presence of the magnetic field is clearly felt by the bullets in our aligned field simulations . clouds in the stronger field cases are less distended ( figs . 1 , 2 , and 6 ) and there is an apparently stable density concentration at the top of the bullet `` c '' . examination of the forces applied there shows that the density is mostly confined by ram pressure , but that magnetic pressure and tension contribute at the 10% level , as anticipated from earlier discussion . at late times in these cases material no longer seems to be stripped from the bullets ( see fig . 6 ) , consistent with our comments above . for the stronger field cases , there is less thinning of the main bullet body , as well . magnetic energy enhancement in the aligned field models begins to rise again after @xmath120 , mostly in response to the development of flux tubes around the bullet and in the associated vortices . our simulations are not able to capture this final rise completely , because the flux tube fine structures are still resolution dependent ( see figs . a2 and a4 ) and because significant magnetic structures begin to leave the grid after @xmath121 . it appears likely , however , that the excess magnetic energy becomes at least comparable in this stage to the peak value noted earlier . @xcite similarly emphasized the lack of convergence in the magnetic field within their simulations . they also used an aligned field geometry , so the issues responsible were analogous . although the details are fairly complex , the summary of aligned - field bullet evolution is straightforward . magnetic fields are initially swept over the bullet , stretched and folded there . eventually reconnection separates the field into flux passing directly through the bullet and flux passing directly around it . except within a thin flux tube formed temporarily along the symmetry axis , there is no place that the magnetic field becomes energetically dominant ; that is , almost everywhere @xmath122 . in the meantime the disruptive , ram pressure force that applies to gasdynamical bullets ( and gasdynamical shocked clouds ) causes the initial cloud to become distended and stripped . magnetic field stretched over the top of the bullet can have a significant stabilizing influence that should prolong bullet coherence even though magnetic energy never becomes dominant . for the transverse cases where the initial field crosses the bullet s path , field lines are also swept and stretched around the bullet . however in this case the field lines do not reconnect around the bullet , except in a `` magnetotail '' along the axis , so that a region of high magnetic pressure develops on the bullet nose as shown in fig . 2 . even in the t5 case with @xmath73 , the field is strong enough that @xmath123 on the bullet nose by @xmath74 . for all the other transverse field cases we computed , @xmath87 along the nose of the bullet by this time . in models t1 and t2 , @xmath124 here and @xmath24 directly on the leading edge of the bullet . except in t5 , @xmath125 along the top and towards the rear of the bullet boundary , partly because the gas pressure is low , but mostly because field lines have been greatly stretched . that characterization of the field lines is obvious in fig . 2 or fig . a2 . even though field lines are compressed by the bow shock , it is stretching , not compression , that is important to the evolution of the magnetic field and to its eventual dynamical role . that supports the expectations expressed by @xcite , based on passive fields . one can see in fig . 6 that the normalized magnetic energy enhancement for the transverse geometry grows to more than @xmath126 for the weakest field cases and more than @xmath127 even for the strongest field cases . since the volume containing highly compressed plasma is never more than a few times the initial bullet volume , the maximum field enhancement through compression would be @xmath128 , emphasizing the importance of stretching . we note that the magnetic energy in the transverse cases seems fairly well converged through the full duration of the simulations and better than in the aligned field geometry . that makes sense , since the transverse fields are not so closely tied to vortical flows behind the bullet . we can write down a crude model for the enhancement of the magnetic field energy in the transverse cases that seems to qualitatively account for what is seen . for ideal mhd the magnetic induction equation can be expressed in a form @xmath129}{b^2 } } , \label{dbdt}\ ] ] where @xmath130 is the convective derivative . at the stagnation point on the bullet nose we can estimate @xmath131 and @xmath132 \sim b^2 u_{b0}/r$ ] , so that @xmath133 where @xmath134 is a `` fudge factor '' accounting for various details . if this field growth occurs within a `` shield '' of volume @xmath135 , we can estimate the associated magnetic energy enhancement to be @xmath136 that growth seems consistent with the results shown in fig . 6 , for @xmath137 . since the field on the bullet nose saturates with @xmath138 , we expect a maximum for @xmath139 . that is also roughly consistent with the results in fig . the early magnetic energy enhancement is similar for all the values of @xmath110 , but it saturates sooner and the dynamical influence of the field is sooner when @xmath110 is smaller . the field lines draped over the bullet are also drawn down near the symmetry axis into the bullet wake , producing a region that resembles the flux rope seen in the aligned field cases . again , this is a region of @xmath140 , but primarily because the gas pressure is very low from the initial evacuation of this region . it is always the case in our simulations that @xmath141 within this feature . in addition , the @xmath142 boundary of our grid separates field lines of opposite direction ; , there is a current sheet there , much as in the earth s magnetotail . that is also unstable to tearing mode instabilities that limit fields in this region . like the earth s magnetosphere does , the penetration of the bullet through a `` quasi - transverse '' field should produce on the bullet nose an induced electric field perpendicular to both the magnetic field and the bullet velocity . in this case that projects out of the computational plane . if the third dimension of the bullet @xmath143 , then the induced potential across the bullet would be @xmath144 . taking numbers that might be appropriate for knots in a young snr like cas a ( @xmath145 gauss , @xmath146 c , @xmath147 cm ) ( , @xcite ) , we find that @xmath148 volt is possible . supposing that reconnection within the bullet magnetotail can generate electric fields aligned with the magnetic fields , then these regions might be important sites for nonthermal particle acceleration . for the weak transverse field cases , the bullet dynamics initially resembles the aligned field and gasdynamical cases to the first approximation . the r - t bubbles seen in those other situations form here , too . in fact at @xmath74 there are no obvious differences in either bullet morphology or flow dynamics between models a5 and t5 , for example ( see figs . 1 and 3 ) . as time progresses , however , the bullet in all transverse field cases becomes significantly influenced by the field . even though the same `` c''-shaped bullet morphology is seen in the two weakest field cases , t4 and t5 , field stretched over the top and back of the `` c''-shaped cloud develops magnetic pressures significantly greater than the gas pressure , so that @xmath149 along the bullet edge . this condition protects the bullet from further disruption . in model t5 that happens quite late , so as late as @xmath86 the bullet morphology is pretty similar to a5 . however , even in model t4 ( @xmath150 ) the field becomes dynamically strong ( @xmath151 along the bullet nose just after @xmath74 ) . that case still expands laterally , but not so fast as in the cases with negligible magnetic influence ( see fig . for all the other transverse cases with @xmath152 , the maxwell stresses grow large enough to completely inhibit lateral expansion of the bullet . the bullets are then enshrouded by a strong magnetic shield . for cases involving an initially weak field , the bullet is partially disrupted , but eventually the shield protects the r - t fingers from further erosion . the bullet embedded in a stronger field is compressed , but then , as the field confines it , develops a streamlined profile and is not strongly eroded . remarkably , fig . 6 shows that the acceleration of the transverse - field bullet increases with the strength of the magnetic field . this trend is reversed from that of aligned - field bullets . there we have observed that the tendency of stronger field to resist lateral expansion reduces the evolution to a greater cross section . it was that increased cross section and the augmented drag that were modified by the field . for the transverse field models , lateral expansion can be halted entirely , yet the drag force clearly is enhanced with the stronger field . this seeming paradox is easily explained by accounting properly for the role of the magnetic pressure in the drag . whereas the aligned field did not contribute directly to the force across the bullet , the transverse field does . the mhd bernoulli equation on the symmetry axis gives the result in the highly supersonic limit that @xmath153 , where @xmath154 on the nose of the bullet in this case . as already noted , @xmath85 increases over the first few crushing times and can become comparable to @xmath155 in that region . although the expansion coefficient @xmath156 in eqs . [ accel ] and [ ub ] the drag coefficient , @xmath102 , is an effectively increasing function of time and that enhances the bullet s acceleration . we find , for example , that eq . [ ub ] gives a good fit to the motion of the strongest field case , t1 , by setting @xmath156 , replacing @xmath102 with @xmath157 , and using the same @xmath158 that we have used for aligned field models . that corresponds to an increase in drag of about 5% at the end of the simulation . thus , the picture that develops for the transverse field bullets is rather different from and considerably simpler than the ones for aligned field . magnetic field is swept around the bullet to form a protective shield . the magnetic pressure becomes comparable to the ram pressure through the bullet bow shock ; thus , the magnetic energy is enhanced by an amount approaching @xmath159 . again taking that to be roughly the volume of the bullet , we recover the observed magnetic energy enhancements with the expression @xmath160 . our bullets have a cylindrical form , so that field lines can not be swept around the sides of the bullet in the @xmath31-direction . such sweeping may reduce the magnetic field enhancement somewhat in a three - dimensional bullet . but we still expect the same qualitative behavior , since much of the field that forms into the shield comes from the field lines that penetrate into the `` skin '' of the bullet , and since irregularities in the spherical bullet would capture field lines much like the cylindrical one does . the brief summary of transverse bullet evolution is the following . even when the initial field is of modest strength measured in terms of the ratio of magnetic pressure to background plasma pressure , the stretched magnetic field effectively confines the bullet and prevents its fragmentation . further , the magnetic pressure applied to the nose of the bullet increases the rate at which the bullet is brought to rest with respect to the ambient medium ; more effectively , in fact , than the lateral expansion that accompanies the acceleration of gasdynamical bullets .

similar effects cause the magnetic field within the bullet itself to be reduced below its initial value over time . for oblique fields , we expect that the transverse field cases modeled here are more generally relevant . what counts is whether field lines threading the face of the bullet are swept around it in a fashion that folds them ( leading to reconnection ) or that keeps them unidirectional one each side of the bullet . in the second instance

we report an extensive set of two - dimensional mhd simulations exploring the role and evolution of magnetic fields in the dynamics of supersonic plasma clumps . we examine the influence of both ambient field strength and orientation on the problem . of those two characteristics , field orientation is far more important in the cases we have considered with . that is due to the geometry - sensitivity of field stretching / amplification from large - scale shearing motions around the bullet . when the ambient magnetic field is transverse to the bullet motion , even a very modest field , well below equipartition strength , can be amplified by field line stretching around the bullet within a couple of bullet crushing times so that maxwell stresses become comparable to the ram pressure associated with the bullet motion . the possibility is discussed that those situations might lead to large , induced electric potentials capable of accelerating charged particles . when the ambient field is aligned to the bullet motion , on the other hand , reconnection - prone topologies develop that shorten the stretched field and release much of the excess energy it contains . in this geometry , the maxwell stresses on the bullet never approach the ram pressure level . in both cases , however , the presence of a field with even moderate initial strength acts to help the flow realign itself around the bullet into a smoother , more laminar form . that reduces bullet fragmentation tendencies caused by destructive instabilities . eddies seem less effective at field amplification than flows around the bullet , because fields within eddies tend to be expelled to the eddy perimeters . similar effects cause the magnetic field within the bullet itself to be reduced below its initial value over time . for oblique fields , we expect that the transverse field cases modeled here are more generally relevant . what counts is whether field lines threading the face of the bullet are swept around it in a fashion that folds them ( leading to reconnection ) or that keeps them unidirectional one each side of the bullet . in the second instance , behaviors should resemble those of the transverse field cases . we estimate that this , quasi - transverse , behavior is appropriate whenever the angle , , between the motion and the field satisfies , where is the bullet mach number . from these simulations , we find support in either field geometry for the conclusions reached in previous studies that nonthermal radio emission associated with supersonic clumps is likely to be controlled largely by the generation of strong magnetic fields around the perimeters of the clumps , rather than local particle acceleration and field compression within the bow shock . in addition , since the magnetic pressure on the nose of the bullet likely becomes comparable to the ram pressure and hence the total pressure behind the bow shock , the gas pressure there could be substantially lower than that in a gasdynamical bullet . that means , as well , that the temperature in the region on the nose of the bullet would be lower than that predicted in the gasdynamical case . that detail could alter expectations of the thermal emission , including x - rays and uv - ir lines . = cmmi10 scaled1 = cmmi10 = cmmi7 = cmmib10 scaled1 = cmmib10 = cmmib10 scaled 833 = cmbsy10 scaled1 = cmbsy10 = cmbsy10 scaled 833 1 = 1 = 1 = 9 = 9 = 9 = 10 = 10 = 10 =

astro-ph9606106

i

we have carried out an extensive set of two - dimensional mhd simulations exploring the role of magnetic field in the dynamics of supersonic clumps of plasma . we have examined the influence of both field strength and orientation on the problem . of those two characteristics field orientation is far more important . even a very modest ambient magnetic field that crosses the path of the bullet tends to be amplified by field line stretching around the bullet until the maxwell stresses become comparable to the ram pressure associated with the bullet motion . a field that is aligned with the bullet motion , on the other hand , develops reconnection - prone topologies that shorten the stretched field and release the excess energy it contains . the field is also swept around the bullet in this geometry and can temporarily become moderately strong . however , the energy in the field is not enhanced so much for this geometry as for the transverse geometry . rather , as a consequence of reconnection , there is a transformation and relaxation of the field over a few bullet crushing times . some magnetic flux passes directly through the bullet , where it can become entrained in vortices and amplified around the vortex perimeter . the remaining flux passes directly around the bullet , where it can act to resist lateral expansion as it is stretched by that expansion . in this geometry , however , the maxwell stresses on the bullet never approach the ram pressure level . even so , a field of even moderate initial strength becomes strong enough to help realign the flow around the bullet into a smoother , more laminar form that reduces the tendency of the bullet to fragment . both of the above field geometries are highly idealized , and more generally the bullet would encounter a field at some oblique angle to its motion . in that situation , we will want to know which of the two special cases is more relevant . the most important detail should be if , as the field lines are swept over the bullet , they are folded over the top as well , thus leading to reconnection . conceptually that depends on the relative rates at which the field lines are swept past the bullet body , on the one hand , and at which the `` foot - points '' of the field lines along the bow shock move past the bullet , on the other hand . if the field - line bow - shock foot - point moves faster ( as it must for transverse field cases ) , the lines are not folded over the top , but stretched directly to the bow shock . if , however , the field - line bow - shock foot - point moves slower ( it is at rest for aligned field cases ) , then the field lines are folded over inside the bow shock on one side of the bullet and likely to reconnect . we can derive an approximate expression for the condition that the field foot - point moves downstream faster than the flow around the bullet , if we take the mach bow shock to be a simple cone with half angle @xmath161 and suppose that the flow speed around the bullet is @xmath162 . defining the motion of the foot - point as the translation of the intersection between the field line and the bow shock , this leads to the constraint @xmath163 where @xmath1 is the angle between the bullet motion and the ambient magnetic field . in the limit @xmath18 , with @xmath164 , this becomes @xmath165 so , we conclude that for supersonic bullets most field directions will lead to behaviors similar to the transverse field cases , while as the motion becomes transsonic the dividing line would be closer to 45 . except in circumstances with preferential alignments between the motion and the field , that would lead to the further conclusion that even a weak magnetic field will have a substantial impact on the evolution and dynamics of supersonic clumps of ionized , conducting gas . in young supernova remnants , polarized radio synchrotron emission indicates that there is a net radial direction to the magnetic field inside the remnants ( @xcite ) . this might suggest that bullets in young remnants would generally encounter a radial field and , hence , one nearly aligned with their motions . that view is somewhat simplistic , however , because the same radio observations also show a very small net polarization ( @xcite ) indicating that , to first order , the field is disordered . that , in turn , argues that a wide range of field orientations may be encountered by small projectiles . in either limiting field geometry and presumably those in between , field line stretching is the dominant process for magnetic field amplification . that supports the conclusions reached by @xcite and @xcite that nonthermal radio emission associated with supersonic clumps in supernova remnants , for example , is likely to be largely controlled by the generation of stretched magnetic fields around the perimeters of the clumps , rather than primarily highlighting the bow shock where field is mostly enhanced by compression . we note that the structures of the bow shock and the bullet boundary may even superficially resemble each other in observations , so that morphology alone can be misleading . the physical difference is important , however , since the bow shock is probably the site of local particle acceleration , while on the bullet perimeter one sees primarily energetic particles that come from some other site ( possibly including the bow shock , of course ) . our estimates of the field strengths expected in the two situations are very different , however . so , observational estimates of the local magnetic field ( based on equipartition , for example ) would possibly lead us to very different conclusions about the local conditions . in addition , since the magnetic pressure on the nose of the bullet may become comparable to the ram pressure and hence the total pressure behind the bow shock , the gas pressure there could be substantially lower than that in a gasdynamical bullet . that means , as well , that the temperature in the region on the nose of the bullet would be lower than that predicted in the gasdynamical case . that detail can alter expectations of the thermal emission , including x - rays and uv - ir lines . in summary , the role of a magnetic field in the evolution and in the appearance of supersonic clumps is very important , even if the magnetic field is nominally not strong in the ambient medium . the importance comes because magnetic field lines can be stretched and amplified if they become draped around the bullet perimeter . that effect seems especially strong when the field lines are `` quasi - transverse '' to the motion , a concept that depends on the speed of the bullet , but seems to include most directions . additional amplification within vortices associated with the destruction of the bullets can also occur , but seems to be less important . if the fields are quasi - transverse , then they can effectively confine the bullet and prevent its disruption . the same amplified fields may be important to emissions used to analyze the bullets . they can control the radio synchrotron emission expected and possibly become strong enough to alter the local thermodynamics of the gas and influence thermal emissions , as well . we are grateful to adam frank , byung - il jun , bob lysak and larry rudnick for fruitful discussions and to mordecai - mark mac low for helpful comments on the manuscript . at the university of minnesota this work was supported in part by nsf ( ast-9318959 ) , nasa ( nagw-2548 ) , and the minnesota supercomputer institute . at chungnam national university this work was supported in part by the basic science research institute program , korean ministry of education 1995 , project no . bsri-95 - 5408 .

we report an extensive set of two - dimensional mhd simulations exploring the role and evolution of magnetic fields in the dynamics of supersonic plasma clumps . we examine the influence of both ambient field strength and orientation on the problem . of those two characteristics , when the ambient magnetic field is transverse to the bullet motion , even a very modest field , well below equipartition strength , can be amplified by field line stretching around the bullet within a couple of bullet crushing times so that maxwell stresses become comparable to the ram pressure associated with the bullet motion . when the ambient field is aligned to the bullet motion , on the other hand , reconnection - prone topologies develop that shorten the stretched field and release much of the excess energy it contains . in this geometry , the maxwell stresses on the bullet never approach the ram pressure level . in both cases , however , the presence of a field with even moderate initial strength acts to help the flow realign itself around the bullet into a smoother , more laminar form . that reduces bullet fragmentation tendencies caused by destructive instabilities . eddies seem less effective at field amplification than flows around the bullet , because fields within eddies tend to be expelled to the eddy perimeters . , behaviors should resemble those of the transverse field cases . we estimate that this , quasi - transverse , behavior is appropriate whenever the angle , , between the motion and the field satisfies , where is the bullet mach number . from these simulations , we find support in either field geometry for the conclusions reached in previous studies that nonthermal radio emission associated with supersonic clumps is likely to be controlled largely by the generation of strong magnetic fields around the perimeters of the clumps , rather than local particle acceleration and field compression within the bow shock . in addition , since the magnetic pressure on the nose of the bullet likely becomes comparable to the ram pressure and hence the total pressure behind the bow shock , the gas pressure there could be substantially lower than that in a gasdynamical bullet . that means , as well , that the temperature in the region on the nose of the bullet would be lower than that predicted in the gasdynamical case . that detail could alter expectations of the thermal emission , including x - rays and uv - ir lines .

we report an extensive set of two - dimensional mhd simulations exploring the role and evolution of magnetic fields in the dynamics of supersonic plasma clumps . we examine the influence of both ambient field strength and orientation on the problem . of those two characteristics , field orientation is far more important in the cases we have considered with . that is due to the geometry - sensitivity of field stretching / amplification from large - scale shearing motions around the bullet . when the ambient magnetic field is transverse to the bullet motion , even a very modest field , well below equipartition strength , can be amplified by field line stretching around the bullet within a couple of bullet crushing times so that maxwell stresses become comparable to the ram pressure associated with the bullet motion . the possibility is discussed that those situations might lead to large , induced electric potentials capable of accelerating charged particles . when the ambient field is aligned to the bullet motion , on the other hand , reconnection - prone topologies develop that shorten the stretched field and release much of the excess energy it contains . in this geometry , the maxwell stresses on the bullet never approach the ram pressure level . in both cases , however , the presence of a field with even moderate initial strength acts to help the flow realign itself around the bullet into a smoother , more laminar form . that reduces bullet fragmentation tendencies caused by destructive instabilities . eddies seem less effective at field amplification than flows around the bullet , because fields within eddies tend to be expelled to the eddy perimeters . similar effects cause the magnetic field within the bullet itself to be reduced below its initial value over time . for oblique fields , we expect that the transverse field cases modeled here are more generally relevant . what counts is whether field lines threading the face of the bullet are swept around it in a fashion that folds them ( leading to reconnection ) or that keeps them unidirectional one each side of the bullet . in the second instance , behaviors should resemble those of the transverse field cases . we estimate that this , quasi - transverse , behavior is appropriate whenever the angle , , between the motion and the field satisfies , where is the bullet mach number . from these simulations , we find support in either field geometry for the conclusions reached in previous studies that nonthermal radio emission associated with supersonic clumps is likely to be controlled largely by the generation of strong magnetic fields around the perimeters of the clumps , rather than local particle acceleration and field compression within the bow shock . in addition , since the magnetic pressure on the nose of the bullet likely becomes comparable to the ram pressure and hence the total pressure behind the bow shock , the gas pressure there could be substantially lower than that in a gasdynamical bullet . that means , as well , that the temperature in the region on the nose of the bullet would be lower than that predicted in the gasdynamical case . that detail could alter expectations of the thermal emission , including x - rays and uv - ir lines . = cmmi10 scaled1 = cmmi10 = cmmi7 = cmmib10 scaled1 = cmmib10 = cmmib10 scaled 833 = cmbsy10 scaled1 = cmbsy10 = cmbsy10 scaled 833 1 = 1 = 1 = 9 = 9 = 9 = 10 = 10 = 10 =

1204.4706

i

observations of the far - ir / submillimeter background with _ cobe _ demonstrated that a substantial fraction of the universe s star formation took place behind a veil of dust @xcite . because these were integrated measurements , however , they could not identify which populations of dust - obscured galaxies contained this vigorous star formation . a breakthrough in resolving the background came in the late 1990s , with imaging by the submillimeter common - user bolometer array ( scuba ) on the james clerk maxwell telescope ( jcmt ) . its initial surveys at 850@xmath4 m @xcite detected a new population of bright ( @xmath8mjy ) galaxies . named after the wavelengths where they are most visible , these submillimeter galaxies ( smgs ) are systems with apparently vast ( @xmath9 ) bolometric luminosities but with such high obscurations that their optical counterparts are faint or absent ( see * ? ? ? * and references therein ) . smgs brighter than scuba s confusion limits could not account for all of the 850@xmath4 m background , but clearly made a substantial contribution to it . over the last fifteen years , much of the effort to understand the origins of the far - ir / submillimeter background has focused on bright smgs selected from 8501200@xmath4 m surveys . smgs are sometimes treated as representatives of a more general category of high - redshift galaxies , dusty star - forming galaxies ( dsfgs ) whose luminosities are dominated by obscured star formation . a major initial hurdle was verifying that bright smgs actually do lie at high redshifts . while two early scuba detections had optical redshifts @xcite , quickly confirmed with co spectroscopy @xcite , progress in measuring redshifts of other smgs foundered due to their very high obscurations . only after @xcite took advantage of radio continuum mapping to determine precise positions for blind optical spectroscopy did it become possible to obtain co detections in large numbers @xcite , and to derive an smg redshift distribution peaking around @xmath102.5 @xcite . heroic efforts to explore the high-@xmath11 tail that radio pre - selection misses when radio counterparts fall below typical survey flux limits have identified a handful of sources at @xmath12 ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , but detailed analysis limits the possible significance of this tail in the @xmath13 mm population @xcite . we now know that bright smgs have large stellar @xcite , molecular gas @xcite , and dynamical @xcite masses , that many of them are mergers @xcite , and that their large luminosities are powered principally by star formation @xcite . explaining the observed properties of bright smgs , their evolutionary states , and their relationships to populations of galaxies selected at other wavelengths is a current major challenge for galaxy evolution models ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in parallel with the growth in our understanding of bright smgs , it is also becoming clear that current samples give an incomplete picture of the full variety of dsfgs . first , 850@xmath4 m sources fainter than scuba s nominal confusion limit of about 2 mjy , although accessible via gravitational lensing ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , must at some point start to resemble optically selected galaxies more than heavily obscured smgs ( e.g. , * ? ? ? * ; * ? ? ? second , even among bright dsfgs , 850@xmath4m - bright smgs have distinct selection biases . dsfg samples selected at longer wavelengths appear to have cooler dust temperatures and higher median redshifts @xcite . dsfg samples selected at shorter wavelengths , conversely , include populations with warmer dust that 850@xmath4m - selected samples can miss , @xcite , and that tend to have both lower redshifts and more bolometrically significant active galactic nuclei ( agns ; e.g. , * ? ? ? * ; * ? ? ? third , existing samples of smgs with spectroscopic redshifts often suffer from biases associated with the steps used to determine those redshifts . for example , precise localization of a submillimeter source usually relies on radio continuum mapping , and while the deepest vla imaging yields counterparts for a high fraction of dsfgs @xcite , more typical vla maps tend to deliver counterparts for only 6070% of smgs . subsequent optical spectroscopy based on these positions fails to yield redshifts for a modest fraction of candidates @xcite , and even when apparently successful , attempts to obtain co detections of the gas reservoirs associated with these massive starbursts can sometimes fail to yield conclusive confirmation , raising questions over either the identification or redshift @xcite . mid - ir spectroscopy can avoid some of these difficulties ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) but suffers from its own problems for sources with power - law spectra or confusion from multiple sources within large beams or slits . finally , many of the seminal studies of smgs mapped relatively small areas on the sky . notwithstanding the large line - of - sight interval probed by 850@xmath4mselection , which can partly compensate for a small area , smgs are such rare sources ( mergers caught at special moments , with the most luminous caught at the most special of moments ) that cosmic variance remains a concern for the derived redshift distributions . new instruments capable of producing deep images of large regions of the sky , and of conducting efficient spectral surveys over wide bandwidths , have accelerated the discovery of high - redshift dsfgs with a broader range of physical properties than could be probed by previous efforts . survey areas at @xmath14 mm have increased substantially ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , with extremely wide - area surveys possible both from the ground @xcite , and from space with the _ herschel space observatory _ @xcite . large - area surveys are identifying many very bright dsfgs whose fluxes are rivaled by those of only a few extreme , serendipitously discovered objects that have been confirmed to be gravitationally lensed ( e.g. , * ? ? ? regardless of the balance between intrinsically hyperluminous systems and less extreme but gravitationally lensed galaxies within these samples , we are no longer missing the rarest dsfgs because of limited sky coverage . _ herschel _ is playing a particularly important role because the wavelength coverage of its spire instrument @xcite allows selection of dsfg samples that are relatively free of dust temperature biases @xcite , although they are limited by confusion to only the most extreme luminosity systems at @xmath15 @xcite . specialized instruments designed for wide - band spectral line surveys now enable the determination of blind co redshifts ( see , e.g. , * ? ? ? * ; * ? ? ? * ) for bright dsfgs , without intermediate radio continuum mapping or optical spectroscopy . an example of the combination of these new developments is the recent use of two wide - bandwidth instruments to obtain co redshifts for a complete sample of five bright _ herschel _ sources @xcite , an essential step in confirming their status as galaxy - galaxy lenses @xcite . expanding on this initial work , we here report on @xmath14 cm spectroscopy of the @xmath0c@xmath1o @xmath2 ground - state rotational transition toward two dozen of the brightest dsfgs in catalogs from the _ herschel _ astrophysical terahertz large area survey ( h - atlas ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) program , using the zpectrometer ultra - wideband spectrometer on the national radio astronomy observatory s 100-meter diameter robert c.byrd green bank telescope ( gbt ) . submillimeter continuum flux ratios provide some coarse redshift information for many sources , but the precise redshifts needed to enable additional observations with narrow - band instruments require spectroscopy of atomic or molecular lines . the zpectrometer is one of several ultra - wideband spectrometers built for this purpose , and is the first instrument to make routine measurements of the co @xmath16 rotational transition from high - redshift galaxies ( e.g. , * ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . with the co molecule s @xmath17 level only 5.4k above the ground state , its low but nonzero permanent dipole moment , and its strong c o bond , the @xmath2 transition is the best tracer of molecular gas over a wide range of conditions in molecular clouds . in addition to giving a spectroscopic marker for redshift measurements , velocity - resolved spectroscopy yields dynamical information , which together with gas masses derived from co intensities provides key inputs to understanding dsfgs star formation efficiencies and overall evolutionary states . subsequent sections of this paper describe the observations and the initial results from this sample . section [ sec : obs ] describes target selection and observations , section [ sec : res ] contains observational results , and section [ sec : disc ] provides further analysis and discussion . calculations use a @xmath18cdm cosmology with @xmath19 , @xmath20 , and @xmath21 @xcite .

we report measurements of the carbon monoxide ground state rotational transition (co ) with the zpectrometer ultra - wideband spectrometer on the 100 m diameter green bank telescope . herschel_-atlas photometric colors from the spire instrument . the co detections confirm the existence of massive gas reservoirs within these luminous dusty star - forming galaxies ( dsfgs ) .

we report measurements of the carbon monoxide ground state rotational transition (co ) with the zpectrometer ultra - wideband spectrometer on the 100 m diameter green bank telescope . the sample comprises 11 galaxies with redshifts between and 3.5 from a total sample of 24 targets identified by _ herschel_-atlas photometric colors from the spire instrument . nine of the co measurements are new redshift determinations , substantially adding to the number of detections of galaxies with rest - frame peak submillimeter emission near 100 m . the co detections confirm the existence of massive gas reservoirs within these luminous dusty star - forming galaxies ( dsfgs ) . the co redshift distribution of the 350m - selected galaxies is strikingly similar to the optical redshifts of 850m - selected submillimeter galaxies ( smgs ) in . spectroscopic redshifts break a temperature - redshift degeneracy ; optically thin dust models fit to the far - infrared photometry indicate characteristic dust temperatures near 34k for most of the galaxies we detect in co. detections of two warmer galaxies and statistically significant nondetections hint at warmer or molecule - poor dsfgs with redshifts difficult determine from from _ herschel_-spire photometric colors alone . many of the galaxies identified by h - atlas photometry are expected to be amplified by foreground gravitational lenses . analysis of co linewidths and luminosities provides a method for finding approximate gravitational lens magnifications from spectroscopic data alone , yielding . corrected for magnification , most galaxy luminosities are consistent with an ultra - luminous infrared galaxy ( ulirg ) classification , but three are candidate hyper - lirgs with luminosities greater than .

1204.4706

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panels in figure [ fig : spectra ] show the spectra and confidence plots for all of the source pairs we observed . the upper panel for each source pair is the spectrum across the zpectrometer band . vertical dashed lines mark line frequencies of detected galaxies . the lower panel shows the detection probabilities @xmath34 from our detection algorithm , versus frequency , given as confidence@xmath35 ( numerically , the scale is equivalent to the number of nines in confidence : 0.9 , 0.99 , 0.999 , etc . for @xmath36 ) . each dot in the plot is an individual channel s confidence measure ( within the algorithm s assumptions ) for a given combination of binning width and starting point . columns of dots at specific frequencies show where a potential detection is relatively immune to exact binning parameters , indicating that a real line is present rather than a favorable binning for a chance fluctuation . our brief comments on individual spectra are : _ j083051.0 + 013224 _ and _ j084933.4 + 021443 _ ( fig . [ fig : spectra ] , 1 - 2 ) : only the second target in the pair ( emission appears in the negative sense ) is detected . riechers ( priv . comm . 2011 ) has detected a single strong line with the carma observatory toward the first in the pair . if the line were co @xmath37 , j083051.0 + 013224 would lie at a redshift with the @xmath38 line in a low - noise region of the zpectrometer band . this is a statistically significant nondetection that we discuss in section [ sec : completeness ] . _ j083929.5 + 023536 _ and _ j084259.9 + 024958 _ ( fig . [ fig : spectra ] , 3 - 4 ) : neither target is clearly detected in this spectrum . _ j090302.9@xmath39014127 _ and _ j091305.0@xmath39005343 _ ( fig . [ fig : spectra ] , a - c ) : clear detections of both targets . the high confidence at slightly lower frequency than the strong positive line is likely an artifact , as even a modest dip can be far from the local amplitude mean , a signature the detection algorithm interprets as a line . _ j091840.8 + 023047 _ and _ j085111.7 + 004933 _ ( fig . [ fig : spectra ] , 5 - 6 ) : clear detection of the first target in the pair . the continuum offset from zero shows that the first target has a higher continuum flux than the second target . _ j091948.8@xmath39005036 _ and _ j092135.6 + 000131 _ ( fig . [ fig : spectra ] , 7 - 8 ) : neither target is clearly detected in this spectrum . residual large - scale structure may obscure what could be tentative detections . even small noise fluctuations at the tops of large - scale positive and negative structures are far from local means , so they register strongly in the confidence plot . _ j113526.3@xmath39014605 _ and _ j113243.1@xmath39005108 _ ( fig . [ fig : spectra ] , 9 - 10 ) : clear detections of both targets . some spurious high confidence peaks are associated with each of the bright lines . _ j113833.3 + 004909 _ and _ j113803.5@xmath39011735 _ ( fig . [ fig : spectra ] , 11 - 12 ) : neither target is clearly detected in this spectrum . _ j114637.9@xmath39001132 _ and _ j115112.3@xmath39012638 _ ( fig . [ fig : spectra ] , 13 - 14 ) : clear detection of the first target . _ j115820.2@xmath39013753 _ and _ j114752.7@xmath39005832 _ ( fig . [ fig : spectra ] , 15 - 16 ) : clear detection of the first target . _ j132426.9 + 284452 _ and _ j133008.3 + 245860 _ ( fig . [ fig : spectra ] , 17 - 18 ) : tentative detection of the first target . baseline structure to slightly higher frequencies makes it difficult to find a local baseline , so the line parameters are uncertain . _ j134429.4 + 303036 _ and _ j133649.9 + 291801 _ ( fig . [ fig : spectra ] , 19 - 20 ) : clear detections of both targets , with one line in the positive sense and two in the negative sense . we attribute the stronger negative line with the spire source . for completeness , we assign the other negative line a tentative formal detection because it is uncharacteristically broad for a spurious signal , but it is close to the positive - sense line where the local mean changes rapidly and may throw off the detection algorithm . _ j141351.9@xmath39000026 _ and _ j142751.0 + 004233 _ ( fig . [ fig : spectra ] , 21 - 22 ) : a strong detection of the first target . the high confidence measures for dips to either side are most likely due to a high local mean in the region . the dips are rather wide to be due to a galaxy , so it is unlikely that they represent detections . the continuum slope indicates a difference in spectral index between the two targets . overall , we detected 11 of the 24 targets in our sample . two of the detections were blind independent confirmations of sources with established redshifts ( id.17b in * ? ? ? * and id.130 in ; * ? ? ? this success rate is similar to that of detections from the plateau de bure millimeter - wave interferometer starting from optical redshift catalogs ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , but without the complications associated with finding optical redshifts for submillimeter sources ( see , e.g. , * ? ? ? section [ sec : completeness ] contains a more extensive discussion of detection completeness . in addition to the 11 detections , we also list two tentative detections , denoted by italics in table [ tab : summary ] and ( for j132426.9 + 284452 ) with open circles in the figures . line parameters for tentative detections were too uncertain for robust error estimates . based on the submillimeter photometric selection and line strength , we initially derived redshifts assuming that the lines were the redshifted co @xmath2 transition rather than co @xmath40 from a @xmath41 galaxy or a line from a species other than co. this assumption has proved correct for all 11 sources , which have other observed lines , most starting with redshifts from the zpectrometer observations ( d.a . riechers , priv . 2011 ; p.p . van der werf , priv . comm . 2011 ; table [ tab : summary ] summarizes observed and derived source parameters . for detected lines , the parameters are from single - component fits to gaussian lineshapes , with errors given by the statistical uncertainties in the fit at the 68% ( `` @xmath42 '' ) confidence level . gaussian fits to the convolutions of gaussian line shapes and the correlator s sinc instrumental profile shows that linewidth corrections are unimportant for linewidths above 200kms@xmath29fwhm ( the correction is 12% when the gaussian line and sinc fwhms are equal , falling below 1% when the gaussian s fwhm is 1.5 times the sinc s fwhm or wider ) . all lines are broader than this , so we make no corrections . the table also contains estimates of the total infrared ( 81000@xmath4 m ) fluxes and dust temperatures obtained from fits to the spire photometry ( h - atlas collaboration , priv . 2010 ) , as discussed later . in addition to the detections from this program , table [ tab : summary ] also includes co @xmath38 data from a previous zpectrometer detection of h - atlas j090311.6 + 003906 ( * ? ? ? * id.81 ) . [ tab : summary ] we have firm detections of 11 of the 24 targets in our program , a number large enough to draw some sample conclusions . here we use the molecular and continuum flux information to explore the detection completeness and to evaluate possible reasons for co nondetections . figure [ fig : scovss350 ] explores the relationship between 350@xmath4mflux density , @xmath43 , and the co @xmath2 integrated flux , @xmath44 . sources without co detections have zero amplitude in this plot , and the open circle denotes a tentative co detection . line nondetections generally fall to lower 350@xmath4 m flux densities , but several galaxies are bright in continuum but not detected in co. we can take the third - brightest @xmath43 source in our sample ( j083051.0 + 013224 , target number 1 in figures and tables ) as an example of a nondetection that implies a galaxy with a redshift outside the zpectrometer band or an abnormally low co to continuum flux ratio . the former seems more likely in this case : as noted above , carma has a clear detection of a mid-@xmath45 co line from this source , but deep integrations by the zpectrometer and other instruments have not found other lines corresponding to a redshift within the zpectrometer s @xmath463.5 band . versus 350@xmath4 m flux density @xmath43 for co - detected and co - undetected sources from our sample . co nondetections have been assigned zero flux . horizontal dashed lines show completeness levels for line detections derived from our 400kms@xmath29 linewidth simulations , with corresponding @xmath43 derived from the power - law fit shown by the smooth curve . all galaxies with co nondetections have 350@xmath4 m flux densities above the 70% completeness limit for detections if a simple co - continuum flux scaling law holds ( see text ) . this implies that chance alone can not explain the fraction of galaxies in the sample that we do not detect , but that some galaxies have redshifts outside the zpectrometer band or contain relatively little molecular gas . points are labeled by target numbers given in the tables . [ fig : scovss350],width=307 ] most likely , some fraction of the nondetected galaxies have redshifts that are not well predicted by continuum properties , while others have co @xmath38 lines that are fainter than our detection threshold . before we simply ascribed co nondetections to galaxies with observed luminosities below some threshold , we first examined the line detection completeness and the relationship between line and continuum fluxes . estimating line detection completeness in broadband spectra is complicated by system temperature and nonideal noise that vary with frequency ; this frustrates any attempt to define a quantity such as the baseline rms in narrowband spectra that could specify a simple detection limit . we estimated completeness levels for nondetections by simulation , adding sets of synthetic lines as frequency combs across subscans for all sources , running the modified spectra through the data reduction pipeline , and inspecting the spectra to see which synthetic lines we could clearly identify . with a comb of seven 400kms@xmath29 wide lines ( a width close to the median of the astronomical source linewidths ) across each spectrum , we recovered 90% of the synthetic lines with co integrated intensity @xmath44 = 800 mjykms@xmath29 , 70% of the lines with @xmath44 = 600 mjykms@xmath29 , and 35% of those with @xmath44 = 400 mjykms@xmath29 . taking @xmath44 = 600 mjykms@xmath29as the typical lower limit for our detections , the simulation gives 70% completeness for 400kms@xmath29 lines , 90% completeness for 200kms@xmath29 lines , and 40% completeness for 800kms@xmath29 lines . this shows that the statistical algorithm is most sensitive to peak intensity for lines near detection thresholds . the average completeness for these three widths is 67% , so 70% is representative for a set of lines with various widths and 600 mjykms@xmath29 . a somewhat monotonic relationship between the continuum and line fluxes in dsfgs must exist : energy balance requires that galaxies with little far - ir continuum luminosity will have weak molecular emission . the exact relationship is unknown , but a power - law fit established a representative correspondence between @xmath44 and 350@xmath4 m flux densities @xmath43 for sources with co detections . this fit yielded equivalent limits of @xmath43 = 150mjy , 90mjy , and 50mjy for 90 , 70 , and 35% completeness for the median ( 400kms@xmath29 ) linewidth , as shown in figure [ fig : scovss350 ] . given the @xmath44@xmath43 distribution , the exact form of the continuum line relationship is unimportant over the relatively small range at low flux densities , and a linear fit gave essentially the same values . excluding the extreme high - flux point from the fit flattens the @xmath44@xmath43 relationship , pushing the completeness limits to lower continuum flux densities . pushing the completeness limits to higher flux densities would require a steeper relationship than could be supported by these data with a simple model . whatever the exact form of the correspondence between @xmath44 and @xmath43 , all of our targets have @xmath43 falling above the 70% completeness level ( probability of detection ) if their co @xmath16 emission falls within the zpectrometer frequency range . we estimated the number of targets we might expect to have missed due to faint co flux alone by considering the targets below @xmath43 = 150mjy , the approximate 90% completeness level . there are 10 sources in our target list below this limit , of which we detect only two . if chance alone dominates , the detection rate will be given by the binomial distribution . taking a lower limit of a 70% detection probability , the distribution finds 7 detections as most likely , with @xmath47 detections accounting for 99% of the total probability . the probability of detecting just two sources is 0.1% . increasing either the detection probability or the flux limit corresponding to a given detection probability reduces the probability of detecting just two of ten sources . if chance alone ruled , we should therefore have detected some 2 to 5 more weak sources . considering the additional four nondetections with 350@xmath4 m flux densities significantly above the nominal 90% completeness limit , this analysis points to a strong disparity between actual and expected detections . we conclude that chance is not the only reason for nondetections , but that systematic effects are also important : some of the sources could not be detected because their redshifts are outside of the zpectrometer s band , some because they have lower @xmath44/@xmath43 ratios than the detected sources , some because their lines are weak and broad ( although there is no sign of these even though the eye is good at picking out correlated channels ) , or some combination . zpectrometer redshifts for the h - atlas sources provide an independent sample for comparison with previous spectroscopic redshift surveys . comparing surveys , we find that the redshift distributions of the `` 350@xmath4 m peaker '' galaxies with zpectrometer detections and those of the radio - preselected smgs @xcite that fall within the zpectrometer s redshift range are strikingly similar , although the source selection and lines used in the redshift measurements were quite different : our galaxies are 350@xmath4m - bright targets from a wide - area survey that highlights lensed sources , while the @xcite galaxies must be bright at 850@xmath4 m and 20 cm radio continuum . figure [ fig : zdistribs]a gives the binned distribution for the galaxies with zpectrometer co detections . the median of the zpectrometer co redshifts is @xmath48 , and the mean is @xmath49 ( 68% confidence levels by bootstrap analysis ) , both well below the band center at @xmath50 . figure [ fig : zdistribs]a shows that the peak of the observed density function is near @xmath51 , agreeing well with the peaks found for optical spectroscopic redshifts of scuba - selected sources @xcite , and for photometric redshifts of both _ herschel_-selected sources bright at 350@xmath4 m @xcite and 870@xmath4m - selected sources identified by laboca @xcite . m - selected galaxies . [ fig : zdistribs],width=307 ] figure [ fig : zdistribs]b gives the cumulative distribution functions of the zpectrometer and the @xcite sample redshifts , allowing a clean comparison free of binning effects . it shows that the distributions are indistinguishable ; a kolmogorov - smirnov test gives a probability of 0.995 that the two underlying distributions are the same . such good agreement must in part reflect random chance in a statistically small sample , but nevertheless it is clear that the two distributions are very similar . there is otherwise no _ a priori _ reason that the distributions should be so similar : for instance , the @xcite sample could be concentrated to lower redshifts because of the radio pre - selection , while the zpectrometer detections could highlight a population of galaxies with strong molecular but very little rest - frame uv line emission . another similarity between the zpectrometer sample and galaxies detected in millimeter - wave co followup from optical redshift catalogs is the distribution of co linewidths . linewidths trace the dynamics , and thus to some extent masses , of the galaxies , and are not strongly affected by lensing . full width at half maximum ( fwhm ) linewidths in the zpectrometer sample range from 210 to 1180kms@xmath29 , with a median width of @xmath52kms@xmath29 ( 68% confidence levels by bootstrap analysis ) . in general this is somewhat narrower than the widths of mid-@xmath45 lines in the millimeter - wave studies of @xcite and @xcite , but a permutation test shows that the difference in median widths between the studies is significant at only the 70% level , and could easily be from small number statistics . combining the samples , a characteristic width of about 500kms@xmath29 is representative for dsfgs . in absolute terms , the widest @xmath38 lines are very broad , however , including two with fwhm linewidths greater than 1100kms@xmath29 . if tracing virialized matter , these widths correspond to emission from very massive galaxies or interacting massive galaxies . spectroscopic redshift measurements unambiguously break the @xmath53-@xmath11 degeneracy ( e.g. , * ? ? ? * ) that renders dust temperature estimates uncertain for galaxies without firm redshift measurements . we fit a simple optically thin single - temperature dust model with dust emissivity @xmath54 to the 250 , 350 , and 500@xmath4 m spire flux densities . to estimate the observed total infrared ( rest - frame 81000@xmath4 m ) luminosity , we joined the far - infrared fit smoothly in slope to a power - law spectrum with form @xmath55 at short wavelengths @xcite . assuming that the same gravitational magnification @xmath4 applies to emission in all far - ir wavebands , lensing should not affect temperature estimates , but it will scale the intrinsic luminosity @xmath56 so the observed infrared luminosity is @xmath57 . table [ tab : summary ] contains the model results and monte - carlo error estimates for individual galaxies . excluding the two @xmath58 galaxies , the dust temperature is @xmath59k averaged over all of the detected sources , with a slight dependence on the observed 350@xmath4mflux density ( fig . [ fig : dustvsalla]b ) or , equivalently , @xmath60 . little temperature scatter is to be expected among the detected galaxies because the source selection criteria favored similar spire - band seds . temperatures near 35k are similar to those derived from other surveys of smgs . the two highest-@xmath11 galaxies in our sample have temperatures of about 40k , a temperature higher than scatter alone can explain . varying the dust emissivity parameter @xmath61 from 1.2 to 1.7 did not change the dust temperatures by more than 3k . dust emission models that allow for dust emission optical depths yield temperatures about 15k higher than those from the optically thin model ; we quote the optically thin results to facilitate comparisons with previous work , most of which uses the same formalism . m flux density @xmath43 , showing that the luminosity scales reasonably well with flux density , even in the presence of a range of redshifts and dust temperatures . panel ( b ) shows that the derived characteristic dust temperatures are nearly constant with @xmath43 , possibly at least in part from selection effects . the highest two points in both panels are from the two galaxies in our sample with @xmath62 . points are labeled by target numbers given in the tables . [ fig : dustvsalla],width=307 ] figure [ fig : dustvsalla]a shows that the 350@xmath4 m flux density is an excellent proxy for the observed infrared luminosity @xmath57 at @xmath103 . the two points falling above the general trend are the two galaxies with the highest redshifts , @xmath58 , in our sample . excluding these two galaxies , we derive @xmath63 . apart from the two galaxies at @xmath58 there is no dependence of @xmath57 on redshift within errors . one of the goals of this project was to provide a data set suitable for evaluating the precision of photometric redshifts against spectroscopic measurements . here we make a first - cut comparison of techniques based on simple spire 3-band colors and on fitting to template galaxy seds . with galaxies chosen as `` 350@xmath4 m peakers , '' the simplest color selection is a flux ratio that estimates the sed s peak wavelength . since the 250@xmath4 m and 500@xmath4 m bands straddle the emission peak their ratio provides this estimate , reflecting some combination of temperature and redshift . as section [ sec : continuum ] shows , our sample of galaxies has a small range of dust temperatures , so we can test whether there is a simple relationship between the observed sed peak wavelength and redshift . figure [ fig : ratiodetz ] shows that there is a relationship between the peak wavelength , as given by the 250@xmath4m/500@xmath4 m flux density ratio , and spectroscopic redshift for galaxies with co detections . for these galaxies the 250@xmath4m/500@xmath4mflux density ratio predicts redshifts within @xmath64 ( standard deviation of the redshift error ) . other combinations of continuum flux densities and ratios are less successful at predicting redshifts than the peak wavelength . for example , both the co - detected and nondetected target galaxies fall along a common locus in a 500@xmath4m/350@xmath4m350@xmath4m/250@xmath4 m color - color diagram , but the galaxies are well mixed in redshift along that locus . a more general method of estimating redshifts is to take seds of galaxies with known redshift and temperature as templates , then find which redshifted template best matches the observed sed . template fits are not very tightly constrained by spire data alone because the 250 , 350 , and 500@xmath4 m bands lie near the peak of the observed - frame sed , however . flux ratios near the peak have little dynamic range and consequently can not provide strong constraints : the maximum @xmath65 and @xmath66 ratios are about 1.6 . figure [ fig : templcmp ] shows the redshift error @xmath67 versus redshift @xmath11 for the detected galaxies comparing results from the simple @xmath68 ratio and those from independent template fitting codes by co - authors clements , gonzlez - nuevo , and wardlow . each estimates the redshift by minimizing the chi - squared deviation of the data points compared with one or more observed seds of galaxies with known redshifts . minimizing chi - squared by shifting the templates in wavelength gives the redshift , while the widths of the chi - squared values versus shift provide redshift error estimates . comparing the template fitting with the linear fit between @xmath11 and @xmath68 shown in fig . [ fig : ratiodetz ] , shows that the linear fit gives the lowest dispersion in @xmath67 for most of the detected galaxies . redshifts from an sed corresponding to the cosmic eyelash galaxy smmj2135@xmath390102 ( * ? ? ? * , with sed template from ; * ? ? ? * and ; * ? ? ? * ) are nearly as accurate as those from the linear fit . comparison with models that choose from libraries of extragalactic seds shows these have generally poorer agreement than constrained models for most of the detected galaxies , with @xmath691 and internal error estimates smaller than the actual redshift deviation between observation and model . their errors are lower than those of the @xmath68 ratio or eyelash fits for the two galaxies at @xmath70 , however . this result emphasizes the difficulty of fitting curves with only a few samples near the peak ; photometric redshifts incorporating substantially longer - wavelength data are substantially more accurate ( see , e.g. , photometric redshifts including mambo 1200@xmath4 m data in * ? ? ? * ) . versus 250@xmath4m/500@xmath4 m continuum flux density ratio ( solid points ; open point for a tentative detection ) . dashed horizontal lines mark the zpectrometer s band edges . co nondetections ( triangles ) are plotted outside the band at an arbitrary @xmath46 . for galaxies with co detections , the figure shows that spire colors give @xmath71 for this carefully filtered homogeneous sample . points are labeled by target numbers given in the tables . [ fig : ratiodetz],width=307 ] redshifts , either the linear fit ( triangles ; fig . [ fig : ratiodetz ] ) or template fitting against the eyelash sed ( crosses ) provides redshift estimates within @xmath72 for @xmath73 . dashed lines highlight grouping by method only . template fits that automatically select from a library of seds ( squares ) generally predict redshift to @xmath69 - 1 ; the grey background shows the typical internal uncertainty for the template fits . models that choose between multiple seds predict redshifts outside the zpectrometer band for several of the nondetected sources , even though the linear and eyelash templates place them within the band , and have lower errors for the @xmath74 sources . as discussed in the text , this indicates that selection effects are important in the agreement between eyelash sed and co detections . [ fig : templcmp],width=307 ] we emphasize that the correspondence between co @xmath2 detections and spire 250@xmath4m/500@xmath4 m color or eyelash template redshifts yields no redshift information about the galaxies that we do _ not _ detect in the co @xmath2 line . galaxies with and without detections span nearly the same 250@xmath4m/500@xmath4 m flux density ratios ( fig . [ fig : ratiodetz ] ) , and the success of the eyelash template may simply arise from its ability to identify the @xmath75k galaxies we find in co. as we discussed in section [ sec : completeness ] , some fraction of galaxies with continuum properties similar to galaxies with co detections very likely fall outside the zpectrometer s band . lens magnifications ( @xmath4 ) are needed to convert the observed fluxes to intrinsic luminosities . determining magnification is generally done by constraining a model of the source - lens pair with an image of the gravitationally - distorted source galaxy . detailed lens models are not yet available for most of our sources . we do have velocity - resolved spectra , however , and can take an alternative approach of comparing observed and intrinsic luminosities established by an empirical luminosity - linewidth relationship similar in spirit to the tully - fisher relation @xcite . without correction for galaxy inclination or dispersion in intrinsic galaxy properties , such a relationship can not be exact , but it can provide approximate estimates of lensing magnifications . since the galaxies with zpectrometer co detections seem to be quite typical of the general smg population , as we discussed above , we assume that only lens magnifications modify the observed typical luminosity distributions of galaxies detected in co @xmath2 . following the method of @xcite , as outlined below , we find an empirical intrinsic integrated line luminosity - linewidth relationship @xmath76 from galaxies with published co @xmath2 intensities , widths , and magnifications . this relationship forms the basis to solve for the unknown magnification @xmath4 that scales the true line luminosity @xmath77 to an apparent luminosity @xmath78 , or @xmath79 figure [ fig : co_tf ] shows @xmath80 for 15 @xmath814 smgs from the literature versus linewidth , with corrections for lens magnification when needed ( co data from * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; magnifications as needed from * ? ? ? points for these galaxies fall close to a power law fit with relatively small scatter . inserting the fit parameters into equation ( [ eq : mu1 ] ) , we obtain @xmath82 with the units for line luminosity @xmath77 as defined in @xcite . apparent line luminosities for the h - atlas galaxies with zpectrometer co measurements , uncorrected for lens magnification , are also plotted in figure [ fig : co_tf ] . as expected for a flux - limited sample , these galaxies have a narrower range of luminosities than the comparison sample from the literature . galaxies with narrower linewidths , which will generally have lower luminosities , require more magnification to reach the observational detection threshold . versus co @xmath2 fwhm linewidths for 15 sources with redshifts , fluxes , and magnifications as needed from the literature ( co data from * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; magnifications as needed from * ? ? ? the solid line shows a power - law fit to these data , representing an estimate of the intrinsic line luminosity versus linewidth for typical galaxies . round points show the observed line luminosities versus widths for the zpectrometer sample ( values from table [ tab : summary ] ) , without correction for lens magnifications . the literature sample has a steep power - law relation with modest scatter , while the zpectrometer sample shows a much flatter trend . intrinsically weaker sources require higher magnification to rise above the observational detection threshold , which is approximately constant in flux . we scaled the observed line luminosity for each of the zpectrometer sources by the prediction from the power - law estimate of its likely magnification @xmath4 , as given in table [ tab : galprops ] . this method yielded a range of @xmath8320 and a median of @xmath84 for the zpectrometer sample . [ fig : co_tf],width=307 ] table [ tab : galprops ] lists the lens magnifications derived from equation ( [ eq : mu ] ) . the empirical magnification distribution is approximately uniform over its range of 3 to 20 , with both median and mean equal to 10 . simple uncertainty estimates for the scaling term and power law index are not available because the two are not independent , but a bootstrap analysis provides @xmath8568% confidence bounds on @xmath4 for each galaxy in table [ tab : galprops ] . fractional uncertainties range from about 30% at a minimum near 500kms@xmath29 , climbing to about 50% at 300 and 1200kms@xmath29 , and about 100% at 200kms@xmath29 . the divergence toward low @xmath86 is also a reminder that the ( unknown ) inclination corrections become large for galaxies with observed low linewidths . it is possible that some of the sources with broad co lines and low inferred amplifications from equation ( [ eq : mu ] ) are intrinsically hyper - luminous systems which are not significantly magnified at all ; the magnification uncertainty encompasses that possibility . lrrrrrrrr j084933.4 + 021443 & @xmath87 & @xmath88 & @xmath89 & @xmath90 & @xmath91 & @xmath92 & @xmath93 + j090302.9@xmath39014127 & @xmath94 & @xmath95 & @xmath96 & @xmath97 & @xmath98 & @xmath99 & @xmath26 + j090311.6 + 003906 & @xmath100 & @xmath101 & @xmath102 & @xmath103 & @xmath104 & @xmath96 & @xmath105 + j091305.0@xmath39005343 & @xmath106 & @xmath107 & @xmath108 & @xmath109 & @xmath110 & @xmath111 & @xmath27 + j091840.8 + 023047 & @xmath112 & @xmath113 & @xmath114 & @xmath115 & @xmath116 & @xmath117 & @xmath118 + j113243.1@xmath39005108 & @xmath119 & @xmath120 & @xmath121 & @xmath122 & @xmath123 & @xmath124 & @xmath125 + j113526.3@xmath39014605 & @xmath126 & @xmath127 & @xmath128 & @xmath129 & @xmath130 & @xmath131 & @xmath132 + j114637.9@xmath39001132 & @xmath133 & @xmath134 & @xmath135 & @xmath136 & @xmath137 & @xmath138 & @xmath139 + j115820.2@xmath39013753 & @xmath140 & @xmath141 & @xmath142 & @xmath143 & @xmath144 & @xmath145 & @xmath146 + j133649.9 + 291801 & @xmath147 & @xmath148 & @xmath149 & @xmath150 & @xmath151 & @xmath152 & @xmath153 + j134429.4 + 303036 & @xmath154 & @xmath155 & @xmath156 & @xmath157 & @xmath158 & @xmath159 & @xmath160 + j141351.9@xmath39000026 & @xmath161 & @xmath162 & @xmath163 & @xmath164 & @xmath165 & @xmath166 & @xmath167 magnifications from the luminosity - linewidth relation ( [ eq : mu ] ) compare well with values from the two galaxies in the h - atlas survey that have both zpectrometer detections and preliminary lens models from image reconstruction with lens and source galaxies at known redshifts . for j090311.6 + 003906 ( id.81 ; co data from * ? ? ? * ) , the co linewidth - luminosity relationship in equation ( [ eq : mu ] ) predicts @xmath168 , while @xcite quote @xmath169 ( range 1831 ) from their modeling . for j091305.0@xmath39005343 ( id.130 ) , equation ( [ eq : mu ] ) predicts @xmath170 while @xcite quote @xmath171 ( range 57 ) . table [ tab : galprops ] provides estimates of the intrinsic luminosities and gas masses corrected by the source - specific magnification factors , and also by the median @xmath84 . most of the galaxies appear to have intrinsic luminosities typical of ulirgs , although three are candidate hyper - lirgs , with luminosities greater than @xmath172 . gas mass estimates use the same co luminosity - to - mass conversion factor as in @xcite and @xcite for ease of comparison , @xmath173 m@xmath174 ( kkms@xmath29pc@xmath175)@xmath29 @xcite . although absolute mass estimates carry double uncertainties from both conversion and magnification factors , they are similar to estimates for smgs selected from 850@xmath4 m observations that use the same conversion factor .

the sample comprises 11 galaxies with redshifts between and 3.5 from a total sample of 24 targets identified by _ nine of the co measurements are new redshift determinations , substantially adding to the number of detections of galaxies with rest - frame peak submillimeter emission near 100 m . the co redshift distribution of the 350m - selected galaxies is strikingly similar to the optical redshifts of 850m - selected submillimeter galaxies ( smgs ) in . spectroscopic redshifts break a temperature - redshift degeneracy ; optically thin dust models fit to the far - infrared photometry indicate characteristic dust temperatures near 34k for most of the galaxies we detect in co. detections of two warmer galaxies and statistically significant nondetections hint at warmer or molecule - poor dsfgs with redshifts difficult determine from from _ herschel_-spire photometric colors alone . analysis of co linewidths and luminosities provides a method for finding approximate gravitational lens magnifications from spectroscopic data alone , yielding . corrected for magnification , most galaxy luminosities are consistent with an ultra - luminous infrared galaxy ( ulirg ) classification , but three are candidate hyper - lirgs with luminosities greater than .

we report measurements of the carbon monoxide ground state rotational transition (co ) with the zpectrometer ultra - wideband spectrometer on the 100 m diameter green bank telescope . the sample comprises 11 galaxies with redshifts between and 3.5 from a total sample of 24 targets identified by _ herschel_-atlas photometric colors from the spire instrument . nine of the co measurements are new redshift determinations , substantially adding to the number of detections of galaxies with rest - frame peak submillimeter emission near 100 m . the co detections confirm the existence of massive gas reservoirs within these luminous dusty star - forming galaxies ( dsfgs ) . the co redshift distribution of the 350m - selected galaxies is strikingly similar to the optical redshifts of 850m - selected submillimeter galaxies ( smgs ) in . spectroscopic redshifts break a temperature - redshift degeneracy ; optically thin dust models fit to the far - infrared photometry indicate characteristic dust temperatures near 34k for most of the galaxies we detect in co. detections of two warmer galaxies and statistically significant nondetections hint at warmer or molecule - poor dsfgs with redshifts difficult determine from from _ herschel_-spire photometric colors alone . many of the galaxies identified by h - atlas photometry are expected to be amplified by foreground gravitational lenses . analysis of co linewidths and luminosities provides a method for finding approximate gravitational lens magnifications from spectroscopic data alone , yielding . corrected for magnification , most galaxy luminosities are consistent with an ultra - luminous infrared galaxy ( ulirg ) classification , but three are candidate hyper - lirgs with luminosities greater than .

1102.2880

i

this paper concerns the computational complexity of an optimisation problem with strong connections to the _ constraint satisfaction problem _ ( csp ) . an instance of the constraint satisfaction problem consists of a finite set of variables , a set of values ( the domain ) , and a finite set of constraints . the goal is to determine whether there is an assignment of values to the variables such that all the constraints are satisfied . csps provide a general framework for modelling a variety of combinatorial decision problems @xcite . various optimisation variations of the constraint satisfaction framework have been proposed and many of them can be seen as special cases of the valued constraint satisfaction problem ( ) , introduced by schiex et al . this is an optimisation problem which is general enough to express such diverse problems as max csp , where the goal is to maximise the number of satisfied constraints , and the minimum cost homomorphism problem ( ) , where all constraints must be satisfied , but each variable - value tuple in the assignment is given an independent cost . to accomplish this , instances of the assign costs ( possibly infinite ) to individual tuples of the constraints . it is then convenient to replace relations by _ cost functions _ , _ i.e. _ functions from tuples of the domain to some set of costs . this set of costs can be relatively general , but much is captured by using @xmath1 , where denotes the set of non - negative rational numbers . we arrive at the following formal definition . let @xmath2 be a finite domain , and let @xmath3 be a set of functions @xmath4 . by vcsp(@xmath3 ) we denote the following minimisation problem : instance : : : a set of variables @xmath5 , and a sum @xmath6 , where @xmath7 , @xmath8 , and @xmath9 is a list of @xmath10 variables from @xmath5 . solution : : : a function @xmath11 . measure : : : @xmath12 , where @xmath13 is the list of elements from @xmath2 obtained by applying @xmath14 component - wise to @xmath9 . the set @xmath3 is often referred to as the _ constraint language_. we will use @xmath3 as our parameter throughout the paper . for instance , when we say that a class of vcsps @xmath15 is polynomial - time solvable , then we mean that vcsp@xmath16 is polynomial - time solvable for every @xmath17 . finite - valued functions , _ i.e. _ functions with a range in , are sometimes called _ soft constraints_. a prominent example is given by functions with a range in @xmath0 ; they can be used to express instances of the well - known min csp and max csp problems ( which , for instance , include max @xmath18-cut , max @xmath18-sat , and nearest codeword as subproblems ) . on the other side we have _ crisp constraints _ which represent the standard type of csp constraints . these can be expressed by cost functions taking values in @xmath19 . a systematic study of the computational complexity of the was initiated by cohen et al . @xcite ; for instance , they prove a complexity dichotomy for @xmath16 over two - element domains . this was the starting point for an intensive research effort leading to a large number of complexity results for vcsp : examples include complete classifications of conservative constraint languages ( _ i.e. _ languages containing all unary cost functions ) @xcite , @xmath0 languages on three elements @xcite , languages containing a single @xmath0 cost function @xcite , and arbitrary languages with @xmath19 cost functions @xcite . we note that some of these results have been proved by computer - assisted search something that drastically reduces the readability , and insight gained from the proofs . we also note that there is no generally accepted conjecture stating which vcsps are polynomial - time solvable . the picture is clearer when considering the approximability of finite - valued vcsp . raghavendra @xcite have presented algorithms for approximating any finite - valued vcsp . these algorithms achieve an optimal approximation ratio for the constraint languages that can not be solved to optimality in polynomial time , given that the unique games conjecture ( ugc ) is true . for the constraint languages that can be solved to optimality , one gets a ptas from these algorithms . furthermore , no characterisation of the set of constraint languages that can be solved to optimality follows from raghavendra s result . thus , raghavendra s result does not imply the complexity results discussed above ( not even conditionally under the ugc ) . the goal of this paper is to prove a dichotomy result for vcsp with @xmath0 cost functions over four - element domains : we show that every such problem is either solvable in polynomial time or np - hard . such a dichotomy result is not known for csps on four - element domains ( and , consequently , not for unrestricted vcsps on four - element domains ) . our result proves that , in contrast to the two - element , three - element , and conservative case , submodularity is not the only source of tractability . in order to outline the proof , let @xmath3 denote a constraint language with @xmath0 cost functions over a four - element domain @xmath2 . we will need two tractability results in our classification . the first one is well - known : if every function in @xmath3 is submodular on a chain ( _ i.e. _ a total ordering of @xmath2 ) , then vcsp@xmath16 is solvable in polynomial time . the second result is new and can be found in section [ sec : tractable ] : we introduce _ 1-defect chain multimorphisms _ and prove that if @xmath3 has such a multimorphism , then vcsp@xmath16 is tractable . a multimorphism is , loosely speaking , a pair of functions such that @xmath3 satisfies certain invariance properties under them . the algorithm we present is based on a combination of submodular and bisubmodular minimisation @xcite . the hardness part of the proof consists of four parts ( sections [ sec : endo][sec : full ] ) . we begin by introducing some tools in section [ sec : endo ] and [ sec : graph ] . section [ sec : endo ] concerns the problem of adding ( crisp ) constant unary relations to @xmath3 without changing the computational complexity of the resulting problem . the main tool for doing this is using the concept of _ indicator problems _ introduced by jeavons et al . @xcite ( see also cohen et al . section [ sec : graph ] introduces a graph construction for studying @xmath3 . in principle , this graph provides information about the complexity of vcsp@xmath16 based on the two - element sublanguages of @xmath3 . similar graphs has been used repeatedly in the study of vcsp , _ cf . _ @xcite . equipped with these tools , we determine the complexity of vcsp@xmath16 over a four - element domain in section [ sec : binary ] . the graph introduced in section [ sec : graph ] allows us to prove that , when @xmath3 is a _ core _ ( _ cf . _ section [ sec : endo ] ) , vcsp@xmath16 is polynomial - time solvable if and only if @xmath3 is submodular on a chain or @xmath3 has a 1-defect chain multimorphism ( theorem [ thm : fourclass ] ) . some proofs of intermediate results are deferred to section [ sec : full ] .

we report new results on the complexity of the valued constraint satisfaction problem ( vcsp ) . under the unique games conjecture , the approximability of finite - valued vcsp is fairly well - understood . however , there is yet no characterisation of vcsps that can be solved exactly in polynomial time . this is unsatisfactory , since such results are interesting from a combinatorial optimisation perspective ; there are deep connections with , for instance , submodular and bisubmodular minimisation . we consider the min and max csp problems ( _ i.e. _ where the cost functions only attain values in ) over four - element domains and identify all tractable fragments . similar classifications were previously known for two- and three - element domains . in the process , we introduce a new class of tractable vcsps based on a generalisation of submodularity . this allow us to prove the result without relying on computer - assisted case analyses ( which otherwise are fairly common when studying the complexity and approximability of vcsps . ) the hardness results are further simplified by the introduction of powerful reduction techniques . * keywords * : constraint satisfaction problems , combinatorial optimisation , computational complexity , submodularity = [ draw , circle , fill = black , text = white , minimum size=4pt , inner sep=0pt ] = [ ] = [ dotted ]

we report new results on the complexity of the valued constraint satisfaction problem ( vcsp ) . under the unique games conjecture , the approximability of finite - valued vcsp is fairly well - understood . however , there is yet no characterisation of vcsps that can be solved exactly in polynomial time . this is unsatisfactory , since such results are interesting from a combinatorial optimisation perspective ; there are deep connections with , for instance , submodular and bisubmodular minimisation . we consider the min and max csp problems ( _ i.e. _ where the cost functions only attain values in ) over four - element domains and identify all tractable fragments . similar classifications were previously known for two- and three - element domains . in the process , we introduce a new class of tractable vcsps based on a generalisation of submodularity . we also extend and modify a graph - based technique by kolmogorov and ivn ( originally introduced by takhanov ) for efficiently obtaining hardness results in our setting . this allow us to prove the result without relying on computer - assisted case analyses ( which otherwise are fairly common when studying the complexity and approximability of vcsps . ) the hardness results are further simplified by the introduction of powerful reduction techniques . * keywords * : constraint satisfaction problems , combinatorial optimisation , computational complexity , submodularity = [ draw , circle , fill = black , text = white , minimum size=4pt , inner sep=0pt ] = [ ] = [ dotted ]

astro-ph0510629

c

this paper contains the first spectroscopic variability study for young accreting brown dwarfs . we obtained , depending on the target , 4 - 13 high - resolution spectra using the magellan / clay 6.5 m telescope , covering timescales from a few hours to several weeks . our targets are six sub - stellar objects in nearby star - forming regions , for which signs of accretion had been noted in previous studies . we measured line widths for the most prominent emission lines , either related to accretion , winds , or both . in all spectra , the continuum is faint , but not seriously affected by incomplete background subtraction or accretion veiling . all our targets are variable in the emission lines . the most dramatic changes are seen for 2m1207 , 2m1101 , and iso217 , whereas the remaining targets ( @xmath3oph-32 , chah@xmath0 - 1 , ls - rcra1 ) show significantly less variability . the most prominent line in all cases is the h@xmath0 feature . our targets exhibit a variety of h@xmath0 profiles , similarly to accreting t tauri stars . two objects ( 2m1207 , iso217 ) have strongly asymmetric and double - peaked profiles at least in parts of the time series , produced by a superposition of broad emission and either a red- ( 2m1207 ) or blue - shifted absorption feature . 2m1101 also exhibits a weak red - shifted absorption feature in parts of our time series . strong changes in the h@xmath0 10% width are seen in 2m1207 and 2m1101 , indicating variations in the accretion rate on timescales of weeks ( 2m1207 ) and hours ( 2m1101 ) . in both cases , this finding is supported by additional accretion indicators in the spectrum . for 2m1101 , the variations are consistent with a scenario of non - steady , clumpy accretion . we also see evidence for strong variability in the outflow rate in at least three targets ( 2m1101 , @xmath3oph-32 , iso217 ) , particularly if we compare our results with literature data . in two cases ( 2m1207 , iso217 ) there are indications for a coupling between infall and outflow rate changes . in some cases the variability is best explained by rotational modulation of the emission line flux . for ls - rcra1 , the variability characterictic supports a close to edge - on view of the disk . one important result from this study is a cautionary note : given that most accreting targets are strongly variable , studies of accretion - related properties have to be based either on large samples or on time series . one example is the recently found accretion rate vs. mass relationship , which shows a suspiciously large scatter . we demonstrate that it is possible to explain this noise by taking into account variability information . for at least two out of six targets , we have to assume asymmetric accretion flows to interpret the emission line shape and variations . this indirectly supports funneling of the accretion , as predicted in the magnetospheric accretion scenario for t tauri stars , and thus provides evidence that this scenario also applies to brown dwarfs . this implies the existence of large - scale magnetic fields , which may have @xmath1 kg field strengths , in accreting substellar objects . some of the observations were carried out by alexis brandeker , whose help is gratefully acknowledged . we thank the las campanas observatory staff for their assistance . the constructive comments from an anonymous referee helped to improve the paper . this research was supported by an nserc grant and university of toronto startup funds to r.j . llccccc 2mass j1207334 - 393254 & 2m1207 & m8 & 11.2 & 13 & 13 & 29 + 2mass j11013205 - 7718249 & 2m1101 & m8 & @xmath47 & - & 7 & 49 + @xmath3oph - iso032 & @xmath3oph-32 & m7.5 & @xmath67 & - & 5 & 17 + chah@xmath0 - 1 & chah@xmath0 - 1 & m7.5 & 15.5 & 7.6 & 5 & 19 + chai - iso217 & iso217 & m6.25 & @xmath47 & - & 5 & 39 + ls - rcra1 & ls - rcra1 & m6.5 & @xmath68 & 18 & 4 & 16 + ccccccccc 29/01 & 05:25 & 035 & @xmath69 & 2m1207 & @xmath70 & 110 & 215 & + 29/01 & 08:08 & & & 2m1207 & @xmath71 & 64 & 215 & + 01/02 & 05:56 & & & 2m1207 & @xmath71 & 86 & 209 & + 17/03 & 00:38 & 10 & @xmath4 & 2m1207 & @xmath72 & 334 & 308 & double - peaked + & 01:15 & & & 2m1101 & @xmath72 & 22 & 131 & + & 06:45 & 07 & & @xmath3oph-32 & @xmath73 & 88 & 270 & + & 08:14 & 10 & & 2m1207 & @xmath72 & 387 & 274 & + & 08:52 & & & 2m1101 & @xmath72 & 17 & 135 & + & 09:28 & & & ls - rcra1 & @xmath74 & 80 & 270 & + 18/03 & 00:23 & 10 & @xmath4 & 2m1207 & @xmath72 & 259 & 291 & double - peaked + & 01:14 & & & 2m1101 & @xmath75 & 12 & 122 & + & 02:06 & & & iso217 & @xmath72 & 109 & 359 & + & 02:41 & & & chah@xmath0 - 1 & @xmath72 & 72 & 139 & + & 05:16 & & & chah@xmath0 - 1 & @xmath72 & 74 & 135 & + & 05:50 & & & iso217 & @xmath75 & 142 & 376 & + & 06:46 & & & @xmath3oph-32 & @xmath73 & 82 & 224 & + & 08:03 & & & 2m1207 & @xmath72 & 229 & 253 & + & 08:42 & & & 2m1101 & @xmath72 & 92 & 232 & accretion burst + & 09:19 & & & ls - rcra1 & @xmath72 & 44 & 266 & + 19/03 & 23:52 & 10 & @xmath4 & chah@xmath0 - 1 & @xmath72 & 180 & 165 & + & 00:28 & & & 2m1207 & @xmath72 & 279 & 283 & double - peaked + & 02:06 & & & 2m1101 & @xmath75 & 85 & 224 & accretion burst + & 03:07 & & & iso217 & @xmath72 & 226 & 367 & + & 03:57 & & & chah@xmath0 - 1 & @xmath72 & 142 & 143 & + & 04:32 & & & 2m1207 & @xmath72 & 308 & 257 & double - peaked + & 05:07 & & & iso217 & @xmath72 & 219 & 363 & + & 06:06 & & & chah@xmath0 - 1 & @xmath74 & 132 & 152 & + & 06:37 & & & @xmath3oph-32 & @xmath73 & 100 & 224 & + & 07:50 & & & 2m1207 & @xmath72 & 258 & 270 & + & 08:27 & & & 2m1101 & @xmath75 & 126 & 194 & accretion burst + & 09:29 & & & ls - rcra1 & @xmath72 & 125 & 291 & + 27/03 & 03:56 & 035 & @xmath69 & 2m1207 & @xmath76 & 192 & 295 & double - peaked + & 06:29 & & @xmath4 & @xmath3oph-32 & @xmath71 & 85 & 241 & + 28/03 & 04:46 & 035 & @xmath69 & 2m1207 & @xmath76 & 183 & 279 & double - peaked + 29/03 & 04:38 & 035 & @xmath69 & 2m1207 & @xmath76 & 261 & 285 & double - peaked + & 05:14 & & @xmath4 & iso217 & @xmath76 & 73 & 342 & + & 05:47 & & & 2m1101 & @xmath76 & 13 & 127 & + & 07:54 & & & @xmath3oph-32 & @xmath76 & 50 & 211 & + 30/03 & 05:12 & 035 & @xmath69 & 2m1207 & @xmath77 & 322 & 304 & double - peaked + & 08:11 & & @xmath4 & ls - rcra1 & @xmath76 & 71 & 304 & +

high - resolution optical spectra of six targets in nearby star - forming regions were obtained over 11 nights between 2005 january - march on the magellan 6.5 m telescope . the most dramatic changes are seen for 2mass j1207334 - 393254 ( 2m1207 ) , 2mass j11013205 - 7718249 ( 2m1101 ) and chai - iso217 . we also see indications for changes in the outflow rate in at least three objects . in one case ( iso217 ) , there appears to be a-hour time lag between outflow and accretion variations , consistent with a scenario in which the wind originates from the inner disk edge . for some objects our variability study supports a close to edge - on inclination for the brown dwarf ls - rcra 1 . the fact that all targets in our sample show variations in accretion and/or outflow indicators suggests that studies of young brown dwarf properties should be based either on large samples or time series . as an example , we demonstrate that the large scatter in the recently found accretion rate vs. mass relationship can be explained primarily with variability .

we report on the first dedicated monitoring campaign of spectroscopic variability in young brown dwarfs . high - resolution optical spectra of six targets in nearby star - forming regions were obtained over 11 nights between 2005 january - march on the magellan 6.5 m telescope . we find significant variability in h and a number of other emission lines related to accretion and outflow processes on a variety of timescales ranging from hours to weeks to years . the most dramatic changes are seen for 2mass j1207334 - 393254 ( 2m1207 ) , 2mass j11013205 - 7718249 ( 2m1101 ) and chai - iso217 . we observe possible accretion rate changes by about an order of magnitude in two of these objects , over timescales of weeks ( 2m1207 ) or hours ( 2m1101 ) . the accretion ` burst ' seen in 2m1101 could be due to a ` clumpy ' flow . we also see indications for changes in the outflow rate in at least three objects . in one case ( iso217 ) , there appears to be a-hour time lag between outflow and accretion variations , consistent with a scenario in which the wind originates from the inner disk edge . for some objects there is evidence for emission line variability induced by rotation . our variability study supports a close to edge - on inclination for the brown dwarf ls - rcra 1 . the fact that all targets in our sample show variations in accretion and/or outflow indicators suggests that studies of young brown dwarf properties should be based either on large samples or time series . as an example , we demonstrate that the large scatter in the recently found accretion rate vs. mass relationship can be explained primarily with variability . the observed profile variations imply asymmetric accretion flows in brown dwarfs , which , in turn , is evidence for magnetic funneling by large - scale fields . we show that accreting sub - stellar objects may harbor magnetic fields with kg strength .

astro-ph0205305

r

the variability results for our sample are presented in table [ tab - sv ] . included are the total number of nights each object was observed and the number of nights in the final data set , the number of good images used in the analysis and the total taken , the number of days the data sets cover ( t@xmath40 ) , the number of good references used for the mean reference and the total number initially considered , the probility the l dwarf is variable ( @xmath35 ) , the standard deviation of the points from the mean level ( @xmath41 ) , and the average error ( @xmath42 ) . we have already defined the variable l dwarfs as those with probabilities above 95.4% . this group constitutes 7 out of the sample of 18 targets . the five objects with @xmath4380% are considered possibly variable , since they are likely to be viewed as variable with higher precision photometry . the six objects with @xmath44 clearly show no variability above the detection limits of this study . supporting of our claim for variability in the l dwarfs , figure [ perhist ] shows the fraction of the total number of objects with a given probability of variability . over 60% of the references have probabilities below 5% , whereas only 10% of the l dwarfs do . in addition , about 40% of the l dwarfs are flagged as variable ( @xmath38% ) compared to about 15% for the references . furthermore , figure [ histogram ] shows the number of variable objects as a function of instrumental magnitude . the fraction of references in a given magnitude bin that are variable does not show any indication of being a strong function of object brightness , suggesting that we are not underestimating the errors in these objects . the slight increase between @xmath45=14 - 15 in the references is likely due to small number statistics . given this evidence , it seems clear that the l dwarfs derive from an inherently more variable population than the reference stars . three of the targets in our sample were also monitored by @xcite : 2mass 1146 + 22ab , 2mass 1439 + 19 , and 2mass 0345 + 12 . our results disagree on the status of 2mass 1146 + 22ab . this object is significantly non - variable in our sample , whereas @xcite detected variability with an rms amplitude of 0.015 mag . our average photometric error for this object is almost four times larger than this amplitude . it is quite possible that 2mass 1146 + 22ab varies with such a small amplitude as to be undetectable in this work . therefore , even though we find that this object does not display statistically significant variations , higher signal - to - noise observations could show that it is still a low - amplitude variable . the second object , 2mass 1439 + 19 , is classified as a possible variable here and a non - variable by bailer - jones & mundt . interestingly , their variability probability is larger than the one we find here ( 90% compared to 80% ) . given that the probabilities are similarly high , this object is likely a low - amplitude variable . we agree with the results of @xcite on the classification of 2mass 0345 + 12 as a variable object . the light curve of 2mass 0345 + 25 ( figure [ 2m0345dif ] ) shows quite a bit of scatter , but no periodic trends are evident . the primary peak in the clean power spectrum occurs at [email protected] hours with a power @xmath18 times higher than the noise . a couple of reference stars have prominent clean peaks at 12 hours , indicating that the period is not intrinsic to any one object . consequently , we list 2mass 0345 + 25 as a variable object in table [ tab - sv ] , but do not present it in table [ tab - pow ] . @xcite presented preliminary results for three l dwarfs in this program . they found 2mass 0036 + 18 and 2mass 0135 + 12 to be variable and 2mass 1412 + 16 to be non - variable . an error was found in the reduction process used to obtain those results . the fwhm used to reject high fwhm frames was only from one star , and not an average of all stars . upon correction of the error , the classification of 2mass 0036 + 18 changed from variable to non - variable . the classifications of the other two objects did not change , but their data sets did change slightly . the new light curve for 2mass 0135 + 12 is shown in ( figure [ 2m0135dif ] ) . this object does not have a significant period ( table [ tab - pow ] ) , contrary to what was reported previously . 2mass 1108 + 68 is another l dwarf displaying statistically significant variations and no significant period . with a baseline of nearly 6 months ( figure [ 2m1108dif ] ) , the data obtained for this object represents the most extensive photometric monitoring of any l dwarf to date . though not as extensive as 2mass 1108 + 68 , 2mass 0746 + 20ab also has very good coverage ( figure [ 2m0746dif ] ) . this binary is the brightest object in our target list and is variable . the most dominant peak in the clean power spectrum ( figure [ 2m0746cln ] ) is quite high compared to other peaks and is present at a period of [email protected] hours . the power of this period is nearly 5 times higher than the noise and the phased data ( figure [ 2m0746phs ] ) shows a roughly sinusoidal light curve . @xcite present @xmath47 measurements for twelve l dwarfs , including 2mass 1439 + 19 and 2mass 1146 + 22ab from this study . the values they derive span from [email protected] to 60@xmath465 km s@xmath48 . for typical brown dwarf radii @xcite , these velocities translate to rotation periods @xmath4910 hours . because the inclination angle of the rotation axis is unknown , this period is an _ upper _ limit to the true rotation period of these objects . consequently , the 31-hour period found here is likely too long to be related to the rotation period . the first 70 days of coverage for 2mass 0746 + 20ab reveal an interesting trend ( figure [ 2m0746zoom ] ) . the data appear to have a rough saw - tooth light curve that repeat with a period of approximately 20 days . after hjd 1950 this pattern is not as prominent . it is unclear what variability source can cause a saw - tooth pattern such as this . spots and clouds should produce more gradual changes in the light curve . a flare would produce a sudden brightening , followed by a gradual dimming , the opposite to what is seen here . furthermore , @xcite estimate an orbital semi - major axis of 3.4 au , giving a period of about 18 years . therefore , both the shape and duration of the feature are not what would be expected for an eclipsing system . 2mass 1300 + 19 also has an interesting feature in its light curve ( figure [ 2m1300dif ] ) . the sequence of points around hjd=2027 ( figure [ 2m1300zoom ] ) show roughly sinusoidal variations . this span of points is approximately the same as the best period for the entire data set , 238 hours , indicating that this feature is the source of the period . the period is much longer than expected for a rotation period . it seems likely that some other cause is responsible for the feature . although the feature is reminiscent of an eclipsing binary light curve , this scenario seems unlikely . the depth of the feature implies a secondary object radius about 18% the radius of the l dwarf , roughly 3 times larger than earth . the duration suggests an orbital separation @xmath50 au . the probability that we should observe an edge - on binary system with an orbital separation @xmath50 au just as it is eclipsing is extremely small ( @xmath51 ) . furthermore , while there are stars with l and t dwarf companions at separations greater than 500 au , there are no known companions to l dwarfs beyond 10 au . it is possible that the 10-day feature in this object s light curve is related only to its surface features . the sudden creation and dissipation of a large storm could possibly produce the changes we see . a similar event happened with saturn several years ago @xcite , but over a longer dissipation timescale . however , features on jupiter and saturn are known to evolve on timescales from hours to years , depending on the features positions and rotation orientations ( beebe 2001 , private communication ) , so the timescale seen here is certainly plausible . a large storm would not only change the brightness of the object , it should also have an effect on the photometric colors . table [ tab - pow ] presents the primary clean periods and their pnr for six variable and five possibly variable l dwarfs . the only periods considered significant are those with pnr values above 3 , 2mass 0746 + 20ab and 2mass 1300 + 19 . we have discussed why we do not believe these periods to be related to the rotation period of these objects . in addition to the objects mentioned above , our sample contains several other objects ( table [ tab - sv ] ) . these objects do not have significant periods , nor do they have any interesting features in their light curves . the light curves for all objects will be found in @xcite .

the periods found for 2mass 0746 + 20ab and 2mass 1300 + 19 are unique but longer than those periods likely from rotation velocity measurements and they do not represent periodic behavior in the light curve that persists through the entire data set . the remaining variable objects show no prominent features in their light curves , suggesting even more rapid evolution of atmospheric features .

we report on the results of an-band photometric variability survey of eighteen l dwarfs . we find that seven exhibit statistically significant variations above the 95.4% confidence level with root - mean - square scatter ( including photometric errors ) between 0.010 and 0.083 mag . another five targets have variability probabilities% , suggesting that these are likely variable objects . three of the variable objects display significant peaks in a clean periodogram that are several times higher than the noise . the period for 2mass 0345 + 25 is clearly not intrinsic to the object and can be dismissed . the periods found for 2mass 0746 + 20ab and 2mass 1300 + 19 are unique but longer than those periods likely from rotation velocity measurements and they do not represent periodic behavior in the light curve that persists through the entire data set . these observations suggest that we are not observing the rotation modulation of a long - lived albedo feature . instead , rapid evolution of atmospheric features is likely causing the non - periodic variability . the remaining variable objects show no prominent features in their light curves , suggesting even more rapid evolution of atmospheric features . we argue against the existence of magnetic spots in these atmospheres and favor the idea that non - uniform condensate coverage is responsible for these variations . the magnetic reynolds number in the atmosphere of l dwarfs is too small to support the formation of magnetic spots . in contrast , silicate and iron clouds are expected to form in the photospheres of l dwarfs . inhomogeneities in such cloud decks and the evolution of the inhomogeneities can plausibly produce the observed photometric variations .

astro-ph0205305

c

we have conducted a photometric monitoring program of eighteen l dwarfs in the @xmath6 photometric filter . we find that seven of these eighteen display statistically significant variations above the 95.4% probability level and with rms scatter between 0.010 and 0.083 mag . an additional five objects have probabilities for variability @xmath180% , suggesting that these objects are possibly variable . the remaining targets have probabilities @xmath9235% , indicating that they are non - variable or have amplitudes below our detectability . only three variable l dwarfs have prominent periods in their clean power spectra that have power @xmath393 times the noise . the 24.1-hour period of 2mass 0345 + 25 is not intrinsic to the l dwarf and needs more investigation . 2mass 1300 + 19 has a 9-day section of its light curve that could be evidence for the creation and dissipation of a large storm . the source of the 31.0-hour period of 2mass 0746 + 20ab is not clear from the light curve . however , it does have a 70-day section with a puzzling saw - tooth pattern with properties unlike any that would be expected . all of these timescales are much longer than the rotation periods expected for these objects . the light curves of the other variable objects are quite random and have no dominant features . non - uniform cloud coverage with features evolving on timescales less than a few days is likely the source of the variations in these objects . indeed , we have shown that the low ionization fraction predicted by l - dwarf models and the accompanyingly low magnetic reynolds numbers strongly argue against magnetic spots as a plausible cause for the photometric variations . on the other hand silicate and iron grains condense in l - dwarf atmospheres within the photosphere . these clouds are likely responsible for the photometric variations discovered in the various studies , particularly for the later l dwarfs ( about l2 and later ) . since the thermal emission of t dwarfs is also influenced by clouds @xcite we predict that variability will also be found in the opacity window regions of these objects . further work with models and more observations are required to better understand cloud composition and dynamics . the authors wish to thank d.h . roberts , j. peterson , and b. goldman for various contributions and discussions . we also wish to acknowledge the useful comments of the referee . c.g . and m.m . acknowledge support from nasa grants nag2 - 6007 and nag5 - 8919 and nsf grants ast-9624878 and ast-0086288 . work by k.l . supported by nsf grant ast-0086487 . ackerman , a. s. , & marley , m. s. 2001 , , 556 , 872 allard , f. , hauschildt , p. h. , baraffe , i. , & chabrier , g. 1996 , , 465 , l123 allard , f. , hauschildt , p. h. , alexander , d. r. , tamanai , a. , & schweitzer , a. 2001 , , 556 , 357 bailer - jones , c. a. l. & mundt , r. 1999 , a&a , 348 , 800 bailer - jones , c. a. l. & mundt , r. 2001 , a&a , 367 , 218 bailer - jones , c. a. l. & mundt , r. 2001 , a&a , 374 , 1071 basri , g. , et al . 2000 , , 538 , 363 beebe , r. f. , barnet , c. , sada , p. v. , & murrell , a. s. , icarus , 95 , 163 berger , e. 2002 , in press ( astro - ph/0111317 ) berger , e. , et al . 2001 , , 410 , 338 bondar , n. i. 1995 , a&as , 111 , 259 burgasser , a. j. , kirkpatrick , j. d. , reid , i. n. , liebert , j. , gizis , j. e. , & brown , m. e. 2000 , , 120 , 1100 burgasser et al . 2002 , apjl , in press ( astro - ph/0205051 ) burrows , a. , et al . 1997 , , 491 , 856 burrows , a. , & sharp , c. m. 1999 , , 512 , 843 clarke , f. j. , tinney , c. g. , & covey , k. r. , , 332 , 361 fleming , t. a. , giampapa , m. s. , & schmitt , j. h. m. m. 2000 , , 533 , 372 gelino , c. r. 2002 , ph.d . dissertation , in preparation gelino , c. r. , & marley , m. s. 2000 , in asp conf . 212 , from giant planet to cool stars , ed . c. a. griffith & m. s. marley ( san francisco : asp ) , 322 gelino , c. r. , marley , m. s. , & holtzman , j. a. 2001 , to appear in the proceedings of the 12th cambridge workshop on cool stars , stellar systems , and the sun gizis , j. e. , monet , d. g. , reid , i. n. , kirkpatrick , j. d. , liebert , j. , & williams , r. j. 2000 , , 120 , 1085 haisch , b. , strong , k. t. , & rodono , m. 1991 , , 29 , 275 hammel , h. b. , & lockwood , g. w. 1997 , icarus , 129 , 466 hawley , s. l. , reid , i. n. , & gizis , j. e. 2000 , in asp conf . ser . 212 , from giant planets to cool stars , ed . c. a. griffith & m. s. marley ( san francisco : asp ) , 252 johns - krull , c. m. , & valenti , j. a. 1996 , , 459 , l95 kirkpatrick , j. d. , et al . 1999 , , 519 , 802 kirkpatrick , j. d. , et al . 2000 , , 120 , 447 kirkpatrick , j. d. , dahn , c. c. , monet , d. g. , reid , i. n. , gizis , j. e. , liebert , j. , & burgasser , a. j. 2001 , , 121 , 3235 koerner , d. w. , kirkpatrick , j. d. , mcelwain , m. w. , & bonaventura , n. r. 1999 , , 526 , l25 lodders , k. 1999 , , 519 , 793 marley , m. s. 2000 , in asp conf . 212 , from giant planets to cool stars , ed . c. a. griffith & m. s. marley ( san francisco : asp ) , 152 marley , m. s. , & ackerman , a. s. 2001 , proceedings of iau symposium 202 , `` planetary systems in the universe : observation , formation and evolution '' in press ( astro - ph/0103269 ) marley , m. s. , saumon , d. , guillot , t. , freedman , r. s. , hubbard , w. b. , burrows , a. , & lunine , j. i. 1996 , science , 272 , 1919 marley , m. s. , seager , s. , saumon , d. , lodders , k. , ackerman , a. s. , freedman , r. , & fan , x. 2002 , , 568 , 335 martn , e. l. , delfosse , x. , basri , g. , goldman , b. , forveille , t. , & zapatero osorio , m. r. 1999 , aj , 118 , 2466 martn , e. l. , zapatero osorio , m. r. , & lehto , h. j. 2001 , , 557 , 822 monet , d. et al . 1998 , usno - sa2.0 , ( u.s . naval observatory , washington dc ) parker , e. n. 1955 , , 121 , 491 press , w. h. , teukolsky , s. a. , vetterling , w. t. , & flannery , b. p. 1992 . numerical recipes in fortran 77 : the art of scientific computing ( 2d ed ; cambridge : cambridge university press ) priest , e. r. 1982 , solar magnetohydrodynamics ( dordrecht , holland : d. reidel publishing ) reid , i. n. , et al . 1999 , , 521 , 613 reid , i. n. , gizis , j. e. , kirkpatrick , j. d. , & koerner , d. w. 2001 , , 121 , 489 reid , i. n. , kirkpatrick , j. d. , gizis , j. e. , dahn , c. c. , monet , d. g. , williams , r. j. , libert , j. , & burgasser , a. j. 2000 , , 119 , 369 roberts , d. h. , lehr , j. , & dreher , j. w. 1987 , , 93 , 968 rutledge , r. e. , basri , g. , martn , e. l. , & bildsten , l. 2000 , , 538 , l141 saar , s. h. 1994 , in iau symp . 154 , infrared solar physics , ed . d. m. rabin et al . ( dordrecht : kluwer ) , 493 schubert , g. , & zhang , k. 2000 , in asp conf . ser . 212 , from giant planets to cool stars , ed . c. a. griffith & m. s. marley ( san francisco : asp ) , 210 somov , b. v. 1992 , physical processes in solar flares ( dordrecht , holland : kluwer academic publishers ) stephens , d. , marley , m. , noll , k. , & chanover , n. 2001 , , 556 , l97 tinney , c. g. 1998 , , 296 , l42 tinney , c. g. , & reid , i. n. 1998 , , 301 , 1031 tinney , c. g. , & tolley , a. j. 1999 , , 304 , 119 tsuji , t. 2001 , proceedings of the iau workshop on `` ultracool dwarfs : surveys , properties and spectral classification '' ed . h. r. a. jones & i. steele , in press tsuji , t. , ohnaka , k. , aoki , w. , & nakajima , t. 1996 , a&a , 308 , l29 westphal , j. a. , matthews , k. , & terrile , r. j. 1974 , , 188 , l111 yelle , r. v. 2000 , in asp conf . 212 , from giant planets to cool stars , ed . c. a. griffith & m. s. marley ( san francisco : asp ) , 267 2mass 0015 + 35 & l2 & 00:15:44.7 & + 35:16:03 & @xmath93 & y & 1 + 2mass 0036 + 18 & l3.5 & 00:36:15.9 & + 18:21:10 & 16.10 & & 1,2 + 2mass 0058@xmath206 & l0 & 00:58:42.5 & @xmath206:51:23 & @xmath94 & y & 1 + 2mass 0135 + 12 & l1.5 & 01:35:35.8 & + 12:05:22 & @xmath95 & y & 1 + 2mass 0345 + 25 & l0 & 03:45:43.2 & + 25:40:23 & 16.98 & & 3 + 2mass 0746 + 20ab & l0.5 & 07:46:42.5 & + 20:00:32 & 15.11 & y & 1,2 + 2mass 1029 + 16 & l2.5 & 10:29:21.6 & + 16:26:52 & @xmath96 & y & 1 + 2mass 1108 + 68 & l1 & 11:08:30.7 & + 68:30:17 & @xmath97 & y & 4 + 2mass 1146 + 22ab & l3 & 11:46:34.5 & + 22:30:53 & 17.62 & & 3 + 2mass 1300 + 19 & l1 & 13:00:42.5 & + 19:12:35 & @xmath98 & & 4 + 2mass 1338 + 41 & l2.5 & 13:38:26.1 & + 41:40:34 & @xmath96 & & 1 + 2mass 1411 + 39 & l1.5 & 14:11:17.5 & + 39:36:36 & @xmath99 & & 1 + 2mass 1412 + 16 & l0.5 & 14:12:24.4 & + 16:33:12 & @xmath100 & y & 1 + 2mass 1439 + 19 & l1 & 14:39:28.4 & + 19:29:15 & 16.02 & & 2,3 + 2mass 1506 + 13 & l3 & 15:06:54.4 & + 13:21:06 & @xmath101 & y & 4 + 2mass 1615 + 35 & l3 & 16:15:44.1 & + 35:59:00 & @xmath102 & & 1 + 2mass 1658 + 70 & l1 & 16:58:03.7 & + 70:27:01 & @xmath103 & & 4 + 2mass 2224@xmath201 & l4.5 & 22:24:43.8 & @xmath201:58:52 & @xmath104 & y & 1 2mass 0345 + 25 & 35/37 & 209/318 & 108.73 & 7/7 & @xmath3999.99 & 0.030 & 0.027 + 2mass 0746 + 20ab&38/45 & 260/421 & 150.88 & 10/12 & @xmath3999.99 & 0.010 & 0.007 + 2mass 1300 + 19 & 37/39 & 275/384 & 137.78 & 5/7 & @xmath3999.99 & 0.015 & 0.012 + 2mass 2224@xmath201 & 5/6 & 15/21 & 26.01 & 5/7 & 99.88 & 0.083 & 0.057 + 2mass 1108 + 68 & 46/52 & 394/536 & 182.80 & 5/8 & 99.75 & 0.016 & 0.016 + 2mass 0135 + 12 & 18/22 & 110/187 & 30.00 & 5/6 & 99.33 & 0.041 & 0.035 + 2mass 1658 + 70 & 10/13 & 27/38 & 31.99 & 9/14 & 97.31 & 0.024 & 0.019 + 2mass 1615 + 35 & 12/15 & 43/61 & 40.92 & 6/6 & 82.69 & 0.073 & 0.067 + 2mass 0015 + 35 & 5/9 & 21/34 & 230.31 & 6/6 & 80.82 & 0.026 & 0.024 + 2mass 0058@xmath206 & 3/3 & 11/12 & 26.95 & 5/5 & 80.23 & 0.034 & 0.028 + 2mass 1439 + 19 & 11/11 & 28/30 & 38.90 & 4/4 & 79.81 & 0.014 & 0.013 + 2mass 1338 + 41 & 27/29 & 112/140 & 123.86 & 8/9 & 77.10 & 0.039 & 0.035 + 2mass 1029 + 16 & 5/5 & 14/18 & 32.96 & 6/6 & 30.39 & 0.057 & 0.063 + 2mass 0036 + 18 & 10/18 & 36/85 & 53.00 & 6/8 & 26.66 & 0.009 & 0.010 + 2mass 1506 + 13 & 3/4 & 9/12 & 35.91 & 5/6 & 22.46 & 0.024 & 0.030 + 2mass 1412 + 16 & 8/11 & 27/39 & 84.92 & 4/4 & 11.40 & 0.018 & 0.025 + 2mass 1146 + 22ab & 10/16 & 28/48 & 36.90 & 5/5 & 0.54 & 0.034 & 0.057 + 2mass 1411 + 39 & 24/30 & 78/132 & 131.86 & 4/5 & 0.12 & 0.047 & 0.056 2mass 0746 + 20ab & [email protected] & 4.85 + 2mass 1300 + 19 & 238.@xmath469 . & 3.38 + 2mass 1108 + 68 & [email protected] & 2.55 + 2mass 1658 + 70 & [email protected] & 1.64 + 2mass 0135 + 12 & [email protected] & 1.48 + 2mass 2224@xmath201 & [email protected] & 0.71 + 2mass 1439 + 19 & [email protected] & 1.85 + 2mass 1615 + 35 & [email protected] & 1.24 + 2mass 1338 + 41 & [email protected] & 1.06 + 2mass 0015 + 35 & [email protected] & 0.85 + 2mass 0058@xmath206 & [email protected] & 0.74

we find that seven exhibit statistically significant variations above the 95.4% confidence level with root - mean - square scatter ( including photometric errors ) between 0.010 and 0.083 mag . another five targets have variability probabilities% , suggesting that these are likely variable objects . the period for 2mass 0345 + 25 is clearly not intrinsic to the object and can be dismissed .

we report on the results of an-band photometric variability survey of eighteen l dwarfs . we find that seven exhibit statistically significant variations above the 95.4% confidence level with root - mean - square scatter ( including photometric errors ) between 0.010 and 0.083 mag . another five targets have variability probabilities% , suggesting that these are likely variable objects . three of the variable objects display significant peaks in a clean periodogram that are several times higher than the noise . the period for 2mass 0345 + 25 is clearly not intrinsic to the object and can be dismissed . the periods found for 2mass 0746 + 20ab and 2mass 1300 + 19 are unique but longer than those periods likely from rotation velocity measurements and they do not represent periodic behavior in the light curve that persists through the entire data set . these observations suggest that we are not observing the rotation modulation of a long - lived albedo feature . instead , rapid evolution of atmospheric features is likely causing the non - periodic variability . the remaining variable objects show no prominent features in their light curves , suggesting even more rapid evolution of atmospheric features . we argue against the existence of magnetic spots in these atmospheres and favor the idea that non - uniform condensate coverage is responsible for these variations . the magnetic reynolds number in the atmosphere of l dwarfs is too small to support the formation of magnetic spots . in contrast , silicate and iron clouds are expected to form in the photospheres of l dwarfs . inhomogeneities in such cloud decks and the evolution of the inhomogeneities can plausibly produce the observed photometric variations .

1405.4165

i

we performed a broad - band and narrow - band ( h@xmath1 ) imaging survey of a radio galaxy field ( 4c65.22 ) at @xmath0 over the 7@xmath224@xmath23 fov ( corresponding to [email protected] mpc@xmath19 ) with moircs / suprime - cam on the subaru telescope . based on this new dataset , we find a rich cluster candidate around the radio galaxy . we also studied an environmental dependence of galaxy properties around this newly discovered structure at @xmath3 . our findings are summarized as the following . \(1 ) with the photo-@xmath16 and h@xmath1 emitter selections , we discovered a strong over - density of galaxies around 4c65.22 . we find that the cluster central region ( @xmath136@xmath5250 kpc from the density peak ) is clearly dominated by passive red - sequence galaxies without h@xmath1 emission , while the h@xmath1-emitting galaxies are preferentially located in the cluster outskirts , showing a sharp decline in the h@xmath1 emitter fraction toward the cluster center . this spatial segregation is similar to that seen in lower redshift clusters , suggesting that the newly discovered structure is a well - matured system . \(2 ) the color density and @xmath7density relations are already in place at @xmath3 . these environmental trends are mostly driven by passive red / massive galaxies residing in the cluster central region , whilst such environmental trends become much weaker when we consider only h@xmath1 emitters . this is also the case for sfr density and ssfr density relation . an excess of non - h@xmath1-emitting red - sequence galaxies in the cluster core strongly suggests that the sf activity is suppressed in the very rich environment at @xmath2 , but the sf activity amongst sf galaxies are almost independent of environment . \(3 ) there may exist a weak correlation between dust attenuation ( derived with sfr@xmath84/sfr@xmath10 ratio ) and local environment for sf galaxies at @xmath2 : galaxies in high - density environments tend to be dustier by @xmath60.51.0 mag level . however , even if we take this point into account , we can not see a detectable environmental variation in the location of the sf main sequence , consistent with recent studies . we do not find any correlation between the sfr offset from the sf main sequence ( @xmath110ms ) and @xmath43 , but we find a tentative hint that galaxies having a close companion ( at a moderate distance of @xmath5200 kpc ) tend to be more largely scattered from the sf main sequence than more isolated galaxies . the broad - band and narrow - band imaging data used in this paper are collected at the subaru telescope , which is operated by the national astronomical observatory of japan ( naoj ) . we thank the referee for reviewing our paper and providing us with useful comments which improved the paper . y.k . , k.t . , and m.h . acknowledge support from the japan society for the promotion of science ( jsps ) through jsps research fellowships for young scientists . this work was financially supported in part by a grant - in - aid for the scientific research ( nos.21340045 ; 24244015 ) by the japanese ministry of education , culture , sports and science . + _ facilities : _ . alberts , s. , pope , a. , brodwin , m. , et al . 2014 , , 437 , 437 balogh , m. , eke , v. , miller , c. , et al . 2004 , , 348 , 1355 bassett , r. , papovich , c. , lotz , j. m. , et al . 2013 , , 770 , 58 bauer , a. e. , conselice , c. j. , prez - gonzlez , p. g. , et al . 2011 , , 417 , 289 bauer , a. e. , grtzbauch , r. , jrgensen , i. , varela , j. , & bergmann , m. 2011 , , 411 , 2009 bertin , e. , & arnouts , s. 1996 , , 117 , 393 best , p. n. , lehnert , m. d. , miley , g. k. , rttgering , h. j. a. 2003 , , 343 , 1 bhringer , h. , voges , w. , huchra , j. p. , et al . 2000 , , 129 , 435 brammer , g. b. , van dokkum , p. g. , & coppi , p. 2008 , , 686 , 1503 brinchmann , j. , charlot , s. , white , s. d. m. , et al . 2004 , , 351 , 1151 brinkmann , w. , chester , m. , kollgaard , r. , et al . 1999 , , 134 , 221 brodwin , m. , stanford , s. a. , gonzalez , a. h. , et al . 2013 , , 779 , 138 buat , v. , boselli , a. , gavazzi , g. , & bonfanti , c. 2002 , , 383 , 801 bunker , a. j. , warren , s. j. , hewett , p. c. , & clements , d. l. 1995 , , 273 , 513 calzetti , d. , armus , l. , bohlin , r. c. , kinney , a. l. , koornneef , j. , & storchi - bergmann , t. 2000 , , 533 , 682 cardelli , j. a. , clayton , g. c. , & mathis , j. s. 1989 , , 345 , 245 cooke , e. a. , hatch , n. a. , muldrew , s. i. , rigby , e. e. , & kurk , j. d. 2014 , , 440 , 3262 cooper , m. c. , coil , a. l. , gerke , b. f. , et al . 2010 , , 409 , 337 cooper , m. c. , newman , j. a. , weiner , b. j. , et al . 2008 , , 383 , 1058 cucciati , o. , iovino , a. , marinoni , c. , et al . 2006 , , 458 , 39 daddi , e. , dickinson , m. , morrison , g. , et al . 2007 , , 670 , 156 dressler , a. 1980 , , 236 , 351 elbaz , d. , dickinson , m. , hwang , h. s. , et al . 2011 , , 533 , a119 elbaz , d. , daddi , e. , le borgne , d. , et al . 2007 , , 468 , 33 fassbender , r. , nastasi , a. , bhringer , h. , et al . 2011 , , 527 , l10 galametz , a. , stern , d. , pentericci , l. , et al . 2013 , , 559 , a2 galametz , a. , stern , d. , stanford , s. a. , et al . 2010 , , 516 , a101 garn , t. , et al . 2010 , , 402 , 2017 garn , t. , & best , p. n. 2010 , , 409 , 421 gobat , r. , daddi , e. , onodera , m. , et al . 2011 , , 526 , a133 gmez , p. l. , et al . 2003 , , 584 , 210 goto , t. , et al . 2003 , , 55 , 757 greene , c. r. , gilbank , d. g. , balogh , m. l. , et al . 2012 , , 425 , 1738 grtzbauch , r. , bauer , a. e. , jrgensen , i. , & varela , j. 2012 , , 423 , 3652 grtzbauch , r. , conselice , c. j. , bauer , a. e. , et al . 2011 , , 418 , 938 gunn , j. e. , & stryker , l. l. 1983 , , 52 , 121 hayashi , m. , kodama , t. , koyama , y. , et al . 2014 , , 439 , 2571 hayashi , m. , kodama , t. , tadaki , k .- , koyama , y. , & tanaka , i. 2012 , , 757 , 15 hayashi , m. , kodama , t. , koyama , y. , tadaki , k .- i . , & tanaka , i. 2011 , , 415 , 2670 hayashi , m. , kodama , t. , koyama , y. , tanaka , i. , shimasaku , k. , & okamura , s. 2010 , , 402 , 1980 hatch , n. a. , kurk , j. d. , pentericci , l. , et al . 2011 , , 415 , 2993 hilton , m. , lloyd - davies , e. , stanford , s. a. , et al . 2010 , , 718 , 133 hwang , h. s. , elbaz , d. , dickinson , m. , et al . 2011 , , 535 , a60 ibar , e. , sobral , d. , best , p. n. , et al . 2013 , , 434 , 3218 ichikawa , t. , et al . 2006 , , 6269 , 38 ideue , y. , nagao , t. , taniguchi , y. , et al . 2009 , , 700 , 971 iye , m. , et al . 2004 , , 56 , 381 kajisawa , m. , ichikawa , t. , yamada , t. , et al . 2010 , , 723 , 129 kajisawa , m. , kodama , t. , tanaka , i. , yamada , t. , & bower , r. 2006 , , 371 , 577 kashino , d. , silverman , j. d. , rodighiero , g. , et al . 2013 , , 777 , l8 kennicutt , r. c. , jr . 1998 , , 36 , 189 kennicutt , r. c. , jr . , & kent , s. m. 1983 , , 88 , 1094 kinney , a. l. , calzetti , d. , bohlin , r. c. , et al . 1996 , , 467 , 38 kodama , t. , hayashi , m. , koyama , y. , et al . 2013 , iau symposium , 295 , 74 kodama , t. , tanaka , i. , kajisawa , m. , et al . 2007 , , 377 , 1717 kodama , t. , balogh , m. l. , smail , i. , bower , r. g. , & nakata , f. 2004 , , 354 , 1103 kodama , t. , smail , i. , nakata , f. , okamura , s. , & bower , r. g. 2001 , , 562 , l9 kodama , t. , arimoto , n. , barger , a. j. , & aragon - salamanca , a. 1998 , , 334 , 99 kollgaard , r. i. , feigelson , e. d. , laurent - muehleisen , s. a. , et al . 1995 , , 449 , 61 kollgaard , r. i. , brinkmann , w. , chester , m. m. , et al . 1994 , , 93 , 145 koyama , y. , smail , i. , kurk , j. , et al . 2013 , , 434 , 423 koyama , y. , kodama , t. , tadaki , k .- i . , et al . 2013 , , 428 , 1551 koyama , y. , kodama , t. , nakata , f. , shimasaku , k. , & okamura , s. 2011 , , 734 , 66 koyama , y. , kodama , t. , shimasaku , k. , hayashi , m. , okamura , s. , tanaka , i. , & tokoku , c. 2010 , , 403 , 1611 koyama , y. , kodama , t. , tanaka , m. , shimasaku , k. , & okamura , s. 2007 , , 382 , 1719 kurk , j. , cimatti , a. , zamorani , g. , et al . 2009 , , 504 , 331 kurk , j. d. , pentericci , l. , rttgering , h. j. a. , & miley , g. k. 2004 , , 428 , 793 kurk , j. d. , rttgering , h. j. a. , pentericci , l. , et al . 2000 , , 358 , l1 lawrence , a. , warren , s. j. , almaini , o. , et al . 2007 , , 379 , 1599 lin , l. , jian , h .- y . , foucaud , s. , et al . 2014 , , 782 , 33 matsuda , y. , smail , i. , geach , j. e. , et al . 2011 , , 416 , 2041 muzzin , a. , wilson , g. , demarco , r. , et al . 2013 , , 767 , 39 muzzin , a. , wilson , g. , yee , h. k. c. , et al . 2012 , , 746 , 188 lacy , m. , hill , g. j. , kaiser , m .- e . , & rawlings , s. 1993 , , 263 , 707 lewis , i. , et al . 2002 , , 334 , 673 li , i. h. , glazebrook , k. , gilbank , d. , et al . 2011 , , 411 , 1869 lidman , c. , rosati , p. , tanaka , m. , et al . 2008 , , 489 , 981 madau , p. , ftac13erguson , h. c. , dickinson , m. e. , et al . 1996 , , 283 , 1388 mcgee , s. l. , balogh , m. l. , wilman , d. j. , et al . 2011 , , 413 , 996 miyazaki , s. , et al . 2002 , , 54 , 833 nastasi , a. , fassbender , r. , bhringer , h. , et al . 2011 , , 532 , l6 newman , a. b. , ellis , r. s. , andreon , s. , et al . 2013 , arxiv:1310.6754 noeske , k. g. , weiner , b. j. , faber , s. m. , et al . 2007 , , 660 , l43 ouchi , m. , et al . 2004 , , 611 , 660 patel , s. g. , kelson , d. d. , holden , b. p. , franx , m. , & illingworth , g. d. 2011 , , 735 , 53 papovich , c. , momcheva , i. , willmer , c. n. a. , et al . 2010 , , 716 , 1503 park , c. , & hwang , h. s. 2009 , , 699 , 1595 peng , y .- j . , lilly , s. j. , renzini , a. , & carollo , m. 2012 , , 757 , 4 peng , y .- j . , lilly , s. j. , kova , k. , et al . 2010 , , 721 , 193 price , s. h. , kriek , m. , brammer , g. b. , et al . 2013 , arxiv:1310.4177 rodighiero , g. , cimatti , a. , gruppioni , c. , et al . 2010 , , 518 , l25 saintonge , a. , tacconi , l. j. , fabello , s. , et al . 2012 , , 758 , 73 salpeter , e. e. 1955 , , 121 , 161 santini , p. , fontana , a. , grazian , a. , et al . 2009 , , 504 , 751 santos , j. s. , altieri , b. , popesso , p. , et al . 2013 , , 433 , 1287 santos , j. s. , fassbender , r. , nastasi , a. , et al . 2011 , , 531 , l15 schlegel , d. j. , finkbeiner , d. p. , & davis , m. 1998 , , 500 , 525 scoville , n. , arnouts , s. , aussel , h. , et al . 2013 , , 206 , 3 shimakawa , r. , et al . , 2014 , mnras , submitted smail , i. , geach , j. e. , swinbank , a. m. , et al . 2014 , , 782 , 19 sobral , d. , smail , i. , best , p. n. , et al . 2013 , , 428 , 1128 sobral , d. , best , p. n. , matsuda , y. , et al . 2012 , , 420 , 1926 sobral , d. , best , p. n. , smail , i. , geach , j. e. , cirasuolo , m. , garn , t. , & dalton , g. b. 2011 , , 411 , 675 stanford , s. a. , brodwin , m. , gonzalez , a. h. , et al . 2012 , , 753 , 164 steidel , c. c. , adelberger , k. l. , shapley , a. e. , et al . 2005 , , 626 , 44 stott , j. p. , smail , i. , edge , a. c. , et al . 2007 , , 661 , 95 suzuki , r. , et al . 2008 , , 60 , 1347 tacconi , l. j. , neri , r. , genzel , r. , et al . 2013 , , 768 , 74 tadaki , k. i. , kodama , t. , tanaka , i. , et al . 2013 , , 778 , 114 tadaki , k. i. , kodama , t. , ota , k. , et al . 2012 , , 423 , 2617 tadaki , k. i. , kodama , t. , koyama , y. , et al . 2011 , , 63 , 437 tanaka , i. , breuck , c. d. , kurk , j. d. , et al . 2011 , , 63 , 415 tanaka , m. , finoguenov , a. , mirkazemi , m. , et al . 2013 , , 65 , 17 tanaka , m. , finoguenov , a. , & ueda , y. 2010 , , 716 , l152 tanaka , m. , goto , t. , okamura , s. , shimasaku , k. , & brinkmann , j. 2004 , , 128 , 2677 tran , k .- v . h. , papovich , c. , saintonge , a. , et al . 2010 , , 719 , l126 venemans , b. p. , rttgering , h. j. a. , miley , g. k. , et al . 2007 , , 461 , 823 venemans , b. p. , kurk , j. d. , miley , g. k. , et al . 2002 , , 569 , l11 villar , v. , gallego , j. , prez - gonzlez , p. g. , pascual , s. , noeske , k. , koo , d. c. , barro , g. , & zamorano , j. 2008 , , 677 , 169 vulcani , b. , poggianti , b. m. , finn , r. a. , et al . 2010 , , 710 , l1 whitaker , k. e. , van dokkum , p. g. , brammer , g. , & franx , m. 2012 , , 754 , l29 wijesinghe , d. b. , hopkins , a. m. , brough , s. , et al . 2012 , , 423 , 3679 wuyts , s. , frster schreiber , n. m. , nelson , e. j. , et al . 2013 , , 779 , 135 wuyts , s. , frster schreiber , n. m. , van der wel , a. , et al . 2011 , , 742 , 96 yagi , m. , kashikawa , n. , sekiguchi , m. , doi , m. , yasuda , n. , shimasaku , k. , & okamura , s. 2002 , , 123 , 66 zeimann , g. r. , stanford , s. a. , brodwin , m. , et al . 2013 , , 779 , 137 ziparo , f. , popesso , p. , finoguenov , a. , et al . 2013 , , 2575

we find that h emitters are located in the outskirts of the density peak ( cluster core ) dominated by passive red - sequence galaxies . density or ssfr density relations amongst sf galaxies , and the location of the sf main sequence does not significantly change with environment . nevertheless , we find a tentative hint that star - bursting galaxies ( up - scattered objects from the main sequence ) are preferentially located in a small group at-mpc away from the main body of the cluster .

we report the discovery of a strong over - density of galaxies in the field of a radio galaxy at ( 4c65.22 ) based on our broad - band and narrow - band ( h ) photometry with subaru telescope . we find that h emitters are located in the outskirts of the density peak ( cluster core ) dominated by passive red - sequence galaxies . this resembles the situation in lower - redshift clusters , suggesting that the newly discovered structure is a well - evolved rich galaxy cluster at . our data suggest that the color density and stellar mass density relations are already in place at , mostly driven by the passive red massive galaxies residing within kpc from the cluster core . these environmental trends almost disappear when we consider only star - forming ( sf ) galaxies . we do not find sfr density or ssfr density relations amongst sf galaxies , and the location of the sf main sequence does not significantly change with environment . nevertheless , we find a tentative hint that star - bursting galaxies ( up - scattered objects from the main sequence ) are preferentially located in a small group at-mpc away from the main body of the cluster . we also argue that the scatter of the sf main sequence could be dependent on the distance to the nearest neighboring galaxy .

1409.5810

i

we have examined the abundance patterns found in stars with high levels of enrichment as indicated by their enhanced [ eu / fe ] ratios . our study differs from the survey of @xcite by deriving abundances from higher - resolution spectra that cover a wider wavelength range . thirteen of the 313 metal - poor stars analyzed by @xcite are identified as members of the class of @xmath0-ii stars after correcting for offsets in the derived [ eu / fe ] ratios ( [ eu / fe ] @xmath150.8 ) . four of these stars are red giants whose high levels of enhancement were known previously . we identify six new subgiants ( including the msto phase ) and three new rhb members of this class . @xcite also identified one such star on the main sequence . once limited to the realm of red giants , highly -- enhanced stars are now known all across a broad range of stellar evolutionary states . the first highly -- enhanced star discovered , , was also enhanced in c and n , which signaled a possible connection between these chemical signatures . only 2 of the 13 stars in our sample ( including ) are enhanced in c and n , however , offering no compelling evidence for such a connection . we also find no compelling evidence to suggest that a disproportionately high fraction of highly -- enhanced stars are members of binary or multiple star systems , confirming the conclusions of a dedicated radial velocity survey by @xcite . the dispersion in the [ sr / ba ] and [ sr / eu ] ratios is larger than the dispersion in the [ ba / eu ] or [ yb / eu ] ratios , indicating that the robust pattern does not extend to the elements between the first and second peaks even within the class of highly -- enhanced stars . we compare the light - element ( @xmath28 30 ) abundance pattern in each highly -- enhanced star with the light - element abundance pattern in a comparison set of stars that have similar stellar parameters but lack high levels of enhancement . this test reveals no obvious light - element abundance signatures that are unique to the highly -- enhanced stars . the nucleosynthetic sites responsible for producing the large enhancement apparently did not produce any detectable light - element abundance signatures distinct from normal core - collapse supernovae responsible for much of the early metal production in the universe .

we also analyze four previously - known-process - enhanced metal - poor red giants . from this sample of 13 stars , we draw the following conclusions . ( 1 ) high levels of-process enhancement are found in a broad range of stellar evolutionary states , reaffirming that this phenomenon is not associated with a chemical peculiarity of red giant atmospheres . ( 2 ) only 1 of 10 stars observed at multiple epochs shows radial velocity variations , reaffirming that stars with high levels of-process enhancement are not preferentially found among binaries . ( 3 ) only 2 of the 13 stars are highly - enhanced in c and n , indicating that there is no connection between high levels of-process enhancement and high levels of c and n. ( 4 ) the dispersions in [ sr / ba ] and [ sr / eu ] are larger than the dispersions in [ ba / eu ] and [ yb / eu ] , suggesting that the elements below the second-process peak do not always scale with those in the rare earth domain , even within the class of highly--process - enhanced stars . ( 5 ) the light - element ( 12 30 ) abundances of highly--process - enhanced stars are indistinguishable from those with normal levels of-process material at the limit of our data , 3.5 per cent ( 0.015 dex ) on average . the nucleosynthetic sites responsible for the large-process enhancements did not produce any detectable light - element abundance signatures distinct from normal core - collapse supernovae . [ firstpage ] nuclear reactions , nucleosynthesis , abundances stars : abundances stars : atmospheres stars : population ii

we report the discovery of nine metal - poor stars with high levels of-process enhancement (.81 [ eu / fe ] .13 ) , including six subgiants and three stars on the red horizontal branch . we also analyze four previously - known-process - enhanced metal - poor red giants . from this sample of 13 stars , we draw the following conclusions . ( 1 ) high levels of-process enhancement are found in a broad range of stellar evolutionary states , reaffirming that this phenomenon is not associated with a chemical peculiarity of red giant atmospheres . ( 2 ) only 1 of 10 stars observed at multiple epochs shows radial velocity variations , reaffirming that stars with high levels of-process enhancement are not preferentially found among binaries . ( 3 ) only 2 of the 13 stars are highly - enhanced in c and n , indicating that there is no connection between high levels of-process enhancement and high levels of c and n. ( 4 ) the dispersions in [ sr / ba ] and [ sr / eu ] are larger than the dispersions in [ ba / eu ] and [ yb / eu ] , suggesting that the elements below the second-process peak do not always scale with those in the rare earth domain , even within the class of highly--process - enhanced stars . ( 5 ) the light - element ( 12 30 ) abundances of highly--process - enhanced stars are indistinguishable from those with normal levels of-process material at the limit of our data , 3.5 per cent ( 0.015 dex ) on average . the nucleosynthetic sites responsible for the large-process enhancements did not produce any detectable light - element abundance signatures distinct from normal core - collapse supernovae . [ firstpage ] nuclear reactions , nucleosynthesis , abundances stars : abundances stars : atmospheres stars : population ii

1412.5674

i

after four years of nearly continuous photometric monitoring and thousands of planet discoveries ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , the primary _ kepler _ mission came to an end in in may 2013 with the failure of the second of four reaction wheels used to stabilize the spacecraft . without at least three functioning reaction wheels , the spacecraft is unable to achieve the fine pointing necessary for high photometric precision on the original target field . however , an extended mission called k2 was enabled by pointing along the ecliptic plane and balancing the spacecraft against solar radiation pressure to mitigate the instability caused by the failed reaction wheels . the recently extended k2 mission enables renewed opportunities for transit science on a new set of bright target stars , albeit with somewhat reduced photometric precision compared to the original _ kepler _ mission @xcite . searching for transiting exoplanets around bright , nearby stars is important because measuring the precise masses and radii of transiting planets allows for characterization of their interior structures and atmospheres @xcite . this is particularly desirable for planets with masses intermediate to those of the earth and uranus , commonly referred to as super earths , because no such planet exists in our solar system @xcite . however , while the radii of _ kepler _ planets are often measured to high precision @xcite , their masses are generally unknown because the host stars are faint ( @xmath10 ) and exposure times needed for radial velocity ( rv ) measurements are prohibitive for all but the brightest _ kepler _ planet candidates ( e.g. * ? ? ? * ; * ? ? ? preparations for the extended two wheeled _ kepler _ mission included a 9day test of the new observing mode in february of 2014 . after the data were released to the public , ( * ? ? ? * hereafter vj14 ) presented a photometric reduction technique that accounts for the motion of the spacecraft , improves photometric precision of raw k2 data by a factor of 25 , and enables photometric precision comparable to that of the original _ kepler _ mission . while the data collected during the engineering test were intended primarily as a test of the new spacecraft operating mode , inspection of light curves produced with this technique nonetheless revealed a single transit event in engineering data taken of hip116454 . in this paper , we provide an analysis of that light curve along with archival and follow up spectroscopy , archival and adaptive optics imaging , radial velocity measurements from the harps - n spectrograph , and photometric observations from the wide angle search for planets ( wasp ) survey and the microvariability and oscillations of stars ( most ) space telescope . these measurements allow us to verify and characterize the first planet discovered by the two - wheeled _ kepler _ mission , a new transiting super - earth orbiting the bright , nearby , high - proper - motion k dwarf hip116454 .

we report the first planet discovery from the two wheeled _ kepler _ ( k2 ) mission : hip116454b . radial velocity observations with the harps - n spectrograph reveal a 1.33 m planet in a 9.1 day orbit , consistent with the transit depth , duration , and ephemeris . follow up photometric measurements from the most satellite

we report the first planet discovery from the two wheeled _ kepler _ ( k2 ) mission : hip116454b . the host star hip116454 is a bright ( , ) k1dwarf with high proper motion , and a parallax based distance of pc . based on high - resolution optical spectroscopy , we find that the host star is metal - poor with [ fe / h ] , and has a radius r and mass m . the star was observed by the _ kepler _ spacecraft during its two - wheeled concept engineering test in february 2014 . during the 9 days of observations , k2 observed a single transit event . using a new k2 photometric analysis technique we are able to correct small telescope drifts and recover the observed transit at high confidence , corresponding to a planetary radius of r . radial velocity observations with the harps - n spectrograph reveal a 1.33 m planet in a 9.1 day orbit , consistent with the transit depth , duration , and ephemeris . follow up photometric measurements from the most satellite confirm the transit observed in the k2 photometry and provide a refined ephemeris , making hip116454b amenable for future follow up observations of this latest addition to the growing population of transiting super - earths around nearby , bright stars .

astro-ph0008467

r

a low resolution x - ray image , covering all of the radio emitting regions and with selected vla radio contours ( from prm ) overlaid , is shown in fig . 1 , while a full resolution x - ray image of the nucleus and structure to the west of the nucleus is shown in fig . the brightest x - ray source is associated with the nucleus of the galaxy . the position of this source , as measured with the chandra aspect system , is within 2@xmath18 of the radio and optical nuclear positions given by prm . the nucleus is so bright in x - rays that it suffers from strong `` pile up '' , so no useful spatial or spectroscopic information can be obtained from this exposure ; a chandra observation with a shorter frame time is scheduled to obtain a reliable nuclear spectrum . a linear feature , visible in both figures , extends 19 ( 110 kpc ) westward from the nucleus and is spatially coincident with the faint radio jet ( prm ) ; we shall refer to this feature as the `` x - ray jet '' . the x - ray jet `` points '' at the western hot spot , which is 42 ( 240 kpc ) from the nucleus . when the nuclear x - ray source is shifted slightly to coincide with the nuclear radio source , the peak of the x - ray emission from the hot spot is within 1@xmath18 of its radio peak . there is also evidence for faint , diffuse x - ray emission around the nucleus and extending @xmath16 1@xmath22 from it , but more sensitive observations are needed to confirm this component . faint x - ray emission extends eastwards from the nucleus to the two eastern radio hot spots , 31 and 34 from the nucleus ( fig . this faint x - ray emission is seen to brighten somewhat within @xmath16 1@xmath22 of these hot spots . there are also four compact x - ray sources within the brightest radio contour around the eastern hot spots ; none of these x - ray sources coincides with either radio hot spot . lastly , we point out a faint ( @xmath30 counts above the background ) , compact x - ray source 323@xmath18 e of the nucleus at @xmath13 = 05@xmath31 20@xmath32 [email protected] , @xmath34 = 45@xmath6 47@xmath22 44@xmath18 ( j2000 ) . this x - ray source is beyond the eastern radio lobe , but it lies in p.a . 101@xmath6 from the nucleus , a direction which is precisely opposite to the direction to the western hot spot ( p.a . 281@xmath6 ) . examination of the digital sky survey reveals a faint point source within @xmath16 1@xmath18 of this position , almost at the limit of the serc - j survey ( we estimate @xmath35 ) , and marginally detected in the second epoch southern ( uk schmidt ) survey . it is unclear whether this compact x - ray source is related to pictor a. images of the western hot spot at radio ( prm ) , optical ( rser 1989 ; prm ) and x - ray wavelengths with similar resolutions are shown in fig . 3 . as described in the introduction , the radio and optical hot spots have a very similar morphology . in a higher resolution ( 045 @xmath8 009 ) radio image ( fig . 19 of prm ) , the bright `` core '' is found to have a sharp leading ( i.e. away from the nucleus ) edge , with a slower decline on the side towards the nucleus . behind this bright region is a linear feature elongated in p.a . 32@xmath6 ( fig . 3 ) , referred to as the `` filament '' by rser & meisenheimer ( 1987 ) and the `` plateau '' by prm . the overall x - ray morphology is remarkably similar to the radio and optical , with both the `` core '' and the `` filament '' detected . much of the apparent elongation of the brighter part of the `` core '' of the x - ray hot spot ( fig . 3 ) reflects the shape of the point spread function ( psf ) . 4 compares profiles along the major and minor axes of the hot spot through both the hot spot and the model psf at the location of the hot spot . at half maximum , the hot spot is somewhat wider than the model , but the model psf does not include broadening by imperfections in the aspect solution . in order to assess the reliability of the model psf , we have compared a compact x - ray source ( visible in fig . 1 ) some 152@xmath18 from the nucleus in p.a . 40@xmath6 with the chandra model psf at this location . the observed profile of this source ( which is at a similar distance from the aim point as the hot spot ) is in good agreement with the model psf , but broader by 02 at the half power point . this number is similar to the excess broadening of the hot spot over the model psf along its minor axis ( fig . 4 ) , suggesting that the brighter part of the hot spot is unresolved in this direction . the excess fwhm of the hot spot over the psf along its major axis ( fig . 4 ) is somewhat larger . nevertheless , we feel that caution is necessary , since other effects ( e.g. the motion of the source on the detector during an observation ) could lead to further broadening compared with the model psf . the conservative conclusion is that the brightest part of the `` core '' is marginally resolved or unresolved in x - rays . there are , however , clear indications of structure in the hot spot at lower brightness levels . as in the radio , the x - ray core has a sharper edge away from the nucleus than towards it . a narrow `` ridge '' extends @xmath2 35 ( 3.4 kpc ) in p.a . 108@xmath6 ( the general direction towards the nucleus ) from the hot spot peak . a weaker feature some 6@xmath18 ( 5.7 kpc ) ssw of the core and elongated towards p.a . 279@xmath6 , is seen in both the radio and x - ray images . in conclusion , when the small differences in resolution of the x - ray and radio images ( fig . 3 ) are taken into account , the x - ray and radio morphologies are remarkably similar . this morphological similarity indicates that the x - ray , optical and radio - emitting regions are physically co - spatial and argues that the x - ray emission does not originate from a bow shock ahead of the radio hot spot . the x - ray spectrum of the hot spot has been modelled in various ways . a hot plasma with solar abundances and in collisional equilibrium ( `` raymond - smith '' model ) provides a poor fit to the data ( table 1 ) and can be ruled out . if the abundances of all elements heavier than helium are allowed to vary , we find that an abundance of @xmath36 10 per cent solar is needed for this thermal model to provide an acceptable description of the data . however , this model ( table 1 ) requires a hydrogen column well below the galactic value of n@xmath37 = 4.2 @xmath8 10@xmath38 atoms @xmath39 towards pictor a ( heiles & cleary 1979 ) , and is thus implausible . fixing the column at the galactic value while allowing the abundances to vary leads to a poor fit ( table 1 ) . further , we shall argue in section 3.2.3 that a thermal model can be excluded on grounds that the required gas density is so high that the radio emission would be faraday depolarized , contrary to observation . lastly , a power law of photon index @xmath0 = 2.07@xmath40 absorbed by a column density of solar abundance gas n@xmath37 = ( 7.1@xmath41 ) @xmath8 10@xmath38 atoms @xmath39 provides an excellent description of the spectrum ( table 1 , fig . 5 ) this column density is only slightly greater than the galactic column density towards pictor a , suggesting that the interstellar medium of our galaxy is responsible for most of the observed absorption . the unabsorbed flux and luminosity of the western hot spot in the 2 - 10 kev band are 3.1 @xmath8 10@xmath42 erg @xmath39 s@xmath10 and 1.7 @xmath8 10@xmath43 erg s@xmath10 , respectively . we first evaluate the thermal model . if we assume a representative intrinsic dimension of 1.9 @xmath8 0.9 @xmath8 0.9 kpc ( i.e. 2@xmath18 @xmath8 1@xmath18 @xmath8 1@xmath18 ) , as suggested for the bright `` core '' by the x - ray image ( figs 3 and 4 ) , the required gas density for the best fitting raymond - smith model is n@xmath44 @xmath2 3 @xmath45 . because the x - rays come from the same general region of space as the radio and optical emission ( fig . 3 ) , we may estimate the magnetic field in this putative thermal gas from the synchrotron emission . for an equipartition magnetic field of 4.7 @xmath8 10@xmath46 gauss ( obtained assuming a total cosmic ray energy equal to twice that of the electrons , @xmath13 = 0.74 [ meisenheimer , yates & rser 1997 ] , lower and upper cut - off frequencies 10@xmath47 and 10@xmath17 hz , respectively , and an emitting volume corresponding to the size of the radio core - 760 @xmath8 190 @xmath8 190 pc [ 08 @xmath8 02 @xmath8 02 ] ) , the rotation measure through the hot spot is expected to be @xmath2 6 @xmath8 10@xmath48 rad m@xmath49 . if the larger volume adopted above for the x - ray source is used to calculate the equipartition field , a value of 1.4 @xmath8 10@xmath46 gauss and a rotation measure through the hot spot of @xmath2 2 @xmath8 10@xmath48 rad m@xmath49 are found . in contrast , the high polarization observed at 6 cm implies a rotation measure internal to the hot spot @xmath12 900 rad m@xmath49 ( n@xmath44 @xmath12 0.014 @xmath45 ) , a factor of @xmath2 200 lower than required for thermal emission . if the 20 cm polarization is used , the upper limit on rotation measure and density are an order of magnitude smaller , but the hot spot is not well resolved at this wavelength . we thus conclude that our upper limit to the gas density renders a thermal model untenable . this conclusion could be wrong if either a ) the magnetic field has a preferred direction but many reversals ; such a field structure can provide the high observed synchrotron polarization but gives little faraday rotation , or b ) the thermal gas is actually in small , dense clumps with a small covering factor . we favor neither of these : the field structure of a ) is physically implausible , and it is very improbable that thermal gas of density 3 @xmath45 , let alone the higher density required if the gas is clumped , exists 240 kpc from the pictor a galaxy . another argument for a low gas density in the hot spot comes from the photoelectrically absorbing column . most or all of this column comes from gas in our galaxy ; any contribution from other regions is @xmath12 3 @xmath8 10@xmath38 atoms @xmath39 ( table 1 ) . if spread uniformly throughout the hot spot `` core '' of average diameter @xmath16 1 kpc , the density is @xmath12 0.1 @xmath45 ( as long as electrons are not stripped from the k shells of the relevant elements ) , a factor of 30 below the density needed for thermal emission . in summary , our finding ( section 3.2.2 ) that a thermal model provides a poor description of the x - ray spectrum , and the upper limits to the gas density from the limits on faraday depolarization and the absorbing column , rule out a thermal model of the x - rays from the hot spot we conclude that the x - rays are non - thermal in origin and discuss relevant models in section 4.2.2 . the x - ray jet extends 19 ( 110 kpc ) westward from the nucleus in p.a . 281@xmath6 ( fig . this direction is only 1@xmath6 away from that quoted for the radio jet out to 3@xmath22 ( 170 kpc ) from the nucleus ( prm ) . such a difference in p.a . is within the errors of measurement , so we can conclude that the x - ray and radio jets are coincident . the profile of x - ray emission along the jet , shown in fig . 6 , consists of a number of ` knots ' , the brightest of which is @xmath50 from the nucleus . in section 4.1 , we shall argue that the western radio lobe is the nearer . the ratio of the x - ray fluxes of the western and eastern jets , using the brightest part of the western jet , is more than a factor of 10 ( fig . 6 ) , suggesting relativistic boosting , as discussed in section 4.3.2 . we have compared the transverse profiles across the jet with the expected psf . after deconvolution from the psf , the jet is found to be transversely extended . the width of the jet varies somewhat along its length , but its typical fwhm = 20 ( 1.9 kpc ) . we are confident of this transverse extent because : a ) the profile of the compact source 152@xmath18 from the nucleus in p.a . 40@xmath6 agrees well with the expected psf at its location ( section 3.2.1 ) , and b ) the linear feature that results from the ccd readout of the strong nuclear source gives a measure of the 1d psf at the nucleus ; this feature is much narrower than the jet . these arguments show that the measured jet width is not a result of poor aspect solution or focus . the jet is so faint in the radio that it is difficult to measure its width . prm state `` no accurate estimate of the jet s width is possible , but it is clearly not greatly resolved by the 75 beam '' . thus the upper limit to the radio width is consistent with the x - ray width . given the low count rate , the background begins to dominate above 2.5 kev . the same models as used for the hot spot were tried for the jet ( table 2 ) . the raymond - smith thermal models provide a poor fit to the spectrum , even when the metal abundance is a free parameter . an absorbed power - law model provides an excellent description of the spectrum of the jet ( fig . the absorbing column density ( @xmath51 = 5.8@xmath52 @xmath8 10@xmath38 atoms @xmath39 ) and photon index ( @xmath0 = 1.94@xmath3 ) are similar to those found for the hot spot . again we conclude that most of the absorption occurs in the interstellar medium of our galaxy . the unabsorbed 2 - 10 kev flux and luminosity of the jet are 2.5 @xmath8 10@xmath53 erg @xmath39 s@xmath10 and 1.4 @xmath8 10@xmath54 erg s@xmath10 , respectively . even if the metal abundance is left as a free parameter , a raymond - smith thermal plasma model provides a poor fit to the jet s spectrum ( section 3.3.2 , table 2 ) . since there is no information on the radio polarization of the jet , we can not argue against a thermal model on grounds of internal faraday depolarization , as we did for the western hot spot . the x - ray absorbing column within the jet must be @xmath36 8.4 @xmath8 10@xmath38 atoms @xmath39 ( the maximum allowed column [ table 2 ] minus the galactic column ) , which implies a density n@xmath55 @xmath12 0.15 @xmath45 . for the observed x - ray emission to be thermal , the average density of hot gas in the jet ( taken to be a cylinder of radius 1@xmath18 and length 19 ) is n@xmath55 @xmath2 0.05 @xmath45 , compatible with the limits from the absorbing column . thus the only argument against thermal emission is the poor description of the spectrum by a raymond - smith model . we will discuss non - thermal models for the jet in section 4.3.2 .

x - ray emission is detected from the nucleus , a 19 ( 110 kpc ) long jet to the west of the nucleus , the western radio hot spot some 42 ( 240 kpc ) from the nucleus , and the eastern radio lobe . the x - ray jet coincides with a weak radio jet and is laterally extended by 20 ( 1.9 kpc ) .

we report x - ray observations of the nearby , powerful radio galaxy pictor a with the chandra observatory and optical and near uv observations of its western radio hot spot with the hubble space telescope . x - ray emission is detected from the nucleus , a 19 ( 110 kpc ) long jet to the west of the nucleus , the western radio hot spot some 42 ( 240 kpc ) from the nucleus , and the eastern radio lobe . the morphology of the western hot spot is remarkably similar to that seen at radio and optical wavelengths , where the emission is known to be synchrotron radiation . the x - ray spectrum of the hot spot is well described by an absorbed power law with photon index = 2.07 0.11 . the x - ray jet coincides with a weak radio jet and is laterally extended by 20 ( 1.9 kpc ) . the observed jet is up to 15 times brighter in x - rays than any counter jet , a difference ascribed to relativistic boosting as the western radio lobe is probably the closer . the jet s spectrum is well modelled by an absorbed power law with = 1.94 and poorly fitted by a raymond - smith thermal plasma model . the emission processes responsible for the x - rays are discussed in detail . the radio - optical spectrum of the hot spot breaks or turns down at 10 hz , and its x - ray spectrum is not a simple extension of the radio - optical spectrum to higher frequencies . thermal models for the hot spot s x - ray emission are ruled out . synchrotron self - compton models involving scattering from the _ known _ population of electrons give the wrong spectral index for the hot spot s x - ray emission and are also excluded . a composite synchrotron plus synchrotron self - compton model can match the x - ray observations but requires similar contributions from the two components in the chandra band . we show that the hot spot s x - ray emission could be synchrotron self - compton emission from a hitherto unobserved population of electrons emitting at low radio frequencies , but do not favor this model in view of the very weak magnetic field required . an inverse compton model of the jet , in which it scatters microwave background photons but moves non - relativistically , requires a magnetic field a factor of 30 below equipartition , and ad hoc conditions to explain why the radio lobes are fainter than the jet in x - rays but brighter in the radio . these problems are alleviated if the jet moves relativistically , but models with an equipartition field require an implausibly small angle ( ) between the jet and the line of sight . a model with 23 and a field a factor of 6 below equipartition seems viable . synchrotron radiation is an alternative process for the x - ray emission . the expected synchrotron spectrum from relativistic electrons accelerated by strong shocks and subject to synchrotron radiation losses is in very good agreement with that observed for both the hot spot and jet . the possibility that the relativistic electrons result via photo - pion production by high energy protons accelerated in shocks ( a ` proton induced cascade ' ) is briefly discussed .

astro-ph0008467

c

the projected distance , d@xmath56 , of the w radio hot spot of pictor a from the nucleus is larger than that , d@xmath55 , of the e radio hot spots . this observation is consistent with the w radio lobe being the nearer one , since the extra light travel time to the more distant lobe implies that it is seen at an earlier phase in its motion away from the nucleus and thus appears closer to the nucleus . further , the east lobe is more depolarized than the west at long radio wavelengths ( prm ) , again suggesting that the w lobe is the nearer ( laing 1988 ) . both the radio and x - ray jets of pictor a are seen on the w side of the nucleus . these considerations strongly suggest that the jet sidedness is a result of relativistic boosting . the angle of the source axis to the line of sight is , of course , unknown , but can be estimated from d@xmath56 and d@xmath55 if the source is assumed to be intrinsically symmetric , since @xmath57 where @xmath58 = v / c , v is the velocity with which the hot spots are receding from the nucleus and @xmath5 is the angle between the radio axis and our line of sight . a recent study ( arshakian & longair 2000 ) has found the mean value of @xmath58 in a sample of frii radio galaxies to be 0.11 @xmath1 0.013 . for pictor a , we may then write @xmath59 so @xmath5 = 23@xmath6 if v = 0.11 c. in view of its sensitivity to v and the assumption of symmetry , this value of @xmath5 should not be taken too seriously . the radio lobes are remarkably round and are well separated in the vla images ( prm ) , although joined by a ` waist ' near the nucleus . the overall radio extent in the plane of the sky is 430 kpc and the outward motions of the vlbi jet components ( tingay et al . 2000 ) are subluminal . all these properties indicate that @xmath5 is not small . a large value of @xmath5 is suggested by the fact that the hot spots project further away from the nucleus than the outer edges of the lobes themselves . tingay et al . ( 2000 ) have estimated that the vlbi - observed jet has @xmath5 @xmath12 51@xmath6 based on a jet - deflection model . 8 shows the broad band spectrum of the western hot spot . all of the radio points and most of the optical and near infrared ones were taken from meisenheimer , yates & rser ( 1997 ) . to these we added the flux densities at @xmath2 2900 and @xmath2 6200 obtained from our analysis of archival hst data ( section 2.2 ) . these hst values may underestimate the true flux densities as some of the emission is resolved out . also included is the original estimate of the x - ray flux density from the einstein observatory ( rser & meisenheimer 1987 ) and the chandra - measured intrinsic spectrum . the einstein point is a factor of @xmath16 2 higher than the chandra measurement ; this may be a result of partial blending of the hot spot with the much stronger nuclear source in the low spatial resolution einstein observation . the radio spectrum of the hot spot is well described by a power law with @xmath13 = 0.740 @xmath1 0.015 ( meisenheimer , yates & rser 1997 ) , but there must be a break or turnover in the spectrum at 10@xmath4 hz to accommodate the near infrared and optical measurements . it is also apparent that the x - ray spectrum is not a simple extension of the radio and optical measurements to higher frequencies . the luminosities of the radio to optical and the x - ray components are given in table 3 . it has long been realised that the outward motion of hot spots in frii radio galaxies is sub - relativistic . the most recent work ( arshakian & longair 2000 ) obtains a mean outward velocity of 0.11c @xmath1 0.013c . while the velocity of a hot spot in any individual object is uncertain , we shall neglect boosting or diminution of the hot spot fluxes by bulk relativistic motion . the broad - band spectrum ( fig . 8) shows that the x - ray emission of the western hot spot can not be synchrotron radiation from a high energy extension of the population of electrons responsible for the radio to optical synchrotron radiation . it is , therefore , natural to consider inverse compton scattering for the x - ray emission . in the bright core of the hot spot , the radiant energy density ( @xmath60 ) of the synchrotron radiation dominates that of the microwave background radiation and the galaxy starlight ( table 3 ) , so it is appropriate to consider a synchrotron self - compton model . when the scattering electrons follow a power - law distribution in @xmath61 (= e / mc@xmath62 ) , n(@xmath61 ) = n@xmath63 over all @xmath61 , then the inverse compton spectrum is a power law with a spectral index @xmath64 , the same index as the synchrotron spectrum . , where @xmath65 is the frequency of the synchrotron photon and @xmath66 is the rest mass energy of the electron . ] the fact that the radio ( @xmath67 = 0.740 @xmath1 0.015 ) and x - ray ( @xmath68 = 1.07@xmath40 ) spectral indices are different then suggests difficulties with an inverse compton model . however , in reality , the electron energy spectrum is a power law over only a certain range of @xmath61 ( from @xmath69 to @xmath70 ) , and the synchrotron spectrum is a power law over only a certain range of @xmath71 ( from @xmath72 to @xmath73 ) . these limited ranges yield `` end effects '' in synchrotron self - compton spectra : the inverse compton scattered spectra must turn down below @xmath74 and above @xmath75 ( e.g. blumenthal & gould 1970 ; rybicki & lightman 1979 ) . further , the synchrotron self - compton spectrum is no longer an exact power law between these limits . in order to provide a more realistic evaluation of inverse compton and synchrotron self - compton models , we have performed numerical calculations of spectra in spherical geometries using the computer code of band & grindlay ( 1985 , 1986 ) , which was kindly provided by dan harris . given the observed radio optical spectrum ( fig . 8) , we have assumed a power law electron spectrum with @xmath76 = 2.48 from @xmath69 to @xmath70 . the magnetic field is treated as a variable . we first computed a synchrotron self - compton spectrum which passes through the chandra - measured flux ( model 1 ) . this was achieved for a magnetic field strength of @xmath77 gauss , a factor of 14 below the equipartition field in the radio `` core '' of the hot spot ( table 4 ) . however , the predicted spectrum is similar to that of the radio source and does not match the measured x - ray spectrum ( fig . 8) . as an alternative to reducing the field strength , the power radiated in inverse compton radiation could be increased by increasing the radiation density . the nucleus of pictor a might emit a narrow , collimated beam of radiation ( like those inferred to be present in bl lac objects ) along the axis of the jet . this beam could illuminate the hot spot , but be invisible to us . however , an ( isotropic ) nuclear luminosity of 1.6 @xmath8 10@xmath78 erg s@xmath10 is needed merely to _ equal _ the radiant energy density in synchrotron radiation in the core of the hot spot . the ( isotropic ) nuclear luminosity would have to be @xmath2 1.5 @xmath8 10@xmath79 erg s@xmath10 to provide sufficient radiation for the hot spot to radiate the observed x - ray flux by inverse compton scattering if the field has its equipartition value . this luminosity is unreasonably large . an alternative is that the x - rays are a combination of synchrotron and inverse compton radiation . in model 2 , we assumed that the turnover in the synchrotron spectrum at 10@xmath4 hz is an effect of synchrotron losses on a continuously injected electron spectrum with energy index @xmath76 = 2.48 . the assumed electron spectrum is thus a broken power law ( kardashev 1962 ) : @xmath80 the synchrotron spectrum then has an index @xmath13 = 0.74 well below the break and @xmath13 = 0.74 + 0.5 = 1.24 is expected well above it ( dotted line in fig . 8) . by adding this spectrum to the predicted synchrotron self - compton component for a magnetic field of @xmath81 gauss ( dot - dashed line in fig . 8) , which is again well below equipartition , we obtain the solid line in fig . 8 , which is a good description of the chandra spectrum . the parameters of model 2 are given in table 4 . because the energy density in magnetic field is @xmath20 an order of magnitude larger than the synchrotron radiation density , the power in the first order synchrotron self - compton component is less than that in the synchrotron radiation ( e. g. rees 1967 ) further , the second order scattered component is even weaker ( 3 orders of magnitude below the first order radiation in the chandra band ) . assuming that the electrons are continuously accelerated in the hot spot , we may interpret the turnover frequency as the frequency at which the `` half - life '' to synchrotron losses of the radiating electrons is equal to their escape time from the hot spot . for the field of @xmath81 gauss needed to match the x - ray spectrum , electrons radiating at 10@xmath17 hz have a synchrotron `` half - life '' of @xmath2 10@xmath82 yrs . for a hot spot radius of @xmath2 250 pc , the corresponding streaming velocity of the relativistic electrons is @xmath2 0.1c . the problem with model 2 is the fine tuning needed : synchrotron and synchrotron self - compton emission must be present in the chandra band with comparable fluxes . in the previous subsection , we showed that the x - ray emission is so strong that the magnetic field in the hot spot must be a factor of @xmath16 14 below equipartition if the x - rays are produced by inverse compton scattering from the electrons that generate the _ observed _ radio emission . even then , the observed x - ray spectrum is different to the predicted one ( fig . 8) , and so this model ( model 1 , table 4 ) may be ruled out . the other process capable of generating the observed x - rays is synchrotron radiation . however , the x - ray emission of the hot spot is not a smooth continuation of the radio optical synchrotron spectrum . in model 2 , we contrived to fit the x - ray spectrum by a combination of synchrotron emission from an extension of the radio - optical spectrum and synchrotron self - compton from the radio - optical synchrotron - emitting electrons . in view of the unsatisfactory nature of these models , we now consider inverse compton and synchrotron models involving hypothetical new electron populations . _ i ) x - rays as inverse compton radiation _ for a successful inverse compton scattering model , a low energy population of relativistic electrons with an index of the energy spectrum p @xmath2 2@xmath83 + 1 is needed . the required value of p is thus p@xmath84 @xmath2 3.14@xmath85 . 9 shows a model ( model 3 , table 4 ) for the hot spot in which a synchrotron - emitting component with a larger spectral index than that observed in the radio has been added at low radio frequencies . the spectrum of the hot spot has not been measured below 327 mhz , but the extension of this hypothetical spectrum down to lower frequencies does not exceed the measured _ integrated _ flux density of pictor a ( the lowest such measurements are at @xmath16 80 mhz , see prm ) . it is envisaged that the population of electrons which emits the _ observed _ synchrotron radio emission is in a relatively strong ( e.g. equipartition , table 3 ) magnetic field , so that the synchrotron self- compton emission from this _ electron _ population is negligible , as shown above . however , the observed radio - optical synchrotron _ radiation _ , as well as the radio synchrotron radiation of the hypothesised component , is available for scattering by the hypothetical low energy electron population . as can be seen from fig . 9 , the low energy electrons must radiate predominantly through the inverse compton channel , requiring a very weak magnetic field ( model 3 , table 4 ) which is @xmath16 100 times weaker than the equipartition field in the core of the western hot spot . the calculation shows that the second order compton scattered component is @xmath20 2 orders of magnitude weaker than the first order compton scattered component in the chandra band . we find that the spectrum of the low energy electrons has to be steep ( p = 3.3 ) as shallower spectra ( p @xmath12 3.3 ) cause the inverse compton spectrum to increase above @xmath86 hz , contrary to our x - ray observations . taking this model to its extreme , the hypothetical electron population could be in a region free of magnetic field , and thus radiate no radio emission at all . this requirement for a weak or absent magnetic field associated with this population is difficult to understand in view of the finding that the x - ray , optical and radio emitting regions of the western hot spot are co - spatial ( section 3.2.1 and fig . high resolution radio observations at lower frequencies would provide stronger constraints on this model . _ ii ) x - rays as synchrotron radiation _ alternatively , the x - ray emission of the hot spot could be synchrotron radiation from a separate population of electrons . in such models ( models 4a and b ) , the energy index of the x - ray emitting electrons would be p@xmath84 @xmath2 3.14@xmath85 , similar to the above inverse compton model . in view of the short synchrotron loss times ( a few years for a 5 kev - emitting electron in the equipartition field ) , the energy index at injection would be p@xmath87 @xmath2 2.14@xmath85 in a steady state , continuous injection model . the synchrotron break frequency must thus be below the x - ray band but above 10@xmath88 hz ( otherwise the emission would exceed the observed flux at the latter frequency ) . models 4b and 4a ( table 4 ) , in which we have adopted the equipartition field , represent these two extremes for the synchrotron break frequency , respectively . thus , in both these models , the extrapolation of the x - ray spectrum to lower frequencies does not exceed the observed radio , infrared or optical flux . interestingly , the required value of p@xmath87 is the same to within the errors as the canonical index for particle acceleration by a strong shock ( p = 2 , e.g. bell 1978 ; blandford & ostriker 1978 ) . in this picture , electrons would have to be continuously reaccelerated by such shocks on pc scales . unfortunately , there is no information on the radio spectrum of the jet . we have only prm s statement that the average excess brightness of the jet above the background lobe emission is estimated to be about 10 mjy ( 75 beam)@xmath10 at @xmath89 20 cm . over the length of the detected x - ray jet , we then estimate a total 20 cm flux density of 152 mjy , with large uncertainties . the spectral index between 20 cm and 1 kev is @xmath90 = 0.87 , which is similar to @xmath91 = 0.85 , the spectral index for the _ entire _ radio source for @xmath71 @xmath92 400 mhz ( prm ) . this value of @xmath90 may also be compared with the index within the chandra band of @xmath93 = 0.94@xmath3 . given the errors , it is not out of the question that the jet has a constant spectral index from ghz frequencies to 10 kev , but the radio spectrum is needed to check this . simply joining the radio and x - ray flux densities with @xmath94 = 0.87 implies a total optical magnitude for the jet of v @xmath2 23 mag , and an optical surface brightness of v @xmath2 29 mag ( arc sec)@xmath49 . the fact that the jet has not been detected in the optical is consistent with these numbers . some estimated parameters of the jet are given in table 5 . it is apparent that the microwave background radiation dominates the radiant energy within the jet , unless the radius of the radio synchrotron - emitting region is much smaller than the observed radius of the x - ray jet . the x - rays from the jet could be either inverse compton or synchrotron radiation , which we discuss in turn . evaluation of these models is limited by our ignorance of the jet s radio spectrum . for concreteness , we shall adopt a jet radius of 1@xmath18 ( 950 pc ) for both the radio and x - ray emission . _ i ) x - rays as inverse compton radiation _ we consider first inverse compton models in which doppler boosting is unimportant , and show that such models of the jet s x - ray emission are implausible . we then consider models including doppler boosting . _ a ) insignificant doppler boosting by the jet _ adopting @xmath95 = 0.87 , s@xmath96 = 152 mjy for the part of the jet detected in x - rays ( section 4.3.1 ) , and the equipartition field h@xmath97 = 2.3 @xmath8 10@xmath98 gauss , the predicted inverse compton scattered x - ray flux falls a factor of @xmath2 500 below that observed . in order to match the observed x - ray flux , we need to reduce the magnetic field to h@xmath97 @xmath2 7 @xmath8 10@xmath99 gauss , a factor of @xmath2 30 below equipartition . alternatively , as for the hot spot , we could invoke a radiation beam from the nucleus to boost the radiation density in the jet . to obtain the observed x - ray flux from the jet while retaining the equipartition field requires an ( isotropic ) nuclear luminosity of @xmath16 2 @xmath8 10@xmath78 erg s@xmath10 , which is implausibly high . we could also suppose , as we did for the hot spot , that the _ observed _ radio jet contains a stronger ( e.g. equipartition ) magnetic field and there is , in addition , a population of electrons in a weak or absent field . because we do not know the radio spectrum of the jet , and have thus not been able to demonstrate that the radio and x - ray spectral indices are different , we can not prove that the radio- and x - ray - emitting electrons represent different populations , as we could for the hot spot . the following simple fact argues against inverse compton scattering for the jet s x - ray emission _ if doppler boosting is unimportant _ : in the radio band , the western lobe dominates the jet , while in x - rays the converse is true . the ratio of the rates of energy loss to inverse compton scattering and synchrotron radiation is @xmath100 the radiant energy density in both the jet and western lobe is dominated by the microwave background radiation . the equipartition magnetic field in the jet is @xmath2 2.3 @xmath8 10@xmath98 gauss ( for r@xmath101 = 1@xmath18 , see table 5 ) and that in the lobe is @xmath16 5 @xmath8 10@xmath102 gauss . thus one expects that the ratio ( de / dt)@xmath103/(de / dt)@xmath104 should be larger for the lobe than the jet . given that the lobe s radio synchrotron radiation overwhelmingly dominates that of the jet , the lobe s inverse compton emission should dominate the jet by an even larger factor , contrary to observation . however , the jet s inverse compton emission would be larger if either a ) its magnetic field is well below equipartition , or b ) a narrow beam of radiation is emitted by the nucleus along the jet , providing a larger @xmath60 than the microwave background , as discussed above . both of these possibilities are _ ad hoc _ and so we consider the prominence of the jet compared to the lobe in the chandra image as an argument against inverse compton scattering in the absence of doppler boosting . _ b ) significant doppler boosting by the jet _ the above discussion neglects relativistic boosting or diminution by possible bulk relativistic motion of the jet . there is now a strong case for energy transport at bulk relativistic velocities to the hot spots in frii sources ( e.g. bridle 1996 ) . for emission which is isotropic in the rest frame and has a power law spectrum , the observed flux density , @xmath105 , is related to the flux density in the rest frame , @xmath106 , by @xmath107 where @xmath108^{-1}$ ] , @xmath0 is the lorentz factor of the bulk flow , @xmath58 is the bulk velocity in units of the speed of light , and @xmath5 is the angle between the velocity vector and the line of sight ( e.g. urry & padovani 1995 ) . this equation assumes that the emission comes from a discrete , moving source . for a smooth , continuous jet , the exponent 3+@xmath13 becomes 2+@xmath13 ( begelman , blandford & rees 1984 ) . equation ( 6 ) will describe relativistic boosting or diminution of the jet s synchrotron radiation , as long as that radiation is isotropic in the jet s rest frame . as noted above ( table 5 ) , the radiation density in the jet is dominated by the microwave background radiation , which is isotropic in the observer s frame and anisotropic in the rest frame of the jet . in this case , the principal dependence of the inverse compton scattered radiation on @xmath5 is given by ( dermer 1995 ) @xmath109 where an additional term which depends slowly on @xmath110 has been omitted ( begelman & sikora 1987 ; dermer 1995 ) . retaining the discrete source model , the ratio of inverse compton scattered to synchrotron spectral flux density is then @xmath111 thus the ratio of inverse compton to synchrotron flux is increased by doppler boosting ( @xmath34 @xmath92 1 ) . our goal is to develop successful models for the jet s x - ray emission for various assumed angles @xmath5 . selection of a given @xmath5 defines a maximum value of @xmath34 ( @xmath112 @xmath2 1/@xmath5 ) , which is achieved when @xmath0 @xmath2 1/@xmath5 . assuming @xmath112 ( which is the most optimistic choice , since it minimises the required reduction of h below equipartition at a given @xmath5 ) , we have computed the value of h required to reproduce the observed x - ray to radio flux ratio , and compared it with the equipartition field which would be inferred from the synchrotron emission by an observer in the rest frame of the jet ( estimated by `` deboosting '' the observed radio flux ; h@xmath22 @xmath16 h@xmath113 ) . the results are given in table 6 . for our canonical @xmath5 = 23@xmath6 ( section 4.1 ) , the field must be at least a factor of 6 below equipartition . an equipartition model demands @xmath5 = 8@xmath6 , which is surely too small for a lobe - dominated frii radio galaxy like pictor a ( see discussion in section 4.1 ) . such an angle would make pictor a one of the largest known radio galaxies ( length 3 mpc ) . we conclude that inverse compton scattering of the microwave background is a viable model for the x - ray emission of the jet of pictor a , but requires a magnetic field which is substantially below equipartition . _ ii ) x - rays as synchrotron radiation _ as already noted , the available data are consistent with a single power law with @xmath90 = 0.87 from 1.4 ghz to 10 kev . this is , however , an unlikely physical situation for a purely synchrotron spectrum in view of the short energy loss times of the x - ray emitting electrons to synchrotron and inverse compton radiation . for electrons emitting synchrotron radiation at 1.4 ghz and 1 kev in the equipartition field of 2.3 @xmath8 10@xmath98 gauss , the times to lose half their energy are @xmath2 4 @xmath8 10@xmath114 and 300 yrs , respectively . if the energies of the radio - emitting electrons are not significantly reduced by synchrotron and inverse compton losses , we would expect the radio spectrum to be flatter than the x - ray spectrum ; in the simplest case involving continuous injection , @xmath95 = @xmath93 0.5 @xmath2 0.4 . it would thus be valuable to measure @xmath95 . for a synchrotron model in which the radiation is isotropic in the frame of bulk jet motion , the observed ratio of flux in the approaching side of the jet to the receding side is given by @xmath115 from x - ray observations @xmath116 and @xmath117 at the brightest part of the x - ray jet . assuming @xmath5 @xmath92 23@xmath6 ( section 4.1 ) , then @xmath58 @xmath92 0.3 . if the x - rays are the result of inverse compton scattering of the microwave background radiation , the exponent 3+@xmath13 in equation ( 9 ) becomes 4 + 2@xmath13 ( cf . equation 7 ) and a somewhat smaller lower limit to @xmath58 is obtained .

the x - ray spectrum of the hot spot is well described by an absorbed power law with photon index = 2.07 0.11 . the observed jet is up to 15 times brighter in x - rays than any counter jet , a difference ascribed to relativistic boosting as the western radio lobe is probably the closer . the jet s spectrum is well modelled by an absorbed power law with = 1.94 and poorly fitted by a raymond - smith thermal plasma model . the radio - optical spectrum of the hot spot breaks or turns down at 10 hz , and its x - ray spectrum is not a simple extension of the radio - optical spectrum to higher frequencies . we show that the hot spot s x - ray emission could be synchrotron self - compton emission from a hitherto unobserved population of electrons emitting at low radio frequencies , but do not favor this model in view of the very weak magnetic field required . an inverse compton model of the jet , in which it scatters microwave background photons but moves non - relativistically , requires a magnetic field a factor of 30 below equipartition , and ad hoc conditions to explain why the radio lobes are fainter than the jet in x - rays but brighter in the radio . a model with 23 and a field a factor of 6 below equipartition seems viable . synchrotron radiation is an alternative process for the x - ray emission . the expected synchrotron spectrum from relativistic electrons accelerated by strong shocks and subject to synchrotron radiation losses is in very good agreement with that observed for both the hot spot and jet .

we report x - ray observations of the nearby , powerful radio galaxy pictor a with the chandra observatory and optical and near uv observations of its western radio hot spot with the hubble space telescope . x - ray emission is detected from the nucleus , a 19 ( 110 kpc ) long jet to the west of the nucleus , the western radio hot spot some 42 ( 240 kpc ) from the nucleus , and the eastern radio lobe . the morphology of the western hot spot is remarkably similar to that seen at radio and optical wavelengths , where the emission is known to be synchrotron radiation . the x - ray spectrum of the hot spot is well described by an absorbed power law with photon index = 2.07 0.11 . the x - ray jet coincides with a weak radio jet and is laterally extended by 20 ( 1.9 kpc ) . the observed jet is up to 15 times brighter in x - rays than any counter jet , a difference ascribed to relativistic boosting as the western radio lobe is probably the closer . the jet s spectrum is well modelled by an absorbed power law with = 1.94 and poorly fitted by a raymond - smith thermal plasma model . the emission processes responsible for the x - rays are discussed in detail . the radio - optical spectrum of the hot spot breaks or turns down at 10 hz , and its x - ray spectrum is not a simple extension of the radio - optical spectrum to higher frequencies . thermal models for the hot spot s x - ray emission are ruled out . synchrotron self - compton models involving scattering from the _ known _ population of electrons give the wrong spectral index for the hot spot s x - ray emission and are also excluded . a composite synchrotron plus synchrotron self - compton model can match the x - ray observations but requires similar contributions from the two components in the chandra band . we show that the hot spot s x - ray emission could be synchrotron self - compton emission from a hitherto unobserved population of electrons emitting at low radio frequencies , but do not favor this model in view of the very weak magnetic field required . an inverse compton model of the jet , in which it scatters microwave background photons but moves non - relativistically , requires a magnetic field a factor of 30 below equipartition , and ad hoc conditions to explain why the radio lobes are fainter than the jet in x - rays but brighter in the radio . these problems are alleviated if the jet moves relativistically , but models with an equipartition field require an implausibly small angle ( ) between the jet and the line of sight . a model with 23 and a field a factor of 6 below equipartition seems viable . synchrotron radiation is an alternative process for the x - ray emission . the expected synchrotron spectrum from relativistic electrons accelerated by strong shocks and subject to synchrotron radiation losses is in very good agreement with that observed for both the hot spot and jet . the possibility that the relativistic electrons result via photo - pion production by high energy protons accelerated in shocks ( a ` proton induced cascade ' ) is briefly discussed .

astro-ph0008467

c

our chandra study of pictor a has shown that the x - ray emissions from the jet and the western hot spot are non - thermal . the spectra of both are well described by an absorbed power law with ( flux density ) spectral index @xmath13 @xmath2 1.0 . the x - ray spectrum of the hot spot is not a smooth extension of the radio to optical synchrotron spectrum , which turns down or cuts off near @xmath16 10@xmath17 hz . inverse compton scattering of the synchrotron radio photons by the relativistic electrons responsible for the radio emission ( i.e. a synchrotron self - compton model ) may be ruled out for the hot spot s x - ray emission , as the predicted spectrum differs from that observed . we considered the possible existence of a population of relativistic electrons in the hot spot that radiates synchrotron emission at frequencies below that at which its spectrum has been measured ( i.e. @xmath12 327 mhz ) . by choosing an appropriate index for the energy spectrum of these electrons , we constructed a successful synchrotron self - compton model for the x - rays at the price of reducing the magnetic field to @xmath16 1% of equipartition ( see fig . 9 and model 3 in table 4 ) . more generally , relativistic electrons could exist in regions with weak or absent magnetic fields . since the properties of such electron populations are unconstrained by radio observations , one can always create inverse compton models that match the x - ray spectra . it is , however , then difficult to understand why the x - rays from both the jet and the hot spot should correlate so well with synchrotron radio emission , which must arise in a relatively strong magnetic field . the x - ray spectrum of the hot spot may be reproduced in a composite synchrotron plus synchrotron self - compton model . in this picture , the spectral index of the synchrotron radiation is supposed to increase by 0.5 above the break near 10@xmath17 hz , as would be expected in a continuous injection model . addition of this synchrotron emission to the synchrotron self - compton emission expected for a magnetic field a factor of 9 below equipartition reproduces the observed spectrum ( see fig . 8 and model 2 , table 4 ) . the model is contrived , requiring similar fluxes from the two components in the chandra band , but can not be ruled out . if the jet is non - relativistic , inverse compton scattering is an implausible model for its x - ray emission , for it requires a magnetic field a factor of 30 below equipartition . further , it is hard to understand why the jet is brighter than the lobe ( the opposite of the situation in the radio ) in such a model . if the jet is relativistic , these difficulties are eased , and we consider inverse compton scattering by such a jet off the microwave background a viable mechanism . however , the magnetic field must still be well below equipartition for plausible angles between the jet and the line of sight in this lobe - dominated , frii radio galaxy . synchrotron radiation is a plausible x - ray emission process for both jet and hot spot . strong , non - relativistic shocks are believed to accelerate relativistic particles yielding an energy spectrum n(e ) @xmath14 e@xmath118 with p = 2 at injection . since the half lives of x - ray emitting electrons to synchrotron losses are very short ( @xmath16 years ) , the spectrum steepens and a synchrotron spectral index of @xmath13 = 1.0 is expected , in excellent accord with observations ( models 4a , b , table 4 ) . the separate population of radio - optical synchrotron emitting electrons remains unexplained ; the radio spectral index - @xmath119 = 0.740 @xmath1 0.015 - is close to the average for non - thermal radio sources . various processes , including acceleration in weak shocks , synchrotron losses and effects of tangled fields ( see summary in longair 1994 , ch . 21 ) , have been invoked to account for the difference between the typical index seen in radio sources and the value @xmath13 = 0.5 expected in the canonical model . hot spots are , of course , associated with two shocks - an internal , mildly relativistic shock in the jet and a non - relativistic bow shock in the intergalactic medium . both may reasonably be expected to accelerate cosmic rays and the resulting fluxes and energy spectra may differ . as well as being directly accelerated in shocks , high @xmath61 relativistic electrons may result from a ` proton induced cascade ' initiated by photopion production ( e.g. sikora et al . 1987 ; biermann & strittmatter 1987 ; mannheim & biermann 1989 ; mannheim , krlls & biermann 1991 ) . in this process , relativistic proton - photon collisions create @xmath120 , @xmath121 and @xmath122 . the last two decay into relativistic electrons , positrons , neutrinos and antineutrinos ( e.g. biermann & strittmatter 1987 ) . the process thus provides a supply of synchrotron x- and @xmath61-ray emitting electrons and positrons from high energy protons accelerated by shocks . mannheim , krlls & biermann ( 1991 ) considered this process for production of synchrotron x - ray emission in radio galaxy hot spots . their calculations suggest that the proton induced cascade produces x - ray emission about an order of magnitude weaker and with a harder spectrum than is observed for the western hot spot of pictor a. as they note , the predicted luminosity can be increased by increasing the number of relativistic protons or the number of photons ( the latter might occur , for example , if the hot spot is illuminated by a beam of radiation from the galaxy nucleus ) . this process seems promising and further calculations of the expected x - ray luminosity and spectrum of a proton induced cascade would be worthwhile . our discussion of the western hot spot has assumed it moves outwards non - relativistically . while this is established for the population of radio hot spots in general , it is not necessarily true for pictor a. the fact that the western hot spot is on the near side and is much brighter than the eastern hot spots at both radio and x - ray wavelengths raises the possibility of relativistic outflow . some of the problems with inverse compton models of the hot spot might then be eased ( as they are for the jet ) , but the difference between the radio and x - ray spectral indices remains a difficulty . this research was supported by nasa through grant nag 81027 and by the graduate school of the university of maryland through a research fellowship to asw . we are extremely grateful to rick perley for providing the radio images published by prm in numerical form . we also wish to thank the staff of the chandra science center , especially dan harris and shanil virani , for their help . bridle , a. h. 1996 , in energy transport in radio galaxies and quasars , asp conference series vol . 100 , eds . e. hardee , a. h. bridle and j. a. zensus , p 383 ( astronomical society of the pacific : san francisco ) raymond - smith & @xmath123 & @xmath124 & solar & @xmath125 & & & 166 / 97 + raymond - smith & 4.2 ( frozen ) & @xmath126 & solar & @xmath127 & & & 232 / 99 + raymond - smith & @xmath128 & @xmath129 & @xmath130 solar & @xmath131 & & & 101 / 96 + raymond - smith & 4.2 ( frozen ) & @xmath132 & @xmath133 solar & @xmath134 & & & 122 / 98 + power law & 7.1@xmath41 & & & & 2.07@xmath40 & ( 1.34@xmath135 ) @xmath8 10@xmath46 & 95 / 98 + lcccccccc raymond - smith & 4.2 ( frozen ) & @xmath136 & solar & @xmath137 & & & 27 / 15 + raymond - smith & 4.2 ( frozen ) & @xmath138 & @xmath139 solar & @xmath140 & & & 19 / 14 + power law & 5.8@xmath52 & & & & 1.94@xmath3 & ( 1.45@xmath141 ) @xmath8 10@xmath98 & 15 / 14 + lc l(327 mhz - optical ) & @xmath2 3 @xmath8 10@xmath142 erg s@xmath10 + l(0.1 - 10 kev ) & 4.9 @xmath8 10@xmath43 erg s@xmath10 + h@xmath143 ( bright core ) & 4.7 @xmath8 10@xmath46 gauss + h@xmath143 ( filament ) & 9.1 @xmath8 10@xmath98 gauss + @xmath60 ( core , synchrotron radn ) & @xmath16 8 @xmath8 10@xmath144 erg @xmath45 + @xmath60 ( filament , synchrotron radn ) & @xmath16 1 @xmath8 10@xmath42 erg @xmath45 + @xmath60 ( microwave background ) & 4 @xmath8 10@xmath42 erg @xmath45 + @xmath60 ( galaxy optical light ) & 4 @xmath8 10@xmath145 erg @xmath45 + 1 & 5.3 & 2.48 & @xmath146 & & & @xmath147 & @xmath77 & 0.07 + 2 & 2.2 & 2.48 & @xmath146 & @xmath148 & & @xmath147 & @xmath81 & 0.11 + 3 & 485.0 & 3.30 & @xmath149 & & @xmath150 & @xmath147 & @xmath151 & 0.01 + 4a & @xmath152 & 2.14 & & @xmath153 & & @xmath147 & @xmath154 & 1 + 4b & @xmath155 & 2.14 & & @xmath156 & & @xmath147 & @xmath154 & 1 + lc h@xmath143 & 2.3 @xmath8 10@xmath98 ( r@xmath157/1 arc sec)@xmath158 gauss + @xmath60 ( synchrotron radn)@xmath159 & @xmath16 1 @xmath8 10@xmath160 ( r@xmath157/1 arc sec)@xmath10 erg @xmath45 + @xmath60 ( microwave background ) & 4 @xmath8 10@xmath42 erg @xmath45 + @xmath60 ( galaxy optical light ) & @xmath16 8 @xmath8 10@xmath160 ( r/1 arc min)@xmath49 erg @xmath45 + lcccccccc any value@xmath161 & 1 & 1 & 7@xmath810@xmath99 & 2.3@xmath810@xmath98 & 0.03 + 23@xmath6 & 2.6 & 2.6 & 2@xmath810@xmath102 & 1.2@xmath810@xmath98 & 0.16 + 8@xmath6 & 7.2 & 7.2 & 6@xmath810@xmath102 & 6@xmath810@xmath102 & 1 +

we report x - ray observations of the nearby , powerful radio galaxy pictor a with the chandra observatory and optical and near uv observations of its western radio hot spot with the hubble space telescope . thermal models for the hot spot s x - ray emission are ruled out . synchrotron self - compton models involving scattering from the _ known _ population of electrons give the wrong spectral index for the hot spot s x - ray emission and are also excluded . a composite synchrotron plus synchrotron self - compton model can match the x - ray observations but requires similar contributions from the two components in the chandra band . these problems are alleviated if the jet moves relativistically , but models with an equipartition field require an implausibly small angle ( ) between the jet and the line of sight . the possibility that the relativistic electrons result via photo - pion production by high energy protons accelerated in shocks ( a ` proton induced cascade ' ) is briefly discussed .

we report x - ray observations of the nearby , powerful radio galaxy pictor a with the chandra observatory and optical and near uv observations of its western radio hot spot with the hubble space telescope . x - ray emission is detected from the nucleus , a 19 ( 110 kpc ) long jet to the west of the nucleus , the western radio hot spot some 42 ( 240 kpc ) from the nucleus , and the eastern radio lobe . the morphology of the western hot spot is remarkably similar to that seen at radio and optical wavelengths , where the emission is known to be synchrotron radiation . the x - ray spectrum of the hot spot is well described by an absorbed power law with photon index = 2.07 0.11 . the x - ray jet coincides with a weak radio jet and is laterally extended by 20 ( 1.9 kpc ) . the observed jet is up to 15 times brighter in x - rays than any counter jet , a difference ascribed to relativistic boosting as the western radio lobe is probably the closer . the jet s spectrum is well modelled by an absorbed power law with = 1.94 and poorly fitted by a raymond - smith thermal plasma model . the emission processes responsible for the x - rays are discussed in detail . the radio - optical spectrum of the hot spot breaks or turns down at 10 hz , and its x - ray spectrum is not a simple extension of the radio - optical spectrum to higher frequencies . thermal models for the hot spot s x - ray emission are ruled out . synchrotron self - compton models involving scattering from the _ known _ population of electrons give the wrong spectral index for the hot spot s x - ray emission and are also excluded . a composite synchrotron plus synchrotron self - compton model can match the x - ray observations but requires similar contributions from the two components in the chandra band . we show that the hot spot s x - ray emission could be synchrotron self - compton emission from a hitherto unobserved population of electrons emitting at low radio frequencies , but do not favor this model in view of the very weak magnetic field required . an inverse compton model of the jet , in which it scatters microwave background photons but moves non - relativistically , requires a magnetic field a factor of 30 below equipartition , and ad hoc conditions to explain why the radio lobes are fainter than the jet in x - rays but brighter in the radio . these problems are alleviated if the jet moves relativistically , but models with an equipartition field require an implausibly small angle ( ) between the jet and the line of sight . a model with 23 and a field a factor of 6 below equipartition seems viable . synchrotron radiation is an alternative process for the x - ray emission . the expected synchrotron spectrum from relativistic electrons accelerated by strong shocks and subject to synchrotron radiation losses is in very good agreement with that observed for both the hot spot and jet . the possibility that the relativistic electrons result via photo - pion production by high energy protons accelerated in shocks ( a ` proton induced cascade ' ) is briefly discussed .

1610.05850

i

the mixed formulation allows us to calculate simultaneously the primary solution of a pde and its flux . for this reason , mixed formulations are very useful for numerical solution of multiphysics systems . the focus of this work is on a single diffusive process that is a part of almost any complex multiphysics system . in this paper , we present design principles used in the derivation of mimetic finite difference ( mfd ) schemes on polygonal and polyhedral meshes and establish bridges to design principles used by a few other discretization frameworks ( finite volumes and finite elements ) . the focus on the design principle allows us to avoid technical details and provide a more clear connection between different frameworks in comparison with the work performed in @xcite . we also illustrate the flexibility of the mimetic framework with two challenging examples : derivation of arbitrary - order accurate schemes for linear problems and convergent schemes for nonlinear problems with degenerate diffusion coefficients . many ideas underpinning the mfd method were originally formulated in the sixties for orthogonal meshes using the finite difference framework from which the name of the method was derived . over the years , the mfd method has been extensively developed for the solution of a wide range of scientific and engineering problems in continuum mechanics @xcite , electromagnetics @xcite , fluid flows @xcite , elasticity @xcite , obstacle and control problems @xcite , diffusion @xcite , discretization of differential forms @xcite , and eigenvalue analysis @xcite . an extensive list of people who contributed to the development of the mfd method can be found in the recent book @xcite and review paper @xcite . the paper summarizes almost all known results on cartesian and curvilinear meshes for various pdes including the lagrangian hydrodynamics . the book complements the paper by providing numerous examples and describing basic tools used in the convergence analysis of mimetic schemes for elliptic pdes . the mfd method preserves or mimic essential mathematical and physical properties of underlying partial differential equations ( pdes ) on general polygonal and polyhedral meshes . for the elliptic equation , these properties include the _ local flux balance _ and the _ duality between gradient and divergence operators_. the latter implies symmetry and positive definiteness of the resulting matrix operator and is desirable for robustness and reliability of numerical simulations . the duality of the primary and derived mimetic operators is one of the major design principles . the _ definition of the primary mimetic operators is coordinate invariant _ , which is another design principle that allows us to build discrete schemes for non - cartesian coordinate systems . the discrete operators are also built to satisfy _ exact identities _ , the property that is critical for avoiding spurious numerical solutions , providing accurate modeling of conservation laws , and making the convergence analysis possible . the related discretization frameworks considered in this paper include the finite volume methods @xcite , the mixed finite element ( mfe ) method @xcite , and the virtual element method ( vem ) @xcite . other finite volume frameworks exist that are based on mimetic principles such as the discrete duality finite volume methods ( ddfv ) , see , e.g. , @xcite , but these methods do not fit in the mfd framework and will not be considered here . the fv methods , originally introduced in @xcite for the heat equation and dubbed as the integrated finite difference method , form , perhaps , the largest class of schemes that can handle unstructured polygonal and polyhedral meshes , non - linear problems , and problems with anisotropic coefficients . an introduction to the finite volume nethoddology can be found in the recent review @xcite . almost all fv methods starts with a discrete representation of the flux balance equation . this representation is exact and this property is so important that all the methods that we consider in this paper use the same discrete form of the balance equation and the difference between them is only in the discretization of the constitutive equation . the classical cell - centered fv scheme uses a two - point flux formula that is second - order accurate for special meshes such as the voronoi tessellations . to overcome this limitation , a class of fv methods , consistent by design , is proposed by introducing additional unknowns on mesh faces . examples of such methods are the _ hybrid finite volume _ method @xcite , and the _ mixed finite volume _ method @xcite . these fv methods start with different definitions of the cell - based discrete gradient that are exact for linear solutions . the formula for the numerical flux based on this gradient needs a stabilization term . construction of the stabilized flux uses two principles . first , the stabilization term should be zero on linear solutions . second , the stabilized flux is defined as the solution of a certain equation with a symmetric and positive definite bilinear form . we will show that these design principles imply the duality principle in the mimetic framework . the vem was originally introduced as an evolution of the mfd method . in the classical finite element spirit , the duality principle is incorporated directly in the weak formulation . the exact identities are replaced by the exact sequence of virtual finite element spaces . a new design principle is the unisolvency property where the space of degrees of freedom is isomorphic to a space of finite element functions and includes polynomial as well as non - polynomial functions . the bilinear forms are split explicitly into consistency and stability forms using problem - dependent @xmath0 and @xmath1 projectors . we discuss how the new design principles are connected to the stability and consistency conditions in the mimetic framework . the recent developments of the mfd framework exploit it flexibility for selecting non - standard degrees of freedom , optimization of inner products , and non - standard approximations of primary operators to build schemes with higher order of accuracy and convergence schemes for nonlinear pdes with degenerate coefficients ( see also section [ sec : divk ] ) . extension to higher - order mixed scheme is almost straightforward in the mimetic framework . the key step is the proper selection of degrees of freedom that ( a ) simplify the discretization of the primary divergence operator and ( b ) allows us to formulate a computable consistency condition . a new design principle is introduced in this case , which states that a commuting relation exists between the interpolation operators defining the degrees of freedom of scalar and vector fields , and the divergence operators in the discrete and continuum settings . all of the aforementioned methods discretize effectively the divergence operator `` _ _ div__@xmath2 '' . to solve nonlinear parabolic equations , we employ new mfd schemes where the primary operator discretizes the combined operator `` _ _ div__@xmath3 '' , where @xmath4 is the non - constant scalar diffusion coefficient . the resulting scheme uses both cell - centered and face - centered values of the diffusion coefficient . this model has applications in heat diffusion @xcite and moisture transport in porous media @xcite . the duality property mentioned above guarantees that the schemes can be formulated as algebraic problems with symmetric and positive definite matrices . matrices with these properties lead to better performance of scalable iterative solvers , such as algebraic multigrid solvers and krylov solvers such as the preconditioned conjugate gradient . finally , we mention other discretization methods that work on general meshes . our necessarily incomplete list include the polygonal / polyhedral finite element method ( pfem ) @xcite , hybrid high - order method @xcite , the discontinuous galerkin ( dg ) method @xcite , hybridized discontinuous galerkin ( hdg ) method @xcite , and the weak galerkin ( wg ) method @xcite . the outline of the paper is as follows . in section [ sec : basic : principles : mfd : framework ] , we review the basic discretization principles of the mimetic framework . in section [ sec : mixed : mimetic : formulation ] , we derive the mimetic finite difference method for elliptic problems through the consistency and stability properties . we also prove that any mixed - hydrid method that uses the same degrees of freedom leads to a member of the mimetic family of schemes . in section [ sec : recent : developments ] , we review the recent progress in the development of mimetic methods for mixed formulations of elliptic problems . our final remarks and conclusions are given in section [ sec : conclusions ] .

we review basic design principles underpinning the construction of mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems . for a class of low - order mixed - hybrid schemes , we show connections between these principles and prove that the consistency and stability conditions must lead to a member of the mimetic family of schemes regardless of the selected discretization framework .

we review basic design principles underpinning the construction of mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems . for a class of low - order mixed - hybrid schemes , we show connections between these principles and prove that the consistency and stability conditions must lead to a member of the mimetic family of schemes regardless of the selected discretization framework . finally , we give two examples of using flexibility of the mimetic framework : derivation of higher - order schemes and convergent schemes for nonlinear problems with small diffusion coefficients .

1011.0732

i

inhomogeneities in the large - scale matter distribution can in many ways affect the light signals coming from very distant objects . these effects need to be understood well if we want to map the expansion history and determine the composition of the universe to a high precision from cosmolgical observations . in particular the evidence for dark energy in the current cosmological concordance model is heavily based on the analysis of the apparent magnitudes of distant type ia supernovae ( sne ) @xcite . inhomogeneities can affect the observed sne magnitude - redshift relation for example through gravitational lensing , in a way which essentially depends on size and composition of the structures through which light passes on its way from source to observer . the fundamental quantity describing this statistical magnification is the lensing probability distribution function ( pdf ) . it is not currently possible to extract the lensing pdf from the observational data and we have to resort to theoretical models . two possible alternatives have been followed in the literature . a first approach ( e.g. ref . @xcite ) relates a `` universal '' form of the lensing pdf to the variance of the convergence , which in turn is fixed by the amplitude of the power spectrum , @xmath0 . moreover the coefficients of the proposed pdf are trained on some specific n - body simulations . a second approach ( e.g. ref . @xcite ) is to build _ ab - initio _ a model for the inhomogeneous universe and directly compute the relative lensing pdf , usually through time - consuming ray - tracing techniques . the flexibility of this method is therefore penalized by the increased computational time . in ref . @xcite we introduced a stochastic approach to cumulative weak lensing ( hereafter sgl method ) which combines the flexibility in modeling with a fast performance in obtaining the lensing pdf . the speed gain is actually a sine - qua - non for likelihood approaches , in which one needs to scan many thousands different models ( see ref . the sgl method is based on the weak lensing approximation and generating stochastic configurations of inhomogeneities along the line of sight . the major improvements introduced here are the use of a realistic halo mass function to determine the halo mass spectrum and the incorporation of large - scale structures in the form of filaments . the improved modeling together with the flexibility to include a wide array of systematic biases and selection effects makes the sgl method a powerful and comprehensive tool to study the impact of lensing on observations . we show in particular that the sgl method , endowed with the new array of inhomogeneities , naturally and accurately reproduces the lensing pdf of the millenium simulation @xcite . we also study a simple selection effect model and show that selection biases can reduce the variance of the observable pdf . such reduction could at least partly cancel the opposite effect coming from large scale inhomogeneities , masking their effect on the observable pdf . we also show how a jdem - like survey could constrain the lensing pdf relative to a given cosmological model . along with this paper , we release an updated version of the package , which is a simple and very fast mathematica implementation of the sgl method @xcite . this paper is organized as follows . in section [ sup ] we introduce the cosmological background , the generic layout of inhomogeneities and review the basic formalism needed to compute the weak lensing convergence . in section [ sec : inhoprop ] we derive the halo mass function and the halo density profiles and define the precise modeling of filaments . in section [ hmf ] we present the revised and extended sgl method . the exact discretization of the model parameters , which is a crucial step in the sgl model building , is explained in section [ mbin ] and in section [ confi ] we explain how the realistic structures where halos are confined in filaments are modelled in the sgl method . section [ results ] contains our numerical results including the comparison with the cosmology of the millennium simulation @xcite and , finally , in section [ conco ] we will give our conclusions .

we revise and extend the stochastic approach to cumulative weak lensing ( hereafter the sgl method ) first introduced in ref . . here we include a realistic halo mass function and density profiles to model the distribution of mass between and within galaxies , galaxy groups and galaxy clusters . we show that the sgl method naturally reproduces the weak lensing results for the millennium simulation . this makes it a useful tool to study how lensing depends on cosmological parameters and its impact on observations . we show how simple selection effects may reduce the variance of observed pdf , which could possibly mask opposite effects from very large scale structures . we also show how a jdem - like survey could constrain the lensing pdf relative to a given cosmological model . the updated code is available at .

we revise and extend the stochastic approach to cumulative weak lensing ( hereafter the sgl method ) first introduced in ref . . here we include a realistic halo mass function and density profiles to model the distribution of mass between and within galaxies , galaxy groups and galaxy clusters . we also introduce a modeling of the filamentary large - scale structures and a method to embed halos into these structures . we show that the sgl method naturally reproduces the weak lensing results for the millennium simulation . the strength of the sgl method is that a numerical code based on it can compute the lensing probability distribution function for a given inhomogeneous model universe in a few seconds . this makes it a useful tool to study how lensing depends on cosmological parameters and its impact on observations . the method can also be used to simulate the effect of a wide array of systematic biases on the observable pdf . as an example we show how simple selection effects may reduce the variance of observed pdf , which could possibly mask opposite effects from very large scale structures . we also show how a jdem - like survey could constrain the lensing pdf relative to a given cosmological model . the updated code is available at .

1206.5830

i

it has been established that a strong link exists between supermassive black holes ( smbhs ) and the galaxies in which they live @xcite and between accreting smbhs ( or active galactic nuclei , agn ) and star formation in particular ( e.g. * ? ? ? * ; * ? ? ? clues to this link can be revealed by detailed analysis of the spectra of galaxies and agn . star formation processes imprint their signatures on the spectrum . stellar populations of various ages produce strong continuum emission in the ultraviolet ( uv ) through near - ir region , while gas photo - ionized by the hot young stars produces prominent emission - lines in the uv , optical , and ir . the accretion disk surrounding the supermassive black hole in an agn produces its own strong uv and optical continuum emission ( the big blue bump @xcite ) . this emission can swamp that of the stellar population of the host galaxy when there is a direct view of the accretion disk ( i.e. in type 1 agn ) . dust in the interstellar medium of the host galaxy will absorb optical and uv light from both stars and the agn and re - radiate this in the ir . in agn , this reprocessing also occurs in the dusty obscuring torus @xcite . in type 2 agn , the direct view of the agn is blocked by the obscuring torus , and the presence of the agn can be inferred by prominent optical and infrared emission lines from highly ionized gas located beyond the torus and the strong mid - ir continuum emission from the torus . in such objects the signatures of host galaxys young stars and star formation are also present in optical and mid - ir spectra . these type 2 agn are therefore ideal laboratories for studying the connection between agn and star formation , provided that the tracers of this activity can be disentangled . multi - wavelength star formation indicators have been extensively studied in samples of quiescent star forming galaxies ( see * ? ? ? * for a review ) . star formation rates ( sfrs ) have been calibrated in the optical based on h@xmath1 emission , which results from recombination following ionization due to energetic photons from massive o and b stars , and in the uv based on the continuum which provides a window into emission from young stars . dust in the galaxy reprocesses optical and uv photons and re - radiates in the infrared ( ir ) , thus revealing obscured star formation . other ir indicators include emission from fine structure lines excited by starburst activity , such as [ neii ] 12.81@xmath2 m and [ neiii ] 15.56@xmath2 m @xcite , as well as spectral emission features associated with polycyclic aromatic hydrocarbons ( pahs ) , since these macro - molecules / small - grains can be ionized by single optical or uv photons @xcite and are prominent in ir spectra of star - forming galaxies @xcite . such host galaxy star formation diagnostics can be contaminated by the presence of an agn . photons emitted by the accretion disk enhance the optical and uv emission used to derive sfrs . the obscuring medium enshrouding the central engine contributes significantly to the infrared emission , constituting approximately 20% of the agn bolometric luminosity @xcite . disentangling the contribution from the agn vs. star formation then becomes a necessary intermediate step in using continuum ir emission as a tracer of star formation in active galaxies , and such a process can be plagued with uncertainties . previous studies have indicated that emission from pahs tend to be suppressed in galaxies hosting an active nucleus , which is sometimes attributed to the harsh radiation field produced by the agn accretion disk destroying pahs ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? a complementary view of the agn and starburst connection is to study spectroscopic signatures that parameterize the relative importance of these two processes . the optical bpt diagram ( a plot of [ oiii]@xmath35007/h@xmath4 vs. [ nii]@xmath36583/h@xmath1 ) provides a useful diagnostic to differentiate between star - forming galaxies , composite systems ( galaxies with comparable amounts of star - formation and agn activity ) and type 2 , or obscured , agn in the local universe @xcite . the optical `` d '' parameter is the distance a source lies from the locus of star forming galaxies on the bpt diagram : a higher d value indicates greater agn dominance @xcite . ratios of ir fine structure lines also parameterize the ionization field hardness . for instance , [ oiv]26@xmath2 m and [ nev]14.32@xmath2 m are primarily ionized by agn @xcite whereas [ neii]12.81@xmath2 m is excited by star formation @xcite . the ratio of these lines can then indicate the relative importance of these two processes @xcite . the mid - infrared ( mir ) spectral slope , @xmath5 , steepens as the amount of emission from cold dust heated by stars increases relative to the amount of emission from hotter dust heated by the agn . it is thus another potentially useful tool to assess the relative amount of star formation in active systems ( e.g. * ? ? ? * ; * ? ? ? the equivalent width ( ew ) of pah grains is another diagnostic to probe the relative amount of star formation to agn activity . an anti - correlation between ionization field hardness and the ratio of pah features at 7.7@xmath2 m and 11.3@xmath2 m has been reported and is interpreted as due to an increasing contribution to the mid - ir continuum emission by agn - heated dust . the selective destruction of smaller pah grains may also play a role ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and so the flux ratios of the different pah features can then also potentially trace the relative contribution of agn and star formation in active galaxies . in this paper , we combine samples of star - forming galaxies , obscured agn ( seyfert 2 galaxies , or sy2s ) and composite systems to study the interplay between agn activity and star formation . using quiescent star forming galaxies as a base - line , we investigate the effects of agn activity on the following star formation diagnostics : optically derived sfrs from the sloan digital sky survey @xcite , the luminosities of the ir fine structure lines [ neii ] 12.81@xmath2 m and [ neiii ] 15.56@xmath2 m @xcite and the luminosities of the polycyclic aromatic hydrocarbons ( pahs ) at 7.7@xmath2 m , 11.3@xmath2 m and 17@xmath2 m @xcite . which of these star formation proxies agree the best among star - forming galaxies and agn and are thus least affected by the presence of an agn ? we expand upon the work of @xcite to test the agreement among diagnostics that parameterize the relative contributions of agn activity and star formation , including the equivalent width ( ew ) of pahs at 7.7 , 11.3 and 17@xmath2 m , ratios of pah fluxes @xcite , ratios of ir fine structure lines @xcite , mid - ir spectral slope ( @xmath5 * ? ? ? * ; * ? ? ? * ) and the optical d parameter @xcite . in @xcite we found that sy2s with stronger pah emission tend to have a softer ionization field and that the mir spectral slope was well correlated with pah ew . by expanding this parameter space into the regime of quiescent star forming galaxies , we test if pah features and the mid - ir spectral slope are dependent on the hardness of the radiation field , regardless of its source , or if ionization by an agn is necessary to appreciably affected observed features . finally , we use the results of this analysis to empirically decompose the mid - ir ( mir ) emission into a star - forming and agn component .

we study a combined sample of 264 star - forming , 51 composite , and 73 active galaxies using optical spectra from sdss and mid - infrared ( mid - ir ) spectra from the spitzer infrared spectrograph . misclassifications of galaxies based on the sdss spectra are rare despite the presence of dust obscuration . the luminosity of the [ neii ] 12.8 emission - line is well correlated with the star formation rate ( sfr ) measured from the sdss spectra , and this holds for the star forming , composite , and agn - dominated systems . we find good qualitative agreement between various parameters that probe the relative contributions of the agn and star formation , including : the mid - ir spectral slope , the ratio of the [ nev ] 14.3 to [ neii ] 12.8 fluxes , the equivalent widths of the 7.7 , 11.3 , and 17 pah features , and the optical d " parameter which measures the distance a source lies from the locus of star forming galaxies in the optical bpt emission - line diagnostic diagram .

we study a combined sample of 264 star - forming , 51 composite , and 73 active galaxies using optical spectra from sdss and mid - infrared ( mid - ir ) spectra from the spitzer infrared spectrograph . we examine optical and mid - ir spectroscopic diagnostics that probe the amount of star formation and relative energetic contributions from star formation and an active galactic nucleus ( agn ) . overall we find good agreement between optical and mid - ir diagnostics . misclassifications of galaxies based on the sdss spectra are rare despite the presence of dust obscuration . the luminosity of the [ neii ] 12.8 emission - line is well correlated with the star formation rate ( sfr ) measured from the sdss spectra , and this holds for the star forming , composite , and agn - dominated systems . agn show a clear excess of [ neiii ] 15.6 emission relative to star forming and composite systems . we find good qualitative agreement between various parameters that probe the relative contributions of the agn and star formation , including : the mid - ir spectral slope , the ratio of the [ nev ] 14.3 to [ neii ] 12.8 fluxes , the equivalent widths of the 7.7 , 11.3 , and 17 pah features , and the optical d " parameter which measures the distance a source lies from the locus of star forming galaxies in the optical bpt emission - line diagnostic diagram . we also consider the behavior of the three individual pah features by examining how their flux ratios depend upon the degree of agn - dominance . we find that the pah 11.3 feature is significantly suppressed in the most agn - dominated systems .

1206.5830

c

we have explored the infrared and optical parameter space where star - forming galaxies , composites and agn live to analyze diagnostics that parameterize host galaxy star formation . using star - forming galaxies as a control sample , we have investigated which star formation diagnostics are least affected by agn activity . we have studied diagnostics that trace the interplay between agn and starburst activity and tested whether a smooth transition exists over a range of radiation field hardness . finally , using the results of this analysis , we present an empirical decomposition of the mir flux into a star - forming and an agn component . _ our overall result is that the optical and mid - ir diagnostics of star formation and of the relative importance of young stars and the agn generally agree well . _ our more specific results are summarized as follows : * sfr diagnostics * the sdss derived sfr@xmath18 and the [ neii ] 12.81@xmath2 m luminosity agree well , and are the most reliable sf proxies we have considered for use in star - forming galaxies , composites and agn . the sum of [ neii ] and [ neiii ] 15.56@xmath2 m is systematically offset to higher values for agn due to the active nucleus boosting the [ neiii ] flux . the aggregate pah luminosity ( l@xmath25 ) relative to l@xmath23}$ ] is suppressed in agn compared with both quiescent and composite galaxies . though the ( l@xmath25)/sfr@xmath18 ratio agrees between star - forming galaxies and sy2s , analysis of pah flux ratios indicate abnormal behavior in some agn dominated systems , such as suppression of the 11.3@xmath2 m feature , suggesting diminished pah emission in strong agn rather than [ neii ] enhancement . the disparate slopes of ( l@xmath25)/sfr@xmath18 between sy2s and star - forming galaxies also hint that agn may contaminate the emission from pah macro - molecules . * ionization field hardness * we have used the optical d parameter , which indicates the distance a source lies from the star - forming galaxy locus on the bpt diagram @xcite , and l@xmath33}$]/l@xmath23}$ ] @xcite as probes of the incident radiation field hardness . the infrared diagnostics that parameterize the relative contributions of agn to star - forming activity that we have considered ( @xmath5 , pah ews and pah flux ratios ) only show significant trends with ionization field hardness in the agn population . this result suggests that rather than parameterizing incident radiation hardness in general , these ir diagnostics are only effective descriptors of ionization field hardness in agn . in agn , the spectral slope between 20 - 30 @xmath2 m ( measured by the spectral index @xmath5 ) has been shown to steepen in the presence of cold dust due to star formation @xcite . for the agn in our sample , @xmath5 is significantly anti - correlated with proxies of ionization field hardness , albeit with wide scatter , however this result does not hold when expanded into the regime of quiescent star forming galaxies . * pah ew * pah ews are significantly anti - correlated with the increasing hardness of radiation field , but this is only true when considering the agn . when considering just the star - forming galaxies , no trend exists between incident radiation hardness and the strength of the resulting pah feature , which agrees with the findings of @xcite and @xcite . this result is consistent with the hypothesis that the mid - ir continuum has a significant contribution from dust heated by the agn only in objects where the ionizing radiation field is dominated by the agn . for the 11.3@xmath2 m pah feature , our analysis of the pah flux ratios suggests that destruction of the pah macro - molecule in strong agn could also contribute to suppression of the pah 11.3@xmath2 m ew . * pah flux ratios * we find that the luminosity of pah 11.3 @xmath0 feature is signifcantly suppressed relative to the luminosities of the pah 7.7 @xmath0 and 17 @xmath0 features and relative to the optical and mid - ir derived star formation rates in the most agn - dominated systems . thus , some care is required in using the pah 11.3@xmath2 m luminosity as a proxy for the sfr in agn - dominated systems . * composite systems * galaxies that are optically classified as composite systems are more akin to quiescent star forming galaxies in terms of the mid - ir parameters that trace star formation : the smaller relative energetic importance of the agn in composites does not seem to affect [ neiii ] and pah luminosities . * [ nev ] as unambiguous agn signature * due to the high ionization potential of [ nev ] ( 97.1 ev ) , it is potentially an unequivocal signature of agn activity @xcite . one galaxy that is optically classied as a quiescent star - forming system in our sample has a [ nev ] detection , yet other ir parameters ( i.e. pah ew values ) are normal for a pure star forming galaxy . the nature of this galaxy as a strong `` hidden '' agn is not clear . * disentangling mir emission * using multiple linear regression , we fit the relation l@xmath38 = @xmath1l@xmath40 + @xmath4l@xmath41 to our full sample to determine @xmath1 and @xmath4 . we set l@xmath40 = l@xmath23}$ ] and l@xmath41=l@xmath42,agn}$ ] where in l@xmath42,agn}$ ] , we have subtracted out the estimated starburst contribution to the [ oiii ] flux using eq . 3 in @xcite . we find @xmath1=89@xmath431 and @xmath4=111@xmath437 . this decomposition can be useful in estimating the mir emission due to the circumnuclear agn obscuration or conversely host galaxy star formation in agn . lccccccc 33 & 160.291 & 56.932 & 0.185 & agn & 8.12@xmath43 0.70 & ... & 3.34@xmath43 0.57 + 61 & 160.952 & 58.197 & 0.073 & agn & 3.19@xmath43 0.08 & ... & 0.30@xmath43 0.05 + 11 & 161.720 & 56.252 & 0.047 & comp & 0.17@xmath43 0.01 & ... & @xmath46 0.06 + 12 & 162.268 & 56.224 & 0.072 & comp & 3.04@xmath43 0.09 & ... & 0.31@xmath43 0.04 + 15 & 161.758 & 56.307 & 0.153 & comp & 4.40@xmath43 0.30 & ... & @xmath46 1.64 + lcccccc 36.380 & -8.419 & 0.055 & agn & 1.16@xmath43 0.05 & ... & 1.02@xmath43 0.07 + 36.435 & -7.868 & 0.077 & agn & 2.72@xmath43 0.12 & ... & 1.03@xmath43 0.08 + 132.186 & 53.746 & 0.083 & agn & 4.72@xmath43 0.14 & 1.18@xmath43 0.09 & 2.54@xmath43 0.08 + 132.714 & 54.823 & 0.081 & agn & 3.17@xmath43 0.11 & ... & 2.25@xmath43 0.07 + 132.815 & 54.986 & 0.083 & agn & 3.64@xmath43 0.16 & ... & 1.68@xmath43 0.09 + ngc 291 & 13.375 & -8.768 & 0.019 & 1.61@xmath43 0.04 & 0.60@xmath43 0.02 & 1.12@xmath43 0.02 + mrk 609 & 51.356 & -6.144 & 0.034 & 5.51@xmath43 0.12 & ... & 1.80@xmath43 0.06 + ic 0486 & 120.087 & 26.614 & 0.027 & 1.10@xmath43 0.10 & 0.55@xmath43 0.06 & 1.04@xmath43 0.05 + 2masx j08035923 + 2345201 & 120.997 & 23.756 & 0.029 & ... & @xmath46 0.14 & @xmath46 0.42 + 2masx j08244333 + 2959238 & 126.180 & 29.990 & 0.025 & 0.54@xmath43 0.06 & 0.55@xmath43 0.07 & 0.70@xmath43 0.06 + iras 00198 - 7926 & 5.473 & -79.169 & 0.073 & agn & 35.65@xmath43 1.45 & 49.05@xmath43 1.53 & 60.06@xmath43 1.31 + ngc 0424 & 17.865 & -38.083 & 0.012 & agn & 3.06@xmath43 0.19 & 4.64@xmath43 0.27 & 5.67@xmath43 0.17 + ngc 1068 & 40.670 & -0.013 & 0.004 & agn & 5.34@xmath43 0.28 & 10.11@xmath43 0.48 & 15.02@xmath43 0.32 + ngc 1144 & 43.790 & -0.178 & 0.028 & agn & 10.79@xmath43 0.26 & 0.61@xmath43 0.10 & 2.88@xmath43 0.05 + ngc 1320 & 51.203 & -3.042 & 0.009 & agn & 0.47@xmath43 0.02 & 0.59@xmath43 0.02 & 0.78@xmath43 0.02 + lccccccc 13 & agn & 16.59@xmath43 0.82 & 1.23 & 7.61@xmath43 0.32 & 0.39 & 6.12@xmath43 1.09 & 0.27 + 21 & agn & 30.66@xmath43 1.73 & 2.95 & 10.80@xmath43 0.60 & 1.43 & 6.44@xmath43 0.49 & 1.09 + 23 & agn & ... & ... & ... & ... & ... & ... + 33 & agn & 157.18@xmath43 6.51 & 3.14 & 53.40@xmath43 1.08 & 1.01 & 37.98@xmath43 3.62 & 0.66 + 50 & agn & ... & ... & ... & ... & ... & ... + lcccccccc 36.380 & -8.419 & agn & 24.01@xmath43 2.34 & 5.74 & 7.92@xmath43 0.71 & 3.62 & 15.13@xmath43 2.76 & 2.28 + 36.435 & -7.868 & agn & 59.59@xmath43 4.64 & 1.44 & 16.41@xmath43 0.62 & 0.53 & 7.79@xmath43 1.54 & 0.28 + 132.186 & 53.746 & agn & 144.14@xmath43 5.69 & 4.81 & 41.27@xmath43 0.81 & 1.81 & 32.40@xmath43 1.82 & 1.38 + 132.714 & 54.823 & agn & 54.59@xmath43 5.05 & 4.51 & 21.61@xmath43 0.71 & 1.89 & 16.96@xmath43 1.69 & 1.04 + 132.815 & 54.986 & agn & 107.85@xmath43 3.30 & 5.05 & 29.54@xmath43 0.49 & 1.62 & 19.68@xmath43 1.23 & 1.17 + lcccccc ngc 0291 & 34.69@xmath43 0.95 & 10.07 & 7.44@xmath43 0.15 & 0.75 & 9.20@xmath43 0.15 & 0.50 + mrk 0609 & ... & ... & 52.35@xmath43 0.78 & 1.08 & 54.58@xmath43 0.54 & 0.94 + ic 0486 & 22.69@xmath43 0.47 & 0.75 & 4.15@xmath43 0.19 & 0.12 & 5.77@xmath43 0.12 & 0.16 + 2masx j08035923 + 2345201 & ... & ... & 1.49@xmath43 0.05 & 0.30 & 2.10@xmath43 0.13 & 0.40 + 2masx j08244333 + 2959238 & ... & ... & 2.80@xmath43 0.16 & 0.04 & 5.67@xmath43 0.29 & 0.10 + ngc 0424 & agn & 10.25@xmath43 0.65 & 0.09 & 4.46@xmath43 0.35 & 0.06 & 8.05@xmath43 0.61 & 0.19 + ngc 1144 & agn & 258.85@xmath43 1.37 & 2.21 & 92.63@xmath43 0.99 & 1.83 & 51.43@xmath43 0.73 & 1.56 + ngc 1320 & agn & 9.69@xmath43 0.38 & 0.52 & 2.45@xmath43 0.08 & 0.16 & 1.31@xmath43 0.12 & 0.11 + ngc 1386 & agn & 0.84@xmath43 0.02 & 0.71 & 0.16@xmath43 0.00 & 0.14 & 0.26@xmath43 0.01 & 0.27 + ngc 1667 & agn & 61.97@xmath43 1.14 & 3.85 & 18.76@xmath43 0.22 & 2.18 & 9.18@xmath43 0.13 & 1.63 + l@xmath23}$]/sfr@xmath18 & 40.97@xmath47 & 223 & 40.91@xmath48 & 32 & 40.92@xmath49 & 39 + ( l@xmath23}$]+l@xmath24}$])/sfr@xmath18 & 40.84@xmath50 & 223 & 40.74@xmath51 & 32 & 41.11@xmath52 & 39 + l@xmath25/sfr@xmath18 & 42.50@xmath53 & 261 & 42.59@xmath54 & 46 & 42.49@xmath55 & 35 + l@xmath25/l@xmath23}$ ] & 1.50 & 207 & 1.59@xmath56 & 31 & 1.33@xmath57 & 21 & pah uls + l@xmath23}$]/l@xmath25 & -1.61 & 141 & -1.62@xmath58 & 25 & -1.50@xmath59 & 17 & [ neii ] uls + l@xmath23}$]/sfr@xmath18 & 0.127 & 255 & 0.598 & 71 & 0.624 & 223 + ( l@xmath23}$]+l@xmath24}$])/sfr@xmath18 & 0.175 & 255 & 0.0005 & 71 & @xmath461@xmath60 & 262 + l@xmath25/sfr@xmath18 & 0.331 & 307 & 0.365 & 81 & 0.758 & 296 + l@xmath25/l@xmath23}$ ] & 0.213 & 238 & 0.0002 & 77 & 0.003 & 253 & pah uls + l@xmath23}$]/l@xmath25 & 0.945 & 166 & 0.006 & 42 & 0.0004 & 158 & [ neii ] uls + l@xmath33}$]/l@xmath23}$ ] vs. d & 0.562 & 4@xmath60 + l@xmath33}$]/l@xmath23}$ ] vs. @xmath5 & -0.568 & 6@xmath60 + l@xmath33}$]/l@xmath23}$ ] vs. pah ew 7.7 @xmath2 m & -0.702 & 1@xmath60 + l@xmath33}$]/l@xmath23}$ ] vs. pah ew 11.3 @xmath2 m & -0.779 & @xmath61 + l@xmath33}$]/l@xmath23}$ ] vs. pah ew 17 @xmath2 m & -0.628 & 2@xmath60 + d vs. pah ew 7.7 @xmath2 m & -0.679 & 344 + d vs. pah ew 11.3 @xmath2 m & -0.747 & 368 + d vs. pah ew 17 @xmath2 m & -0.658 & 281 + + + + d vs. pah ew 7.7 @xmath2 m & -0.227 & 291 + d vs. pah ew 11.3 @xmath2 m & -0.125 & 303 + d vs. pah ew 17 @xmath2 m & -0.230 & 221 + + + + d vs. pah ew 7.7 @xmath2 m & -0.566 & 318 + d vs. pah ew 11.3 @xmath2 m & -0.653 & 336 + d vs. pah ew 17 @xmath2 m & -0.549 & 249 + + + l@xmath35/l@xmath36 & -0.241 & 33 + l@xmath37/l@xmath36 & -0.564 & 37 + l@xmath35/l@xmath37 & 0.611 & 34 + + + + l@xmath35/l@xmath36 & -0.193 & 266 + l@xmath37/l@xmath36 & -0.364 & 278 + l@xmath35/l@xmath37 & 0.179 & 340 + + + + l@xmath35/l@xmath36 & 0.082 & 47 + l@xmath37/l@xmath36 & -0.247 & 58 + l@xmath35/l@xmath37 & 0.431 & 51 + + + + l@xmath35/l@xmath36 & -0.283 & 240 + l@xmath37/l@xmath36 & -0.356 & 246 + l@xmath35/l@xmath37 & 0.084 & 314 + + + + l@xmath35/l@xmath36 & -0.208 & 22 + l@xmath37/l@xmath36 & -0.554 & 27 + l@xmath35/l@xmath37 & 0.590 & 26 +

we examine optical and mid - ir spectroscopic diagnostics that probe the amount of star formation and relative energetic contributions from star formation and an active galactic nucleus ( agn ) . overall we find good agreement between optical and mid - ir diagnostics . we also consider the behavior of the three individual pah features by examining how their flux ratios depend upon the degree of agn - dominance . we find that the pah 11.3 feature is significantly suppressed in the most agn - dominated systems .

we study a combined sample of 264 star - forming , 51 composite , and 73 active galaxies using optical spectra from sdss and mid - infrared ( mid - ir ) spectra from the spitzer infrared spectrograph . we examine optical and mid - ir spectroscopic diagnostics that probe the amount of star formation and relative energetic contributions from star formation and an active galactic nucleus ( agn ) . overall we find good agreement between optical and mid - ir diagnostics . misclassifications of galaxies based on the sdss spectra are rare despite the presence of dust obscuration . the luminosity of the [ neii ] 12.8 emission - line is well correlated with the star formation rate ( sfr ) measured from the sdss spectra , and this holds for the star forming , composite , and agn - dominated systems . agn show a clear excess of [ neiii ] 15.6 emission relative to star forming and composite systems . we find good qualitative agreement between various parameters that probe the relative contributions of the agn and star formation , including : the mid - ir spectral slope , the ratio of the [ nev ] 14.3 to [ neii ] 12.8 fluxes , the equivalent widths of the 7.7 , 11.3 , and 17 pah features , and the optical d " parameter which measures the distance a source lies from the locus of star forming galaxies in the optical bpt emission - line diagnostic diagram . we also consider the behavior of the three individual pah features by examining how their flux ratios depend upon the degree of agn - dominance . we find that the pah 11.3 feature is significantly suppressed in the most agn - dominated systems .

1003.0366

i

quantum brownian motion ( qbm ) of a particle or charge in a tilted periodic potential is one of the basic subjects of nonequilibrium quantum - statistical mechanics and a key model for a multitude of quantum transport phenomena in condensed matter @xcite . of particular interest is a duality symmetry between the weak- and strong - binding representations of the model @xcite . there is a close correspondence of the qbm model with seemingly different models : ( i ) a resistively shunted josephson junction @xcite , ( ii ) a quantum impurities in a 1d wire @xcite , ( iii ) tunneling of edge currents through constrictions in fractional quantum - hall devices @xcite , and ( iv ) a coherent one - channel conductor in a resistive electromagnetic environment @xcite . in fact , all these models are directly related to each other . the calculation of the dynamics may be done with the use of the feynman - vernon influence functional method @xcite or the equivalent nonequilibrium keldysh technique . in this theory , the reduced density matrix ( rdm ) is expressed as a double path sum over all possible paths on the rdm - plane . the path sum problem is formally equivalent to the grand - canonical sum of a charge gas with complex - valued interactions . of particular interest is the scaling or field theory limit . until now the respective real - time coulomb gas has not been solved analytically barring special cases . one may also consider the system in imaginary time compactified on a circle of length @xmath1 , where @xmath2 is the temperature . in the field theory limit , the charges of the respective coulomb gas interact with a `` log - sine '' long range interaction . the compactified coulomb gas has been solved analytically for particular unphysical values of the bias with the tool of jack symmetric functions @xcite . the consideration of nonequilibrium quantum transport requires ( i ) analytic continuation of the calculated partition function to the physical bias , and ( ii ) a conjectured relation between the analytically continued partition function and transport quantities @xcite . here we analyze this route in different parameter regimes , and we compare the findings with results available by different methods . our paper is organized as follows . in section [ sgtm ] we introduce several related models , which may describe nonequilibrium quantum transport of a particle or a charge , josephson junction dynamics , scattering off an impurity embedded in a luttinger liquid , and conductance of one - channel conductors in a resistive electromagnetic environment . in section [ scgr ] we review the solution of the `` log - sine '' coulomb gas on a circle with winding numbers . in section [ scond ] we study the conjecture for the nonlinear conductance in the weak - tunneling regime , in the classical regime , and in the zero temperature limit . in section [ snoise ] we compare the results of the imaginary time approach with those of the real - time keldysh method . we also address the issue of statistical fluctuations . section [ sconcl ] is devoted to concluding remarks .

they have calculated the perturbative series of twisted partition functions , which require particular ( unphysical ) imaginary values of the bias , by applying the tools of jack symmetric functions to the `` log - sine '' coulomb gas on a circle . we have analyzed the conjectured relation between the analytically continued free energy and the nonlinear conductance in various limits . we confirm the conjecture for weak and strong tunneling , in the classical regime , and in the zero temperature limit . we also shed light on this special variant of the-method and compare it with the real - time keldysh approach . in addition , we address the issue of quantum statistical fluctuations .

we study a conjecture by fendley , ludwig and saleur for the nonlinear conductance in the boundary sine - gordon model . they have calculated the perturbative series of twisted partition functions , which require particular ( unphysical ) imaginary values of the bias , by applying the tools of jack symmetric functions to the `` log - sine '' coulomb gas on a circle . we have analyzed the conjectured relation between the analytically continued free energy and the nonlinear conductance in various limits . we confirm the conjecture for weak and strong tunneling , in the classical regime , and in the zero temperature limit . we also shed light on this special variant of the-method and compare it with the real - time keldysh approach . in addition , we address the issue of quantum statistical fluctuations . quantum transport , full counting statistics , quantum impurity problem , coulomb gas , jack polynomials 05.60.gg , 05.40.ca , 71.10.pm , 73.50.td

1206.2656

i

classical ldpc codes , it hardly needs to be recalled , come together with very efficient and fast decoding algorithms and overall display extremely good performance for a variety of channels . quantum error - correcting codes on the other hand , under the guise of the css @xcite scheme , are in some ways strikingly similar to classical codes , and in particular can be decoded with purely classical means . it is therefore natural to try to import the classical ldpc know - how to the quantum setting . there is however a structural obstacle . a quantum css code is defined by two binary parity - check matrices whose row - spaces must be orthogonal to each other . to have a quantum ldpc code decodable by message - passing these two matrices should be sparse , as in the classical case . therefore , randomly choosing these matrices , the generic method which works very well in the classical case , is simply not an option in the quantum case , because the probability of finding two sparse row - orthogonal matrices is extremely small . a number of constructions have been suggested by classical coding theorists nevertheless @xcite but they do not produce families of quantum ldpc codes with a minimum distance growing with the blocklength . while this may be tolerable for practical constructions of fixed size , this is clearly an undesirable feature of any asymptotic construction and it raises the intriguing theoretical question of how large can the minimum distance of sparse ( or ldpc ) css codes be . families of sparse css codes with a growing minimum distance do exist , the most well - known of these being kitaev s toric code @xcite , which has been generalised to codes based on tesselations of surfaces ( see _ e.g. _ @xcite ) and higher - dimensional objects . these constructions exhibit minimum distances that scale at most as a square root of the blocklength @xmath5 ( to be precise , @xmath6 is achieved in @xcite ) though this often comes at the cost of a very low dimension ( recall that the dimension of the toric code is @xmath7 ) . it is an open question as to whether families of sparse css codes exist with a minimum distance that grows at least as @xmath8 for @xmath9 , even for quantum codes with dimension @xmath10 . the recent construction @xcite manages to reconcile a minimum distance of the order of @xmath11 with a dimension linear in the blocklength . all these constructions borrow ideas from topology and can be seen as some generalisation of kitaev s toric code . in a follow - up to the paper @xcite mackay , mitchison and shokrollahi @xcite proposed a construction that seemingly owes very little to the topological approach . they noticed that the adjacency matrix of any cayley graph over @xmath12 with an even set of generators is self - dual and can therefore be used to define a sparse css code . experiments with some cayley graphs were encouraging . in the present work we take up the theoretical study of the parameters of these css codes which was left open by mackay _ et al . _ the quantum code in the construction is defined by a classical @xmath13 $ ] linear binary code where @xmath14 must be even . its length is @xmath15 , and the row - weight of the parity - check matrix is @xmath14 . the dimension and the minimum distance of the quantum code does not depend solely on the classical code s parameters , but depend more subtly on its structure . we solve the problem in the first non - trivial case , which was an explicit question of mackay _ et al . _ , namely the case when the classical code is the @xmath3 $ ] repetition code . computing the parameters of the associated quantum code turns out to be not easy , even in this apparently simple case . our main result , theorem [ thm : main ] , gives the exact parameters for this quantum code , namely : @xmath16.\ ] ] the construction therefore hits the @xmath11 barrier for the minimum distance , but it is quite noteworthy that it does so using a construction that breaks significantly with the topological connection . for quantum codes based on more complicated classical @xmath13 $ ] structures , similarly precise results seem quite difficult to obtain , but we managed to prove a lower bound on the quantum minimum distance of the form @xmath17 for some constant @xmath18 ( theorem [ thm : min_dist ] ) . notice that the constructed quantum ldpc codes have not a constant row - weight . indeed , this weight is logarithmic in the blocklength . this has its drawbacks since decoding will be slightly more complex , we remark however that the best families of classical ldpc codes ( i.e. capacity - achieving ldpc codes ) all have row weights that grow logarithmically in the block length . we note also that it was recently proved in @xcite that quantum ldpc stabilizer codes can not achieve the capacity of the quantum erasure channel if their stabilizer matrices have constant row weight . some prerequisites on quantum and quantum css codes together with some basic notions on cayley graphs are recalled in section [ sec : prelim ] . in sections [ sec : basic ] , we describe some basic properties of cayley graphs associated to the group @xmath0 . in section [ sec : hamm ] , we focus on the properties of the _ hamming hypercube _ , that is the cayley graph @xmath19 , where @xmath20 denotes the canonical basis . in particular , we observe some nice property : for almost all families @xmath21 of generators of @xmath22 , the cayley graph @xmath23 looks locally like the hamming hypercube of dimension @xmath24 . in section [ sec : dist ] , we study the minimum distance of a quantum code associated to a cayley graph of @xmath0 and show that this distance is at least quadratic in @xmath14 . finally in section [ sec : repet ] , we focus on the example studied by mitchison _ _ in @xcite and give the exact parameters of this family of quantum codes .

we study a construction of quantum ldpc codes proposed by mackay , mitchison and shokrollahi . it is based on the cayley graph of together with a set of generators regarded as the columns of the parity check matrix of a classical code . * msc : * 94c15 , 05c99 , 94b99 * key words : * quantum codes , ldpc codes , cayley graphs , graph covers . * notes . * the material in this paper was presented in part at isit 2011 . this article is published in _ we point out that the second step of the proof of proposition vi.2 in the published version ( proposition [ prop : wrong_proof ] in the present version and proposition 18 in the isit extended abstract ) is not strictly correct . this issue is addressed in the present version .

we study a construction of quantum ldpc codes proposed by mackay , mitchison and shokrollahi . it is based on the cayley graph of together with a set of generators regarded as the columns of the parity check matrix of a classical code . we give a general lower bound on the minimum distance of the quantum code in where is the minimum distance of the classical code . when the classical code is the $ ] repetition code , we are able to compute the exact parameters of the associated quantum code which are $ ] . * msc : * 94c15 , 05c99 , 94b99 * key words : * quantum codes , ldpc codes , cayley graphs , graph covers . * notes . * the material in this paper was presented in part at isit 2011 . this article is published in _ ieee transactions on information theory _ . we point out that the second step of the proof of proposition vi.2 in the published version ( proposition [ prop : wrong_proof ] in the present version and proposition 18 in the isit extended abstract ) is not strictly correct . this issue is addressed in the present version .

nucl-th9709062

i

there exist many nucleon - nucleon potentials which reproduce phase shifts and nuclear properties with remarkable accuracy @xcite . three fundamental features are shared by these potential models : ( i ) pions dominate at long distances , ( ii ) there is some source of intermediate - range attraction , and ( iii ) there is some source of short - distance repulsion . however , in general , distinct physical mechanisms in these models account for the same feature of the nuclear force . agreement with experiment is maintained in spite of these differences because of the large number of fit parameters . it would be a considerable advance if a systematic approach to the nucleon - nucleon interaction could be developed based solely on symmetries and general physical principles . systematic approaches to the scattering of strongly interacting particles , such as chiral perturbation theory , are based on the ideas of effective field theory ( eft ) . effective field theory says that for probes of a system at momentum @xmath2 , details of the dynamics at scale @xmath3 are unimportant . what is important at low energies is the physics that can be captured in operators of increasing dimensionality which take the form of a power - series in the quantity @xmath4 it is important to realize that even if eft ideas can be applied to the @xmath0 system they will probably not lead to any startlingly new predictions for @xmath0 scattering . indeed , it is entirely possible that the resulting fits to phase shifts will not be as good as those produced by conventional @xmath0 potentials with the same number of parameters . however , the real motivation for constructing an eft is to relate one process to another . for instance , one would like to relate @xmath0 scattering systematically to scattering processes with more nucleons , such as @xmath5 and @xmath6 scattering , and to say something predictive about processes involving pionic and photonic probes of few - nucleon systems . one reason to hope that this can be achieved in nuclear physics is provided by the pattern of chiral symmetry breaking in qcd . the fact that chiral symmetry is spontaneously broken implies that the pion is light and interacts weakly at low energies of course the lightness of the pion in itself guarantees that it should play a fundamental role in nuclear physics . the weakness of pion interactions at low energies allows pion interactions with nucleons to be systematized using chiral perturbation theory . this procedure has proved remarkably successful in describing the interactions of pions with a single nucleon @xcite . these ideas have been extended to processes involving more than one nucleon , leading to arguments concerning the relative importance of various pion - exchange mechanisms in the nuclear force @xcite . however , these eft arguments assume the existence of a systematic power - counting scheme for multi - nucleon processes . in our view there is no convincing argument in the literature that such a power counting exists . the purpose of this paper is to investigate this issue in the simplest possible context . naive transposition of eft ideas to nuclear physics immediately suggests a puzzle . in nuclear physics there are bound states whose energy is unnaturally small on the scale of hadronic physics . in order to generate such bound states within a `` natural '' theory it is clear that one must sum a series to all orders . therefore , weinberg proposed @xcite implementing the eft program in nuclear physics by applying the power - counting arguments of chiral perturbation theory to an @xmath7-nucleon effective potential rather than directly to the s - matrix . only @xmath7-nucleon irreducible graphs should be included in the @xmath7-nucleon effective potential . the potential obtained in this way is then to be inserted into a lippmann - schwinger or schrdinger equation and iterated to all orders . there will of course be unknown coefficients in the effective potential , but these can be fit to experimental data as in ordinary chiral perturbation theory @xcite . thus , an eft treatment of the @xmath0 interaction differs in a fundamental way from conventional eft applications like @xmath8 scattering in chiral perturbation theory . in both cases operators are ordered in an effective lagrangian in the same way . however , in @xmath9 scattering the operator expansion in the effective lagrangian maps to a power series in @xmath4 in the scattering amplitude . it is straightforward to see that eft treatments where there is a direct mapping from the lagrangian to the s - matrix are systematic @xcite . on the other hand , when the mapping is from the lagrangian to an effective potential which is subsequently iterated to all orders , many issues arise which lead one to question the existence of a systematic power counting in the potential . in order to raise some of these issues , consider @xmath0 scattering in the @xmath10 channel at momentum scales @xmath11 . the eft at these scales involves only nucleons since the pion is heavy and may therefore be `` integrated out '' . the effective lagrangian thus consists of contact operators of increasing dimensionality constrained by spin and isospin . throughout the paper this is the eft which we consider . we do not intend that this eft should provide a quantitative description of the @xmath0 phase shifts . instead , we study it because scattering amplitudes can be calculated analytically . it therefore allows us to elucidate issues of principle in eft for @xmath0 scattering . one might naively expect to be able to calculate the @xmath0 scattering amplitude directly from the effective lagrangian as a power series in @xmath12 , where @xmath13 is the heavy scale in this problem . it is instructive to show in some detail why this fails and one is led to consider an expansion in the potential . consider an expansion of the amplitude in the @xmath14-wave channels : @xmath15 where @xmath16 , and , with the prevailing prejudice of eft , we anticipate that the dimensionless coefficients @xmath17 , @xmath18 , etc . will be natural ; i.e. of order unity . we know that in the @xmath10 and @xmath19 channels there are , respectively , a quasi - bound state and a bound state at low energies . the power series expansion ( [ eq : texp ] ) with natural coefficients can only be correct if these bound states are at energies @xmath20 . however , in these channels the bound states occur at unnaturally low energies , i.e. at energies @xmath21 . therefore , the coefficients in the expansion must be unnatural they are fixed by the pole positions of the low - lying bound states rather than by the scale of the physics that has been integrated out . this limits the usefulness of an expansion in the amplitude to an extremely restricted domain of validity . on the other hand , if one makes the following expansion of the potential in @xmath14-wave channels : @xmath22 and iterates it via the lippmann - schwinger equation ( see fig . [ fig1 ] ) @xmath23 one may hope to generate ( quasi-)bound states at the appropriate energies while maintaining natural coefficients in the potential . at face value this procedure appears promising . the expansion ( [ eq : vexp ] ) may be truncated at some finite order in the quantities @xmath24 and @xmath25 and , provided @xmath26 the neglected terms will be small . however , in making the expansion in the potential of eq . ( [ eq : vexp ] ) and then iterating , a number of issues arise which are absent in standard eft treatments , and which render this procedure suspect . in what follows we will identify and clarify some of these issues . first , the physical scattering amplitude that is generated when the potential ( [ eq : vexp ] ) is iterated is exactly unitary and therefore necessarily contains arbitrarily high powers in energy or momenta . this occurs regardless of the order to which one is working in the momentum expansion of the potential @xmath27 . this suggests that as long as one is interested in physics near the bound state pole where exact unitarity is important the scattering amplitude may be sensitive to physics at arbitrarily short - distance scales . while this observation does not necessarily invalidate the eft approach , it does mean that one should not simply translate intuition gained about how short - distance physics decouples in perturbative eft calculations ( e.g. in chiral perturbation theory ) to the non - perturbative problem at hand . thus , the first question we face is whether a systematic expansion in the potential translates to a systematic determination of the scattering amplitude . a necessary condition for this to occur is that the integrals in the ls equation , which formally extend up to infinity , be dominated by momenta of order @xmath28 , where @xmath29 is the on - shell momentum , since otherwise there is no small parameter in the expansion ( [ eq : vexp ] ) for @xmath27 . second , non - perturbative regularization and renormalization is required when iterating to all orders using the ls equation . this is an issue because of the presence of ultraviolet divergences , which generally can arise in two ways . when explicit pions are included in the eft , the potential itself may contain loop graphs which require regularization and renormalization . these divergences are easily handled using standard perturbative methods . a second type of ultraviolet divergence arises because in solving the ls equation one integrates the potential over all momenta . given the hard asymptotic behavior inherent to the momentum expansion this necessarily introduces new divergences . the divergences which arise from iterating the potential become more severe as one goes to higher order in the eft expansion . these divergences apparently violate the assumption that @xmath30 , so the existence of a procedure to regularize these divergences and renormalize in such a way that the momentum scales probed inside loops are ultimately well below @xmath13 provides a non - trivial condition on the existence of an eft . in ordinary perturbative eft , all regularization schemes lead to the same renormalized amplitude . this insensitivity to the short - distance physics implied by the regulator makes perturbative eft methods like chiral perturbation theory possible . similarly , there is no hope of defining a sensible eft for @xmath0 scattering unless there is some degree of regulator independence . an interesting feature that arises when regularizing and renormalizing the lippmann - schwinger equation is that not all regulators lead to the same physical results . for instance , we will show that dimensional regularization ( dr ) and cutoff schemes lead to different physical scattering amplitudes . this result should give practitioners of eft pause , since it suggests a sensitivity to short - distance physics which violates the basic tenets of eft . we further demonstrate that in order to generate low - energy ( quasi-)bound states in the @xmath0 system within this eft , one must use a scale - dependent regulator . cutoff schemes provide the most physical means of regularizing the effective theory . we therefore focus on whether it is possible to implement the regularization and renormalization program in a consistent fashion using cutoff schemes . within this restricted class of regulators physical results are insensitive to the specific choice of regulator . however , we find that taking the cutoff to infinity requires that the effective range parameter in the scattering amplitude be negative . in physical processes of interest the effective range parameter is positive . the impossibility of maintaining a positive effective range when the cutoff is removed follows from an old theorem of wigner , which depends only on general physical principles @xcite . therefore , either the cutoff must be kept finite or else all orders in the effective potential must be retained . using an extension of wigner s theorem to the eft where pions are explicitly included , we further argue that the inclusion of pions as explicit degrees of freedom in the eft does not resolve these difficulties . having found that an eft with only nucleons as explicit degrees of freedom can work only if there is a finite cutoff or regulator scale , we investigate the possibility of a cutoff effective field theory . in cutoff eft , cutoff dependence in physical observables is removed systematically by adding higher - dimensional operators to the effective action . however , this procedure makes sense only if there is a small parameter which allows one to conclude that higher - order operators in the action are negligible . we show that there is no such small parameter in @xmath0 scattering when there are low - energy ( quasi-)bound states . we stress that we _ are not _ questioning the existence of an effective field theory of @xmath0 scattering . since the principles underlying eft are causality and locality , an eft of @xmath0 scattering must exist unless a sacred principle is violated . the question we address is : `` what are the relevant low - energy degrees of freedom which must be included explicitly in the eft ? '' the problem of @xmath0 scattering is subtle in this respect because generally there are singularities at unnaturally low energies ( e.g. , the deuteron ) in scattering amplitudes . these singularities are not present as fields in the effective action . what our analysis here shows is that if low - lying bound states are present then there is no systematic eft for @xmath0 scattering in which there are only nucleon fields in the effective lagrangian . this would suggest the necessity of introducing the physics of ( quasi-)bound states in terms of explicit degrees of freedom in the eft description . a step in this direction has been taken in ref . @xcite , but in this paper we will not discuss such ideas further . therefore , we use the term eft to mean an effective field theory in which low - energy bound states are not included as fields in the effective action , i.e. an eft in which only nucleons ( and pions ) are explicit degrees of freedom . in sec . 2 we discuss the @xmath10 channel in @xmath0 scattering and introduce a simple potential model that reproduces data remarkably well . this model demonstrates how an unnaturally small scale can emerge from a theory with only large scales . in sec . 3 we review the effective field theory power - counting argument for @xmath0 scattering , originally proposed by weinberg . in particular , we examine arguments for power counting in the potential rather than in the amplitude in the @xmath0 problem . in sec . 4 we perform a `` leading - order '' eft calculation for @xmath0 scattering in the @xmath10 channel and show that all regularization schemes give the same scattering amplitude . in sec . 5 we perform a `` second - order '' eft calculation using cutoff regularization . we show that if a cutoff is introduced such that the regulated theory respects all physical principles , then the cutoff can not be taken to infinity . we discuss how this result relates to an old theorem of wigner . in sec . 6 we compare dimensional regularization ( dr ) and cutoff regularization schemes . we show that dr and cutoff regularization give different physical scattering amplitudes in the second - order eft calculation , indicating that there is a sensitivity to the choice of regulator , and therefore to short - distance physics . we find that the presence of a regulator scale is necessary to reproduce unnaturally low - lying ( quasi- ) bound states . in sec . 7 we consider the possibility of an effective field theory with a finite cutoff . we find that although a procedure whereby cutoff dependence in the amplitude is removed by adding higher orders in the effective potential can be defined , the small parameter which is necessary to conclude that this is systematic is simply not present . we summarize and conclude in sec .

the potential is conjectured to be the sum of a delta function and its derivatives . regularizing the lippmann - schwinger equation using a cutoff we find that the cutoff can be taken to infinity only if the effective range is negative . comparison of cutoff schemes and dimensional regularization reveals that the physical scattering amplitude is sensitive to the choice of regulator . we also show that one can define a procedure where finite cutoff dependence in the scattering amplitude is removed order by order in the effective potential . it follows that in the presence of a finite cutoff there is no small parameter in the effective potential , and consequently no systematic truncation of the derivative expansion can be made . pp # 98 - 024 + + department of physics , university of maryland , college park , md , 20742 - 4111

we study an effective field theory of interacting nucleons at distances much greater than the pion s compton wavelength . in this regime the potential is conjectured to be the sum of a delta function and its derivatives . the question we address is whether this sum can be consistently truncated at a given order in the derivative expansion , and systematically improved by going to higher orders . regularizing the lippmann - schwinger equation using a cutoff we find that the cutoff can be taken to infinity only if the effective range is negative . a positive effective range which occurs in nature requires that the cutoff be kept finite and below the scale of the physics which has been integrated out , i.e. . comparison of cutoff schemes and dimensional regularization reveals that the physical scattering amplitude is sensitive to the choice of regulator . moreover , we show that the presence of some regulator scale , a feature absent in dimensional regularization , is essential if the effective field theory of scattering is to be useful . we also show that one can define a procedure where finite cutoff dependence in the scattering amplitude is removed order by order in the effective potential . however , the characteristic momentum in the problem is given by the cutoff , and not by the external momentum . it follows that in the presence of a finite cutoff there is no small parameter in the effective potential , and consequently no systematic truncation of the derivative expansion can be made . we conclude that there is no effective field theory of scattering with nucleons alone . = 0.0 in = 0.0 in = 6.5 in = 8.9 in = 0.0 in = 0.0 in = 0.0 in = 0.25 in = -1 cm u.md . pp # 98 - 024 + + department of physics , university of maryland , college park , md , 20742 - 4111

nucl-th9709062

c

our results are discouraging for any effective field theory description of @xmath0 scattering in which low - lying bound states are not included as explicit degrees of freedom . these low - energy bound and quasi - bound states exist in nuclear physics , and so , if efts in which they are not explicitly included are to be useful , power - counting arguments can only apply to the @xmath0 potential , rather than to the @xmath0 amplitude . solving such an eft with nucleons would appear to be a simple problem in non - relativistic quantum mechanics . however , the problem is complicated by the appearance of power - law divergences which arise from the internal loop integrations in the lippmann - schwinger equation . in perturbative efts such divergences are renormalized away and have no effect on the physical amplitude . in fact , if this were not the case there would be no consistent power counting in these theories . by contrast , when the second - order eft potential is iterated to all orders , we find that the resulting scattering amplitude is inevitably regularization scheme dependent : dimensional regularization and cutoff regularization give different renormalized scattering amplitudes . we are therefore forced to conclude that the physical scattering amplitude is sensitive to the power - law divergences arising from loop integrations . one way to understand this sensitivity is to realize that when cutoff regularization is used the potential acquires a range , which is naively @xmath73 . when the schrdinger equation is solved all physical observables depend on the upper limit in internal loop integrations , @xmath71 . in any perturbative calculation this dependence can be removed by the introduction of a finite number of higher - dimensional operators in the lagrangian . however , for some observables , e.g. the effective range , this can not be achieved for arbitrary cutoff in our non - perturbative calculation : these observables still depend on the cutoff ( equivalently , on the `` range '' of the potential ) , even after renormalization , as evidenced by the bound ( [ eq : wb ] ) . when dimensional regularization discards all power - law divergences in order to maintain its scale independence it removes , by fiat , the power - law divergences which represent an important part of the physics of the range of the @xmath0 interaction . this suggests dr should not be used to regularize this potential . it is straightforward to show that if dr is used to regularize a potential which generates low - energy bound or quasi - bound states , the resulting coefficients in the dimensionally regularized potential will be governed by the bound - state energy , and not by the underlying scale of the eft @xcite . thus , if dr is used to regularize the eft @xmath0 potential the radius of convergence of the resulting expansion will be small as seen in the work of kaplan _ et al . _ @xcite . again , this may be thought of as a consequence of dr s discarding power - law divergences : such power - law divergences implement the cancellation between `` range '' and `` strength '' which was seen in the simple model of sec . [ sec - sm ] ( see also ref . @xcite ) to be the key to allowing a theory with natural scales to produce `` unnaturally '' low - lying bound states . _ therefore the only hope for a systematic and successful eft description of @xmath0 scattering with nucleons alone lies with methods of regularization which preserve information on these power - law divergences . _ cutoff regularization is such a regularization scheme . however , the effective range is positive in nature , and so we discover that if we wish to use an effective field theory with a cutoff to describe the real world we must keep the cutoff finite and below the scale @xmath41 of the short - distance physics . while this may provide a procedure for fitting low - energy scattering data , such an approach can only be regarded as systematic if the important momenta inside internal loops are well below the cutoff scale . if this is not true physical observables will be sensitive to details of the potential in precisely the region where the artificially - introduced cutoff plays an important role . as we saw in sec . [ sec - coeft ] there will then be no justification for keeping some terms in the eft potential and neglecting others . now , while the external momentum @xmath29 can clearly be kept small compared to the cutoff , we have just argued that in order to have a successful eft in the presence of low - lying bound states the virtual momenta of order the cutoff must play a significant role ! this becomes apparent mathematically through the strong cutoff dependence of the quantum averages of momentum operators . _ we therefore conclude that there is no small parameter which allows one to consistently truncate the regularized @xmath0 potential at some finite order in the derivative expansion . _ the preceding argument that power counting fails might be regarded as incomplete since we have demonstrated a violation of power counting at the level of the bare parameters in the regularized potential . in general one does not expect power counting in effective field theories to be respected at the level of the bare parameters in the lagrangian but rather at the level of the renormalized parameters . for example , in ordinary chiral perturbation theory , the bare parameters which enter the perturbative calculations are strictly infinite , while the renormalized amplitudes have natural power counting . here we have shown that sensible regularization schemes inevitably involve a finite cutoff and therefore the only object in which systematic power counting can be defined is the potential with bare parameters ; _ there simply is no renormalized potential_. one might attempt to _ define _ the renormalized potential as the @xmath191 matrix , @xmath192)^{-1}$ ] . this quantity is certainly well defined . however , as discussed elsewhere in this paper , the entire reason for doing eft at the level of the potential is that we are interested in developing an eft in the vicinity of the low - energy pole , and power counting in @xmath66 or @xmath191 fails in the presence of this pole . it might also be suggested that the inclusion of pions as explicit degrees of freedom in the effective field theory will ameliorate the situation . however , we do not believe this to be the case . after all , provided the energy under consideration is low enough , nothing in the general eft arguments applied to the @xmath0 potential in refs . @xcite requires the inclusion of explicit pions . when pions are added as fields in the lagrangian of the eft the basic object of the calculation remains an eft potential which is to be iterated via the lippmann - schwinger equation . this potential still requires regularization . if cutoff regularization is used a generalization of the wigner bound implies that even in this eft with explicit pions the cutoff can not be taken to infinity @xcite . dr could also be used to render finite the divergent integrals which arise upon iteration , but again , doing this implicitly assumes that details of the short - distance physics do not affect the physical scattering amplitude . ( in fact , additional problems , beyond those discussed here , arise when dr is applied to the eft with pions , as noted in ref . therefore it seems that cutoff eft , with a finite cutoff @xmath71 , is the safest way to regularize the eft with explicit pions . whether the inclusion of explicit pions modifies our conclusions about cutoff eft is a matter for numerical investigation . previous numerical calculations indicate that the inclusion of explicit pions does not change the scales of the coefficients @xmath87 and @xmath88 @xcite . hence , it does not appear that the explicit inclusion of pions in the eft will modify our conclusion that there is no systematic eft for @xmath0 scattering . richardson _ et al . _ have independently argued that the eft approach to @xmath0 scattering is not systematic @xcite . however , their definition of systematic is more restrictive than ours . they define systematicity to mean that the scattering length @xmath33 should receive no contribution from the term with two derivatives in the effective lagrangian ( the coefficient @xmath88 ) . since @xmath33 does receive a contribution from this term ( see eq . ( [ eq : cbeta ] ) ) they claim that the eft ( [ eq : lag ] ) is not systematic . this definition of systematicity is patterned on perturbative eft , and may be unduly rigid . we would argue that the appearance of @xmath88 in @xmath33 does not of itself imply non - systematicity . after all , the contribution of @xmath88 to @xmath33 might be systematically small . this happens , for instance , if a finite cutoff @xmath163 is used to regularize the divergences and the physical observables are all natural . on the other hand , in the case of interest here , where @xmath49 is unnaturally large , we saw in the previous section that the contribution of the appropriately - rescaled @xmath88 to @xmath33 _ is _ of order one . the coefficients @xmath87 that are obtained in the zeroth and second - order calculations then differ significantly . perhaps this is only symptomatic of the more general malaise already diagnosed : the higher - order terms in the effective action can not be safely ignored . in summary , the appearance of higher - order coefficients in the expression for low - momentum observables does not necessarily imply non - systematicity . but here we expect the contribution of these higher - order operators to low - momentum observables to be large , because the effective potential can not be systematically truncated . the potential of eft for the @xmath0 interaction lies partly in embedding the @xmath0 scattering amplitude derived in the eft in scattering processes involving three or more nucleons . one would hope to apply power - counting arguments to determine those contributions that are important in the nuclear force and those that are systematically suppressed . in principle , this approach has predictive power . for example , as noted by weinberg , in a nucleus three - body forces are characteristically down by two powers of @xmath193 compared to two - body forces , and so might be expected to yield small contributions to nuclear observables . furthermore , four - body forces are down by four powers of @xmath193 and thus could be expected to be negligible @xcite . this suggests that at some reasonably crude level one might simply neglect @xmath194-body force effects , @xmath195 in nuclei . an analysis of realistic phenomenological nuclear force calculations @xcite and the relative contributions of @xmath194-body forces to nuclear binding energies shows qualitative agreement with this prediction . unfortunately , in light of the results of this paper one must question in what sense it is valid to use power counting to deduce a hierarchy of @xmath194-body forces . if eft power counting is a valid way to deduce that certain terms in the hamiltonian are suppressed then we would have seen that higher - derivative terms in the potential were negligible . in fact , in none of the regularization schemes discussed here was this the case . nevertheless , we stress that effective field theory continues to be the most promising method of systematizing nuclear physics . what we have found here is that an eft for @xmath0 scattering with only nucleons must contain _ all _ operators in the effective action , and therefore is not useful . this has a simple physical interpretation . the @xmath0 scattering amplitude is sensitive to all operators in the effective action because it has a singularity corresponding to the ( quasi-)bound state pole . by definition , this pole `` feels '' all distance scales and therefore naturally requires that operators to all orders in momentum in the effective action be present in order to describe it . the only way around this dilemma is to include the ( quasi-)bound state pole as a `` fundamental '' degree of freedom in the effective theory , while retaining the four - point @xmath0 interactions of the lagrangian ( [ eq : lag ] ) @xcite . in the resulting eft , these @xmath0 contact interactions can be treated perturbatively with consistent power counting . application of these ideas in the three - nucleon scattering problem is being pursued in ref .

the question we address is whether this sum can be consistently truncated at a given order in the derivative expansion , and systematically improved by going to higher orders . a positive effective range which occurs in nature requires that the cutoff be kept finite and below the scale of the physics which has been integrated out , i.e. .

we study an effective field theory of interacting nucleons at distances much greater than the pion s compton wavelength . in this regime the potential is conjectured to be the sum of a delta function and its derivatives . the question we address is whether this sum can be consistently truncated at a given order in the derivative expansion , and systematically improved by going to higher orders . regularizing the lippmann - schwinger equation using a cutoff we find that the cutoff can be taken to infinity only if the effective range is negative . a positive effective range which occurs in nature requires that the cutoff be kept finite and below the scale of the physics which has been integrated out , i.e. . comparison of cutoff schemes and dimensional regularization reveals that the physical scattering amplitude is sensitive to the choice of regulator . moreover , we show that the presence of some regulator scale , a feature absent in dimensional regularization , is essential if the effective field theory of scattering is to be useful . we also show that one can define a procedure where finite cutoff dependence in the scattering amplitude is removed order by order in the effective potential . however , the characteristic momentum in the problem is given by the cutoff , and not by the external momentum . it follows that in the presence of a finite cutoff there is no small parameter in the effective potential , and consequently no systematic truncation of the derivative expansion can be made . we conclude that there is no effective field theory of scattering with nucleons alone . = 0.0 in = 0.0 in = 6.5 in = 8.9 in = 0.0 in = 0.0 in = 0.0 in = 0.25 in = -1 cm u.md . pp # 98 - 024 + + department of physics , university of maryland , college park , md , 20742 - 4111

1203.4063

i

_ coefficient extraction _ can be seen as a general method for designing algorithms , recently in particular in the area of exact algorithms for various np - hard problems @xcite ( cf . @xcite for an introduction to exact algorithms ) . the approach of the method is the following ( see also @xcite ) : 1 . define a variable ( the so - called coefficient ) whose value ( almost ) immediately gives the solution of the problem to be solved , 2 . show that the variable can be expressed by a relatively small formula or circuit over a ( cleverly chosen ) large algebraic object like a ring or field , 3 . show how to perform operations in the algebraic object relatively efficiently . in a typical application of the method , the first two steps are derived from an existing dynamic programming ( dp ) algorithm , and the third step deploys a carefully selected algebraic isomorphism , such as the discrete fourier transform to extract the desired solution / coefficient . algorithms based on coefficient extraction have two key advantages over dp algorithms ; namely , they are space - efficient and they parallelise well ( see , for example , @xcite ) . yet , dp has an advantage if the problem instance is _ sparse_. by this we mean that the number of candidate / partial solutions that need to be considered during dp is small , that is , most entries in the dp table are not used at all . in such a case we can readily adjust the dp algorithm to take this into account through _ memorization _ so that both the running time and space usage become proportional to the number of partial solutions considered . unfortunately , it is difficult to parallelise or lower the space usage of memorization . coefficient extraction algorithms relying on interpolation of sparse polynomials @xcite improve over memorization by scaling proportionally only to the number of _ candidate _ solutions , but their space usage is still not satisfactory ( see also @xcite ) . this paper aims at obtaining what is essentially the best of both worlds , by investigating the systematic use of homomorphisms to `` hash down '' circuit - based coefficient extraction algorithms so that the domain of coefficient extraction and hence the running time matches or improves that of memorization - based dp algorithms , while providing space - efficiency and efficient parallelisation . the key idea is to take an existing algebraic circuit for coefficient extraction ( over a sparsely populated algebraic domain such as a ring or field ) , and transform the circuit into a circuit over a smaller domain by a homomorphic hash function , and only then perform the actual coefficient extraction . because the function is homomorphic , by hashing the values at the input gates and evaluating the circuit , the output evaluates to the hash of the original output value . because the function is a hash function , the coefficient to be extracted collides with other coefficients only with negligible probability in the smaller domain , and coefficient extraction can be successfully used on the new ( hashed - down ) circuit . we call this approach _ homomorphic hashing_. we study sparse dp / coefficient extraction in three domains : ( a ) the univariate polynomial ring @xmath0 $ ] in section [ sec : sss ] , ( b ) the group algebra @xmath1 $ ] in section [ sec : setpart ] and ( c ) the mbius algebra of the subset lattice in section [ sec : unionhashing ] . the subject of sparse dp or coefficient extraction is highly motivated and well - studied @xcite . in @xcite , a sparse polynomial interpolation algorithm using exponential space was already given for ( a ) and ( b ) ; our algorithms improve these domains to polynomial space . in @xcite a polynomial - space algorithm for finding a small multilinear monomial in @xmath1 $ ] was given . in @xcite a general study of settings ( a ) and ( b ) was initiated , but sparsity was not addressed . our main technical contribution occurs with ( c ) and hashing down to the `` solomon algebra '' of a poset . our methods work for general arithmetic circuits similarly as in @xcite , and most of our algorithms work for counting variants as well . but , for concreteness , we will work here with specific decision problems . although we mainly give improvements for sparse variants of these problems , we feel the results will be useful to deal with the general case as well ( as we will see in section [ sec : setpart ] ) . [ [ subset - sum ] ] subset sum + + + + + + + + + + the problem is the following : given a vector @xmath2 and integer @xmath3 , determine whether there exists a subset @xmath4 $ ] such that @xmath5 . it is known to be solvable @xmath6 time and @xmath7 space @xcite , and solving it faster , or even in @xmath8 time and polynomial space are interesting open questions @xcite . recently , a polynomial space algorithm using @xmath9 time was given in @xcite . [ thm : mainsss ] an instance @xmath10 of the problem can be solved 1 . in @xmath11 expected time and polynomial space , and 2 . in @xmath12 time and polynomial space , where @xmath13 is the number of distinct sums , i.e. @xmath14\}|$ ] . here it should be noted that standard sparse dp gives an @xmath11 time and space algorithm . informally stated , our algorithms hash the instances by working modulo randomly chosen prime numbers and applying the algoritm of @xcite . while interesting on their own , these results may be useful in resolving the above open questions when combined with other techniques . [ [ linear - sat ] ] linear sat + + + + + + + + + + the linear sat problem is defined as follows : given a matrix @xmath15 , vectors @xmath16 and @xmath17 , and an integer @xmath18 , determine whether there is there a vector @xmath19 such that @xmath20 and @xmath21 . variants of linear sat have been studied , perhaps most notably in @xcite , where approximability was studied . in @xcite the fixed parameter tractability was studied for parameterizations of various above guarantees . there , it was also quoted from @xcite that ( a variant of ) linear sat is `` as basic as satisfiability '' . it can be observed that using the approach from @xcite , linear sat can be solved in @xmath22 time and @xmath22 space . also , using standard `` sparse dynamic programming '' , it can be solved in @xmath23 time and @xmath23 space , where @xmath24 is the rank of @xmath25 . we obtain the following polynomial - space variants : [ thm : mainls ] an instance @xmath26 of can be solved by algorithms with constant one - sided error probability in 1 . @xmath23 time and polynomial space , and 2 . @xmath27 time and polynomial space . the first algorithm hashes the input down using a random linear map and afterwards determines the answer using the walsh - hadamard transform . the second algorithm uses a win / win approach , combining the first algorithm with the fact that an @xmath25 with high rank can be solved with a complementary algorithm . [ [ satisfiability ] ] satisfiability + + + + + + + + + + + + + + the cnf - sat problem is defined as follows : given a cnf - formula @xmath28 over @xmath29 variables , determine whether @xmath30 is satisfiable . there are many interesting open questions related to this problem , a major one being whether it can be solved in time @xmath31 ( the ` strong exponential time hypothesis ' @xcite states this is not possible ) , and another being whether the number of satisfying assignments can be counted in time @xmath31 for some @xmath32 ( e.g. @xcite ) . a _ prefix assignment _ is an assignment of 0/1 values to the variables @xmath33 for some @xmath34 . a _ projection _ ( _ prefix projection _ ) of a cnf - formula is a subset @xmath35 $ ] such that there exists an assignment ( prefix assignment ) of the variables such that for every @xmath36 it satisfies @xmath37 if and only if @xmath38 . an algorithm for cnf - sat running in time linear in the number of _ prefix _ projections can be obtained by standard sparse dp . however , it is sensible to ask about complexity of cnf - sat if the number of projections is small . we give a positive answer : [ thm : maincnf ] satisfiability of a formula @xmath39 can be determined in @xmath40 time and @xmath41 space , where @xmath42 : \pi \text { is a projection of } \phi \}|$ ] . we are not aware of previous work that studies instances with few projections . although most instances will have many projections , we think our result opens up a fresh technical perspective that may contribute towards solving the above mentioned and related questions . underlying theorem [ thm : maincnf ] is our main technical contribution ( theorem [ thm : unionhashsmallsupp ] ) that enables us to circumvent partial projections and access projections directly , namely homomorphic hashing from the mbius algebra of the lattice of subsets of @xmath43 $ ] to the solomon algebra of a poset . a full proof of theorem [ thm : unionhashsmallsupp ] is given in the appendix ; we give a specialized , more direct proof of theorem [ thm : maincnf ] in section 5 . the proofs of claims marked with a `` @xmath44 '' are relegated to the appendix in order to not break the flow of the paper .

we study classes of dynamic programming ( dp ) algorithms which , due to their algebraic definitions , are closely related to coefficient extraction methods . dp algorithms can easily be modified to exploit sparseness in the dp table through memorization . coefficient extraction techniques on the other hand are both space - efficient and parallelisable , but no tools have been available to exploit sparseness . we investigate the systematic use of homomorphic hash functions to combine the best of these methods and obtain improved space - efficient algorithms for problems including linear sat , set partition , and subset sum . the last property also gives an improved algorithm for cnf sat with sparse projections .

we study classes of dynamic programming ( dp ) algorithms which , due to their algebraic definitions , are closely related to coefficient extraction methods . dp algorithms can easily be modified to exploit sparseness in the dp table through memorization . coefficient extraction techniques on the other hand are both space - efficient and parallelisable , but no tools have been available to exploit sparseness . we investigate the systematic use of homomorphic hash functions to combine the best of these methods and obtain improved space - efficient algorithms for problems including linear sat , set partition , and subset sum . our algorithms run in time proportional to the number of nonzero entries of the last segment of the dp table , which presents a strict improvement over sparse dp . the last property also gives an improved algorithm for cnf sat with sparse projections .

1508.07055

i

one of the most intriguing theoretical results in quantum field theory ( qft henceforth ) has been the realization that fermions can emerge out of purely bosonic lagrangians as solitonic excitations ( for a detailed review see @xcite ) . the clearest demonstration that the importance of this result goes far beyond pure theoretical physics is given by the skyrme theory @xcite which is one of the most important models of nuclear and particle physics . the skyrme term @xcite allows the existence of static soliton solutions with finite energy , called _ skyrmions _ ( see @xcite ) describing fermionic degrees of freedom ( see @xcite and references therein ) . the wide range of applications of the theory in other areas ( such as astrophysics , bose - einstein condensates , nematic liquids , multi - ferric materials , chiral magnets and condensed matter physics in general @xcite ) is well recognized by now . it is also worth to emphasize that the skyrme model appears in a very natural way in the context of the ads / cft correspondence @xcite . from the point of view of nuclear physics , it is very important to have analytic tools allowing to analyse the skyrme model when interacting skyrmions are present within bounded regions . this case is relevant whenever one wants to take into account the effects of the finite size on the topological properties of the skyrmions themselves . it is commonly believed that many - nucleons systems ( such as the ones occurring in nuclear pasta @xcite ; for a review see @xcite ) are completely out of reach of the analytical techniques provided by soliton theory already in the @xmath4 case ( while , at a first glance , the @xmath5 case is even worse ) . in particular , the task to compute physical parameters of such multi - nucleon systems with analytic multi - skyrmionic configurations is believed to be completely hopeless . recently , the generalized hedgehog ansatz in the @xmath4 case , introduced in @xcite , allowed the construction of the first multi - skyrmions at finite volume : namely , the first exact solutions of the skyrme model representing interacting elementary skyrmions with a non - trivial winding number , in which finite - volume effects can be explicitly taken into account ( arriving at a good prediction for the compression modulus ) , was obtained @xcite . the way to do this is to write the system in a modified cylinder - like " metric whose curvature is parametrized by a length @xmath6 . then multi - skyrmionic configurations look like necklaces of elementary skyrmions interacting in bounded tube - shaped regions . the ground state of such multi - skyrmions has the remarkable property that , although the bps bound in terms of the winding can not be saturated , a new topological charge exists which leads to a different bps bound , which can instead be saturated . in this paper , we consider the @xmath5 case . a very powerful technique to construct multi - skyrmionic configurations in unbounded regions is given by an ansatz for @xmath5 skyrmions introduced in @xcite and @xcite , based on harmonic maps of @xmath0 into @xmath1 , which allowed the construction of many interesting numerical multi - skyrmionic configurations . here we will exploit the fact that the metric we use is spherically symmetric , just like flat space , so the harmonic map ansatz can be used also in the present case without modifications . we shall see that in the new metric the equations simplify with respect to those studied in @xcite and @xcite ; in particular they become autonomous , thus techniques from dynamical systems theory become available . thanks to the choice of the background geometry , a novel type of large @xmath2 limit becomes possible in which @xmath2 is large and the curvature is small in such a way that their product is constant . in this way one can see that both the effects of the curvature become negligible and the field equations remain autonomous ( so that , in such a limit , one can kill the curvature of the metric but keeping all the advantages of the technique of @xcite ) . it is also worth to emphasize that it is precisely the large @xmath2 limit which discloses in the clearest possible way the role of the skyrme model as low energy limit of qcd . a non constructive proof of the existence of such nontrivial solutions is also provided and a few numerical solutions are exhibited as well . this paper is organized as follows : in the second section , the @xmath4 case treated in @xcite will be briefly reviewed in order to set the stage . in the third section , the ansatz for the skyrmions will be described . in the fourth section , the general equations of motion are written down and the flat - large @xmath2 limit is discussed . in the fifth section , we study the system using techniques from the theory of dynamical systems ; in particular , the stability of the fixed points in the @xmath7 case is analyzed , and their dependence on the geometric t hooft parameter is discussed . in the sixth section , some nontrivial numerical solution of the equations of motion in the @xmath8 case will be studied . in the seventh section , some conclusions will be drawn . in the appendix , it is proved on general grounds that the equations of motion do have nontrivial solutions which can be interpreted as genuine @xmath5 skyrmions .

we study multi - soliton solutions of the four - dimensional su(n ) skyrme model by combining the hedgehog ansatz for su(n ) based on the harmonic maps of into and a geometrical trick which allows to analyze explicitly finite - volume effects without breaking the relevant symmetries of the ansatz . the geometric set - up allows to introduce a parameter which is related to the t hooft coupling of a suitable large limit , in which and the curvature of the background metric approaches zero , in such a way that their product is constant . the relevance of such a parameter to the physics of the system is pointed out . in particular , we discuss how the discrete symmetries of the configurations depend on it .

we study multi - soliton solutions of the four - dimensional su(n ) skyrme model by combining the hedgehog ansatz for su(n ) based on the harmonic maps of into and a geometrical trick which allows to analyze explicitly finite - volume effects without breaking the relevant symmetries of the ansatz . the geometric set - up allows to introduce a parameter which is related to the t hooft coupling of a suitable large limit , in which and the curvature of the background metric approaches zero , in such a way that their product is constant . the relevance of such a parameter to the physics of the system is pointed out . in particular , we discuss how the discrete symmetries of the configurations depend on it .

cond-mat9901267

i

the dynamics of systems close to a glass transition remains a central problem in statistical physics @xcite . because the glass transition is a many - body phenomenon , models for it invariably involve some approximation and it is important to disentangle the physical phenomena from the approximation scheme used . in mode - coupling theories , for example , the dynamics are dominated by a small number of collective degrees of freedom @xcite . this is appealing , but ignores activated processes , and obscures the fact that glassy materials are dynamically heterogeneous with a variety of local environments @xcite . another approach is to use disordered hopping models , which treat instead single - particle degrees of freedom coupled to a random environment , and this is the route followed here . such models , though unrealistic in some respects , are likely to give a better account of those properties , such as self - diffusion , which are not dominated by relaxation of collective modes . an important breakthrough in the approach based on hopping models was that of bouchaud @xcite , who showed that an ensemble of _ non - interacting _ particles , moving by thermally activated hopping at temperature @xmath0 in an uncorrelated fashion through a sequence of traps , can show a glass transition . this occurs if and only if the density of states ( the prior probability distribution of trap depths ) @xmath1 has an exponential tail . though grossly over - simplified , this allows many properties of the model to be calculated exactly . the exponential tail to the prior distribution @xmath1 , which leads to a power - law spectrum of relaxation times and is vital to the appearance of a glass transition , is supported by evidence from theory on spin glasses @xcite and experiments on low - temperature fluids @xcite . such a power - law relaxation spectrum was the point of departure for a related model of glasses @xcite , and similar features appear in models of dispersive transport in disordered semiconductors @xcite . the original model of bouchaud has no explicit spatial coordinates . nevertheless , the extension to self - diffusion is unambiguous ( if each hop corresponds to a spatial displacement with a well - defined second moment ) and indeed monthus and bouchaud @xcite gave an expression for the distribution of displacements on a hypercubic lattice . for flow properties , more choices are possible in the way spatial coordinates are treated , but a minimal extension of the model was offered by sollich et al . this model , which we call the gr ( glassy rheology ) model allows both linear and nonlinear rheological properties to be calculated . details of it are recalled in section [ gr ] below . the model introduced in ref . @xcite was in fact proposed to describe a class of soft glassy materials " ( argued to include foams , dense emulsions , etc . ) , in which context it was found necessary to replace the thermodynamic temperature @xmath0 in bouchaud s model by an effective ( noise ) temperature @xmath2 . this replacement converts the gr model studied below into the _ soft _ glassy rheology model of refs . @xcite , and can be made throughout our calculations . the glass transition in the gr model shows interesting features which may need further explanation for readers whose background lies in conventional glasses . specifically , in bouchaud s model the glass transition @xmath3 is identified as the temperature below which the system shows weak ergodicity breaking " : its boltzmann distribution is not normalizable . this means the system will evolve into deeper and deeper traps as time goes by , and will never attain a steady state although at no finite time are there infinite barriers partitioning phase space . when flow - related degrees of freedom are included in the model ( see section [ gr ] below ) , one finds , as expected , that the system has a finite elastic modulus ( at zero frequency ) for temperatures @xmath4 . less obviously , the _ viscosity _ of the material diverges , not at @xmath5 but at @xmath6 . between these two temperatures , the static modulus is zero but the viscosity infinite ; the material is what is known in rheological language as a power - law fluid " . for applications of the model to soft glassy materials this is a very attractive feature , since such viscoelastic behaviour is frequently observed in these systems @xcite . in a model of conventional glasses , on the other hand , it might be considered undesirable . however , with the introduction of a high energy cutoff in the prior distribution @xmath1 , the phenomenology of the gr model can be adapted to model that of conventional glasses . we discuss the conceptual features of this modification at the end of section [ concl ] ; for the actual calculations in the present paper we restrict ourselves to the simpler case without cutoff . below we calculate the statistics ( additional to the results of ref . @xcite ) of self - diffusion in the gr model , and explore quantitatively the breakdown , near the glass transition , of the ( generalized ) stokes - einstein relation [ ( g)ser ] between self - diffusion of a representative particle in the fluid and the ( frequency - dependent ) viscosity of the system as a whole . ( this breakdown does not , of course , imply that gser also fails for _ macroscopic _ probe particles which see the surrounding material as a continuum . ) we also investigate the effect of shear flow on self - diffusion and show that this causes a finite diffusivity in the low - temperature regime where this was previously zero . in the next section we review the status of the gser in both conventional and soft glassy systems . the gr model is described in section [ gr ] and used in section [ test ] to study and discuss the breakdown of the gser . in section [ analysis ] , we further elucidate the physics of particle transport in glassy systems , using both analysis and simulation of the model . in section [ shear ] we calculate the effects of shear on the rate of self - diffusion , finding the diffusion constant in the presence of continuous and periodic shear strains of various rates and amplitudes . in section [ concl ] we conclude with a discussion of our results in the context of both conventional super - cooled / glass - forming liquids and soft glassy materials .

bouchaud , _ rev . we investigate the breakdown , near the glass transition , of the ( generalized ) stokes - einstein relation between self - diffusion of a tracer particle and the ( frequency - dependent ) viscosity of the system as a whole . we also investigate the effect of flow ( oscillatory shear ) on self - diffusion and show that this causes a finite diffusivity in the temperature regime below the glass transition ( where this was previously zero ) . at higher temperatures the diffusivity is enhanced by a power law frequency dependence that also characterises the rheological response . the relevance of these findings to soft glassy materials ( foams , emulsions etc . ) as well as to conventional glass - forming liquids is discussed .

we study self - diffusion within a simple hopping model for glassy materials . ( the model is bouchaud s model of glasses [ j .- p . bouchaud , _ j. physique i _ * 2 * 1705 ( 1992 ) ] , as extended to describe rheological properties [ p. sollich , f. lequeux , p. hbraud and m.e . cates , _ phys . rev . lett . _ * 78 * 2020 ( 1997 ) ] . ) we investigate the breakdown , near the glass transition , of the ( generalized ) stokes - einstein relation between self - diffusion of a tracer particle and the ( frequency - dependent ) viscosity of the system as a whole . this stems from the presence of a broad distribution of relaxation times of which different moments control diffusion and rheology . we also investigate the effect of flow ( oscillatory shear ) on self - diffusion and show that this causes a finite diffusivity in the temperature regime below the glass transition ( where this was previously zero ) . at higher temperatures the diffusivity is enhanced by a power law frequency dependence that also characterises the rheological response . the relevance of these findings to soft glassy materials ( foams , emulsions etc . ) as well as to conventional glass - forming liquids is discussed .

cond-mat9901267

c

we have studied quantitatively , within a simple hopping model of glassy dynamics , the relation between diffusion and rheological responses ( in the linear response regime ) and ( for the nonlinear regime ) the coupling between these two aspects of the dynamics . in the presence of a broad distribution of relaxation times , as the model possesses ( and as is generic in hopping models of the glass transition ) one can expect strong violations of the generalized stokes - einstein relation ( eq.[gser ] ) when applied @xcite to the self - diffusion of representative particles in the medium ( small probes ) . the relation holds only for probe particles large enough that their surroundings are properly viewed as a continuum @xcite . effective - medium theories , and also simple forms of mode - coupling theory @xcite ( in which a single mode of slow relaxation dominates ) can give misleading predictions under these conditions . for glassy systems , use of the gser will under - predict the diffusivity of particles and/or the rheological viscoelastic moduli . this is because the latter are dominated by the most immobile and the former is dominated by the most mobile particles . in fact , the nature of diffusion in the model is quite subtle ( see section [ analysis ] ) : close to ( but above ) the glass transition one has an apparently bimodal behaviour . starting from any initial equilibrium state , a fraction of particles remain stuck for a long time , but any particle that has hopped once remains mobile thereafter . it is peculiar that , despite this , the diffusive behaviour conspires to be relatively normal ( at least for low order moments of the displacement distribution ; moments of fractional negative order would presumably reveal a different story ) . an additional peculiarity of diffusion , which our model does not include , but which could also lead to enhanced diffusivity near the glass temperature , has been observed in a recent molecular dynamics simulation @xcite . in ref.@xcite the effective dimensionality of the most mobile random walks was observed to decrease with temperature . at low temperature , particles moved along string - like clusters ( also seen in ref . @xcite ) , and therefore covered greater distances than in an uncorrelated random walk in three dimensions . we have also applied our gr model to calculate the change in the self - diffusion constant when a material is sheared . after subtraction of affine motion ( including taylor dispersion ) @xcite , or equivalently restricting attention to diffusion perpendicular to the shear direction , one finds a strong effect of imposed flow on the mean jump rate @xcite and hence on the diffusion constant . the effect is particularly extreme below the glass transition , where an anomalous ( sub - diffusive ) behaviour is converted to a finite diffusivity which has , instead , a power law dependence on the steady shear rate . such effects should be accessible in scattering experiments ( with wavevector almost perpendicular to the flow direction ) on labelled small probes . in oscillatory shear , an enhancement in @xmath20 was predicted in section [ shear ] for systems above ( but near ) the glass temperature ; this could also be probed via scattering . the gr model as described in section [ gr ] was originally developed in ref . @xcite to reproduce the generic rheology of a class of soft glassy materials " . ( we comment further below on its relevance to conventional glasses . ) this class was argued to include , for example , foams , emulsions , pastes and slurries . experimentally , their linear viscoelastic behaviour is often characterized by a nearly constant ratio of the elastic and loss moduli @xmath7 , @xmath8 ( @xmath252 is usually about 0.1 ) with a frequency dependence that is either a weak power law ( clay slurries , paints , microgels ) or negligible ( tomato paste , dense emulsions , dense multi - layer vesicles ) @xcite . this behaviour persists down to the lowest experimentally accessible frequencies . sometimes a regime is seen at small @xmath9 where @xmath70 is constant and @xmath71 is decreasing ( which can be interpreted in terms of the model s behaviour below @xmath3 @xcite ) . as mentioned in sections [ introd ] and [ gr ] , there are two differences between the gr model used in this paper and its soft counterpart in @xcite . the first is that the _ soft _ gr model refers not to particles , as we have done , but to mesoscopic material elements " , large enough for a local elastic strain variable to be defined but small enough to have strong heterogeneity in local yield energies . ( for the case of a foam , say , an element " could correspond to a domain of several bubbles , and yield " to a local topological change . ) it is not necessarily clear what is meant by self - diffusion of such elements , so in the present paper we have retained a particle picture , although this is more natural for conventional glass - forming liquids than for soft glassy materials . the second difference is that in the _ soft _ gr model , @xmath0 is replaced by an effective noise temperature " @xmath253 . it was argued in @xcite that the resemblance to thermal activation is formal : the activated " yield processes are viewed as arising primarily by coupling to structural rearrangements elsewhere in the system . indeed , the elastic energies associated with local rearrangements in foams and the like are many orders of magnitude in excess of @xmath26 , so any interpretation of @xmath253 as a true temperature is somewhat unconvincing for these materials ( in contrast to conventional glasses ) . although this interpretation remains problematical , as discussed in @xcite , with it the soft gr model is able to reproduce many of the rheological properties of soft glassy materials . the results we have obtained for the gr model , concerning breakdown of the gser and the nature of shear - induced diffusion , equally apply ( with @xmath254 ) to the _ soft _ gr model . the breakdown of gser , arising from the fact that diffusion and rheology probe different aspects of the relaxation spectrum , is equally natural in this case ; the other contribution to its breakdown discussed in [ breakdown ] , arising from the temperature dependence of the local attempt frequency , even more so ( since @xmath253 is anyway not a true temperature ) . the results of section [ shear ] for shear - induced diffusion could also be quite interesting for soft glassy materials , in which it is easy to apply shear strains large enough to strongly perturb the intrinsic relaxation times . the length scales in these materials can be probed via light scattering ; index matching is often possible so that true tracer diffusion ( of a small subset of unmatched droplets or particles ) can be measured @xcite . for oscillatory flows , an important innovation is the echo technique @xcite in which the positions of a given scatter at identical points in the shear cycle are compared . results on dense emulsions @xcite suggest , in fact , that not only are shear - induced reorganizations easily detectable , but that these have strong temporal and spatial correlations regions that reorganize at a given point in the shear cycle will do so again in the next one . such correlations are not included in the ( soft ) gr model(s ) although they might be added in principle @xcite . ( it would require escape from a shallow trap to be preferentially into another shallow trap , though we do not advocate appending such ad - hoc correlations to this simplified model . ) it would be very interesting to know whether the same applies in conventional glasses ; preliminary work on colloidal suspensions ( which are traditionally thought of in these terms ) suggests not @xcite . finally , we return to the phenomenology of the gr model in relation to conventional glass - forming liquids . as explained in section [ gr]b , the gr model in its basic form predicts a viscosity divergence at @xmath128 , while the diffusion constant vanishes only at @xmath149 , where the system has a glass transition to a non - ergodic state . this existence of a temperature range with finite diffusivity but infinite viscosity appears to be at odds with the experimentally observed behaviour of conventional glasses . a common divergence of viscosity and inverse diffusion constant can however be incorporated into the gr model through a cutoff @xmath255 on the distribution of yield energies @xmath1 ; this modification of the model has in fact already been discussed in ref . it yields a viscosity which initially follows the original power - law divergence as @xmath128 is approached , but then crosses over to @xmath256 as @xmath0 is lowered further . similarly , the predicted @xmath257 would first seem to diverge as @xmath149 is approached from above , but actually remain finite there and eventually approach infinity at the same temperature as the viscosity ( @xmath258 ) . the shear moduli obey the power laws ( eq . [ powerlaws ] ) down to a cutoff frequency @xmath259 , but then cross over to low - frequency maxwell behaviour ( @xmath260 , @xmath261 ) . the above simple temperature dependences apply if , as we did throughout , we assume that the ( prior ) density of yield energies is temperature independent . this is of course an approximation ; odagaki , for example , suggested that the width of @xmath1 may in fact scale as the inverse of the amount of free volume @xmath262 in the system @xcite . in all temperature dependences , @xmath263 then replaces @xmath0 . as a consequence , if the free volume decreases smoothly to zero at a finite temperature @xmath264 , a vogel - fulcher - like divergence of @xmath16 and @xmath257 at @xmath264 ( rather than the above arrhenius behaviour ) would be predicted by the gr model with energy cutoff . one would then be inclined to locate the glass transition at that point ; if we revert to temperature independent @xmath1 , this corresponds to @xmath258 ( rather than @xmath149 , which is the appropriate choice in the absence of an energy cutoff ) . results in the range @xmath265 for the gr model with cutoff may therefore actually apply to supercooled liquids _ above _ the glass transition . these include a dynamic modulus @xmath266 which becomes _ more _ maxwellian in the low - frequency range as @xmath0 is lowered ( for @xmath75 , one has @xmath267 . and @xmath268 above the cutoff frequency @xmath269 @xcite , and hence maxwell behaviour with relaxation time @xmath270 for @xmath271 ) , in an intriguing correspondence with data taken by menon et al . @xcite . this work was funded by epsrc grant no . gr / k56025 ( rmle ) and a royal society dorothy hodgkin fellowship ( ps ) . we wish to thank p. n. pusey , f. lequeux , p. hbraud and j .- p . bouchaud for helpful discussions .

we study self - diffusion within a simple hopping model for glassy materials . j. physique i _ * 2 * 1705 ( 1992 ) ] , as extended to describe rheological properties [ p. sollich , f. lequeux , p. hbraud and m.e . this stems from the presence of a broad distribution of relaxation times of which different moments control diffusion and rheology .

we study self - diffusion within a simple hopping model for glassy materials . ( the model is bouchaud s model of glasses [ j .- p . bouchaud , _ j. physique i _ * 2 * 1705 ( 1992 ) ] , as extended to describe rheological properties [ p. sollich , f. lequeux , p. hbraud and m.e . cates , _ phys . rev . lett . _ * 78 * 2020 ( 1997 ) ] . ) we investigate the breakdown , near the glass transition , of the ( generalized ) stokes - einstein relation between self - diffusion of a tracer particle and the ( frequency - dependent ) viscosity of the system as a whole . this stems from the presence of a broad distribution of relaxation times of which different moments control diffusion and rheology . we also investigate the effect of flow ( oscillatory shear ) on self - diffusion and show that this causes a finite diffusivity in the temperature regime below the glass transition ( where this was previously zero ) . at higher temperatures the diffusivity is enhanced by a power law frequency dependence that also characterises the rheological response . the relevance of these findings to soft glassy materials ( foams , emulsions etc . ) as well as to conventional glass - forming liquids is discussed .

cond-mat0602288

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switching between coexisting stable states underlies many phenomena in physics , from diffusion in solids to protein folding . for classical systems in thermal equilibrium switching is often described by the activation law , with the switching probability being , where @xmath2 is the activation energy . as temperature is decreased , quantum fluctuations become more and more important , and below a certain crossover temperature switching occurs via tunneling @xcite . the behavior of systems away from thermal equilibrium is far more complicated . still , for classical systems switching is often described by an activation type law , with the temperature replaced by the characteristic intensity of the noise that leads to fluctuations @xcite . quantum nonequilibrium systems can also switch via tunneling between classically accessible regions of their phase space @xcite . in addition to classical activation and quantum tunneling , nonequilibrium systems have another somewhat counterintuitive mechanism of transitions between stable states . we call this mechanism quantum activation and study it in the present paper . it describes escape from a metastable state due to quantum fluctuations that accompany relaxation of the system @xcite . these fluctuations lead to diffusion away from the metastable state and , ultimately , to transitions over the classical `` barrier '' , that is , the boundary of the basin of attraction to the metastable state . we study quantum activation for periodically modulated systems . switching mechanisms for such systems are shown schematically in fig . [ fig : d ] , where @xmath3 is the effective potential of the system in the rotating frame . this figure describes , in particular , a nonlinear oscillator studied in the present paper , which displays period doubling when its frequency is periodically modulated in time . the energy of periodically modulated systems is not conserved . instead they are characterized by quasienergy @xmath4 . it gives the change of the wave function @xmath5 when time is incremented by the modulation period @xmath6 , @xmath7 , and is defined modulo @xmath8 fr fr . of a parametrically modulated oscillator . sketched are scaled period - two quasienergy levels ( see sec . [ sec : dynamics ] ) in the neglect of interwell tunneling . the minima of @xmath9 correspond to classically stable states of period two motion . the arrows indicate relaxation , diffusion over quasienergy away from the minima , and interwell tunneling . the effective hamiltonian @xmath10 is defined by eq . ( [ eq : g ] ) , and @xmath11 ; the figure refers to @xmath12 in eq . ( [ eq : g]).,width=288 ] coupling to a thermal reservoir leads to transitions between the states of the system . for @xmath0 the transitions are accompanied by the creation of excitations in the thermal reservoir . the energy of the system decreases in each transition . however , the quasienergy may decrease or increase , albeit with different probabilities @xmath13 and @xmath14 . this effect has quantum origin . it is due to the functions @xmath15 being superpositions of the eigenfunctions @xmath16 of the energy operator of the system in the absence of modulation . therefore bath - induced transitions down in energy @xmath17 lead to transitions @xmath18 with @xmath19 . the values of @xmath13 , @xmath14 for the latter transitions are determined by the appropriate overlap integrals and depend on @xmath20 . more probable transitions determine in which direction , with respect to quasienergy , the system will most likely move . such motion corresponds to relaxation over quasienergy . [ fig : d ] refers to the case @xmath21 . in this case relaxation corresponds to quasienergy decrease . the minima of @xmath3 are the classical stable states . however , quantum transitions in which quasienergy increases have a nonzero probability even for @xmath0 . because this probability is less than @xmath14 , such transitions lead to diffusion over quasienergy @xmath4 away from the minima of @xmath3 . in turn , the diffusion leads to a finite - width distribution over @xmath4 and ultimately to activated - type overbarrier transitions between the wells in fig . [ fig : d ] . in fact , discussed in this paper and sketched in fig . [ fig : d ] are period - two quasienergy states , with quasienergy @xmath4 defined by the condition @xmath22 . they are more convenient for the present problem ; their relation to the standard quasienergy states is explained in sec . [ sec : dynamics ] . of interest for the problem of switching is the semiclassical situation where the basins of attraction to the metastable states ( the wells in fig . [ fig : d ] ) have a large number @xmath23 of localized states . in this case the rate of tunneling decay is exponentially small . the activation rate is also exponentially small since it is determined by the ratio of transition probabilities @xmath24 raised to the power @xmath23 . both the tunneling and activation exponents are @xmath25 for the situation sketched in fig . [ fig : d ] . indeed , the tunneling exponent is given by the action , in the units of @xmath26 , for classical motion in the inverted effective potential @xmath27 from one maximum of @xmath27 to the other . it is easy to see that this action is of order @xmath23 , unless @xmath3 has a special form . therefore for @xmath28 the activation exponent is either much larger or much smaller than the tunneling exponent . in this paper we develop a theory of the statistical distribution and consider switching of a parametrically modulated quantum oscillator . we show that , irrespective of temperature , the activation exponent is smaller than the tunneling exponent . therefore switching always occurs via activation , not tunneling , as long as the relaxation rate exceeds the tunneling rate . we study a nonlinear oscillator with frequency modulated at nearly twice the natural frequency @xmath29 . when the modulation is sufficiently strong , the oscillator has two stable vibrational states with periods @xmath30 . these states differ in phase by @xmath31 but otherwise are identical @xcite . they correspond to the minima of the effective potential in fig . [ fig : d ] . the lowest quantized states in fig . [ fig : d ] are squeezed . squeezing in a parametric oscillator has attracted interest in many areas , from quantum optics @xcite to phonons @xcite , microcantilevers @xcite and electrons and ions in penning traps @xcite . recent progress in systems based on josephson junctions and nanoelectromechanical systems @xcite makes it possible to study squeezed states in a well controlled and versatile environment . both classical and quantum fluctuations can be investigated and the nature of switching between the states can be explored . the results can be further used in quantum measurements for quantum computing , as in the case of switching between coexisting states of a resonantly driven oscillator @xcite . the probability distribution and interstate transitions of a parametrically modulated oscillator have attracted considerable attention . much theoretical work has been done for models where fluctuations satisfy the detailed balance condition either in the classical limit @xcite or for @xmath0 @xcite . generally this condition does not hold in systems away from equilibrium . in particular a classical nonlinear parametric oscillator does not have detailed balance . switching of such an oscillator was studied experimentally for electrons in penning traps @xcite . the measured switching rate @xcite agreed quantitatively with the theory @xcite . of the distribution over scaled period - two quasienergy @xmath9 of a parametrically modulated oscillator for different oscillator planck numbers @xmath32 in the limit of a large number of intrawell quasienergy states . the figure refers to @xmath33 . , width=288 ] a quantum parametric oscillator also does not have detailed balance in the general case . the results presented below show that breaking the special condition where detailed balance holds leads to a sharp change of the statistical distribution and the switching rate . this change occurs already for an infinitesimally small deviation from detailed balance , in the semiclassical limit . the fragility of the detailed balance solution is previewed in fig . [ fig : fr ] . this figure shows the effective inverse temperature of the intrawell distribution over the scaled period - two quasienergy @xmath9 . the function @xmath34 is the exponent of the distribution @xmath35 , where @xmath36 is the population of an @xmath37-th state and @xmath38 is the scaled planck constant defined in eq . ( [ eq : l ] ) below . the effective inverse temperature @xmath39 depends on @xmath9 and differs from the inverse temperature of the bath @xmath40 . the @xmath41 result for @xmath42 is obtained from the solution with detailed balance ( here @xmath43^{-1}$ ] is the planck number of the oscillator ) . it is seen from fig . [ fig : fr ] that the @xmath44 ( @xmath45 ) limit of the solution without detailed balance does not go over into the @xmath0 result . the effective quantum activation energy @xmath46 , which gives the exponent of the switching rate @xmath47 , is shown in fig . [ fig : acte2 ] . it is equal to @xmath48 , where @xmath49 and @xmath50 are , respectively , the values of @xmath3 at the top and the minimum of the wells in fig . [ fig : d ] . the @xmath51 detailed balance value for @xmath52 strongly differs from the @xmath53 value in a broad range of the control parameter @xmath54 that characterizes the detuning of the modulation frequency from @xmath55 , see eq . ( [ eq : mu ] ) below . it is also seen from fig . [ fig : acte2 ] that the quantum activation energy @xmath52 decreases with increasing temperature . ultimately when the planck number of the oscillator becomes large , @xmath56 , we have @xmath57 , the law of thermal activation , and the results coincide with the results @xcite obtained by a different method . , where @xmath58 , eq . ( [ eq : l ] ) , is the effective planck constant . the scaled switching exponent @xmath52 is plotted as a function of the single scaled parameter @xmath54 that controls oscillator dynamics , eq . ( [ eq : mu ] ) , for different values of the oscillator planck number @xmath32 . , width=288 ] in sec . [ sec : dynamics ] we obtain an effective hamiltonian that describes the oscillator dynamics in the rotating frame . we describe the classical dynamics and calculate semiclassical matrix elements of the coordinate and momentum . in sec . [ sec : balance_equation ] we derive the balance equation for the distribution over quasienergy levels . this distribution is found in the eikonal approximation in sec . [ sec : distribution ] . its explicit form is obtained in several physically important limiting cases in sec . [ sec : limiting_cases ] . in sec . [ sec : switching_exponent ] the probability of interstate switching due to quantum activation is analyzed . in sec . [ sec : fragility ] it is shown that the distribution obtained for @xmath59 , where the system has detailed balance , is fragile : in the limit of a large number of intrawell states it differs from the distribution for @xmath1 . it is also dramatically changed by even weak dephasing due to external noise . in sec . [ sec : tunneling ] we discuss tunneling between the coexisting states of period two vibrations and show that interstate switching occurs via quantum activation rather than tunneling , if the relaxation rate exceeds the tunneling rate . in sec . [ sec : conclusions ] we summarize the model , the approximations , and the major results .

we study switching between period - two states of an underdamped quantum oscillator modulated at nearly twice its natural frequency . for all temperatures and parameter values switching we find the semiclassical distribution over quasienergy . for , where the system has detailed balance , this distribution differs from the distribution for ; the distribution is also destroyed by small dephasing of the oscillator .

we study switching between period - two states of an underdamped quantum oscillator modulated at nearly twice its natural frequency . for all temperatures and parameter values switching occurs via quantum activation : it is determined by diffusion over oscillator quasienergy , provided the relaxation rate exceeds the rate of interstate tunneling . the diffusion has quantum origin and accompanies relaxation to the stable state . we find the semiclassical distribution over quasienergy . for , where the system has detailed balance , this distribution differs from the distribution for ; the distribution is also destroyed by small dephasing of the oscillator . the characteristic quantum activation energy of switching displays a typical dependence on temperature and scaling behavior near the bifurcation point where period doubling occurs .

1702.04705

i

the goal of this paper is to study symplectic aspects of monodromy map for second order linear equation on a riemann surface of genus @xmath1 with meromorphic potential admitting @xmath2 simple zeros . our results generalize results of the recent paper by m.bertola , c.norton and the author @xcite where the case of holomorphic potential was treated in detail ( see also an earlier paper by s.kawai for another approach to this problem @xcite ) . the condition of coordinate invariance of the equation @xmath3 on a riemann surface @xmath4 of genus @xmath1 implies that the function @xmath5 transforms as a projective connection under a coordinate change while the solution @xmath6 locally transforms as @xmath7-differential @xcite . thus any meromorphic potential @xmath8 with simple poles can be represented as @xmath9 where @xmath10 is a fixed holomorphic projective connection on @xmath4 and @xmath11 is a meromorphic quadratic differential with @xmath2 simple poles . this is a parameterization of the space of meromorphic potentials on a given riemann surface is natural since meromorphic quadratic differentials with @xmath2 simple poles form the cotangent space @xmath0 to moduli space of riemann surfaces of genus @xmath1 with @xmath2 marked points . however , there remains a freedom in the choice of the `` base '' holomorphic projective connection @xmath10 for a given riemann surface . in this paper , following @xcite we assume that @xmath10 holomorphically depends on moduli of @xmath4 ( in particular , this requirements rules out the use of fuchsian projective connection as @xmath10 ) . furthermore , following @xcite we choose @xmath10 to be the bergman projective connection @xmath12 ( up to the factor @xmath13 this projective connection is the zeroth order term in the expansion of the canonical normalized meromorphic bidifferential @xmath14 near the diagonal @xmath15 @xcite ; @xmath16 is the prime - form ) . therefore , we are going to study the equation written in the form + ( s_b+q)=0 . the ratio @xmath17 of two linearly independent solutions of ( [ sint ] ) solves the schwarzian equation @xmath18 where @xmath19 is an arbitrary local parameter on @xmath4 and @xmath20 denotes schwarzian derivative . the schwarzian equation determines a @xmath21 monodromy representation of the fundamental group @xmath22 which turns out to be liftable to an @xmath23 representation @xcite ( the lift to an @xmath24 representation is a non - trivial fact due to spinorial nature of solutions @xmath25 ) . following @xcite , we define an @xmath23 monodromy representation of equation ( [ sint ] ) directly , by an appropriate change of dependent variable @xmath6 . denote the standard generators of the fundamental group by @xmath26 ; these generators obey the relation @xmath27 . since all poles @xmath28 of the potential of equation ( [ sint ] ) are simple then both eigenvalues of monodromy matrices @xmath29 equal to @xmath30 for each @xmath31 ; all other monodromies are @xmath32 matrices satisfying certain genericity conditions @xcite . our goal is to study symplectic properties of the monodromy map for equation ( [ sint ] ) . since monodromy matrices depend on the choice of normalization point of solutions of ( [ sint ] ) it is natural to work with the corresponding character variety which we denote by @xmath33 ; a point of @xmath33 is an equivalence class of monodromy representations which differ by a simultaneous conjugation with the same matrix . the index @xmath34 indicates that the monodromies around poles @xmath35 are not generic : all of their eigenvalues are equal to @xmath30 . the main result of this paper states that the canonical poisson structure on @xmath0 implies the goldman bracket on the character variety @xmath36 under the monodromy map of equation ( [ sint ] ) , therefore generalizing the result of @xcite to potentials with simple poles . moreover , similar to @xcite and @xcite , we prove that the same statement holds for equation ( [ sint ] ) where the bergman base projective connection is replaced either by schottky or quasi - fuchsian ( bers ) projective connection . we follow the same strategy as in @xcite ; it is based on the use of the `` abelian periods '' of the quadratic differential @xmath11 as coordinates on the underlying moduli space @xmath0 . these coordinates are periods of the abelian differential @xmath37 on the canonical covering @xmath38 of @xmath4 ( the genus of @xmath38 equals @xmath39 ) . we call them `` abelian periods '' or simply `` periods '' to distinguish from monodromy matrices of equation ( [ sint ] ) which are also called sometimes `` periods of quadratic differentials '' @xcite ; following the terminology of @xcite the monodromy matrices should probably be rather called `` non - abelian periods '' . in the theory of dynamical systems the abelian periods of the quadratic differential @xmath11 are known under the name of `` homological coordinates '' ( see @xcite and numerous recent papers ; a substantial reference list can be found in @xcite ) . the phase space associated to equation ( [ sint ] ) is the space of pairs ( riemann surface @xmath4 of genus @xmath1 , meromorphic quadratic differential @xmath11 on @xmath4 with @xmath2 simple poles ) . this phase space is nothing but the cotangent bundle @xmath0 ( up to subspaces of codimension one and higher ; these subspaces contain differentials with multiple zeros ) . the natural symplectic structure on @xmath0 is defined by @xmath40 , where @xmath41 are local coordinates on the moduli space @xmath42 while @xmath43 are corresponding momenta ( coefficients in the decomposition of a cotangent vector in the basis @xmath44 ) . the set of holomorphic local coordinates @xmath45 on @xmath42 can be chosen as follows . to determine locally the conformal structure of @xmath4 we pick ( outside of hyperelliptic locus and for @xmath46 ) a set of @xmath47 entries of the period matrix @xmath48 of @xmath4 ; in different neighbourhoods of the moduli space these entries might have to be chosen differently . the quadratic differentials corresponding to cotangent vectors @xmath49 are products @xmath50 of normalized holomorphic differentials . an additional set of @xmath2 coordinates which determine the positions of punctures @xmath51 on @xmath4 we choose to be @xmath52 where @xmath53 and @xmath54 form a pair of normalized holomorphic 1-forms on @xmath4 corresponding to some torelli marking ( these coordinates are also local : in different coordinate charts on @xmath42 one might need to choose another pair of normalized holomorphic differentials and/or different torelli markings ) . the quadratic differential corresponding to cotangent vector @xmath55 is the meromorphic quadratic differential ( given by the formula ( [ qk ] ) below ) whose only simple pole is at @xmath56 . the momenta @xmath43 are then defined to be coefficients of decomposition of an arbitrary meromorphic quadratic differential with simple poles in the basis described above . an alternative set of darboux coordinates on @xmath0 ( more precisely , on the subset @xmath57 which contains quadratic differentials with all simple zeros ) is given by abelian periods of the quadratic differential @xmath11 which are defined as integrals of @xmath37 over odd part of homology group @xmath58 of canonical covering @xmath38 . the canonical two - sheeted covering @xmath38 is defined by equation @xmath59 in @xmath60 ; the branch points of @xmath38 lie at zeros and poles of @xmath11 ( in modern literature @xmath38 is sometimes attributed to seiberg - witten @xcite or hitchin @xcite , although this two - sheeted covering was extensively used starting from early days of teichmller theory @xcite ) . the genus of @xmath38 equals @xmath39 ; it admits a natural holomorphic involution which we denote by @xmath61 . the homology group @xmath58 can be decomposed into direct sum @xmath62 of even and odd subspaces under the action of @xmath61 ; the dimension of @xmath63 equals @xmath64 while @xmath65 . choosing a symplectic basis @xmath66 in @xmath67 with the intersection matrix @xmath68 we define periods of @xmath11 by a_i=_a_i^-v,0.7 cm b_i=_b_i^-v . the intersection pairing in @xmath67 defines the natural symplectic form @xmath69 which turns out to coincide with the canonical symplectic form @xmath70 on @xmath71 restricted to the space of quadratic differentials with simple zeros . moreover , we show that the function generating the transformation from canonical darboux coordinates @xmath72 to darboux coordinates given by periods @xmath73 is given by @xmath74 which generalizes the formula obtained in @xcite to the case @xmath75 . the symplectic form @xmath76 induces a poisson structure on the character variety @xmath33 via the monodromy map of equation ( [ sint ] ) . we emphasize that this monodromy map essentially depends on the choice of the base projective connection . the choice of bergman projective connection @xmath12 as the base is not unique since @xmath12 transforms non - trivially under the change of torelli marking of @xmath4 . the bers projective connection chosen as the base in @xcite carries even more freedom , since it depends on a choice of a point in the teichmller space as a parameter . nevertheless , as it was shown in @xcite , the poisson structure induced on the character variety is the same for the bergman projective connection ( independently of torelli marking used ) and bers projective connection used in @xcite ( independently of the choice of the initial point in the teichmller space ) . technically , it is convenient to work with the matrix first order equation constructed by introducing functions @xmath77 where @xmath25 are two linearly independent solutions of ( [ sint ] ) . denote by @xmath78 the wronskian matrix of @xmath79 and @xmath80 . the matrix @xmath78 satisfies the first order matrix equation = ( 0 & v + uv & 0 ) where the meromorphic function @xmath81 on @xmath4 is given by u= --1 , and @xmath82 is the schwarzian derivative of the coordinate @xmath83 with respect to a local coordinate @xmath19 . notice that the coefficients @xmath84 and @xmath85 in ( [ lsi ] ) are ( holomorphic and meromorphic respectively ) differentials on @xmath38 , not on @xmath4 itself . the poisson bracket between @xmath86 and @xmath87 ( assuming that the coordinates @xmath88 and @xmath89 are independent of moduli ) is given by the following expression : \{u(z ) , u ( ) } = _z- _ , where the bimeromorphic function @xmath90 on @xmath91 is given by @xmath92 ; the differential operator @xmath93 is known as the `` lenard s operator '' in the theory of integrable systems . the computation of the poisson bracket ( [ pbpot ] ) from the fundamental poisson bracket @xmath94 ( and , therefore , also from fundamental poisson bracket on @xmath0 ) is based on variational formulas for the canonical bidifferential @xmath95 proved in @xcite . the monodromy map for equation ( [ lsi ] ) gives an @xmath23 representation of @xmath96 . a technical computation originally performed in @xcite allows to find the poisson bracket between traces of monodromy matrices of equation ( [ lsi ] ) along two arbitrary loops @xmath97 and @xmath98 . the result is the goldman s bracket @xcite : \{trm_,m_}=_p trm__p - trm__p ^-1 where the monodromy matrices @xmath99 ; cycles @xmath100 and @xmath101 are cycles obtained by resolving the intersection point @xmath102 in two different ways ( see @xcite ) . the paper is organized as follows . in section [ cancov ] we describe main objects associated to the canonical two - sheeted covering . in section [ seceq ] we define the @xmath23 monodromy representation for equation ( [ sint ] ) via an appropriate matrix reformulation . in section [ varfo ] we derive variational formulas for the main objects : the potential of the matrix equation and for monodromy matrices . in section [ canper ] we show that the period coordinates are darboux coordinates for the canonical symplectic structure on @xmath0 . in section [ cango ] we outline the modifications which have to be made in the scheme of @xcite to cover the case of meromorphic differentials with first order poles .

we study symplectic properties of monodromy map of second order linear equation with meromorphic potential having only simple poles on a riemann surface . we show that the canonical symplectic structure on the cotangent bundle implies the goldman poisson structure on the corresponding character variety under monodromy map , thereby extending the recent results of the paper of m.bertola , c.norton and the author from the case of holomorphic to meromorphic potentials with simple poles .

we study symplectic properties of monodromy map of second order linear equation with meromorphic potential having only simple poles on a riemann surface . we show that the canonical symplectic structure on the cotangent bundle implies the goldman poisson structure on the corresponding character variety under monodromy map , thereby extending the recent results of the paper of m.bertola , c.norton and the author from the case of holomorphic to meromorphic potentials with simple poles .

1508.03038

i

the theory of hyperplane arrangements has deep connections with many areas of mathematics , such as combinatorics , representation theory , algebraic geometry , algebraic topology , singularity theory , and the theory of hypergeometric functions . one beautiful application of the use of hyperplane arrangements in algebraic geometry is the proof of brieskorn s conjecture by deligne @xcite in 1972 . real hyperplane arrangements serve as the motivation for the axioms that define oriented matroids . see @xcite for detailed reviews of the theory of hyperplane arrangements . real hyperplane arrangements have been used recently in the physics literature to analyze the fiber structure and the network of flop transitions between different resolutions of elliptically fibered calabi - yau threefolds @xcite . compactifications of m - theory on calabi - yau threefolds form an elegant bridge between the study of supersymmetric gauge theories in five dimensional spacetime and certain types of highly structured hyperplane arrangements defined by a lie algebra @xmath2 and a representation @xmath3 of @xmath2 . these hyperplane arrangements have the peculiarity of being defined not in the full affine space as they are restricted to the dual fundamental weyl chamber of the lie algebra @xmath2 . [ def : incgeogeneral ] let @xmath2 be a reductive lie algebra over @xmath4 , let @xmath5 be a split , real form of a cartan subalgebra of @xmath6 and let @xmath7 be a representation of @xmath2 . we denote by @xmath8 the real hyperplane arrangement consisting of the kernels of the weights of @xmath7 restricted to a dual fundamental weyl chamber in @xmath5 . because all cartan subalgebras are conjugate and all fundamental weyl chambers canonically related by the weyl group action , the incidence geometry @xmath8 is independent of the choice of @xmath5 and of a dual fundamental weyl chamber in @xmath5 . in the rest of the paper , we call the dual fundamental weyl chamber " the _ weyl chamber_. an arrangement of hyperplanes stratifies the ambient space into open polyhedral cones called _ faces_. a non - empty intersection of a finite number of hyperplanes of the arrangement is called a _ flat_. a @xmath9-face ( resp . @xmath9-flat ) is a face ( resp . a flat ) that generates a @xmath9-dimensional linear space . faces of maximum dimension are called _ a classical combinatorial problem asks how many @xmath9-flats and @xmath9-faces a given hyperplane arrangement contains . zaslasky @xcite enumerated chambers and bounded chambers of an affine hyperplane arrangement using the mbius function of its semi - lattice of flats . the purpose of this paper is to count the numbers of @xmath9-faces and @xmath9-flats of hyperplane arrangements @xmath10 where @xmath11 is the vector representation of @xmath0 ( the first fundamental representation ) and @xmath12 is its second exterior power ( the second fundamental representation ) . since our arrangements are restricted to the weyl chamber , we can not apply zaslasky s result directly . however , the highly symmetric nature of the hyperplane arrangements under consideration allows us to study them via their extreme rays . we also analyze the geometries @xmath13 when @xmath2 is not simply laced . the case of @xmath14 is discussed in @xcite . the counting problem solved in this paper is formulated purely in terms of representation theory . however , its motivation comes from the geometry of string theory . in this subsection , we review the motivation . the reader uninterested in the interface of string theory and algebraic geometry can safely ignore this subsection . hyperplane arrangements of the form @xmath15 arise naturally in the study _ coulomb branch _ of a gauge theory in five - dimensional supersymmetric theory with eight supercharges @xcite . such theories contain different types of particles organized into representations of the supersymmetric algebra called _ supermultiplets_. we will consider only vector multiplets and hypermultiplets . when a gauge theory is defined in a five dimensional supersymmetric theory , the vector multiplets transform in the adjoint representation while the hypermultiplets transform in some representation @xmath3 of @xmath2 . the hypermultiplets can become massive through the higgs mechanism along hyperplanes passing through the origin of the weyl chamber of @xmath2 . these hyperplanes partition the weyl chamber into different connected regions called _ coulomb phases _ of the gauge theory , which are characterized by a cubic prepotential depending on real coordinates @xmath16 of the weight space . intriligator - morrision - seiberg computed the prepotential of a five dimensional gauge theory for a theory in which hypermultiplets transform in the representation @xmath17 of a lie algebra @xmath2 . the result is the real function @xcite : @xmath18 depending on the real vector @xmath19 in the weight space . we only wrote the terms of @xmath20 that are relevant for our purposes . the variable @xmath21 runs through the simple roots of @xmath2 , and @xmath22 through the weights of the representation @xmath7 under which the hypermultiplets transform . the cubic absolute values generate singularities , which correspond to hyperplanes along which new massless particles are generated . a well - defined phase of the coulomb branch of the theory is a connected region in which the quantities @xmath23 and @xmath24 each take fixed signs . we fix the sign of @xmath23 by requiring @xmath19 to be in the fundamental weyl chamber . the condition that @xmath25 for all @xmath26 restricts us inside a specific chamber of the arrangement @xmath27 . the counting of flats is connected to the enumeration of mixed _ coulomb - higgs branches _ of the gauge theory . a five dimensional gauge theory with 8 supercharges can be geometrically engineered by a compactification of m - theory on a calabi - yau threefold @xcite . when the calabi - yau threefold is elliptically fibered , its singular fibers determine the lie algebra @xmath2 and the matter representation @xmath3 of the gauge theory . a smooth elliptic fibration with a rational section is a resolution of a singular weierstrass model , and flop transitions join pairs of crepant resolutions of the weierstrass model . it is conjectured that the network of ( partial ) crepant resolutions of the weierstrass model is isomorphic to the adjacency graph of the faces of the hyperplane arrangement @xmath15 . more precisely , it is conjectured that each crepant resolution corresponds to a unique chamber of @xmath15 @xcite , and that two crepant resolutions are connected by a flop if and only if the intersection of the corresponding chambers is a face of codimension one . their common face is then conjectured to correspond to a unique partial resolution of the weierstrass model . see @xcite for examples of explicit matchings between ( partial ) resolutions and faces of a hyperplane arrangements @xmath15 . there are subtleties in presence of non - trivial @xmath28-factorial terminal singularities , see for example @xcite . a proof of this conjecture will likely rely heavily on ideas from mori s program along the lines of @xcite . the intriligator - morrision - seiberg prepotential @xmath29 can also be obtained geometrically @xcite . in the case of @xmath30 , the gauge group is @xmath1 , and therefore the relevant elliptic fibrations each have a mordell - well group of rank one and a singular fiber of type i@xmath31 over a divisor of the discriminant locus . models for elliptic fibrations with a mordell - weil group of rank one are discussed in @xcite and @xcite . elliptic fibrations for geometric engineering of @xmath1 gauge theories have been extensively studied recently in the physics literature ( see for example @xcite and references therein ) . we are now ready to discuss the enumerations performed in this paper . we denote the number of @xmath9-faces of @xmath32 by @xmath33 and collect these numbers in the following formal power series ( generating function ) : @xmath34 the following theorem enumerates faces of @xmath30 . it is proved in sec : genfuncfaces . [ thm : facecount ] the generating function counting faces of @xmath35 by dimension is given by the following rational function : @xmath36 thm : facecount implies a simple recurrence relation for @xmath33 . [ cor : facerecurse ] the sequence @xmath33 obeys the recurrence relation : @xmath37 for @xmath38 . we can also obtain formulas for the generating polynomials @xmath39 g(s , t ) = \sum_{k=0}^n g(n , k)t^k.\ ] ] [ cor : facegenpoly ] the generating polynomials @xmath40 are given by @xmath41 cor : facegenpoly yields the following values of @xmath40 : .3 cm from the above formulae , we can read off the value of @xmath33 for @xmath42 as the coefficient of @xmath43 in @xmath40 : @xmath44 we can also extract formulae for @xmath33 for @xmath9 small and @xmath45 small from thm : facecount . [ cor : facesmalllarge ] we have @xmath46 and @xmath47 cor : facesmalllarge yields the following formulae for @xmath33 and @xmath48 for @xmath49 : @xmath50 thm : facecount and corollaries [ cor : facerecurse ] , [ cor : facegenpoly ] , and [ cor : facesmalllarge ] are proved in sec : genfuncfaces . we denote the number of @xmath9-flats of @xmath32 by @xmath51 and collect these numbers in the following formal power series ( generating function ) : @xmath52 the following theorem enumerates flats of @xmath30 . [ thm : flatcount ] the generating function counting flats of @xmath35 by dimension is given by the following rational function : @xmath53 thm : flatcount is proven sec : genfuncflats . it implies a simple recurrence relation for @xmath51 , the analogue of cor : facerecurse for flats . [ cor : flatrecurse ] the sequence @xmath51 obeys the recurrence relation @xmath54 for @xmath55 . the taylor expansion of thm : flatcount to order 10 in @xmath56 is : from the above formula , we can read off the value of @xmath51 for @xmath42 as the coefficient of @xmath57 in @xmath58 : @xmath59 the form of the series @xmath58 does not allow simple explicit formulae for @xmath60 or for @xmath51 as in corollaries [ cor : facegenpoly ] and [ cor : facesmalllarge ] , respectively . thm : flatcount is proved in sec : genfuncflats . ( 1,1 ) & ( 1,2 ) & ( 1,3 ) & & ( 1,n ) + & ( 2,2 ) & ( 2,3 ) & & ( 2,n ) + & & ( 3,3 ) & & ( 3,n ) + & & & & + & & & & ( n , n ) a face is determined by assigning signs to @xmath61 for all values of @xmath62 such that @xmath63 . these weights can be organized in a right - justified young tableau as in figure [ fig : signtableau ] . it is important to realize that not all sign patterns are allowed . since we are in the weyl chamber , we have @xmath64 using the identities @xmath65 one can prove the following simple sign rules called _ sign flows _ in the physics literature @xcite : the signs in a tableau corresponding to a chamber satisfy the following conditions . * all the boxes above or on the left of a box with positive entries are also positive . * all the boxes below or on the right of a box with negative entries are also negative . a tableau satisfying these two rules corresponds to a unique chamber of @xmath66 . however , a different notation for chambers will be more convenient for dealing with extreme rays . a different notation for chambers will be more convenient for dealing with extreme rays . the sign rules implies that the positive entries of each row are next to each other and start on the left border of the table . it is therefore efficient to denote a given chamber by the numbers of positive entries on each row . the sign rules is then automatically satisfied if these numbers form a decreasing sequence @xmath67 , where we denote by @xmath68 the number of positive entries on the @xmath69th row of the tableau . we do nt count the rows that do not have any positive entries . an entry of the tableau located on the @xmath69th row and the @xmath70th column ( with @xmath71 ) is positive if and only if @xmath72 and @xmath73 . it is negative otherwise . this justifies the following definition . [ def : subsettochamber ] for @xmath74 $ ] , define a face @xmath75 of @xmath35 as the subset of @xmath5 on which @xmath76 we can equivalently write a subset @xmath77 $ ] as a _ characteristic vector _ @xmath78 , where @xmath79 and @xmath80 . a characteristic vector @xmath79 defines a subset @xmath81 $ ] such that @xmath82 ( resp . @xmath83 ) if and only if @xmath84 ( resp . @xmath85 ) . the notation of def : subsettochamber allows us to state the following classification of chambers and extreme rays . [ thm : chamberstructure ] the chambers and extreme rays of @xmath30 satisfy the following properties . a. [ assert : chamberbiject ] the map @xmath86 defines a bijection from @xmath87}$ ] to the set of chambers of @xmath35 . in particular , @xmath35 has @xmath88 chambers . b. [ assert : chamberraysprelim ] the extreme rays of @xmath75 are generated by the vectors @xmath89 where @xmath90 where @xmath91 where @xmath91 counts the elements of @xmath92 that are greater or equal to @xmath93 , and the vectors @xmath94 non - negatively span @xmath75 . in particular , the geometry @xmath30 is simplicial . the enumeration of chambers of @xmath30 announced in thm : chamberstructureassert : chamberbiject recovers the count of phases of @xmath1 with fundamental and antisymmetric matter from the physics literature @xcite . theorem [ thm : chamberstructure ] is proven in sec : extremerayschambers . suppose that @xmath95 with @xmath96 . a direct calculation shows that the box diagram associated to @xmath75 has @xmath97 plusses in the @xmath69th row for @xmath98 and all minus signs in the @xmath69th row for @xmath99 . see tables [ tab : example.gl2 ] and [ tab : example.gl3 ] for examples . c | l|c| l sign tableau & subset of @xmath100 $ ] & characteristic vector & interior points + ' '' '' & @xmath101 & @xmath102 & @xmath103 + ' '' '' & @xmath104 & @xmath105 & @xmath106 + ' '' '' & @xmath107 & @xmath108 & @xmath109 + ' '' '' & @xmath110 & @xmath111 & @xmath112 l | c| c | l sign tableau & subset of @xmath100 $ ] & characteristic vector & interior points of the chamber + ' '' '' - & - & - + & - & - + & & - & @xmath110 & @xmath113 & @xmath114 + ' '' '' + & - & - + & - & - + & & - & @xmath107 & @xmath115 & @xmath116 + ' '' '' + & + & - + & - & - + & & - & @xmath104 & @xmath117 & @xmath118 + ' '' '' + & + & + + & - & - + & & - & @xmath119 & @xmath120 & @xmath121 + ' '' '' + & + & + + & + & - + & & - & @xmath122 & @xmath123 & @xmath124 + ' '' '' + & + & - + & + & - + & & - & @xmath101 & @xmath125 & @xmath126 + ' '' '' + & + & + + & + & + + & & - & @xmath127 & @xmath128 & @xmath129 + ' '' '' + & + & + + & + & + + & & + & @xmath130 & @xmath131 & @xmath132 in light of thm : chamberstructure , we can introduce additional structure on the set of extreme rays of @xmath30 . we will equip the set of extreme rays with a partial order and use the combinatorics of the resulting partially ordered set ( poset ) to study faces and flats in @xmath30 . the following definitions describe the posets that will be relevant to us . [ def : quarterplaneposet ] the _ discrete quarter plane poset _ is the set @xmath133 endowed with the cartesian order induced by the usual order of the set @xmath134 of non - negative integers : @xmath135 this is a graded poset with grading function @xmath136 . we call @xmath137 the _ level _ of @xmath138 . [ def : posetforextrays ] we denote by @xmath139 the subset of the discrete quarter plane that consists of points at level less or equal to @xmath140 . @xmath139 is a poset with the order induced by the cartesian order defined above . we denote by @xmath141 the poset @xmath142 where @xmath143 is greater than all the elements of @xmath139 . we denote by @xmath144 the poset @xmath139 with the origin removed : @xmath145 we are now ready to relate @xmath144 to the set of extreme rays of @xmath30 . [ def : vfn ] define a function @xmath146 by @xmath147 the following theorem follows directly from thm : chamberstructure . [ thm : raystruture ] the extreme rays of @xmath35 satisfy the following properties . a. the function @xmath148 defines a bijection from @xmath144 to the set of extreme rays of @xmath35 . b. the set of extreme rays that lie in a chamber @xmath75 are the extreme rays @xmath149 where @xmath150 . we will characterize faces and flats by the extreme rays they contain . for that reason we define a function which returns the extreme rays lying in a given subset of the weyl chamber . [ def : raysoperator ] define a function @xmath151 from @xmath152 to the power set of the set of extreme rays of @xmath30 as follows . for @xmath153 let @xmath154 be the set of extreme rays of @xmath30 that lie in @xmath155 . the following theorem , proven in sec : extremeraysfaces relates faces in @xmath30 to the combinatorics of @xmath144 . [ thm : characterization.faces ] for all @xmath9 , the function @xmath156 induces a bijection from the set of @xmath9-faces of @xmath30 to the set of @xmath9-chains in @xmath144 . here , we say that @xmath157 is a @xmath9-chain if @xmath92 is a chain and @xmath158 . to state an analogue of thm : characterization.faces for flats , we will need to define structures called _ ensembles _ that will play the role of chains . [ def : ensemble ] an _ ensemble _ is the restriction to @xmath144 of a union @xmath159 \right)\cap { \mathbb{e}^\ast}_n\ ] ] of intervals @xmath160 $ ] of @xmath141 satisfying the following four conditions : 1 . @xmath161 2 . @xmath162 for @xmath163 ; 3 . @xmath164 for @xmath165 ; and 4 . @xmath166 or @xmath167 . we say that @xmath168 is a _ @xmath9-ensemble _ if @xmath169 , so that @xmath9 counts the number of distinct levels of elements of @xmath168 . figure [ fig : ensembleoneeg ] . shows one example of an ensemble . 2 -ensemble in @xmath170 . * figure ( a ) represents the @xmath171-ensemble @xmath92 which is the restriction to @xmath172 of the union of intervals @xmath173 \cup [ ( 3,3),(4,4 ) ] \cup [ ( 5,5),\infty]$ ] . theorem [ thm : characterization.flats ] guarantees that @xmath174 is the set of extreme rays of a unique 10-flat in @xmath175 . figure ( b ) illustrates a maximal chain of @xmath92 , which corresponds to a @xmath171-face of @xmath175 . ] -ensemble in @xmath170 . * figure ( a ) represents the @xmath171-ensemble @xmath92 which is the restriction to @xmath172 of the union of intervals @xmath173 \cup [ ( 3,3),(4,4 ) ] \cup [ ( 5,5),\infty]$ ] . theorem [ thm : characterization.flats ] guarantees that @xmath174 is the set of extreme rays of a unique 10-flat in @xmath175 . figure ( b ) illustrates a maximal chain of @xmath92 , which corresponds to a @xmath171-face of @xmath175 . ] [ thm : characterization.flats ] for all @xmath9 , the function @xmath156 induces a bijection from the set of @xmath9-flats of @xmath30 to the set of @xmath9-ensembles of @xmath144 . theorem [ thm : characterization.flats ] is proven in section [ sec : extremeraysflats ] on page . denote by @xmath11 the vector representation of @xmath176 and of @xmath177 . recall that the representation @xmath178 of @xmath177 factors as @xmath179 , where @xmath180 is irreducible . let @xmath181 ( resp . @xmath182 ) denote the unique 26-dimensional ( resp . 7-dimensional ) irreducible representation of @xmath183 ( resp . @xmath184 ) . we are now ready to discuss the geometry @xmath185 when @xmath2 is non - simply laced simple lie algebra . [ thm : nonsimplylaced ] suppose that @xmath186 and suppose that @xmath2 has rank @xmath140 . the geometry @xmath185 is a cone over a simplex @xmath187 . in particular , there is 1 chamber and the number of @xmath9-faces ( resp . @xmath9-flats ) is @xmath188 . there is only one other geometry @xmath13 when @xmath2 is simple and non - simply laced and @xmath7 is a direct sum of minuscule and quasi - minuscule representation . this is the geometry @xmath189 it is mentioned in ( * ? ? ? * section 6.3 ) that @xmath190 and @xmath191 have no chambers . this is in contradiction with the conclusion of thm : nonsimplylaced . a direct calculation shows that all the weights of @xmath7 are scalar multiples of the roots of @xmath2 in the cases discussed in the theorem . therefore , the hyperplanes @xmath192 for @xmath22 a weight of @xmath7 coincide with vanishing loci of roots of @xmath2 . the theorem then follows from the fact that the weyl chamber is simplicial . . * the geometry contains 4 chambers , 5 half - lines and the origin . there is one 2-flat ( the half - plane below the line @xmath193 ) , three 1-flats ( the interior walls @xmath194 , @xmath195 , @xmath196 ) , and one 0-flat ( the origin ) . ] in sec : prelims , we recall basic facts regarding the lie algebra @xmath0 and from the theory of hyperplane arrangements . in sec : extrayschmfaces , we prove theorems [ thm : chamberstructure ] , [ thm : raystruture ] , and [ thm : characterization.faces ] . in sec : facecount , we prove thm : facecount , and in sec : flatcount , we prove theorems [ thm : flatcount ] and [ thm : characterization.flats ] . m.e . is grateful to shu - heng shao and shing - tung yau for helpful discussions . m.e . and a.n . thank william massey and all the organizers of the 20th conference for african american researchers in mathematical sciences ( caarms 20 ) where this started . is supported in part by the national science foundation ( nsf ) grant dms-1406925 elliptic fibrations and string theory " . is supported by the harvard college research program .

we study the central hyperplane arrangement whose hyperplanes are the vanishing loci of the weights of the first and the second fundamental representations of restricted to the dual fundamental weyl chamber . we obtain generating functions that count flats and faces of a given dimension . this counting is interpreted in physics as the enumeration of the phases of the coulomb and mixed coulomb - higgs branches of a five dimensional gauge theory with 8 supercharges in presence of hypermultiplets transforming in the fundamental and antisymmetric representation of a gauge group as described by the intriligator - morrison - seiberg superpotential .

we study the central hyperplane arrangement whose hyperplanes are the vanishing loci of the weights of the first and the second fundamental representations of restricted to the dual fundamental weyl chamber . we obtain generating functions that count flats and faces of a given dimension . this counting is interpreted in physics as the enumeration of the phases of the coulomb and mixed coulomb - higgs branches of a five dimensional gauge theory with 8 supercharges in presence of hypermultiplets transforming in the fundamental and antisymmetric representation of a gauge group as described by the intriligator - morrison - seiberg superpotential .

1002.0732

i

we propose a continuous model of the elasticity and plasticity of disordered , discrete materials such as cellular patterns ( for instance liquid foams or emulsions ) and assemblies of particles ( for instance colloids ) . it is based on statistical quantities including ( i ) the elastic strain @xmath35 , a dimensionless quantity measurable on images , which facilitates the comparison between different experiments or models , and makes apparent the effect of shear on the material s structure ; ( ii ) the yield strain @xmath40 , a classical criterion for the transition between reversible , elastic and irreversible , plastic regimes ; ( iii ) and the yield function @xmath133 , which describes how progressive this transition is , by measuring the relative proportion of elastic and plastic deformation . they suffice to relate the discrete scale with the collective , global scale . at this global scale , the material behaves as a continuous medium ; it is described with tensors such as strain , stress and velocity gradient . we give the differential equations which predict the elastic and plastic behaviour . the model is fully tensorial and thus general , in 2d or in 3d . we study in detail the case of simple shear . an original representation , suitable for 2d incompressible materials , is introduced to follow the evolution of the material during shear . since @xmath35 is a tensor , it has an orientation and an amplitude , which both evolve under shear . it can continuously decrease its amplitude , change direction and increase again its amplitude without ever vanishing ( as opposed to a scalar , which can change sign only when it is equal to zero ) . predictions of the model regarding orientation and stretching are plotted . they include a rotation of the structure , which can induce an overshoot of the shear strain or shear stress ( and a smaller , rarer overshoot in normal stress differences ) even without overshoot in the elastic strain amplitude . this purely tensorial effect exists if @xmath70 is at least of order of 0.3 . independently , the shear can also induce a change in the material s structure , sometimes resulting in a ( purely scalar ) overshoot in the modulus of the elastic strain . the model extends a classical plasticity criterion to disordered media . it can be solved numerically and yields testable predictions . we successfully compare them with carefully converged quasistatic simulations of shear cycles in 2d foams : the elastic strain increases , saturates and reverses . from this comparison between model and simulation we determine @xmath70 and estimate @xmath52 . this method is similar to that which we have used in experiments to extract @xmath70 @xcite , and a rough estimate of @xmath52 . we still lack a model to predict @xmath70 and @xmath52 . both quantities evolve throughout the simulation , probably due to the evolution of the foam s internal structure , as well as the disorder and fluctuations . in short , the material obeys a continuous description determined by its average properties , while @xmath70 and @xmath52 account for the effect at large scale of its fluctuations . all quantities involved in the model are directly measurable , as tensors , in the current state of the material ; this includes trapped stresses which we discuss ( we also explain how to relax them ) : the history of the sample which led to this current state plays no other direct , explicit role . we explain how and when to use the model in practice , and provide a set of curves and analytical approximations , including a discussion and an extension of the poynting relation . at low strain , typically below 0.2 , tensorial effects vanish and an approximate scalar simplification holds .

we study the elasto - plastic behaviour of materials made of individual ( discrete ) objects , such as a liquid foam made of bubbles . the evolution of positions and mutual arrangements of individual objects is taken into account through statistical quantities , such as the elastic strain of the structure , the yield strain and the yield function . the past history of the sample plays no explicit role , except through its effect on these statistical quantities . they suffice to relate the discrete scale with the collective , global scale . at this global scale , the material behaves as a continuous medium ; it is described with tensors such as elastic strain , stress and velocity gradient . we write the differential equations which predict their elastic and plastic behaviour in both the general case and the case of simple shear . an overshoot in the shear strain or shear stress is interpreted as a rotation of the deformed structure , which is a purely tensorial effect that exists only if the yield strain is at least of order 0.3 . we suggest practical applications , including : when to choose a scalar formalism rather than a tensorial one ; how to relax trapped stresses ; and how to model materials with a low , or a high , yield strain .

we study the elasto - plastic behaviour of materials made of individual ( discrete ) objects , such as a liquid foam made of bubbles . the evolution of positions and mutual arrangements of individual objects is taken into account through statistical quantities , such as the elastic strain of the structure , the yield strain and the yield function . the past history of the sample plays no explicit role , except through its effect on these statistical quantities . they suffice to relate the discrete scale with the collective , global scale . at this global scale , the material behaves as a continuous medium ; it is described with tensors such as elastic strain , stress and velocity gradient . we write the differential equations which predict their elastic and plastic behaviour in both the general case and the case of simple shear . an overshoot in the shear strain or shear stress is interpreted as a rotation of the deformed structure , which is a purely tensorial effect that exists only if the yield strain is at least of order 0.3 . we suggest practical applications , including : when to choose a scalar formalism rather than a tensorial one ; how to relax trapped stresses ; and how to model materials with a low , or a high , yield strain .

0910.5858

c

we have studied the entanglement creation process of two uniformly accelerated ud detectors moving in opposite directions in the minkowski vacuum of a massless scalar field . the two detectors are causally disconnected during the whole history and are far apart at late times . for two detectors initially in their ground states , entanglement creation does occur under some specific conditions : if the initial time is negative and not very close to zero , the coupling strength @xmath156 between each detector and the field is not too large , and the ratio of the proper acceleration @xmath5 to the natural frequency of the detectors @xmath22 is at some moderate value . the moment of entanglement creation , if any , is always at positive @xmath4 . once quantum entanglement is created it can last for a lifetime much longer than the natural period of the detectors in some parameter range , while entanglement always disappears in a finite time . for two detectors each initially in a squeezed state , similar entanglement creation can also occur if the squeeze parameters in the initial state of both detectors are sufficiently small so the initial state is close enough to the direct product of the ground states . moreover , we find that the rdm of two oscillators each with a truncated spectrum up to the first excited state contains the complete information about the separability of the oscillators in gaussian states . in appendices a and b we see that in tdpt@xmath191 regime , where the integration domain has been extended to @xmath190 , the growing rates of the matrix elements of the truncated rdm can be estimated well , but one has to be careful in obtaining the ratio of different matrix elements . while tdpt@xmath191 results are markovian , we find tdpt still keeps some of the non - markovian features . the dependence of entanglement dynamics on the initial state , the fiducial time , and the non - markovian features shown above are beyond the scope of massar and spindel s steady - state calculation @xcite . in addition , there are some other interesting differences between our findings in ( 3 + 1)d ud detector theory and ms s in ( 1 + 1)d u - rsg model . first , in our analysis @xmath113 and @xmath114 corresponding to the ultraviolet cutoffs in ( 3 + 1)d ud detector theory explicitly enter the entanglement dynamics , while the infrared cutoff in ( 1 + 1)d u - rsg model does not affect the degree of entanglement in ms s result because they only considered the cases where their constant @xmath204 , which is a product of the coupling strength and the very long duration of the interaction corresponding to the infrared divergence , is always much greater than all other parameters , such that the higher - order terms in the @xmath204-expansion of the logarithmic negativity can be neglected . second , while in both cases quantum entanglement between the detectors can be created after the moment in minkowski time that the distance between the detectors is a minimum , the lifetimes of the created entanglement in our case are usually much longer than the natural period of the detectors , in contrast to the short lifetimes of entanglement in ms s ( 1 + 1)d results . finally , in our ( 3 + 1)d case entanglement creation is totally suppressed in the strong coupling regime and can manifest in the weak coupling limit , while in ms s result entanglement generation is a non - pertubative phenomena so there is no entanglement creation in their weak coupling regime . entanglement creation between two causally disconnected objects as we have captured in this work may be viewed as _ a manifestation of quantum nonlocality " _ in quantum physics . quantum entanglement between two localized objects can be generated by allowing them to interact with a common quantum field even though they do not exchange any classical information . foremost our results testify to the important fact that _ quantum nonlocality does not violate causality _ notice that quantum entanglement can be recognized and put to use ( as in qip ) only by those spectators " who can access the information from both detectors . from the viewpoint of the separate detectors each can never find out the existence of the other from its own rdm , nor the quantum entanglement between them . there is no transmittal of physical information between them and causality ( of information ) is always respected . this fact also means that the existence of aspectator " is essential when we refer to the dynamics of entanglement between the two localized parties outside of causal contact . the spectator is causally connected to ( and thus can see " ) both parties and can recognize the quantum entanglement between them through its own observation of both . recall that in ref . @xcite we found that entanglement dynamics for two quantum objects in relativistic motion depend on the choice of reference frames or coordinates ( minkowski or rindler , for example ) . one may debate on which coordinate is better " or more objective " for the depiction of entanglement dynamics . our results show that the only physically meaningful one in a given physical setup for describing the entanglement dynamics of the system is that of the spectator . this is of course not unique , but there are well - established ways to relate what is measured by one spectator to another with considerations of time - slicing ( see , e.g. , @xcite ) and transformation laws of reference frames in relativity theory . the setup of our problem can also mimic the situation of two ions of the same charge in a head - on collision . quantum entanglement is generated in the later stage of the collision when the two ions are moving apart , once the trajectories of the ions possess the right kind of symmetry to enhance the field correlations as those in the present problem ( see appendix [ dpridge ] ) . there is no energy exchange between the two ions during the entanglement creation process of this kind . it has been shown that two atoms coupled with a common field vacuum in a cavity can get entangled in a collision " @xcite . these entangling processes could be interpreted as a consequence of virtual quanta exchange in a van der waal potential , analogous to those with the coulomb interaction in electron - electron scattering . in @xcite the interaction time is much longer than the propagation time of photons across the spatial separation between the atoms , and energy exchange between two atoms is clearly present . these cases where entanglement generation occurring well inside the light cone is different from the present setup but closer to the situation we considered in @xcite , where quantum entanglement is established mainly by retarded mutual influences . note that particle ( or atom , molecule ) collisions in non - relativistic classical and quantum mechanics are usually described by an effective hamiltonian with a direct , nonlocal , inter - particle interaction ( e.g. a potential @xmath205 , where @xmath206 are the positions of the particles ) . direct interaction always generates correlation between the particles , classical or quantum . the nonlocality of the interaction , on the other hand , is a consequence of coarse graining from a more fundamental local theory , resulting in an effective theory description . the particles in this non - relativistic regime can not resolve the time scale for information propagating back and forth between them . thus the generation of correlation by this kind of nonlocal direct interaction happens in a time scale during which two particles have causal contact for a long time . one can not tell whether correlations can be created between two causally disconnected particles in this kind of effective theories . moreover , with this kind of nonlocal direct interaction , if one does not further introduce a spatial range of interaction associated with a coarse - graining in time , even classical correlation will be nonlocal and can not be described by any local hidden - variable theory . + * acknowledgment * syl wishes to thank daniel braun for illuminating discussions during his visit to the joint quantum institute , university of maryland and national institute of standards and technology , where this work was first motivated and commenced . blh wishes to thank the hospitality of national center for theoretical sciences and the qis group at national cheng kung university of taiwan . this work is supported partially by grants from lps , nsf grants phy-0426696 , phy-0801368 and darpa - hr0011 - 09 - 1 - 0008 .

we study the full entanglement dynamics of two uniformly accelerated unruh - dewitt detectors with no direct interaction in between but each coupled to a common quantum field and moving back - to - back in the field vacuum . for two detectors initially prepared in a separable state our exact results show that quantum entanglement between the detectors can be created by the quantum field under some specific circumstances , though each detector never enters the other s light cone in this setup . in the weak coupling limit , this entanglement creation can occur only if the initial moment is placed early enough and the proper acceleration of the detectors is not too large or too small compared to the natural frequency of the detectors . once entanglement is created it lasts only a finite duration , and always disappears at late times .

we study the full entanglement dynamics of two uniformly accelerated unruh - dewitt detectors with no direct interaction in between but each coupled to a common quantum field and moving back - to - back in the field vacuum . for two detectors initially prepared in a separable state our exact results show that quantum entanglement between the detectors can be created by the quantum field under some specific circumstances , though each detector never enters the other s light cone in this setup . in the weak coupling limit , this entanglement creation can occur only if the initial moment is placed early enough and the proper acceleration of the detectors is not too large or too small compared to the natural frequency of the detectors . once entanglement is created it lasts only a finite duration , and always disappears at late times . prior result by reznik derived using the time - dependent perturbation theory with extended integration domain is shown to be a limiting case of our exact solutions at some specific moment . in the strong coupling and high acceleration regime , vacuum fluctuations experienced by each detector locally always dominate over the cross correlations between the detectors , so entanglement between the detectors will never be generated .

0811.0388

i

quantum phase transitions in systems of itinerant fermions continue to attract considerable interest.@xcite on one hand this attention is due to the relevance of quantum critical points for understanding collective phenomena like high-@xmath1 superconductivity and other non - conventional properties of experimentally investigated compounds.@xcite on the other , it is related to peculiarities that so far prohibited the emergence of a fully convincing theoretical description of most systems exhibiting quantum criticality.@xcite the standard approach in describing quantum critical phenomena in systems of itinerant fermions - the hertz - millis theory @xcite - relies on an order parameter field , which is introduced by a stratonovich - hubbard transformation . in a subsequent step the fermionic degrees of freedom are integrated out . the resulting representation of the partition function as a path integral over a bosonic field is usually useful only provided the action may be expanded in the order parameter , and the relevant vertex functions can be evaluated for the values of momentum and frequency that correspond to the anticipated instability . the validity of such an expansion was questioned for both zero and finite momentum instabilities in the magnetic channel . in case of ferromagnetic transitions it was argued that the correct effective action involves additional terms @xcite leading to a first order transition , @xcite while for the case of antiferromagnetic transition in @xmath4 integrating out gapless fermionic modes can yield singular vertex functions all of which were argued to be marginal . @xcite despite these theoretical insufficiencies , hertz - millis theory is successful in explaining a number of nonconventional properties of many systems exhibiting quantum criticality . @xcite in recent years this theory was further extended to account for a number of systems not described by the original approach . these include metamagnetic quantum critical points,@xcite field - tuned quantum critical points where a term describing precession of the order parameter has to be retained in the action,@xcite and phase transitions induced by a nonequilibrium drive . @xcite an interesting issue concerns the actual order of specific quantum phase transitions . hertz - millis theory by construction allows for continuous transitions only . however , microscopic models , which usually rely on fermionic degrees of freedom and meanfield - like treatment , often predict a first order scenario in case of both magnetic and charge instabilities occurring at @xmath5 , and for specific cases corresponding to @xmath6 . @xcite theoretical studies of the interplay between first and second order scenarios are further motivated by experimental results , where the order of the quantum phase transitions in specific compounds is altered by varying external magnetic field @xmath7.@xcite upon increasing @xmath7 , the tricritical point separating the first order transition at @xmath8 from the second order at @xmath9 , is shifted towards lower values of @xmath10 and finally vanishes at @xmath11 . therefore , the order of the transition at small @xmath10 can be controlled by varying @xmath7 . of particular interest is the case @xmath12 , where the transition is second order for all @xmath13 , but scaling behavior of physical quantities at low temperatures is in variance with that predicted by hertz - millis theory . @xcite an interesting scenario of quantum criticality occurs also in systems exhibiting a metamagnetic first order transition terminating with a critical end point.@xcite by tuning pressure the critical end point is suppressed to @xmath11 resulting in a distinct type of a quantum critical point . in this work we investigate the possibility of altering the order of quantum phase transitions by order parameter fluctuations . subsequently , we study shapes of phase boundaries , focusing mainly on the cases where such change occurs . we rely on the conventional bosonic hertz action adapted to phases with broken symmetry and retaining also a @xmath0 term in the effective potential . we analyze two- and three- dimensional systems where discrete symmetry - breaking occurs at @xmath5 ( the dynamical exponent @xmath14 ) . our results should apply whenever an action of this type can be constructed . possible examples are magnetic transitions with ising - like symmetry and the so - called pomeranchuk instabilities @xcite where the discrete point - group lattice symmetry of the fermi surface is broken . for these transitions mean - field studies typically predict a first order scenario at @xmath11 but second order for slightly higher temperatures ( for @xmath9).@xcite we argue that the tricritical temperature is lowered by including the order - parameter fluctuations . under appropriate conditions the tricritical point may be suppressed to @xmath11 , in which case a quantum critical or tricritical point is realized . our study is based on the one - particle irreducible version of the functional renormalization group ( rg).@xcite this framework was applied extensively in the context of classical critical phenomena , where it yields a unified description of @xmath15-symmetric scalar models including systems in @xmath4.@xcite it also provides a suitable framework to treat quantum criticality.@xcite we apply the derivative expansion to quadratic order , and the effective potential is parametrized in a form allowing for the occurrence of both - first and second order transition . an advantage of the functional rg is that it allows control over effects occurring at different energy scales , and treatment of quantities that need not be universal . the outline of this work is as follows : in sec . ii we introduce the bare action to be applied in the rg procedure and provide a phase diagram of the unrenormalized theory . in sec . iii we discuss the applied truncation of the functional rg flow equation and derive equations governing the evolution of quantities parametrizing the effective potential and the inverse propagator upon reducing the cutoff scale . iv is devoted to results obtained for the renormalized phase diagrams in the case @xmath11 . in sec . v we consider @xmath13 . we discuss the computed phase diagrams for cases where the phase transition is second order for @xmath13 and terminates at a quantum critical or tricritical point at @xmath11 . we also analyze the case where a tricritical point situated at @xmath13 occurs . for @xmath16 and a choice of system parameters corresponding to proximity to the quantum tricritical scenario we compute the crossovers of the shift exponent @xmath3 , characterizing the shape of the critical line , from the hertz - millis value @xmath17 to @xmath18 . this latter value of the shift exponent is specific to quantum tricritical behavior in @xmath19 . the obtained value of @xmath20 is justified by invoking a scaling argument in sec . vi , where we also classify and discuss scaling regimes emergent from our analysis . finally , sec . vii contains a summary of the work .

we study the impact of quantum and thermal fluctuations on properties of quantum phase transitions occurring in systems of itinerant fermions with main focus on the order of these transitions . our approach is based on a set of flow equations derived within the functional renormalization group framework , in which the order parameter is retained as the only degree of freedom , and where the effective potential is parametrized with a form allowing for both first and second order scenarios . we find a tendency to turn the first order transitions within the bare model into second order transitions upon accounting for the order parameter fluctuations .

we study the impact of quantum and thermal fluctuations on properties of quantum phase transitions occurring in systems of itinerant fermions with main focus on the order of these transitions . our approach is based on a set of flow equations derived within the functional renormalization group framework , in which the order parameter is retained as the only degree of freedom , and where the effective potential is parametrized with a form allowing for both first and second order scenarios . we find a tendency to turn the first order transitions within the bare model into second order transitions upon accounting for the order parameter fluctuations . we compute the first and second order phase boundary lines as a function of a non - thermal control parameter in the vicinity of a quantum phase transition . we analyze crossovers of the shift exponent governing the shape of the line when the system is tuned close to a quantum tricritical scenario , where a second order phase transition line terminates at a quantum tricritical point .

1406.7277

i

the standard model of cosmology , @xmath4cdm , explains anisotropies on cosmic microwave background ( cmb ) radiation @xcite and the large scale structure ( lss ) observations with good accuracies @xcite . this model is based on the assumption of cold dark matter as the skeleton of the structures in the universe @xcite and the cosmological constant as the source of late time acceleration while the initial conditions are set by the inflationary paradigm @xcite . inflation generates nearly scale - invariant , nearly gaussian and nearly adiabatic perturbations which are imprinted on the temperature map of cmb and also provides the initial distribution for the seeds of structures in the early universe @xcite . accordingly , one of the triumphs of modern cosmology is the compatibility of the dark matter tracers distribution with the statistics of cmb temperature anisotropy @xcite . thanks to vast cosmological data available during last decade , models of early universe are well - constrained by cosmological observations . in particular , the high precision maps of cmb have been studied extensively to put constraints on inflationary models @xcite . any deviation from the gaussian , adiabatic , isotropic and scale - invariant initial conditions will open distinct fingerprints on cmb map as tools to study the physics of early universe such as inflation @xcite . on the other hand , the lss observables , by transferring the initial condition of perturbations to the late time observables , are potentially very useful tools to test models of early universe in sub - cmb scales @xcite . the abundance of the structures in the universe @xcite , the scale - dependence of bias parameter between dark matter halos as the host of galaxies and the dark matter perturbations @xcite and higher order statistics of dark matter tracers ( e.g. the bispectrum of galaxies ) @xcite are all used to probe the deviations from the standard initial conditions . there are indications for anomalous features in cmb map such as power asymmetry between the two cmb hemispheres @xcite , power deficit in low multipoles @xcite and the coincidence of the quadrupole and octupole directions @xcite . these observations trigger the motivation to study the predictions of inflationary models with anomalous features in lss observables . we note that the cmb maps cover the first few e - folds of the inflationary period , say the first 5 - 7 e - folds , while the remaining 50 or so e - folds are below the cmb scales . it is likely that the primordial power spectrum may have non - trivial features not only on cmb scales but also on scales which are beyond the probe of cmb but are accessible to lss observations . in this work we investigate the framework under which one can study the probable observational fingerprints of anomalous inflationary power spectrum on lss , specially in the abundance of the structure . having this said , there are open questions in lss , specially on galactic scale , such as the missing satellite " problem @xcite and the too big to fail " problem @xcite which may be considered as hints for anomalies / features in primordial curvature perturbation power spectrum on galactic scales ( for a recent work addressing this idea see @xcite ) . it is worth to mention that the theoretical predictions of standard model for matter power spectrum are in reasonable agreements with the observational data in the range of wavenumber ( scales ) @xmath5 . however , the amplitude of small scale dark matter power spectrum is not strongly constrained by lss observables . accordingly , there are freedoms on the amplitude of the power on galactic scales which in turn can be used as an explanation for the missing satellite problem . therefore the anomalous inflationary models , by modifying the power on small scales , can be considered as a possible solutions to the tension between observations and theory on galactic scales . the rest of the paper is organized as follows . in section [ sec - ii ] first we review the procedure for obtaining the number density of structures based on excursion set theory @xcite and then we study the effects of the primordial feature on the number density of structures in a model - independent way . in section [ theory ] we present the theoretical motivations for generating primordial features studied in this paper . in section [ sec - iii ] , we study the predictions of each anomalous inflationary model on the abundance of the structures . the reader who is not interested in theoretical realization of the features can skip section [ theory ] and go directly to section [ sec - iii ] . the conclusion and future prospects are presented in section [ sec - iv ] .

we study the predictions of anomalous inflationary models on the abundance of structures in large scale structure observations . models with localized feature can alleviate the tension between observations and numerical simulations of cold dark matter structures on galactic scales as a possible solution to the missing satellite problem . in models with hemispherical asymmetry

we study the predictions of anomalous inflationary models on the abundance of structures in large scale structure observations . the anomalous features encoded in primordial curvature perturbation power spectrum are ( a ) : localized feature in momentum space , ( b ) : hemispherical asymmetry and ( c ) : statistical anisotropies . we present a model - independent expression relating the number density of structures to the changes in the matter density variance . models with localized feature can alleviate the tension between observations and numerical simulations of cold dark matter structures on galactic scales as a possible solution to the missing satellite problem . in models with hemispherical asymmetry we show that the abundance of structures becomes asymmetric depending on the direction of observation to sky . in addition , we study the effects of scale - dependent dipole amplitude on the abundance of structures . using the quasars data and adopting the power - law scaling for the amplitude of dipole we find the upper bound for the spectral index of the dipole asymmetry . in all cases there is a critical mass scale in which for the enhancement in variance induced from anomalous feature decreases ( increases ) the abundance of dark matter structures in universe .

0809.4035

i

one of the primary goals of modern condensed matter physics is the characterization of strongly correlated quantum systems . a large class of such materials is represented by frustrated antiferromagnets , which are believed to exhibit a variety of novel states of matter at sufficiently strong coupling . growing experimental evidence indicates that layered materials such as @xmath2 @xcite , @xmath3 @xcite and @xmath4 @xcite can be adequately described by an antiferromagnetic heisenberg model with frustrating next- and next - next - nearest neighbor interactions . as a result , the study of low - dimensional magnets and their frustration - driven quantum phase transitions have attracted a lot of theoretical attention in the last decade @xcite . a paradigmatic system , illustrating the effects of frustrating couplings , is the spin-@xmath5 heisenberg model on a square lattice with competing nearest ( @xmath0 ) , and next - nearest ( @xmath1 ) neighbor antiferromagnetic ( af ) interactions ( @xmath0-@xmath1 model ) . despite numerous analytical and numerical efforts , its phase diagram , which exhibits a two sublattice nel af , quantum paramagnetic , and a four sublattice columnar af states , continues to stir certain controversy ( for a review of recent achievements , see ref . ) . while existence of the nel - ordered phase at small frustration ratio @xmath6 , and of the columnar af state at large @xmath6 is widely established , properties of the intermediate non - magnetic phase , which occurs around the maximum frustration value @xmath7 , are still under debate . particularly , the correlated nature of the intermediate state and the kind of quantum phase transition separating it from the nel state , attract most attention . various methods have been recently applied to characterize the quantum paramagnetic phase , such as green s function monte carlo @xcite , coupled cluster methods @xcite , series expansions @xcite and field - theoretical methods @xcite . as a result , several possible candidate ground states were proposed , namely : spin liquid @xcite , preserving translational and rotational symmetries of the lattice , as well as various lattice symmetry breaking phases , out of which the dimer @xcite , and the _ plaquette resonating valence bond _ phases @xcite are worth mentioning . not surprisingly , the nature of the quantum phase transition separating the nel - ordered and quantum paramagnetic phases is also under scrutiny . the most dramatic , and at the same time original , scenario @xcite is believed to violate the ginzburg - landau - wilson paradigm of phase transitions @xcite which revolves around the concept of an order parameter . such point of view is based on the observation that there are different spontaneously broken symmetries in the nel and quantum paramagnetic phases , which thus can not be connected by a group - subgroup relation . the former , of course , breaks the @xmath8 invariance of the hamiltonian and lattice translational symmetry @xmath9 @xcite , but preserves the four - fold rotational symmetry of the square @xmath10 . on the other hand , the paramagnetic phase is known to restore the spin - rotational symmetry and is believed to break @xmath9 and @xmath10 , due to spontaneous formation of dimers along the links of the lattice @xcite . it follows then , that these two phases can not be joined by the usual landau second - order critical point . this phase transition can either be of the first - order @xcite ( the latest coupled cluster calculations @xcite , however , seem to rule out this possibility ) , or represent an example of a second order critical point , which can not be described in terms of a bulk order parameter , but rather in terms of emergent fractional excitations ( spinons ) , which become deconfined right at the critical point @xcite . however , evidence regarding the structure of the non - magnetic phase is quite controversial . indeed , the results of spin - wave calculations @xcite , large-@xmath11 expansions @xcite , and calculations using the density matrix renormalization group combined with monte - carlo simulations @xcite are believed to indicate the emergence of a dimer order . on the other hand , monte - carlo @xcite and coupled cluster calculations @xcite , and analytical results @xcite seem to support the presence of @xmath10 symmetry ( plaquette - type ordering ) in the paramagnetic phase . in the absence of a reliable numerical or analytical proof of existence of any particular order in the non - magnetic region , there is no apparent reason to believe in the exotic deconfined quantum criticality scenario . although there apparently exists numerical evidence @xcite , at the moment of writing the authors are unaware of a local hamiltonian in space dimensions larger than one , rigorously proven to exhibit the type of quantum critical point discussed in ref . . interestingly , it was demonstrated in ref . that a two - dimensional ( 2d ) lattice model can possess a _ first order _ quantum critical point , which exhibits deconfined excitations . all in all , the complexity of methods used to infer properties of the paramagnetic phase and the variety of different conclusions have created a certain degree of confusion . our goal in the present paper is to try to clarify some of this controversy by proposing a controlled and manifestly symmetry preserving method , geared to computing ground state properties of the @xmath0-@xmath1 model . our approach is based on the recently proposed systematic methodology to investigate the behavior of strongly coupled systems @xcite , whose main idea consists of identifying _ relevant _ degrees of freedom and performing an educated approximation , called the hierarchical mean - field ( hmf ) , to uncover the phase diagram and other properties of the system of interest . in a future work these ideas will be coupled to a new , variational with respect to the energy , renormalization group approach , which thus adapts to the concept of relevant degrees of freedom . -@xmath1 model , summarizing our results . in each phase we show spontaneously broken ( framed symbols ) and unbroken symmetries ( usual symbols ) . the translational invariance is broken along both directions in the nel and paramagnetic phases , and only along the @xmath12direction in the columnar phase this fact is indicated by the subscripts @xmath13 and @xmath12 after @xmath9 . conclusions regarding the order of the phase transition , separating nel and plaquette crystal phases , as well as symmetries of various phases , are based upon extrapolation of our results towards the thermodynamic limit . ] in the present work we construct hmf approximations for the @xmath0-@xmath1 model . the crux of our method is the identification of a _ plaquette _ ( spin cluster @xmath14 or even larger @xmath15 ( _ superplaquette _ ) symmetry - preserving cluster ) as the relevant elementary degree of freedom , which captures necessary quantum correlations to represent essential features of the phase diagram . the importance of this degree of freedom was realized only recently in the present context @xcite , and somewhat earlier in connection with @xmath16 spin - orbital @xcite , and hubbard @xcite models . besides being variational , our formalism has the attractive feature of preserving fundamental lattice point symmetries and the @xmath8 symmetry of the hamiltonian , by utilizing the schwinger boson - type representation and racah algebra technology . remarkably , such simple mean - field calculation already yields all known results , concerning the phase diagram of the @xmath0-@xmath1 model , with a good accuracy , namely : existence of a nel - ordered phase with antiferromagnetic wavevector @xmath17 and spin - wave type excitations for @xmath18 , a non - magnetic intermediate gapped phase , separated by a second order quantum phase transition , and a first order transition point , which is characterized by the discontinuous disappearance of the energy gap and connects the paramagnetic state with the columnar antiferromagnetic phase at @xmath19 and @xmath20 for @xmath21 . we emphasize that our investigation primarily focuses on the symmetry analysis of the various phases . out of many possible coarse graining scenarios , such as covering of the 2d lattice with plaquettes , dimers and crosses , only the @xmath10-_symmetry preserving _ plaquette ( or superplaquette ) covering ( which reproduces the original bravais lattice ) displays the correct phase diagram . in particular , the intermediate paramagnetic phase is shown to be a _ plaquette crystal _ , which preserves spin and lattice rotational symmetries . for all other scenarios , including dimerized ( bond - ordered ) phases , we were unable to reproduce all known quantum phase transition points of the model . we notice that the hmf coarse graining procedure leads to an explicit breaking of a particular translational symmetry . as a result , one can not draw rigorous conclusions on the order of the phase transitions , based solely on a fixed coarse graining . nevertheless , it is still possible to make some predictions , using a finite - size scaling of the relevant degree of freedom towards the thermodynamic limit , where the effects associated with coarse graining should disappear . next two sections are devoted to the formulation of the hmf approach . then , we present results of our calculations and close the paper with a discussion . our main conclusions are summarized in fig . [ fig_phase_diagram ] , which emphasizes symmetry relations between different phases of the model .

we study the quantum phase diagram and excitation spectrum of the frustrated- spin-1/2 heisenberg hamiltonian . a hierarchical mean - field approach , at the heart of which lies the idea of identifying _ relevant _ degrees of freedom , is developed . thus , by performing educated , manifestly symmetry preserving mean - field approximations , we unveil fundamental properties of the system . we then compare various coverings of the square lattice with plaquettes , dimers and other degrees of freedom , and show that only the _ symmetric plaquette _ covering , which reproduces the original bravais lattice , leads to the known phase diagram . we also introduce fluctuations around the hierarchical mean - field solutions , and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap , which closes in the nel and columnar phases .

we study the quantum phase diagram and excitation spectrum of the frustrated- spin-1/2 heisenberg hamiltonian . a hierarchical mean - field approach , at the heart of which lies the idea of identifying _ relevant _ degrees of freedom , is developed . thus , by performing educated , manifestly symmetry preserving mean - field approximations , we unveil fundamental properties of the system . we then compare various coverings of the square lattice with plaquettes , dimers and other degrees of freedom , and show that only the _ symmetric plaquette _ covering , which reproduces the original bravais lattice , leads to the known phase diagram . the intermediate quantum paramagnetic phase is shown to be a ( singlet ) _ plaquette crystal _ , connected with the neighbouring nel phase by a continuous phase transition . we also introduce fluctuations around the hierarchical mean - field solutions , and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap , which closes in the nel and columnar phases . our results suggest that the quantum phase transition between nel and paramagnetic phases can be properly described within the ginzburg - landau - wilson paradigm .

1211.4465

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the concept of ergodicity is at the core of classical statistical mechanics : it establishes a connection between long - time averages of observables and statistical ensemble averages @xcite . the extension of the ergodic theorem to quantum mechanics was pioneered by von neumann @xcite in a seminal paper on the unitary dynamics of closed quantum systems . the experimental possibility of studying the nonequilibrium dynamics of `` virtually '' isolated quantum systems most notably cold atomic species in optical lattices @xcite has stimulated new interest in this issue . the simplest setting for such a nonequilibrium situation is that of a sudden quench of the hamiltonian , @xmath1 , governing the dynamics of the isolated quantum system : the after - quench ( @xmath2 ) unitary evolution is simply @xmath3 but the initial state @xmath4 for instance , the ground state of @xmath5 is generally a complicated superposition of the eigenstates of @xmath6 . since the energy is conserved , @xmath7 , it is reasonable to expect that a `` generic '' ergodic evolution in the hilbert space will lead to time averages which are reproduced by the microcanonical ensemble : this is what von neumann discussed for `` macroscopic '' observables @xcite , and is generally expected to occur @xcite , independently of the initial state @xmath4 . classical physics teaches us also when to expect violations of ergodicity : on one extreme , for systems that are integrable @xcite or close enough to being integrable @xcite ; on the other , for systems with a glassy dynamics , be it due to interactions providing dynamical constraints @xcite , or to genuine disorder @xcite . quantum mechanically , dangers to ergodicity come from very similar sources : integrability , interactions , and disorder . integrability implies the existence of many constants of motion @xmath8 , and this clearly restricts the ergodic exploration of the microcanonical energy shell , leading to what one might call a `` breakdown of thermalization '' @xcite . it often results in a kind of `` generalized thermalization '' described by a statistical ensemble which maximizes entropy in the presence of the constraints @xmath9 , an ensemble introduced long ago by jaynes @xcite and known as generalized gibbs ensemble ( gge ) @xcite @xmath10 } \;,\ ] ] where @xmath11 are lagrange multipliers which constrain the mean value of each @xmath12 to its @xmath13 value : @xmath14 $ ] . on the theory side , the approach to equilibrium has been carefully investigated for one - dimensional bose - hubbard models describing quench experiments in optical lattices and superlattices @xcite . starting from nonhomogeneous initial states ( density waves ) , such as @xmath15 , and evolving the system with a bose - hubbard @xmath16 both at the integrable points @xmath17 ( free bosons ) and @xmath18 ( free hard - core bosons / spinless fermions ) , where analytic solutions are possible @xcite , and at general ( nonintegrable ) values of @xmath19 ( through time - dependent density - matrix renormalization group @xcite ) , the physical picture emerging has led to the so - called _ local relaxation conjecture_@xcite : although the system is , _ sensu stricto _ , in a pure state @xmath20 , when measured upon locally in a finite region @xmath21 , the resulting ( mixed ) reduced density matrix @xmath22 relaxes towards a stationary gibbs state of maximum entropy compatible with all the constants of motion . this relaxation is strongly tight to the `` locality '' of the observable @xmath23 one measures , and results from `` information transfer '' carried by the excitations along the system @xcite , which eventually `` thermalizes '' any finite region @xmath21 , the rest of the system acting as an effective bath for @xmath21 . remarkably , such an approach to equilibrium does not require time averages @xcite . experimentally , a fast dynamical relaxation was recently observed @xcite in a system of cold atoms , where the long - time stationary state was compatible with gge . a far more dangerous type of `` ergodicity crisis '' derives , apparently , from dynamical constraints imposed by interactions@xcite : when quenching a bose - hubbard model starting , for instance , from @xmath24 i.e , with an average density of bosons per site @xmath25 where , in equilibrium , a mott phase transition occurs for @xmath26 the ensuing dynamics leads to a fast relaxation / thermalization for quenches at small @xmath19 , while the relaxation is extremely slow ( and the more so , the more the size of the system increases ) and the dynamics appears effectively _ freezed _ for @xmath27 @xcite . concerning ergodicity breaking due to genuine disorder , both anderson localization , at the single - particle level @xcite , and many - body localization , in the presence of interactions @xcite , are well - known examples of disorder - induced phenomena occurring in equilibrium physics . quantum quenches in the presence of disorder and interactions have also been studied , in the framework of many - body localization @xcite , but the physical picture is far from being fully understood . while breaking of translational invariance and disorder in the initial state @xmath4 have apparently little or no effect on the ensuing relaxation towards a stationary state if the after - quench hamiltonian @xmath6 is translationally invariant @xcite , disorder in the final hamiltonian @xmath6 seems to play a quite crucial role : this has been seen in numerical studies of nonintegrable fermion models with disordered long - range hopping and nearest - neighbor interaction @xcite , and has been recently corroborated through analytical arguments on integrable quantum spin chains of the ising/@xmath0 class @xcite . our present study extends that of ref . , where it was shown that , in the presence of disorder in @xmath6 , the long - time after - quench dynamics _ does not relax _ towards a stationary state , and time fluctuations generally persist in the expectation values of local operators , even in the thermodynamic limit ; this is , essentially , due to the presence of a _ pure - point spectrum _ of @xmath6 associated to localized wave functions , as opposed to the smooth continuum of a system with extended states . one can view this persistence of time fluctuations in local measurements as a result of the inability of the system to carry information around @xcite , due to localization . time averages are , therefore , mandatory in comparing dynamical quantities to statistical ensemble averages . but here a further surprise emerges , which will be the main focus of this study : while time averages of one - body local observables are perfectly well reproduced by the relevant statistical ensemble the gge , being the considered models , essentially , free - fermion ones time averages of many - body local operators show clear deviations from the corresponding gge prediction , in agreement with recent numerical findings @xcite . we will exemplify these ideas on a model of disordered one - dimensional fermions with long - range hoppings , showing a transition between extended and localized eigenstates , and on disordered ising/@xmath0 models . we will start , sec . [ sec : problem ] , by stating in a more precise way the problem we want to analyze . next , in sec . [ sec : models ] , we describe the models we have investigated . in sec . [ sec : gge - one - body ] we will analyze the essential reason why gge works perfectly well in predicting infinite - time averages of _ one - body operators _ , even for finite systems ( as long as one integrates over revivals ) . in sec . [ sec : gge - many - body ] we will discuss why this is not generally the case for many - body operators , unless time fluctuations of one - body green s functions vanish for large @xmath28 . next , in secs . [ sec : spinless ] and [ sec : ising ] we will present our results for the two models we have considered . section [ discussion : sec ] contains a final discussion , and our conclusions and perspectives .

[ phys . rev . lett . 109 , 247205 ( 2012 ) ] . with analytical and numerical arguments we present results on two one - dimensional ( 1d ) models , the disordered 1d fermionic chain with long - range hopping and the disordered ising/ spin chain . we analytically prove that , while time averages of one - body operators are perfectly reproduced by gge ( even for finite - size systems , if time integrals are extended beyond revivals ) , time averages of many - body operators might show clear deviations from the gge prediction when disorder - induced localization of the eigenstates is at play .

we study the unitary dynamics and the thermalization properties of free - fermion - like hamiltonians after a sudden quantum quench , extending the results of s. ziraldo _ et al . _ [ phys . rev . lett . 109 , 247205 ( 2012 ) ] . with analytical and numerical arguments , we show that the existence of a stationary state and its description with a generalized gibbs ensemble ( gge ) depend crucially on the observable considered ( local versus extensive ) and on the localization properties of the final hamiltonian . we present results on two one - dimensional ( 1d ) models , the disordered 1d fermionic chain with long - range hopping and the disordered ising/ spin chain . we analytically prove that , while time averages of one - body operators are perfectly reproduced by gge ( even for finite - size systems , if time integrals are extended beyond revivals ) , time averages of many - body operators might show clear deviations from the gge prediction when disorder - induced localization of the eigenstates is at play .

math0510615

i

in this paper we will study properties of the _ sparse _ or @xmath0-discriminant . given a configuration @xmath1 of @xmath2 points in @xmath3 we may construct an ideal @xmath4 $ ] and , if @xmath5 is homogeneous , a projective toric variety @xmath6 . the dual variety @xmath7 is , by definition , the zariski closure of the locus of hyperplanes in @xmath8 which are tangent to @xmath9 at a smooth point . generically , @xmath7 is a hypersurface and its defining equation @xmath10 , suitably normalized , is called the @xmath0-discriminant . if @xmath7 has codimension greater than one then @xmath9 is called a dual defect variety and we define @xmath11 . the @xmath0-discriminant generalizes the classical notion of the discriminant of univariate polynomials . it was introduced by gelfand , kapranov , and zelevinsky ( their book @xcite serves as the basic reference of our work ) and it arises naturally in a variety of contexts including the study of hypergeometric functions @xcite and in some recent formulations of mirror duality @xcite . when studying the @xmath0-discriminant it is often convenient to consider a gale dual of @xmath0 . this is a configuration @xmath12 , where @xmath13 is the codimension of @xmath9 in @xmath14 . the configuration @xmath15 , and by extension @xmath0 , is said to be irreducible if no two vectors in @xmath15 lie on the same line . equivalently , if the matroid @xmath16 defined by the family , @xmath17 , of linearly independent subsets of @xmath15 is _ simple_. in theorem [ resformula ] , we prove a univariate resultant formula which reduces the computation of the @xmath0-discriminant to the case of irreducible configurations . this implies , in particular , that the newton polytope of the discriminant is unchanged , up to affine isomorphism , if we replace @xmath15 by the configuration obtained by adding up all subsets of collinear vectors . this generalizes a result of @xcite for codimension - two configurations . we point out that , in their case , this is a consequence of a complete description of the newton polytope of the discriminant . in the study of rational hypergeometric functions , one is interested in understanding the behavior of the @xmath0-discriminant when specializing a variable @xmath18 to zero and its relation to the discriminant of the configuration obtained by removing the corresponding point @xmath19 from @xmath0 . theorem [ specialization ] generalizes the known results in this direction ( ( * ? ? ? * lemma 3.2 ) ; ( * ? ? ? * lemma 3.2 ) ) . this specialization result was first proved by the first author in his phd dissertation @xcite , using the theory of coherent polyhedral subdivisions . we give a greatly simplified proof in 4 , where we derive the specialization theorem as a corollary of our resultant formula . using tropical geometry methods , dickenstein , feitchner , and sturmfels have been able to compute the dimension of the dual of a projective toric variety @xmath9 and this , in particular , makes it possible to decide if a given toric variety is dual defect , i.e. if the dual variety has codimension greater than one . their formula ( * ? ? ? * corollary 4.5 ) involves the configuration @xmath0 and the geometric lattice , @xmath20 , whose elements are the supports , ordered by inclusion , of the vectors in @xmath21 . the information contained in @xmath20 is essentially the same as that contained in a family of flats in @xmath22 , for a gale dual configuration @xmath15 of @xmath0 . thus , one could say that the formula by dickenstein , feitchner , and sturmfels involves both @xmath0 and @xmath15 information . in theorem [ goodflags ] , we use theorem [ specialization ] to show that we can decide whether a configuration is dual defect purely in terms of certain _ non - splitting _ flags of flats in the matroid @xmath22 . in theorem [ th : decomposition ] we obtain a decomposition of the gale dual configuration of a toric variety and give , in terms of this decomposition , a sufficient condition for the variety to be dual defect . although we believe this condition to also be necessary , we are not able to prove it at this point . dual defect varieties have been extensively studied : @xcite . in particular , dickenstein and sturmfels have classified codimension - two dual defect varieties @xcite and , by completely different methods , @xcite has classified dual defect projective embeddings of smooth toric varieties in terms of their associated polytopes . we give a complete classification of of dual defect toric varieties of codimension less than or equal to four in terms of the gale duals . this implies , in particular , that in these cases the condition in theorem [ th : decomposition ] is necessary and sufficient . we conclude 5 by comparing di rocco s list , for codimension less than or equal to four , with our classification .

we study the-discriminant of toric varieties . we reduce its computation to the case of irreducible configurations and describe its behavior under specialization of some of the variables to zero . we give characterizations of dual defect toric varieties in terms of their gale dual and classify dual defect toric varieties of codimension less than or equal to four . sparse discriminant , dual defect varieties . + ams subject classification : primary 14m25 , secondary 13p05 .

we study the-discriminant of toric varieties . we reduce its computation to the case of irreducible configurations and describe its behavior under specialization of some of the variables to zero . we give characterizations of dual defect toric varieties in terms of their gale dual and classify dual defect toric varieties of codimension less than or equal to four . sparse discriminant , dual defect varieties . + ams subject classification : primary 14m25 , secondary 13p05 .

1311.4209

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the newtonian @xmath2-body problem studies the motion of @xmath2 point masses moving in the euclidean space , under the influence of their mutual gravitational attraction . the motion is determined by the system of differential equations : @xmath3 where @xmath4 and @xmath5 represent the position and the mass of the i - th mass respectively . one of the difficulties in studying the @xmath1body problem is due to the large number of variables . therefore , sub - problems of the @xmath1body problem that have lower degrees of freedom , which are usually obtained by adding constraints on the configurations , have received considerable attention . two very popular examples are the collinear three - body problem and the isosceles three - body problem . on one hand , a well - known periodic orbit in the collinear three - body problem is the so called schubart orbit , formed by two equal masses @xmath6 and another mass @xmath7 , bouncing in between and having binary collisions with @xmath8 , @xmath9 alternatively . this orbit was numerically found by schubart @xcite . moeckel @xcite and venturelli @xcite separately proved its existence by using topological shooting arguments and variational methods . on the other hand , in the isosceles three - body problem , broucke found a symmetric periodic orbit @xcite , called broucke orbit or a schubart - like " orbit , formed by two equal masses @xmath6 whose positions are symmetric with respect to a fixed axes , along with a third mass @xmath7 that is moving up and down on the axes . see table [ orbits_table](a ) for the broucke orbit . broucke orbit has been proved to exist by shibayama @xcite and martnez @xcite separately . schubart - like"(broucke ) orbit is similar to schubart orbit in the sense that in one period , they both have two singularities due to binary collisions , and that when a binary collision occurs , the third mass reaches its maximum distance to the origin . the motivation for this paper comes from the work of martnez @xcite and chen @xcite . martnez @xcite studies certain hamiltonian systems with two degrees of freedom and provides sufficient conditions for the existence of doubly symmetric schubart - like " periodic orbits ( dssp orbits ) in these systems . these sufficient conditions are applied to three examples , namely the @xmath1pyramidal problem , the @xmath10-planar problem , and the double - polygon problem . however , the double - polygon problem fails one of these sufficient conditions . recently , martnez @xcite extended her previous results . while the previously proved schubart - like orbits have only one singularity in a half period ( called 0-dssp orbits ) , the orbits in the new paper have a sufficiently large number of singularities in a half period ( called k - dssp orbits ) , yet the existence proof requires one hypothesis that is verified only for several values of @xmath2 . on the other hand , another six families of periodic orbits in the isosceles three - body problem are proved to be existed by using topological shooting arguments @xcite . these are the so called brake orbits ; that is , these orbits have zero initial velocity . in this paper , we apply the framework from @xcite to the following three problems : the @xmath1pyramidal problem , the planar double - polygon problem , and the spatial double - polygon problem . see table [ summary ] . first , the @xmath1pyramidal problem is a spatial problem which consists of @xmath2 masses whose configuration forms a planar regular @xmath1gon , along with an additional mass lying on the vertical axes crossing the center of the @xmath1gon . we remark that when @xmath11 , the @xmath1pyramidal problem is identical to the planar isosceles three - body problem . second , in the planar double - polygon problem , the configuration of the @xmath10 bodies forms two regular @xmath1gons in the plane . third , in the spatial double - polygon problem , the configuration of the @xmath10 bodies forms an anti - prism . we remark that the spatial double - polygon problem is a new example that has not appeared in @xcite , and it is a special case of the dihedral n - body problem . the dihedral n - body problem is proposed by ferrario and portaluri in @xcite , where they find all central configurations and compute the dimensions of the stable / unstable manifolds , while the existence of other periodic orbits , except for the relative equilibria , has not been studied . we prove the existence of several families of periodic orbits in the @xmath1pyramidal problem and the spatial double - polygon problem . representative orbits in the isosceles problem can be found in table [ orbits_table ] . to picture orbits of the same types in other problems , for the @xmath1pyramidal problem , one may imagine replacing the two symmetric bodies in the isosceles problem with @xmath2 bodies lying on the vertices of a regular @xmath1gon ; for the spatial double - polygon problem , one furthermore replaces the third body with another @xmath2 bodies lying on the vertices of another regular @xmath1gon . as for the planar double - polygon problem , unfortunately , as in @xcite , there are difficulties to apply our arguments . nonetheless , we complete martnez s existence proof for 0-dssp orbits , in which one of her three sufficient conditions fails , by showing that two of those conditions are enough to ensure the existence of 0-dssp orbits . existence of general k - dssp orbits for the planar double - polygon problem are not proved here and will require further work . we summarize our conclusions in table [ summary ] . compared to martnez s work @xcite , we have found new families of periodic orbits , and our proofs are significantly simplified ; we provide sufficient conditions that are looser and rigorously verified . moreover , while the orbits in @xcite must have either one or a sufficiently large number of singularities , we prove the existence of periodic orbits for any positive number of singularities in a half period . the paper is organized as follows . section 2 introduces two coordinate systems , both of which will be used in our proofs . section 3 provides sufficient conditions for the existence of periodic brake orbits and schubart - like orbit ; it turns out that our sufficient conditions will be boiled down to the behaviours of two orbits . section 4 proves theorems about the two orbits just mentioned . finally , in section 5 , we apply our theorems to the three problems .

we study three sub - problems of the-body problem that have two degrees of freedom , namely thepyramidal problem , the planar double - polygon problem , and the spatial double - polygon problem . we prove the existence of several families of symmetric periodic orbits , including schubart - like " orbits and brake orbits , by using topological shooting arguments . nai - chia chen ( communicated by the associate editor name )

we study three sub - problems of the-body problem that have two degrees of freedom , namely thepyramidal problem , the planar double - polygon problem , and the spatial double - polygon problem . we prove the existence of several families of symmetric periodic orbits , including schubart - like " orbits and brake orbits , by using topological shooting arguments . nai - chia chen ( communicated by the associate editor name )

1510.06686

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there are many lattice models of a single polymer in solution that take account of different physical scenarios and capture different aspects of such a system , for example by modelling the inclusion of hydrogen bonding or stiffness . the first ingredient in these models is the type of lattice path that is considered . the simplest example is the unrestricted random walk , which is a lattice path that may visit sites and bonds of the lattice multiple times . on the other hand the classical model of polymers is based on the _ self - avoiding walk _ , which is a lattice path that can not visit either bonds or sites of the lattice more than once . there are however several configuration systems used that lie between these two extremes . one commonly used for modelling polymers is the self - avoiding trail , which is a lattice path that is bond avoiding but may visit sites multiple times . importantly , this path may both touch at a site , or may cross . consider the subset , @xmath1 , of @xmath2-step trails @xmath3 on the square lattice with the added restriction that no crossings are allowed . this is an important type of configuration since they appear in the high temperature expansion of the @xmath4 model on the square lattice ( see @xcite for a recent example ) . let us call these configurations _ grooves_. the second ingredient in a lattice model of polymers in solution is the set of interactions that are associated with various combinatorial features of the configurations . given a groove @xmath5 , we associate the following set of boltzmann weights : a weight @xmath6 for _ site interaction _ , i.e. for a site that the groove visits more than once , such as occuring in the interacting self - avoiding trail model ( isat ) , a weight @xmath7 for every straight segment , which moderates stiffness in the polymer , and finally a weight @xmath8 for each _ nearest - neighbour interaction _ , i.e. for a pair of visited sites that are nearest - neighbours on the lattice but non sequential in the groove . this nearest - neighbour interaction occurs in the canonical interacting self - avoiding walk ( isaw ) model of polymer collapse . figure [ fig : configuration1 ] shows an example of a configuration belonging to @xmath9 and its associated weights . steps with one ( @xmath10 ) collision , five ( @xmath11 ) straight segments , and four ( @xmath12 ) nearest neighbours . there are @xmath13 singly visited sites and @xmath14 doubly visited sites . the total weight of this configuration is @xmath15 . ] there has been long term interest in special cases of this model over and above the canonical isaw model , which has a weak second order phase transition between a high temperature expanded phase and a low - temperature phase . one can distinguish these phases for example by the different scaling of the size of the polymer as given by its radius of gyration . the associated exponent takes the value @xmath16 in the high - temperature phase and @xmath17 in the low - temperature phase . in the low temperature phase the polymer is disordered and dense , but not maximally dense : it has been described as a liquid - like disordered drop . the phase transition known as the @xmath18-point is conjectured in two dimensions to have a cusp singularity in a convergent specific heat with the associate finite length exponent @xmath19 . the size exponent at the transition is @xmath20 . the isaw model is realised by letting @xmath21 and @xmath22 . on the other hand setting @xmath23 and @xmath22 gives the so - called vertex interacting self - avoiding walk " ( visaw ) , which is a misnomer since the configurations are actually grooves ( as described above ) and not self - avoiding walks . this model first arose as a specialisation of an integrable lattice model introduced by blte and nienhuis in 1989 @xcite related to the izergin - korepin vertex model . in fact , that model included more generally a stiffness parameter @xmath7 . the model was studied numerically @xcite for various values of @xmath7 including @xmath22 . it has also been studied as part of a generalisation of the interacting self - avoiding trail model ( asymmetric isat ) that distinguishes collisions from crossings , using transfer matrix calculations @xcite and monte carlo simulations @xcite . the monte carlo work @xcite concluded that the transition in the visaw @xmath24 would apparently seem to be a strong second order transition . the exponent describing the finite length singularity in the specific heat has been estimated @xcite as @xmath25 , which is in accord with the divergence seen in the isat model of @xmath26 @xcite , estimated from much longer configurations . the size exponent of visaw has not been measured using monte carlo , though the isat model has @xmath17 with a scaling form containing multiplicative logarithmic corrections : this clearly differs from the @xmath18-point isaw value of @xmath27 . in work on the asymmetric isat @xcite the low temperature phase of visaw ( with @xmath22 ) was considered ; it was found to have a similar structure to the low temperature phase in the isat model . this low temperature phase is not the same as the globular , liquid - like phase in the low temperature region of isaw : for visaw and isat the low temperature phase is maximally dense , i.e. every site of the path , apart from those on the outside of a dense ball , is associated with a doubly visited site of the lattice . in contrast , setting @xmath28 excludes the possibility of straight segments and by also setting @xmath29 the model is known as interacting self - avoiding trails on the l - lattice ( _ lsat _ ) . note that by setting @xmath30 the trails do not cross themselves and so are actually _ grooves_. the model can also be mapped onto isaw on the manhattan lattice @xcite . a kinetic growth algorithm that produces long l - lattice trails maps to configurations with boltzmann weights @xmath31 : an analysis of simulations of very long configurations @xcite has shown that the transition is @xmath18-like with a weak second order transition with an exponent conjectured to be the same as the @xmath18-point value of @xmath19 . the scaling of the size of the polymer given by the radius of gyration or similar is described by the exponent @xmath20 . interestingly , the low temperature phase of the lsat model has not been previously considered . of course it has been implicitly assumed that it would be like the isaw model , i.e. disordered and dense but not maximally dense . the parameter space of the semi - flexible visaw model ( @xmath29 ) also includes the special multi - critical point of the @xmath4 model found in @xcite , known as the blte - nienhuis point or bn - point . the location of this point is given by @xmath32 with @xmath33 , and @xmath34 . recently there have been various investigations of the bn - point itself @xcite . in the monte carlo work @xcite the size exponent was estimated as close to @xmath20 in agreement with earlier work @xcite . the specific heat exponent was not estimated and since the study looked at just that point the low temperature phase was not considered . very recently , a theoretical framework for the bn - point has been elucidated where it has been proposed that this point is related to a particularly unusual conformal field theory with continuous exponents @xcite . so while the semi - flexible visaw model has been studied previously by monte carlo at several values of @xmath7 , there are clearly some outstanding gaps in our knowledge . to gain a wider perspective , the generalised model we study here allows us to interpolate between the semiflexible visaw model and the canonical interacting self - avoiding walk ( isaw ) model directly . the set of @xmath2-step self - avoiding walks @xmath35 is a subset of grooves , @xmath36 . hence , if we set @xmath37 we suppress all multiple visits to sites and recover self - avoiding walks as configurations . we are now left with two boltzmann weights @xmath8 and @xmath7 which gives us the semi - flexible interacting self - avoiding walk model or semi - flexible isaw model . this model was studied on the square lattice in @xcite . to present a phase diagram that can be readily compared to the data we describe below , we present the schematic phase diagram for semi - flexible isaw . this has been obtained from our own data and is in accord with the phase diagram elucidated in @xcite previously . in figure [ fig : sfisawpd ] we see a density plot of a generalised specific heat and a schematic phase diagram as per @xcite . ) and a schematic phase diagram inferred from this that is in accord with previous work . darker shades indicate larger values of the fluctuations . later we shall see that appropriate order parameters / indicator variables reinforce these conclusions . there are three phases : extended , collapsed ( globular ) and @xmath0-sheet - like . solid lines represent the approximate location of a second - order phase transitions . the dashed line indicates first order behaviour.,scaledwidth=80.0% ] the data in figure [ fig : sfisawpd ] is a slice obtained from the dataset 3p by fixing @xmath37 ( see table [ appendix : table ] ) . there are three phases : two that occur in the canonical isaw model , that is the extended and globular phases , and a third which is an anisotropic collapsed phase that can be described as @xmath0-sheets . these two - dimensional @xmath0-sheets are actually parallel lines of polymer in the @xmath38 or @xmath39 directions . the extended and globular collapsed phases are separated by a line of weak second - order transitions . the @xmath18-point lies on this line and the conjecture is that the entire line belongs to the @xmath18-universality class . on the other hand the extended phase and @xmath0-sheet - like phase are separated by a line of first order transition points . according to @xcite , the @xmath0-sheet - like phase and the collapsed phase are separated by a line of second - order phase transitions associated with a positive @xmath40-exponent ( around @xmath41 ) and therefore a diverging specific - heat . as can be seen from this summary of the models that are contained within our model there are very different transitions and different collapsed low temperature phases . here we investigate our generalised model filling in the gaps in our knowledge and providing a coherent picture of how the transitions and where the different low temperature phases exist .

we study via monte carlo simulation a generalisation of the so - called vertex interacting self - avoiding walk ( visaw ) model on the square lattice . the configurations are actually not self - avoiding walks but rather restricted self - avoiding trails ( bond avoiding paths ) which may visit a site of the lattice twice provided the path does not cross itself : to distinguish this subset of trails we shall call these configurations _

we study via monte carlo simulation a generalisation of the so - called vertex interacting self - avoiding walk ( visaw ) model on the square lattice . the configurations are actually not self - avoiding walks but rather restricted self - avoiding trails ( bond avoiding paths ) which may visit a site of the lattice twice provided the path does not cross itself : to distinguish this subset of trails we shall call these configurations _ grooves_. three distinct interactions are added to the configurations : firstly the visaw interaction , which is associated with doubly visited sites , secondly a nearest neighbour interaction in the same fashion as the canonical interacting self - avoiding walk ( isaw ) and thirdly , a stiffness energy to enhance or decrease the probability of bends in the configuration . in addition to the normal high temperature phase we find three low temperature phases : ( i ) the usual amorphous liquid drop - like globular " phase , ( ii ) an anisotropic ``-sheet '' phase with dominant configurations consisting of aligned long straight segments , which has been found in semi - flexible nearest neighbour isaw models , and ( iii ) a maximally dense phase , where the all sites of the path are associated with doubly visited sites ( except those of the boundary of the configuration ) , previously observed in interacting self - avoiding trails . we construct a phase diagram using the fluctuations of the energy parameters and three order parameters . the-sheet and maximally dense phases do not seem to meet in the phase space and are always separated by either the extended or globular phases . we focus attention on the transition between the extended and maximally dense phases , as that is the transition in the original visaw model . we find that for the path lengths considered there is a range of parameters where the transition is first order and it is otherwise continuous .

1410.0338

c

in this paper we have reconstructed the null - test , that can be used to probe potential deviations from and was first presented in ref . @xcite , by using the @xmath0 , snia and 8 data . we performed the reconstruction in two different ways : by directly binning the data and by fitting the data to various dark energy models like the and @xmath16cdm and then calculating the null - test . we find that both methods have different advantages ; the former uses as few assumptions as possible while the latter directly tests the standard cosmological model . we have also generalized the null - test and extended it for modified gravity models and models with strong de perturbations , by taking into account the @xmath15 term in eq . ( [ ode ] ) . we have explicitly checked that when this term is taken into account , then the null - test is constant as expected for modified gravity models . this allows us to verify that deviations from unity in the original version of the null - test presented in ref . @xcite can indeed also be attributed to modifications of gravity . we have found that deviations from unity could be due to several reasons , either new physics including modifications of gravity and strong dark energy perturbations , or breakdowns of one of the basic assumptions of the standard cosmological model , i.e. deviation from the flrw metric and homogeneity or finally , a possible tension between @xmath0 ( obtained directly or derived ) and the @xmath53 data . in all cases due to the nature of the null - tests and that they have to be constant at all redshifts , it is enough to a have a statistically significant deviation at one redshift to detect one of the above reasons . a possible limitation at the moment is that the null - test can not tell us which of the above reasons would be responsible for that deviation though . however , our growth null - test will be extremely useful if joined with other null - tests , like the @xmath26 presented in @xcite which is able to test the assumptions of homogeneity and isotropy of the universe . we also examined how well the null - test can be reconstructed by future data by creating mock catalogs based on a lsst - like survey and on the model , a model with strong de perturbations , the @xmath1 and @xmath2 models , and the large void ltb model that exhibit different evolution of the matter perturbations . this was done so as to examine how well our null - test can be reconstructed using the data from upcoming surveys . our results were presented in figs . [ fig : binrealvsmock - null]-[fig : frrealsniavshz ] . we found that when reconstructed with real data the null - test is consistent with unity at the @xmath183 level , with both the binning and the model testing methods . however , when we reconstruct it with the mock data based on the specifications of a lsst - like survey and various models that go beyond the , ie the @xmath1 , @xmath2 models and the ltb , we find that the null - test can detect deviations from unity at the @xmath3 and also @xmath186 level . overall , the novelty of our null - test is that it can directly test the fundamental assumptions of the standard cosmological model with as few assumptions as possible . therefore , it will definitely prove to be an invaluable tool in the near future given the plethora of upcoming surveys that will produce high quality data . & & & & & + z & @xmath121 & @xmath56 s & @xmath121 & @xmath56 s & @xmath121 & @xmath56 s & @xmath121 & @xmath56 s & @xmath121 & @xmath56 s + @xmath102 & @xmath142 & @xmath143 & @xmath142 & @xmath143 & @xmath142 & @xmath143 & @xmath144 & @xmath143 & @xmath145 & @xmath143 + @xmath146 & @xmath147 & @xmath148 & @xmath149 & @xmath150 & @xmath151 & @xmath152 & @xmath153 & @xmath154 & @xmath155 & @xmath156 + @xmath157 & @xmath158 & @xmath159 & @xmath160 & @xmath161 & @xmath162 & @xmath163 & @xmath164 & @xmath165 & @xmath166 & @xmath167 + @xmath168 & @xmath169 & @xmath170 & @xmath171 & @xmath172 & @xmath173 & @xmath174 & @xmath175 & @xmath176 & @xmath177 & @xmath178 + @xmath213 & @xmath214 & @xmath215 & @xmath216 & @xmath217 & @xmath218 & @xmath219 & @xmath220 & @xmath221 & @xmath222 & @xmath223 + @xmath224 & @xmath225 & @xmath226 & @xmath227 & @xmath228 & @xmath229 & @xmath230 & @xmath231 & @xmath232 & @xmath233 & @xmath234 + @xmath235 & @xmath236 & @xmath237 & @xmath238 & @xmath239 & @xmath240 & @xmath241 & @xmath242 & @xmath243 & @xmath244 & @xmath245 + @xmath246 & @xmath247 & @xmath248 & @xmath249 & @xmath250 & @xmath251 & @xmath252 & @xmath253 & @xmath254 & @xmath255 & @xmath256 + @xmath257 & @xmath258 & @xmath259 & @xmath260 & @xmath261 & @xmath262 & @xmath263 & @xmath264 & @xmath265 & @xmath266 & @xmath267 + @xmath268 & @xmath269 & @xmath270 & @xmath271 & @xmath272 & @xmath273 & @xmath274 & @xmath275 & @xmath276 & @xmath277 & @xmath278 +

we perform the reconstruction in two different ways , either by directly binning the data or by fitting various dark energy models . we also examine how well the null - test can be reconstructed by future data by creating mock catalogs based on the cosmological constant model , a model with strong dark energy perturbations , the and models , and the large void ltb model that exhibit different evolution of the matter perturbations . we find that with future data similar to an lsst - like survey , the null - test will be able to successfully discriminate between these different cases at the level .

we systematically study the null - test for the growth rate data first presented in and we reconstruct it using various combinations of data sets , such as the 8 and or type ia supernovae ( snia ) data . we perform the reconstruction in two different ways , either by directly binning the data or by fitting various dark energy models . we also examine how well the null - test can be reconstructed by future data by creating mock catalogs based on the cosmological constant model , a model with strong dark energy perturbations , the and models , and the large void ltb model that exhibit different evolution of the matter perturbations . we find that with future data similar to an lsst - like survey , the null - test will be able to successfully discriminate between these different cases at the level .

astro-ph0504172

r

in section [ section : results : cross ] , we quantify the amplitude of the dla - galaxy cross - correlation relative to the galaxy - galaxy autocorrelation in the sph simulations . we show how to invert the cross - correlation results into a mass constraint in section [ section : converttomass ] . we show that this method is independent of the galaxy sample that one uses ( [ section : samplevariation ] ) . finally , we compare these results to observational results in section [ section : compareobservations ] . the filled circles in figure [ fig : all : all ] show the dla - galaxy cross - correlation @xmath100 using the entire sample of 115,000 dlas and the 651 resolved galaxies . we computed @xmath2 with the estimator @xmath107 where @xmath108 is the observed number of galaxies between @xmath109 and @xmath110 from a dla and @xmath111 is the expected number of galaxies if they were uniformly distributed , i.e. , @xmath112 where @xmath113 is the galaxy surface density . @xmath114 denotes the average over the number of selected dlas ( @xmath115 ) . in counting the pairs , we took into account the periodic boundary conditions of the simulations . there are several reasons not to use other estimators such as the ( * ? ? ? * ls ) estimator . first , we want to duplicate as closely as possible the method ( and estimator ) used in the observations of @xcite and bl04 . but , more importantly , the ls estimator is symmetric under the exchange of the galaxies with the absorbers , whereas here and for the observations of bl04 , the symmetry is broken . this is due to the absorber redshift being well known , while galaxies have photometric redshifts with larger uncertainties and , therefore , are distributed along the line of sight . this broken symmetry is also fundamental in the derivation of equations [ eq : auto : result][eq : cross : result ] . had we used spectroscopic redshifts and @xmath93 instead of @xmath90 , the ls estimator would be superior . given that we use the galaxy surface density @xmath113 to estimate the unconditional galaxy density ( see eq . [ eq : cross ] ) , the integral of @xmath116 over the survey area @xmath117 will be equal to the total number of galaxies , i.e. , @xmath118 . as a consequence , @xmath119 , and the correlation will be negative on the largest scales , i.e. , biased low . this is the known `` integral constraint '' . in the case of our @xmath120 mpc@xmath59 survey geometry , we estimated the integral constraint to be @xmath121 , or 2% of the cross - correlation strength at 1 . we added @xmath122 to @xmath100 estimated from equation [ eq : estimator ] . the uncertainty to @xmath100 , @xmath123 , has two terms , the poisson noise and the clustering variance ( see * ? ? ? * and references therein ; appendix [ appendix : errors ] ) . in appendix [ appendix : errors ] , we show that @xmath123 is proportional to @xmath124 ( eq . [ cluster : eq : crossxi : variance ] ) . there are several ways to compute @xmath123 in practice . the proper way to compute @xmath123 would be to resample the dlas , since this would include the uncertainty due to the finite the number of lines of sight . however , this is valid for independent lines of sight , as in the case of an observational sample ( provided that @xmath115 is large , say greater than @xmath125 ) , and will not be correct here given that we have only one simulation and that we have to use the same galaxies for each simulated line of sight . the uncertainty @xmath123 must then reflect that we used only one realization of the large - scale structure . for this reason , we elected to use the jackknife estimator @xcite , i.e. , by dividing the @xmath126 mpc@xmath59 area into nine equal parts and each time leaving one part out . this will accurately reflect the uncertainty in @xmath127 due to the one large - scale structure used , but the signal - to - nois ratio ( s / n@xmath128 ) will not increase with @xmath129 as expected ( appendix b ) : it will saturate after a certain value of @xmath115 . we find that indeed the snr saturates at @xmath130 ( not shown ) . this is a major difference from observational samples , where each field is independent . in that case , equation [ cluster : eq : crossxi : variance ] applies and the s / n is proportional to @xmath129 . we computed the full covariance matrix from the @xmath131 realizations as @xmath132\cdot [ w_k(r_{\theta_j})-\overline w(r_{\theta_j})]\ ; , \label{eq : covariance}\ ] ] where @xmath133 is the @xmath134th measurement of the cross - correlation and @xmath135 is the average of the @xmath136 measurements of the cross - correlation . the error bars in figure [ fig : all : all ] show the diagonal elements of the covariance matrix , i.e. , @xmath137 . we computed the projected autocorrelation @xmath3 of the same simulated galaxies used for @xmath2 in a similar manner . we used the estimator shown in equation [ eq : estimator ] to compute @xmath3 , where @xmath138 is now the number of galaxies between @xmath139 and @xmath140 from another galaxy . the open triangles in figure [ fig : all : all ] show the projected autocorrelation @xmath3 of the 651 galaxies . we fitted the galaxy autocorrelation with a power law model ( @xmath141 ) by minimizing @xmath142^t \mathrm{cov}^{-1}[\mathbf{w}-\mathbf{\hat w}]$ ] , where @xmath143 and @xmath144 are the vector data and model , respectively , and @xmath145 is the inverse of the covariance matrix . we used single value decomposition ( svd ) techniques to invert the covariance matrix , @xmath146 , since it is singular and the inversion is unstable ( see discussion in * ? ? ? * ) . we then use that fit as a template to constrain the amplitude of @xmath100 , i.e. , @xmath147 where @xmath148 is the amplitude ratio @xmath149 of the correlation functions . this assumes that the two correlation functions have the same slope ( see [ section : clustering ] ) . this method also closely matches the method used by bl04 ( see [ section : compareobservations ] below ) and makes comparison to those observations straightforward . the solid line in figure [ fig : all : all ] shows the fit to @xmath100 using equation [ eq : compareamplitude ] , where the best amplitude @xmath148 is @xmath150 the top panel shows the @xmath151 distribution with the @xmath152 range . in other words , the bias ratio @xmath87 is @xmath153 . this can be converted into a correlation length for @xmath100 of @xmath154 times that of the galaxy autocorrelation , i.e. , @xmath155 . several authors ( e.g. , * ? ? ? * ; * ? ? ? * and references therein ) have shown that the small scales ( @xmath156 mpc ) of the correlation function are the scales sensitive to variations in the halo occupation number . at those scales , @xmath93 is very susceptible to galaxy pairs that are in the same halo . therefore , when we repeated our analysis with the six subsamples , we restricted ourselves to @xmath157 . in this case , for the full sample , we find the amplitude ratio to be @xmath158 , in good agreement with equation [ eq : result : besta ] . the reader should not use these results ( e.g. , eq . [ eq : result : besta ] ) , obtained with 651 galaxies and 115,000 dlas , to scale the errors to smaller samples , because we use the same large - scale structure for all the 115,000 simulated dlas . as mentioned earlier , the large - scale structure dominates the uncertainty at large @xmath115 , and this is seen in the fact that the s / n saturates after @xmath130 . we come back to this point at the end of [ section : compareobservations ] . equation [ eq : result : besta ] , i.e. , the bias ratio @xmath87 , can be converted into a mean halo mass for dlas if one knows the functional form of @xmath83 and @xmath79 . one can use the ps formalism ( e.g. , * ? ? ? * ) or the autocorrelation of several galaxy subsamples to constrain the shape of @xmath83 . we refer to these as the `` theoretical method '' and as the `` empirical method , '' respectively . one can compute the theoretical biases for any population ( eq . [ eq : bias : integral ] ) and predict the bias ratio a priori if the mass probability distribution @xmath82 is known . naturally , @xmath82 is known in our simulation ( fig . [ fig : distribution ] ) . we show that the predicted bias ratio is well within the @xmath152 range of our results ( eq . [ eq : result : besta ] ) , demonstrating the reliability of the method . given that galaxies and the dlas actually lie in halos of different masses , the theoretical biases are found from equation [ eq : bias : integral ] , i.e. , @xmath159 where @xmath82 is the appropriate mass distribution [ @xmath160 normalized such that @xmath161 and @xmath83 is the bias of halos of a given mass @xmath89 . the bias function @xmath83 is also a function of redshift @xmath162 , i.e. , @xmath163 , and can be computed at a given @xmath162 from the extended ps formalism ( e.g. , * ? ? ? it is shown in figgure [ fig : bias : theory ] for @xmath4 on a linear - linear ( _ left _ ) and log - linear ( _ right _ ) plot . the mass distributions @xmath164 and @xmath165 are shown in figgure [ fig : distribution ] . because @xmath82 is bounded at some low - mass limit @xmath166 ( due to limited resolution or to observational selection ) , the mean bias @xmath0 of a given galaxy sample is defined by @xmath167 . the predicted biases @xmath0 are shown in the left panel of figure [ fig : bias : compare ] . the predicted biases @xmath0 for the subsamples , the 651 galaxies , and the dlas are represented by open squares , the filled square and the filled circle , respectively . from @xmath0 for the 651 galaxies ( _ filled square _ ) and for dlas ( _ filled circle _ ) , the theoretical bias ratio @xmath168 is found to be , very close to the bias ratio measured from the clustering of galaxies around the dlas ( eq . [ eq : result : besta ] ) . when the distributions @xmath82 are not known , we can infer a mass ratio from the bias ratio using the approximation @xmath169 , instead , and replace @xmath57 by @xmath170 in the remaining of the discussion . ] over a restricted mass range . in each panel in figure [ fig : bias : theory ] , the dashed line shows such a linear fit over the mass range @xmath171@xmath172 . using this approximation , the mean bias @xmath0 is given by @xmath173 where @xmath57 is the first moment of the distribution @xmath82 . thus , the mean bias for the galaxies and the dlas are @xmath174 , and @xmath175 , respectively , where @xmath114 denote the first moment of the appropriate mass distribution . in figure [ fig : bias : compare ] ( _ left _ ) the solid line is a linear fit to the theoretical biases @xmath176 , and is 5% away ( in amplitude ) from the linear approximation ( eq . [ eq : bias : approx ] ) shown by the thick dashed line . the vertical dashed line indicates the mean dla halo mass @xmath177 that is found from the first moment of the mass distribution in figure [ fig : distribution ] . this shows that using a linear approximation of @xmath83 is equivalent to using the bias function @xmath83 from @xcite , provided that the dla - galaxy mass ratio is not larger than a decade . indeed , the 5% difference in amplitude cancels out when taking the bias ratio . to infer @xmath177 from equation [ eq : result : besta ] or from observations , one needs to find the coefficients @xmath178 and @xmath179 . to do so , one can either use the ps formalism @xcite or use the fact that @xmath0 is proportional to @xmath180 ( eq . [ eq : biascdm ] ) , where @xmath181 is measured for each of the galaxy subsamples covering the mass range @xmath182@xmath172 . figure [ fig : bias : compare ] ( _ right _ ) illustrates this point . the thick dashed line is again the linear approximation shown in figure [ fig : bias : theory ] . the open ( filled ) triangles show the mean biases @xmath0 of the subsamples ( full sample ) assuming that @xmath183 ( eq . [ eq : biascdm ] ) . the normalization is set to match the dashed line , and is not relevant , since we measure a ratio of two biases . this shows that one can use either the ps formalism @xcite or use @xmath180 to find the coefficients @xmath178 and @xmath179 . in the case where the autocorrelation length @xmath184 has been determined , one can use the right @xmath185axis scale of figure [ fig : bias : compare ] the infer the dla halo mass from the measured bias ratio . to actually determine @xmath177 from our cross - correlation result ( eq . [ eq : result : besta ] ) , we used ( 1 ) the linear approximation to the ps bias ( fig . [ fig : bias : compare ] , _ thick dashed line _ ) , and ( 2 ) @xmath186 for the 651 galaxies . we infer a mean dla halo mass of @xmath187 , shown by the vertical shaded area on the right panel of figure [ fig : bias : compare ] . our cross - correlation result ( eq . [ eq : result : besta ] ) is shown by the horizontal shaded area . the `` true '' dla mass derived from @xmath164 ( fig . [ fig : distribution ] ) and equation [ eq : bias : dla ] is shown by the vertical dashed line at @xmath188 . similarly , using fits to @xmath83 in linear space ( fig . [ fig : bias : theory ] , _ left _ ) , we infer @xmath189 , close to `` true '' mean @xmath190 . in summary , the amplitude of @xmath100 relative to @xmath94 , @xmath191 ( eq . [ eq : result : besta ] ) , measured in this simulation implies that dlas have halos of ( logarithmically ) averaged mass @xmath192 close to the true . this shows that the cross - correlation technique uniquely constrain the mean of the halo mass distribution , despite the fact that dlas occupy a range of halo masses and some halos contain multiple galaxies and multiple dla systems . in [ section : samplevariation ] , we show that the technique is reliable in the sense that it will lead to the same answer regardless of the galaxy sample used . from the right panel of figure [ fig : bias : compare ] , we can now predict the cross - correlation strength for real @xmath4 lbgs , which have a correlation length of @xmath193 mpc ( e.g. , assp03 ; * ? ? ? * ) , corresponding to a halo mass of @xmath194 . from the figure , one expects that the correlation ratio or the bias ratio is @xmath195 , and thus the dla - lbg cross - correlation would have a correlation length @xmath196 mpc . potential systematic errors include the few massive halos ( @xmath197 ) that are missed due to the limited volume ( @xmath198 mpc@xmath199 ) of our simulation . however , since dlas are cross section selected these few massive halos are too scarce to change the mean @xmath177 of the dla mass probability distribution ( fig . [ fig : distribution ] , _ right _ ) . naturally , if there were such massive halos in our simulations , the amplitude of the cross - correlation would be different . we address this point in a general way in [ section : samplevariation ] and show that the derived @xmath177 is independent of the galaxy sample used . our treatment of feedback is limited to energy injection of supernovae , and thus does not treat phenomena like winds . @xcite included winds in similar simulations and showed that the dla abundance decreases with increasing wind strength , but the mean dla halo mass will be shifted towards higher mass in the presence of winds . @xcite also showed that the dla abundance ( extrapolated to @xmath200 , i.e. , below the resolution limit , using the ps formalism ) also decreases with increasing resolution , but again , the mean dla halo mass will be shifted toward higher mass in higher resolution runs . given that ( 1 ) a fraction of dlas are expected to arise in halos below our mass resolution of @xmath5 and ( 2 ) our total dla abundance extrapolated to @xmath200 , as in @xcite , over - predicts the observed dla abundance , equation [ eq : result : massdla ] is an upper limit . furthermore , given the results of @xcite showed that both winds and better resolution increase the mean dla halo mass , we conclude that a simulation with sne winds and with a better mass resolution would lower our mean dla mass . reading from figure 5 in @xcite , we estimate that @xmath177 is @xmath201 in their high - resolution run with strong winds , or a factor of @xmath202 smaller than here . thus , equation [ eq : result : massdla ] is an upper limit . from equations [ eq : biascdm ] and [ eq : biascross ] , we expect the relative amplitude @xmath148 to vary as a function of the halo mass of the galaxy sample @xmath203 . we therefore performed the same cross - correlation calculations for each of the six subsamples presented in [ section : simulation ] ( see also fig . [ cluster : fig : sim : mass ] ) , and ask the question , is the inferred @xmath204 the same in each case ? we restricted ourselves to scales @xmath205 ( from the discussion in [ section : results : cross ] ) . figure [ fig : compareb ] shows the measured amplitude or bias ratio @xmath148 for each of the subsamples . the amplitude ratio @xmath148 for the subsamples ( full sample ) is represented by the open squares ( filled circle ) with solid error bars . the filled circle with dotted error bars represents the full sample shown in figure [ fig : all : all ] from which we inferred @xmath191 and @xmath206 . as expected , @xmath148 increases with larger subsamples , or with decreasing galaxy halo mass @xmath203 . for the method to be self - consistent , the derived dla halo mass @xmath177 should be the same for all the subsamples . given equation [ eq : bias : approx ] , @xmath207 determined in [ section : converttomass ] , and a mean galaxy halo mass @xmath208 , we can predict the bias ratio @xmath148 . the solid line in figure [ fig : compareb ] represents this prediction . one sees that the measured bias ratio for the subsamples ( _ open squares _ ) follow the expected bias ratio ( _ solid line _ ) . for comparison , the dashed lines show the expected amplitude ratios @xmath148 if dlas were in halos of mean mass @xmath209 , 11.5 , and 12 ( from bottom to top ) instead of the inferred @xmath207 . we conclude that the method is reliable and self - consistent , i.e. , the mass @xmath177 is independent of the galaxy sample used , that the clustering statistics of dlas with galaxies can be used to infer their mass , and that large observational samples will shed new light on their nature . a direct observational measure of the relative amplitude @xmath148 ( j. cooke 2005 , private communication ) , will show whether or not dlas are massive disks ( @xmath18 ) as proposed by @xcite and @xcite . in this section , we first briefly review past and recent observations of clustering between galaxies and dlas ( [ section : currentobservations ] ) . we then ( [ section : smallsample ] ) focus on comparing the simulated dla - lbg cross - correlation to the observational results of bl04 , in a meaningful way , i.e. , with a sample of similar size . early attempts to detect diffuse emission from dlas at @xmath210 using deep narrow band imaging @xcite did not reveal the absorber but unveiled a few companion emitters @xcite , hinting at the clustering of galaxies around dlas . this prompted @xcite to calculate the two - point correlation function at @xmath211 and to conclude that , indeed , emitters are clustered near dlas at the @xmath212% or greater confidence level . some recent searches have succeeded in unveiling the absorber ( e.g. , * ? ? ? @xcite reported the discovery of super - clustering of sub - dlas at @xmath213 and @xmath214 : a total of four clouds are seen in a qso pair separated by 8 , each being at the same velocity . recent results from narrow - band imaging of the francis & hewett field show that spectroscopically confirmed emitters are clustered at the redshift of the strongest cloud at @xmath215 ( @xmath216 ) towards q2138 - 4427 @xcite . @xcite identified eight emitting galaxies near the dla at @xmath217 towards phl 957 in addition to the previously discovered coup fourr galaxy @xcite , implying the presence of a group , filament , or proto - cluster associated with the dla . other evidence of clustering includes the work of @xcite , who found that the dla at @xmath218 towards q0201 + 1120 is part of a concentration of matter that includes at least four galaxies ( including the dla ) over transverse scales greater than @xmath219 mpc , and of @xcite who showed that out of 10 dlas in qso pairs , five are matching systems within 1000 . they concluded that this result indicates a highly significant over - density of strong absorption systems over separation lengths from @xmath220 to @xmath221 mpc . @xcite studied the cross - correlation of lbgs around one @xmath222 dla . probably due to the high redshift of their dla , @xcite found that @xmath2 is consistent with 0 , i.e. , they found that the distribution of the eight galaxies in that field ( with spectroscopic redshifts ) is indistinguishable from a random distribution . their data did not allow them to put limits on the amplitude of @xmath100 . recently , assp03 found a lack of galaxies near four dlas and concluded that the dla - lbg cross - correlation is significantly weaker than the lbg - lbg autocorrelation at the 90% confidence level . they found two lbgs within @xmath223 and within @xmath224 ( @xmath225 ) whereas @xmath226 were expected if the cross - correlation has the same amplitude as the galaxy autocorrelation . because of the field of view available , both @xcite and assp03 were not sensitive to scales larger than @xmath227 mpc , which is important since the relevant scales to measure the dla - lbg cross - correlation extend up to @xmath228 mpc . however , the results of assp03 can be used to put an upper limit on @xmath6 through the following steps : first , note that the two galaxies ( in @xmath229 fields ) observed by assp03 give @xmath230 and the six galaxies expected if @xmath231 give @xmath232 , where @xmath233 is the volume average of the correlation function . second , for the lbg autocorrelation published in assp03 , we find @xmath234 , averaged over a sphere centered on the dlas with an effective radius of @xmath226 , i.e. , with the same volume as the cylindrical cell used by assp03 . thus , the expected number of galaxies per dla field is @xmath235 if @xmath236 , and the total number of galaxies is @xmath237 . clearly their measurement of two galaxies is consistent with no cross - correlation . from equation [ eq : adelberger ] , we can infer that @xmath238 using @xmath235 . third , the uncertainty to @xmath239 , @xmath240 , can be estimated using the results shown in appendix [ appendix : errors ] . the variance @xmath241 is made of two terms , the shot noise variance @xmath242 and the clustering variance @xmath243 . the shot noise variance to @xmath244 is @xmath245 ( eq . [ cluster : eq : crossvariance : sn ] ) . the two - point clustering variance ( eq . [ cluster : eq : crossvariance:2pt : peebles ] ) is simply @xmath246 where @xmath247 . the three - point clustering variance ( eq . [ cluster : eq : crossvariance:3pt : peebles ] ) is @xmath248 since @xmath249 . finally , from equation [ cluster : eq : crossxi : variance ] , @xmath250 , and a 1-@xmath251 ( 2-@xmath251 ) upper limit to @xmath239 is @xmath252 . since @xmath253 , the 1-@xmath251 ( 2-@xmath251 ) upper limit to the amplitude ratio is @xmath254 , respectively . this rough calculation is quite consistent with adelberger s results where it was found that @xmath255 at the 90% confidence level using monte carlo simulations . given that the relevant scales to measure the dla - lbg cross - correlation extend up to @xmath256 , @xcite were able to first detect and measure a dla - lbg cross - correlation signal ( bl04 ) using the wide - field ( @xmath257 deg@xmath59 or @xmath258 mpc@xmath59 comoving at redshift @xmath4 ) imager mosaic on the kitt peak 4 m telescope . @xcite showed that there was an over - density of lbgs by a factor of @xmath259 ( with 95% confidence ) around the @xmath260 dla towards the quasar apm 08279 + 5255 ( @xmath261 ) on scales @xmath262 . extending the results of @xcite to three @xmath263 dla fields , bl04 probed the dla - lbg cross - correlation on scales @xmath264@xmath265 and found ( 1 ) a dla - lbg cross - correlation with a relative amplitude @xmath266 that is greater than zero at the @xmath267% confidence level , and ( 2 ) that @xmath100 is most significant on scales 510 . in other words , dlas are clustered with lbgs , but unfortunately the sample size did not allow bl04 to test whether @xmath148 is greater or smaller than 1 . soon , the ongoing survey of 9 @xmath268 dlas of @xcite will triple the sample of bl04 . in a slightly different context , @xcite applied successfully the technique presented here to 212 @xmath269 systems ( of which 50% are expected to be dlas ) using luminous red galaxies ( lrgs ) in the sloan digital sky survey data release 1 . they found that the lrg cross - correlation has an amplitude times that of the lrg lrg autocorrelation , over comoving scales up to @xmath270 . since lrgs have halo - masses greater than for @xmath271 , this relative amplitude implies that the host galaxies have halo masses greater than @xmath272@xmath273 . these results show how powerful the cross - correlation technique is . to summarize the current observational situation on the @xmath4 dla - lbg cross - correlation , assp03 finds that the amplitude ratio is @xmath274 , and bl04 finds that @xmath275 , both at the 1-@xmath251 level . using monte carlo simulations , assp03 finds @xmath276 , at the 90% confidence level , and bl04 finds @xmath277 , at the 95% confidence level . the dla halo mass range allowed by these observations is still large : it covers @xmath278@xmath279 . . their mass estimates come from the emission - absorption redshift difference as a proxy for a rotation curve . ] there are many significant differences between the observational sample of bl04 and the present simulated one . first , the shape of the volume is very different : the survey volume of bl04 is @xmath280 mpc@xmath199 ( comoving ) , while these simulations are @xmath281 mpc ( comoving ) on a side . given that the survey of bl04 contains about 80120 lbgs per field , their observed lbg number density corresponds to about seven galaxies per @xmath198 mpc@xmath199 . naturally , seven galaxies are not a fair sample of the lbg luminosity function . this is an inherent problem due to the size of the simulation , rendering the comparison between the observed and the simulated cross - correlation difficult . second , as mentioned in [ section : simulation ] , the simulated lbgs are selected according to their sfr , while the observed lbgs are color selected . third , the same galaxies are used for every simulated line of sight . these differences limit our ability to perform a direct comparison to observations . with these caveats in mind , we can repeat our analysis of section [ section : converttomass ] in the limit of small @xmath115 and with similar galaxy number densities . because , to first order , @xmath282 ( eq . [ cluster : eq : crossxi : variance ] ) , a sample made of 10 dlas and 25 galaxies per @xmath283 mpc@xmath284 `` field '' is expected to have similar errors to the sample of bl04 made of three dlas and 100 galaxies per @xmath285 mpc@xmath284 field . as for the full sample , we restricted ourselves to scales @xmath286 , which also corresponds to the most relevant scales 510 @xmath37 mpc of the observations of bl04 . we find that the relative amplitude of the cross - correlation with 10 lines of sight and 25 galaxies is @xmath287 , whereas bl04 found @xmath288 , i.e. , both with the same s / n . this confirms the results of bl04 . more importantly , one can now use the result for this sample made of 10 dlas and 25 galaxies ( with a surface density @xmath289 mpc@xmath290 ) as a benchmark to predict the s / n for the larger samples of future observations , given that the s / n will be proportional to @xmath291 ( eq . [ cluster : eq : crossxi : variance ] ) .

, we focus on dlas . we demonstrate that the cross - correlation method robustly constrains the mean dla halo mass using smoothed particle hydrodynamics ( sph ) cosmological simulations that resolve dlas and galaxies in halos of mass . direct measurement of these correlation functions from the simulations yields , in excellent agreement with that prediction . the cross - correlation method thus appear to yield a robust estimate of the average host halo mass even though the dlas and the galaxies occupy a broad mass spectrum of halos , and massive halos contain multiple galaxies with dlas . the inferred mean dla halo mass , , is an upper limit since the simulations do not resolve halos less massive than .

we test the reliability of a method to measure the mean halo mass of absorption line systems such as damped absorbers ( dlas ) . the method is based on measuring the ratio of the cross - correlation between dlas and galaxies to the autocorrelation of the galaxies themselves , which is ( in linear theory ) the ratio of their bias factor . we show that the ratio of the projected cross- and autocorrelation functions ( ) is also the ratio of their bias factor irrespective of the galaxy distribution , provided that one uses the same galaxies for and . thus , the method requires only multi - band imaging of dla fields , and is applicable to all redshifts . here , we focus on dlas . we demonstrate that the cross - correlation method robustly constrains the mean dla halo mass using smoothed particle hydrodynamics ( sph ) cosmological simulations that resolve dlas and galaxies in halos of mass . if we use the bias formalism of mo & white ( 2002 ) with the dla and galaxy mass distributions of these simulations , we predict an amplitude ratio of . direct measurement of these correlation functions from the simulations yields , in excellent agreement with that prediction . equivalently , inverting the measured correlation ratio to infer the ( logarithmically ) averaged dla halo mass yields , in excellent agreement with the true value in the simulations : is the probability weighted mean mass of the dla host halos in the simulations . the cross - correlation method thus appear to yield a robust estimate of the average host halo mass even though the dlas and the galaxies occupy a broad mass spectrum of halos , and massive halos contain multiple galaxies with dlas . if we consider subsets of the simulated galaxies with high star formation rates ( representing lyman break galaxies [ lbgs ] ) , then both correlations are higher , but their ratio still implies the same dla host mass , irrespective of the galaxy subsamples , i.e. , the cross - correlation technique is also reliable . the inferred mean dla halo mass , , is an upper limit since the simulations do not resolve halos less massive than . thus , our results imply that the correlation length between dlas and lbgs is predicted to be , at most , given that lbgs have a correlation length of . while the small size of current observational samples does not allow strong conclusions , future measurements of this cross - correlation can definitively distinguish models in which many dlas reside in low mass halos from those in which dlas are massive disks occupying only high mass halos .

astro-ph0504172

c

motivated by the fact that ( 1 ) the amplitude of the cross - correlation is a measurement of the mean dla halo mass and ( 2 ) observational constraints ( @xcite @xcite ; assp03 ; bl04 ; j. cooke et al . 2005 , private communication ) are reaching a turning point and the dla halo masses are starting to be constrained , we tested the cross - correlation technique using treesph cosmological simulations . the method uses the ratio of the cross - correlation between dlas and high - redshift galaxies to the autocorrelation of the galaxies themselves , which is ( in linear theory ) the ratio of their bias factor , to infer the mean dla halo mass . in a treesph simulation @xcite parallelized by @xcite with @xmath50 particles in a volume 22.222@xmath199 @xmath292 mpc@xmath199 ( comoving ) , we find the following : 1 . scales @xmath29315 are the most relevant scales to constrain the mean dla halo mass using the projected cross - correlation @xmath2 . the dla - galaxy cross - correlation has an amplitude @xmath294 close to the predicted value of using the @xcite formalism . the inferred mean dla halo mass is @xmath295 in excellent agreement with the true values of the simulations , i.e. , @xmath296 . thus , even though dlas and galaxies occupy a broad range of halos with massive halos containing multiple galaxies with dlas , the cross - correlation technique yields the first moment of the dla halo mass distribution . if we consider subsets of the simulated galaxies with higher star - formation rates ( representing lbgs ) , the cross - correlation technique is self - consistent , i.e. , the dla mass inferred from the ratio of the correlation functions does not depend on the galaxy sample used . this demonstrates the reliability of the method . 5 . for real @xmath4 lbgs with a correlation length @xmath297 ( assp03 ; * ? ? ? * ) , our results imply that the dla - lbg cross - correlation is expected to have a correlation length @xmath298 mpc . 6 . with small samples ( with 10 lines of sight and 25 galaxies ) matching the statistics of bl04 , the relative amplitude of the cross - correlation is @xmath287 , i.e. , with a signal - to - noise ratio ( s / n@xmath299@xmath300 ) comparable to bl04 , where they found @xmath288 . in short , the cross - correlation between galaxies and dlas is a powerful and self - consistent technique to constrain the mean mass of dlas , and we have demonstrated its reliability . given the resolution limits of the simulation used here ( @xmath5 ) , our values are strictly upper limits . these simulation results suggest that dlas are expected to be less massive than @xmath4 lbgs by a factor of at least @xmath301 . recently , @xcite studied the morphology of @xmath302-selected galaxies at redshifts up to @xmath303 and found that the late type fraction drops beyond @xmath210 . @xcite show that the kinematics of 13 @xmath210 morphologically elongated galaxies are not consistent with those of an inclined disk . furthermore , the virial mass of these galaxies is in the range of a few times @xmath304 up to @xmath305 . these results and the ones presented here disfavor the presence of large , massive @xmath18 disks at @xmath210 and therefore the massive disk hypothesis for dlas . while current observational samples are just starting to put constraints on @xmath6 for @xmath4 dlas bl04 found @xmath306 at the 95% confidence level , and assp03 found @xmath307 at the 90% confidence level , allowing the mass range @xmath308@xmath279 future observations will be able to distinguish between models in which dlas reside in low mass halos from those in which dlas are massive disks occupying only high mass halos thanks to planned wide - field imagers .

the method is based on measuring the ratio of the cross - correlation between dlas and galaxies to the autocorrelation of the galaxies themselves , which is ( in linear theory ) the ratio of their bias factor . equivalently , inverting the measured correlation ratio to infer the ( logarithmically ) averaged dla halo mass yields , in excellent agreement with the true value in the simulations : is the probability weighted mean mass of the dla host halos in the simulations . if we consider subsets of the simulated galaxies with high star formation rates ( representing lyman break galaxies [ lbgs ] ) , then both correlations are higher , but their ratio still implies the same dla host mass , irrespective of the galaxy subsamples , i.e. , the cross - correlation technique is also reliable . thus , our results imply that the correlation length between dlas and lbgs is predicted to be , at most , given that lbgs have a correlation length of . while the small size of current observational samples does not allow strong conclusions , future measurements of this cross - correlation can definitively distinguish models in which many dlas reside in low mass halos from those in which dlas are massive disks occupying only high mass halos .

we test the reliability of a method to measure the mean halo mass of absorption line systems such as damped absorbers ( dlas ) . the method is based on measuring the ratio of the cross - correlation between dlas and galaxies to the autocorrelation of the galaxies themselves , which is ( in linear theory ) the ratio of their bias factor . we show that the ratio of the projected cross- and autocorrelation functions ( ) is also the ratio of their bias factor irrespective of the galaxy distribution , provided that one uses the same galaxies for and . thus , the method requires only multi - band imaging of dla fields , and is applicable to all redshifts . here , we focus on dlas . we demonstrate that the cross - correlation method robustly constrains the mean dla halo mass using smoothed particle hydrodynamics ( sph ) cosmological simulations that resolve dlas and galaxies in halos of mass . if we use the bias formalism of mo & white ( 2002 ) with the dla and galaxy mass distributions of these simulations , we predict an amplitude ratio of . direct measurement of these correlation functions from the simulations yields , in excellent agreement with that prediction . equivalently , inverting the measured correlation ratio to infer the ( logarithmically ) averaged dla halo mass yields , in excellent agreement with the true value in the simulations : is the probability weighted mean mass of the dla host halos in the simulations . the cross - correlation method thus appear to yield a robust estimate of the average host halo mass even though the dlas and the galaxies occupy a broad mass spectrum of halos , and massive halos contain multiple galaxies with dlas . if we consider subsets of the simulated galaxies with high star formation rates ( representing lyman break galaxies [ lbgs ] ) , then both correlations are higher , but their ratio still implies the same dla host mass , irrespective of the galaxy subsamples , i.e. , the cross - correlation technique is also reliable . the inferred mean dla halo mass , , is an upper limit since the simulations do not resolve halos less massive than . thus , our results imply that the correlation length between dlas and lbgs is predicted to be , at most , given that lbgs have a correlation length of . while the small size of current observational samples does not allow strong conclusions , future measurements of this cross - correlation can definitively distinguish models in which many dlas reside in low mass halos from those in which dlas are massive disks occupying only high mass halos .

1510.04697

c

in this work , we have theoretically proposed a scheme to realize non - trivial topological models in classical systems of coupled pendula or coupled lumped - element rlc circuits through a periodic time - modulation of system parameters . within a floquet framework , we have shown that suitably - designed temporal modulations of the natural oscillation frequencies effectively produce the complex coupling amplitudes of the hh model , where the synthetic magnetic flux is easily tunable . we have assessed the accuracy of the floquet picture by numerically solving the full equations of motion and we have shown that hallmarks of the hh model , such as the topologically - robust chiral edge states and the hofstadter butterfly pattern , can be observed in the excitations of the system . furthermore , we have illustrated a protocol to extract the topological chern number of the bands in a classical counterpart of the integer quantum hall effect . finally , we extended our investigation to the regime where the analogy with the quantum lattice model breaks down , investigating the crucial role played by the counter - rotating - wave terms in the stability of the system and the persistence of topological effects . the exploration of topological effect in classical - mechanical systems is opening up many interesting new avenues of research . the use of floquet modulation schemes to engineer topological models brings with it particular advantages . firstly , time - modulation can naturally be used to break time - reversal symmetry and so to create edge states that are fully topologically protected . secondly , the scheme discussed here is only one of many possible floquet modulation schemes that could be applied to arrays of classical oscillators ; other schemes may open up the way to build classical simulators of topological models with other interesting properties and with even more exotic topological invariants @xcite . looking to the future , our proposal can be naturally extended to include a confining external potential , leading to novel oscillation features associated with analogue momentum - space magnetism @xcite . beyond the small oscillation regime considered so far , systems of pendula also show nonlinear effects such as amplitude - dependent oscillation frequencies . the interplay of such nonlinearities with topological features may lead to a variety of new and unexpected effects .

we theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators , such as classical pendula or lumped - element electric circuits , whose oscillation frequency is modulated fast in time . making use of floquet theory in the high frequency limit , we identify a regime in which the system is accurately described by a harper - hofstadter model where the synthetic magnetic field can be externally tuned via the phase of the frequency - modulation of the different oscillators . finally we discuss the regime where the analogy with the harper - hofstadter model breaks down .

we theoretically propose how to observe topological effects in a generic classical system of coupled harmonic oscillators , such as classical pendula or lumped - element electric circuits , whose oscillation frequency is modulated fast in time . making use of floquet theory in the high frequency limit , we identify a regime in which the system is accurately described by a harper - hofstadter model where the synthetic magnetic field can be externally tuned via the phase of the frequency - modulation of the different oscillators . we illustrate how the topologically - protected chiral edge states , as well as the hofstadter butterfly of bulk bands , can be observed in the driven - dissipative steady state under a monochromatic drive . in analogy with the integer quantum hall effect , we show how the topological chern numbers of the bands can be extracted from the mean transverse shift of the steady - state oscillation amplitude distribution . finally we discuss the regime where the analogy with the harper - hofstadter model breaks down .

1109.0900

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we have analyzed a large set of _ hst _ and ground - based images of the galactic globular cluster ngc 104 ( 47 tuc ) in nine photometric bands , finding multiple sequences throughout the various cmds , from the main sequence all the way to the horizontal branch . exploiting this wealth of _ hst _ data to investigate the behavior of the multiple populations as seen in several different combinations of magnitudes and colors , we found that among the rainbow of possible cmds , those involving the f275w and f336w filters are particularly effective in separating components of otherwise entangled cluster populations . taking a cue from _ hst _ , we were able to construct a color system based on the @xmath56 band that exhibited a similarly effective separation of the populations in ground - based data . we found that the distribution of stars along the ms , sgb , rgb , and hb was in every case bimodal in the @xmath87 vs. @xmath48 two - color diagram , and we finally put together the groups of stars that we had separated in this way , so as to draw a continuous connection between their successive evolutionary phases . near the cluster center all evolutionary phases split into two near - parallel sequences , with the richer one making up about 80% of the cluster stars , and the poorer one the remaining 20% . wide - field ground - based photometry allowed us to identify and separate the two sub - populations at larger radial distances from the cluster center , with the result that the majority population is more centrally concentrated , but its relative fraction decreases outward and approaches 50/50 in the outskirts of the cluster . globally , the majority population accounts for @xmath83 of the whole population of 47 tuc , most of the remainder consisting of the minority population . radial gradients in the stellar populations of this cluster have been known for a long time , with a cn - strong population more centrally concentrated than the cn - weak one . this suggests that the numerically dominant population is cn - strong . along these same lines , we used cn band strengths and na and o abundances that are available from the literature for some rgb and hb stars of both populations , to investigate their chemical content . it appears that the more populous rgbb and hbb sequences consist of cn - strong / na - rich / o - poor stars , while the bulk of the cn - weak / na - poor / o - rich stars belong to the numerically poorer rgba and hba . on the theoretical side , we calculated synthetic spectra of main - sequence stars with different chemical compositions , derived the corresponding colors for our filter set , and compared them with the observed colors in the two distinct populations . the colors of the minority population are well reproduced by stars with primordial helium abundance and an oxygen - rich / nitrogen - poor composition that is typical of halo stars of metallicity similar to that of 47 tuc . on the other hand , the colors of the majority population stars are well reproduced by a composition in which nitrogen is greatly enhanced , along with a slightly increased helium , while carbon and oxygen are depleted . synthetic spectra for rgb and hb stars confirm this result . the most straightforward interpretation of these differences is that the minority population is the remnant of the first stellar generation , which formed out of the interstellar medium of its time , and shared its chemical composition . the chemical composition of the majority population , by contrast , carries the signatures of cno and proton - capture processing at high temperatures , such as depletion of oxygen in favor of nitrogen and sodium , accompanied by helium enhancement . therefore the majority population should be regarded as the second stellar generation of 47 tuc , which formed out of material that had been partly processed through stars of the first generation . since both populations share the same iron abundance , one can exclude from the enrichment history of the second - generation material any significant contribution by massive stars , exploding as core - collapse supernovae . this leaves intermediate - mass stars of the first generation as the obvious candidates for having processed the material that is now incorporated into the second generation , a view that is indeed widely entertained in the literature . furthermore , it is certainly striking that the second generation is today more populous than the first . this sets strong constraints on the nature of the progenitor of the present cluster 47 tuc , and on the initial mass of the first generation , which must have been one to two orders of magnitude more massive than the portion that is still bound to the cluster . finally , we must again remind the reader that besides the two populations that we have called first and second , we have found unmistakable evidence for the presence of a third population , including some @xmath2 of the stars , which we can distinguish it only on the sgb , but it appears to have the abundance distribution of the `` b '' population . this remains as a strident reminder that the stellar populations in 47 tuc are more complex than the two - generation picture that we have just sketched . , s.l . , and a.p . acknowledge partial support by prin miur 20075tp5k9 and prin inaf " formation and early evolution of massive star clusters . , s.c . , and a.r . acknowledge partial support by asi under the program asi - inaf i/016/07/0 . j. a. and i. r. k. acknowledge support from stsci grant go-12311 .

we calculate theoretical stellar atmospheres for main sequence stars , assuming different chemical composition mixtures , and we compare their predicted colors through the _ hst _ filters with our observed colors . we present evidence that the color - magnitude diagram of 47 tuc consists of intertwined sequences of the two populations , whose separate identities can be followed continuously from the main sequence up to the red giant branch , and thence to the horizontal branch . a third population is visible only in the subgiant branch , where it includes of the stars .

we use _ hubble space telescope ( hst ) _ and ground - based imaging to study the multiple populations of 47 tuc , combining high - precision photometry with calculations of synthetic spectra . using filters covering a wide range of wavelengths , our _ hst _ photometry splits the main sequence into two branches , and we find that this duality is repeated in the subgiant and red - giant regions , and on the horizontal branch . we calculate theoretical stellar atmospheres for main sequence stars , assuming different chemical composition mixtures , and we compare their predicted colors through the _ hst _ filters with our observed colors . we find that we can match the complex of observed colors with a pair of populations , one with primeval abundance and another with enhanced nitrogen and a small helium enhancement , but with depleted c and o. we confirm that models of red giant and red horizontal branch stars with that pair of compositions also give colors that fit our observations . we suggest that the different strengths of molecular bands of oh , cn , ch and nh , falling in different photometric bands , are responsible for the color splits of the two populations . near the cluster center , in each portion of the color - magnitude diagram the population with primeval abundances makes up only of the stars , a fraction that increases outwards , approachng equality in the outskirts of the cluster , with a fraction averaged over the whole cluster . thus the second , he / n - enriched population is more concentrated and contributes the majority of the present - day stellar content of the cluster . we present evidence that the color - magnitude diagram of 47 tuc consists of intertwined sequences of the two populations , whose separate identities can be followed continuously from the main sequence up to the red giant branch , and thence to the horizontal branch . a third population is visible only in the subgiant branch , where it includes of the stars .

cond-mat0409039

i

we have presented both improved and parallel algorithms for the enumeration of self - avoiding polygons and walks on the triangular lattice . these algorithms have enabled us to obtain polygons up to perimeter length 60 , their radius of gyration and area - weighted moments up to perimeter 58 , while for self - avoiding walks to length 40 we calculated the number of walks as well as the metric properties of mean - square end - to - end distance , mean - square radius of gyration and the mean - square distance of a monomer from the end points . the analysis of the polygon series enabled us to obtain a very precise estimate for the connective constant @xmath0 . we confirmed to a very high degree of accuracy the predicted exponent values @xmath128 , @xmath147 and @xmath129 . we noticed that , as is the case for the square lattice problem , the saw asymptotics is worse behaved than the sap asymptotics , i.e. , estimates for @xmath19 and the critical exponents are at least an order of magnitude more accurate in the sap case . it quite is possible that this behaviour is due to the leading correction - to - scaling exponent @xmath253 . in the sap case this correction simply becomes part of the analytic background term and the sap generating function is therefore simpler since it only has analytic corrections to scaling . we also obtained very accurate estimates for the leading amplitude of the sequence @xmath9 of sap coefficients @xmath163 and using the exact expression for the amplitude combination @xmath171 we find @xmath172 . our data for the area - weighted moments was used @xcite to confirm the correctness of theoretical predictions for the values of the amplitude combinations @xmath41 . finally we obtained accurate estimates for the critical amplitudes @xmath243 , @xmath247 , @xmath248 , and @xmath249 . the estimate for the ratio @xmath254 is in very good agreement with the theoretical estimate @xmath34 @xcite . the amplitude estimates led to a high precision confirmation of the cscps relation ( [ eq : cscps ] ) @xmath255 .

walks to length 40 we also calculate series for the metric properties of mean - square end - to - end distance , mean - square radius of gyration and the mean - square distance of a monomer from the end points . for self - avoiding polygons to length 58 we calculate series for the mean - square radius of gyration and the first 10 moments of the area .

we use new algorithms , based on the finite lattice method of series expansion , to extend the enumeration of self - avoiding walks and polygons on the triangular lattice to length 40 and 60 , respectively . for self - avoiding walks to length 40 we also calculate series for the metric properties of mean - square end - to - end distance , mean - square radius of gyration and the mean - square distance of a monomer from the end points . for self - avoiding polygons to length 58 we calculate series for the mean - square radius of gyration and the first 10 moments of the area . analysis of the series yields accurate estimates for the connective constant of triangular self - avoiding walks , , and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations .

astro-ph0512047

i

variability is observed in the x - ray pwn of psr b1509@xmath058 on time scales possibly as short as one week and up to twelve years . our primary results are as follows : 1 . the compact , small - scale knots appearing within 20@xmath1 of the pulsar exhibit transient behavior which may be attributed to turbulence in the flows surrounding the pulsar . possible knot motion is indicated with a velocity of @xmath121 . apparent outflow along the jet is observed with velocities of @xmath3 . this outflow alone can not account for the @xmath430% brightening of the jet between 1991/1992 and 2000 . the alfvn crossing time for the jet is 1.3@xmath02 years , therefore , mhd kink or sausage instabilities can account for the rapid morphological variations and perhaps the partial jet brightening . the outer arc has possibly moved inward with a velocity of @xmath80 , however the transverse structural changes seen in the outer arc may account for the apparent motion . we can not determine at this time if the outer arc is truly quasi - stationary or if we are witnessing aliasing . the diffuse pwn has not evolved significantly in structure or brightness over the 12-year time span . using the summed _ images , we identify two possible arc structures exterior to the outer arc . the photon indices of the diffuse pwn and possibly the jet steepen with increasing radius indicating synchrotron cooling at x - ray energies . although our imaging capabilities have improved substantially since the first optical observations of time variability in the crab nebula @xcite , our understanding of these variations in pwne is still quite limited . for instance , while we expect magnetic fields to play an important dynamical role in jets , and indeed we do see variations on the appropriate alfvn crossing times , we do not know for certain if mhd instabilities are the root cause of the observed variations . the arc structures we observe in [email protected] are equally enigmatic . we do not yet know if they are in steady motion or are quasi - stationary wave phenomena . the striking changes in the small - scale knots near the pulsar may simply be `` weather , '' diagnosing unimportant details in the pwn flow , or they may indicate important flow structure which is essential to understanding , for instance , diffusion of particles from the equatorial flow to higher latitudes , a loss essential to a post pair shock second - order fermi acceleration model . certainly deeper , and appropriately spaced , x - ray observations will help resolve some issues such as the possible spatial aliasing of the outer arc . also , the higher signal - to - noise will provide better constraints on the spatial spectral index variations and allow us to determine if and how much mixing has occurred in the diffuse pwn . finally , we are excited by the recent development of relativistic mhd models and we hope that some of the variability we observe here can eventually be observed in those simulations . we thank fred seward for assistance with _ rosat _ data analysis , elena amato , niccol bucciantini , and serguei komissarov for helpful discussions , and the anonymous referee for a careful reading of the manuscript . this research has made use of data obtained from the high energy astrophysics science archive research center ( heasarc ) , provided by nasa s goddard space flight center . t. d. & b. m. g. acknowledge the support of nasa through sao grant go3 - 4063a . j.a . acknowledges support from nasa chandra theory grant tm4 - 5005x , nasa atp grant nag5 - 12031 , and from the taxpayers of california . aharonian , f. et al . 2005 , , 435 , l17 bauciska - church , m. , & mccammon , d. 1992 , , 400 , 699 begelman , m. c. 1998 , , 493 , 291 begelman , m. c. 1999 , , 512 , 755 bietenholz , m. f. , hester , j. j. , frail , d. a. , & bartel , n. 2004 , , 615 , 794 bogovalov , s. v. , chechetkin , v. m. , koldoba , a. v. , & ustyugova , g. g. 2005 , , 358 , 705 bogovalov , s. v. & khangoulian , d. v. 2002 , , 336 , l53 brazier , k. & becker , w. 1997 , , 284 , 335 cusumano , g. , mineo , t. , massaro , e. , nicastro , l. , trussoni , e. , massaglia , s. , hermsen , w. , & kuiper , l. 2001 , , 375 , 397 davis , j. e. 2001 , , 562 , 575 del zanna , l. , amato , e. , & bucciantini , n. 2004 , , 421 , 1063 gaensler , b. m. , arons , j. , kaspi , v. m. , pivovaroff , m. j. , kawai , n. , & tamura , k. 2002 , , 569 , 878 ( g02 ) gaensler , b. m. , brazier , k. t. s. , manchester , r. n. , johnston , s. , & green , a. j. 1999 , , 305 , 724 gallant , y. a. & arons , j. 1994 , , 435 , 230 gonzalez , m. & safi - harb , s. 2003 , , 583 , l91 greiveldinger , c. , caucino , s. , massaglia , s. , gelman , h. , & trussoni , e. 1995 , , 454 , 855 helfand , d. j. , gotthelf , e. v. , & halpern , j. p. 2001 , , 556 , 380 hester , j. j. et al . 2002 , , 577 , l49 hester , j. j. et al . 1995 , , 448 , 240 jerius , d. , donnelly , r. h. , tibbetts , m. s. , edgar , r. j. , gaetz , t. j. , schwartz , d. a. , van speybroeck , l. p. , zhao , p. 2000 , proc spie , 4012 , 17 kaspi , v. , manchester , r. , siegman , b. , johnston , s. , & lyne , a. 1994 , , 422 , l83 kardashev , n. s. 1962 , soviet astron . , 6 , 317 kennel , c. f. & coroniti , f. v. 1984 , , 283 , 694 komissarov , s. s. & lyubarsky , y. e. 2003 , , 344 , l93 komissarov , s. s. & lyubarsky , y. e. 2004 , , 349 , 779 livingstone , m. a. , kaspi , v. m. , gavriil , f. p. , & manchester , r. n. 2005 , , 619 , 1046 lou , y. 1998 , , 294 , 443 lu , f. j. , wang , q. d. , aschenbach , b. , durouchoux , p. , & song , l. m. 2002 , , 568 , l49 lyubarsky , y. e. 2002 , , 329 , l34 melatos , a. , scheltus , d. , whiting , m. t. , eikenberry , s. s. , romani , r. w. , rigaut , f. , spitkovsky , a. , arons , j. , & payne , d. j. b. 2005 , , in press ( astro - ph/0509914 ) mori , k. , burrows , d. n. , hester , j. j. , pavlov , g. g. , shibata , s. , & tsunemi , h. 2004 , , 609 , 186 mori , k. , burrows , d. n. , pavlov , g. g. , hester , j. j. , shibata , shinpei , & tsunemi , h. 2004 , young neutron stars and their environments , iau symposiom vol . 218 muzzio , j. c. 1979 , , 84 , 639 ouyed , r. & pudritz , r. 1997 , , 484 , 794 ouyed , r. , pudritz , r. , & stone , m. 1997 , nature , 385 , 409 pacholczyk , a. g. 1970 , radio astrophysics ( san francisco : freeman ) pacini , f. & salvati , m. 1973 , apj , 186 , 249 pavlov , g. g. , kargaltsev , o. y. , sanwal , d. , & garmire , g. p. 2001 , , 554 , l189 pavlov , g. g. , teter , m. a. , kargaltsev , o. , & sanwal , d. 2003 , , 591 , 1157 pfeffermann , e. , et al . 1987 , proc spie , 733 , 519 reynolds , s. p. 2003 , in proc . iau colloquium 192 , supernovae : 10 years of sn 1993j , ed . j. m. marcaide & k. w. weiler ( berlin : springer ) , posters supplement , 161 roberts , m. s. et al . 2003 , , 588 , 992 rodgers , a. w. , campbell , c. t. , & whiteoak , j. b. 1960 , , 121 , 103 safi - harb , s. , harrus , i. m. , petre , r. , pavlov , g. g. , koptsevich , a. b. , & sanwal , d. 2001 , , 561 , 308 scargle , j. d. 1969 , , 156 , 401 seward , f. d. , harnden jr . , f. r. , murdin , p. , & clark , d. h. 1983 , , 267 , 698 slane , p. , helfand , d. j. , van der swaluw , e. , & murray , s. s. 2004 , , 616 , 403 spitkovsky , a. & arons , j. 2000 , in iau colloq . 177 , pulsar astronomy : 2000 and beyond , eds . m. kramer , n. wex , & r. wielebinski ( san francisco : asp ) , 507 spitkovsky , a. & arons , j. 2004 , , 603 , 669 ( sa04 ) tanvir , n. r. , thomson , r. c. , & tsikarishvili , e. g. 1997 , newa , 1 , 311 trmper , j. 1982 , adv . space res . , 2 , 241 trussoni , e. , massaglia , s. , caucino , s. , brinkman , w. , & aschenbach , b. 1996 , , 306 , 581 weisskopf m. c. et al . 2000 , , 536 , l81 yatsu , y. , kataoka , j. , kawai , n. , kotani , t. , tamura , k. , & brinkmann , w. 2005 , astro - ph/0507049

we use new and archival _ chandra _ and _ rosat _ data to study the time variability of the x - ray emission from the pulsar wind nebula ( pwn ) powered by psr b1509 on timescales of one week to twelve years the transient nature of these knots may indicate that they are produced by turbulence in the flows surrounding the pulsar . however , outflow alone can not account for the changes in the jet on such short timescales . the photon indices of the diffuse pwn and possibly the jet steepen with increasing radius , likely indicating synchrotron cooling at x - ray energies .

we use new and archival _ chandra _ and _ rosat _ data to study the time variability of the x - ray emission from the pulsar wind nebula ( pwn ) powered by psr b1509 on timescales of one week to twelve years . there is variability in the size , number , and brightness of compact knots appearing within 20 of the pulsar , with at least one knot showing a possible outflow velocity of ( assuming a distance to the source of 5.2 kpc ) . the transient nature of these knots may indicate that they are produced by turbulence in the flows surrounding the pulsar . a previously identified prominent jet extending 12 pc to the southeast of the pulsar increased in brightness by 30% over 9 years ; apparent outflow of material along this jet is observed with a velocity of . however , outflow alone can not account for the changes in the jet on such short timescales . magnetohydrodynamic sausage or kink instabilities are feasible explanations for the jet variability with timescale of 1.3 years . an arc structure , located 30 north of the pulsar , shows transverse structural variations and appears to have moved inward with a velocity of over three years . the overall structure and brightness of the diffuse pwn exterior to this arc and excluding the jet has remained the same over the twelve year span . the photon indices of the diffuse pwn and possibly the jet steepen with increasing radius , likely indicating synchrotron cooling at x - ray energies .

0806.0246

i

great advances in nanotechnology over the past few years led to the fabrication and intense experimental study of low - dimensional electron systems ( quantum dots and wires ) . from a long - term perspective , such systems are of interest as they give insight into the physics of more complicated nanodevices needed for quantum information processing @xcite . the smallness of quantum dots leads to fairly large energy level spacings and at sufficiently low temperatures only a few levels are relevant for the description of the physics . the latter is then strongly affected by the repulsive interaction between the electrons , manifesting e.g. in coulomb blockade behavior @xcite or kondo screening @xcite . the physics of quantum wires is described by the luttinger rather than the fermi liquid theory , in clear contrast to most bulk materials where the effects of coulomb correlations do not extend beyond mild renormalization of fermi liquid parameters . @xcite . from the theoretical point of view , a many - particle method is needed to properly account for the electron - electron interaction @xmath0 , which is a vital ingredient to any model one might devise to describe the experimental setups . a perturbative approach works in some cases , but it fails to describe strong correlations ( such as kondo physics @xcite ) . moreover , it breaks down completely for certain classes of low - dimensional systems because of infrared divergences in low - order feynman diagrams @xcite . the latter motivates the application of renormalization group ( rg ) based methods which successively address all energy scales of the system , starting from high energies where infrared singularities are cut out . one particular implementation of wilson s general rg idea @xcite is the numerical renormalization group ( nrg ) , which was originally developed to address the kondo model @xcite but later on applied to various kinds of quantum impurity systems @xcite . it provides a very reliable tool to investigate physical properties of models with coulomb interaction at low energies . however , its applicability is practically limited to small systems with a few correlated degrees of freedom because of the computational resources required . a different rg based approach to solve the quantum many - particle problem is the functional renormalization group ( frg ) which exactly describes all vertex functions of the corresponding system in terms of an infinite hierarchy of coupled flow equations @xcite . in practice , this hierarchy needs to be truncated ( usually by neglecting the flow of the three - particle vertex ) , rendering frg an approximate method . moreover , in the context of quantum dots and wires the frequency dependence of the flowing two - particle vertex was discarded , alltogether resulting in a closed finite set of coupled differential equations whose numerical solution gives renormalized frequency - independent system parameters embodying the effects of the two - particle interaction @xcite . this approximation scheme was successfully applied to describe luttinger liquid behavior of one - dimensional quantum wires with local inhomogeneities @xcite , whereas ordinary perturbation theory in the two - particle interaction @xmath0 is plagued by infrared singularities . in contrast , perturbation theory is usually regular for quantum dot models ( such as the single impurity anderson model ) and there is no inherent need for an rg based framework . however , the appearance of the exponentially ( in @xmath0 ) small kondo energy scale @xmath1 motivates rg resummations of certain classes of diagrams . the application of the frequency - independent functional renormalization group to single- as well as multi - level spinful and spin - polarized quantum dot geometries turned out to give surprisingly good results in the strong coupling limit , even though the approximation can a priori be justified only for small to intermediate @xmath0 @xcite . the most striking observation is that the frg describes aspects of kondo physics ( e.g. , an exponential energy scale ) contained within the single impurity anderson model ( siam ) very accurately @xcite . the frequency - independent approximation can thus be viewed as a kind of rg - enhanced hartree - fock theory which does not suffer from typical mean - field artifacts ( such as the breaking of spin symmetry ) . by construction , a truncation procedure which disregards all frequency dependencies can not be expected to give reliable results for finite - energy properties . indeed , the siam linear - response conductance at zero temperature @xmath2 ( which is a zero - energy quantity ) is described well by this level of approximation @xcite , whereas the conductance at @xmath3 ( which is a finite - energy property ) is not . in addition , finite energy effects become important if one is interested in extending the method to the non - equilibrium situation . it is thus very reasonable to devise a truncation procedure which includes the frequency - dependence of the two - particle vertex in order to describe finite - energy properties . a first step in this direction was done in ref . @xcite where results for the siam were presented , illustrating that such a generalization is in principle possible @xcite . however , there was no systematic study of all system parameters ( in particular finite temperatures and finite magnetic fields ) and the question whether strong - coupling physics is captured ( as it is partially by the frequency - independent approximation ) was not answered conclusively . finally , technical details about how the flow equations are actually implemented numerically were not elaborated on . it is the first goal of this paper to systematically study the siam using a frequency - dependent frg scheme , benchmarking this approximation against data we obtain from the numerical rg framework . the second objective is to present technical details of this generalization in order to address the issue of numerical artifacts originating from the discretization of the matsubara frequency axis . even though little is to be learned about the physics , we think that systematically discussing the details of this very natural and obvious generalization of a frequency - independent frg truncation scheme in its application to the siam is of importance , particularly if one aims at treating more complex ( multi - level or multi - impurity ) quantum dot systems . in short , the strong - coupling behavior extracted from the frg approximation turns out to be worse than one might have expected , particularly if one has in mind the success of the frequency - independent approach . however , at small to intermediate @xmath4 ( @xmath5 being the impurity - lead hybridization ) the agreement with nrg reference data improves if the more elaborate finite - frequency frg scheme is employed . the same holds if the two - particle vertex is parametrized not by three independent energy variables but ( numerically far less demanding ) by three functions each depending on a single argument . since the computational effort in solving the flow equations grows only as a power law ( and not exponentially ) with the number of impurities and channels and since there is no numerical need to stick to special ( symmetric ) system parameters , the frequency - dependent frg approximation presented in this paper can be regarded as a fast and reliable tool to describe the small- to intermediate - coupling physics of correlated quantum dot models which can not be treated using the nrg . the paper is organized as follows . in sec . [ sec : model ] , the single impurity anderson model is introduced briefly . next ( sec . [ sec : method.frg ] ) , we recapitulate the general idea of the matsubara functional renormalization group . the flow equations for the siam are derived explicitly in sec . [ sec : method.siam ] and [ sec : appu ] . we present a cutoff procedure which allows for treating both the zero - temperature limit as well as finite @xmath3 ( sec . [ sec : method.cutoff ] ) . numerical issues which come along with the need for discretizing frequency space are commented on in sec . [ sec : method.numerics ] . finally , we introduce three functions each of a single energy variable to parametrize the two - particle vertex in order to speed up numerics ( sec . [ sec : method.appr ] ) . in sec . [ sec : results.sf ] , spectral functions obtained from the various frg schemes are benchmarked against nrg reference calculations . we discuss the average impurity occupation and the zero - temperature spectral weight at the chemical potential in sec . [ sec : results.bn ] and try to extract the kondo temperature from the frg formalism by considering effective masses and static spin susceptibilities ( sec . [ sec : results.tk ] ) . an outlook is given in sec . [ sec : conclusion ] .

we use the matsubara functional renormalization group ( frg ) to describe electronic correlations within the single impurity anderson model . in contrast to standard frg calculations , we account for the frequency - dependence of the two - particle vertex in order to address finite - energy properties ( e.g , spectral functions ) . by comparing with data obtained from the numerical renormalization group ( nrg ) framework , in contrast , at small to intermediate the results obtained by the more elaborate scheme agree better with nrg data . we suggest to parametrize the two - particle vertex not by three independent energy variables but by introducing three functions each of a single frequency .

we use the matsubara functional renormalization group ( frg ) to describe electronic correlations within the single impurity anderson model . in contrast to standard frg calculations , we account for the frequency - dependence of the two - particle vertex in order to address finite - energy properties ( e.g , spectral functions ) . by comparing with data obtained from the numerical renormalization group ( nrg ) framework , the frg approximation is shown to work well for arbitrary parameters ( particularly finite temperatures ) provided that the electron - electron interaction is not too large . we demonstrate that aspects of ( large ) kondo physics which are described well by a simpler frequency - independent truncation scheme are no longer captured by the ` higher - order ' frequency - dependent approximation . in contrast , at small to intermediate the results obtained by the more elaborate scheme agree better with nrg data . we suggest to parametrize the two - particle vertex not by three independent energy variables but by introducing three functions each of a single frequency . this considerably reduces the numerical effort to integrate the frg flow equations .

0806.0246

c

in this paper , we have introduced a truncation scheme for the infinite hierarchy of frg flow equations which accounts for the frequency dependence of the two - particle vertex . the flow equations for the single impurity anderson model were derived explicitly . using a variety of parametrization procedures , we carefully addressed the issue of numerical artifacts originating from the discretization of the matsubara axis . we showed that at intermediate coulomb interaction @xmath4 one can obtain data which is independent of any numerical parameters . in contrast , different ways to parametrize the three frequency arguments of the two - particle vertex do not give coinciding results in the strong - coupling regime , even though it is reasonable to assume that this is merely a question of numerical resources . in addition , there are strong ( conceptional and practical ) arguments favoring the use of a certain set of bosonic frequencies . we thus employed this parametrization to carry out calculations at large @xmath0 , carefully ensuring that the results are independent of any remaining numerical parameters ( particularly the number of frequencies @xmath79 ) . in general , it turned out that at small to intermediate @xmath4 the frg approximation works well ( benchmarking our results against numerical rg reference data ) , and properties such as spectral functions , which are certainly of both experimental and theoretical interest , can be computed accurately for arbitrary parameters ( particularly finite temperatures ) . using a simplified set of flow equations , such reliable calculations are possible within minutes of cpu time . in contrast , it proved impossible to tackle the strong - coupling limit , and zero - energy aspects of kondo physics which are captured by a simple frequency - independent frg scheme ( e.g. , the static spin susceptibility @xmath175 being governed by an exponential energy scale @xcite ) are no longer described by the ` higher - order ' frequency - dependent approximation . however , it is imperative to keep in mind that it was neither possible to clarify why one particular ( unmodified ) frg scheme breaks down in the strong - coupling limit nor practically manageable to obtain data independent of all numerical parameters ( namely the parametrization of the two - particle vertex ) . on the other hand , at small to intermediate @xmath0 the agreement with nrg or bethe ansatz data is improved quantitatively by employing the more elaborate finite - frequency scheme . these observations are consistent with the fact that the latter contains all terms up to order @xmath42 ( but gives results superior to second - order perturbation theory ) , whereas the frequency - independent approximation is only correct to first order in @xmath0 . however , the frequency - independent approach does not suffer from typical mean - field artifacts ( e.g. , breaking of spin symmetry ) and gives results which are in significantly better agreement ( compared to hartree - fock ) with reference calculations ( concerning the low - energy physics of quantum dots @xcite ) . it can thus be pragmatically viewed as a reliable tool to derive effective noninteracting parameters which accurately describe zero - energy aspects ( e.g. , the @xmath2 linear - response conductance ) of correlation phenomena ( rg enhanced hartree - fock theory ) . concerning prospects for future work , it would be interesting to apply the frequency - dependent frg scheme presented in this paper to such multi - impurity systems which can not be accessed easily using the nrg framework ( the numerical effort growing only as a power law but not exponentially with the number of impurities and the number of channels ) . in the context of quantum wires , a renormalization group - based approach to any microscopic model is inherently necessary because of infrared divergences in perturbation theory . generalizing the method to the non - equilibrium situation is certainly an issue of interest . there is ongoing work in all these directions ( see refs . @xcite ) . from a conceptional point of view , it would be favorable to set up an frg scheme in real frequency space which does not suffer from the need for an ill - controlled ( particularly at finite temperatures ) analytic continuation . there is ongoing research in this direction as well , and first results were published @xcite .

the frg approximation is shown to work well for arbitrary parameters ( particularly finite temperatures ) provided that the electron - electron interaction is not too large . we demonstrate that aspects of ( large ) kondo physics which are described well by a simpler frequency - independent truncation scheme are no longer captured by the ` higher - order ' frequency - dependent approximation . this considerably reduces the numerical effort to integrate the frg flow equations .

we use the matsubara functional renormalization group ( frg ) to describe electronic correlations within the single impurity anderson model . in contrast to standard frg calculations , we account for the frequency - dependence of the two - particle vertex in order to address finite - energy properties ( e.g , spectral functions ) . by comparing with data obtained from the numerical renormalization group ( nrg ) framework , the frg approximation is shown to work well for arbitrary parameters ( particularly finite temperatures ) provided that the electron - electron interaction is not too large . we demonstrate that aspects of ( large ) kondo physics which are described well by a simpler frequency - independent truncation scheme are no longer captured by the ` higher - order ' frequency - dependent approximation . in contrast , at small to intermediate the results obtained by the more elaborate scheme agree better with nrg data . we suggest to parametrize the two - particle vertex not by three independent energy variables but by introducing three functions each of a single frequency . this considerably reduces the numerical effort to integrate the frg flow equations .

0812.1396

i

the tunnel leveling theorem of h. goda , m. scharlemann , and a. thompson @xcite says that when a tunnel number one knot is in minimal bridge position , any of its tunnel arcs can be slid to lie in a single horizontal level . using the theory of tunnel number @xmath0 knots developed in @xcite , we will prove the _ tunnel leveling addendum . _ roughly speaking , it says that when a tunnel arc is in level position as in the conclusion of the tunnel leveling theorem , the other two knots from the @xmath5-curve which is the union of the knot and its tunnel arc are also ( after trivial repositioning ) in minimal bridge position . its full statement is given near the start of section [ sec : efficient ] . the tunnel leveling addendum gives a great deal of information about bridge numbers of tunnel number @xmath0 knots . some of these applications involve the _ depth _ invariant , which is defined using the theory from @xcite . the depth of a tunnel , @xmath6 , is somewhat similar to the ( hempel ) distance @xmath7 ( see j. johnson @xcite and y. minsky , y. moriah , and s. schleimer @xcite ) , but unlike the distance , the depth is very easy to calculate in terms of the parameter description of tunnels given in @xcite . the two invariants are related by the inequality @xmath8 but the depth can be much larger than the distance . indeed , the `` middle '' tunnels of torus knots that we examine below are easily seen to have distance @xmath9 , but we will see their depths can be arbitrarily large . the depth invariant can be defined geometrically in terms of the cabling constructions of @xcite , but it also has a geometric interpretation in terms of a construction that first appeared in @xcite . that construction , which we call a giant step , is studied in @xcite . there is no upper bound for the bridge number of a knot in terms of the depths of its tunnels , but among our applications of the tunnel leveling addendum is a sharp lower bound : for @xmath10 , the minimum bridge number of a knot having a tunnel of depth @xmath1 is given recursively by @xmath11 , where @xmath12 , @xmath13 , and @xmath14 for @xmath15 . explicitly , @xmath16 and consequently @xmath17 . this improves lemma 2 of @xcite , which is that bridge number grows at least linearly with distance . it also improves proposition 1.11 of @xcite , which implies that bridge number grows at least as fast as @xmath18 . actually , the minimum bridge number theorem can be proven using only the tunnel leveling theorem , which give the lower bounds , and some explicit constructions to realize the minimum values . our upper bound result , however , uses the full strength of the tunnel leveling addendum : write the fibonacci sequence @xmath19 as @xmath20 . the maximum bridge number of a knot having a tunnel produced by @xmath3 cabling constructions , of which the first @xmath21 produce simple or semisimple tunnels , is @xmath22 . ( the terms `` simple '' and `` semisimple '' are recalled in section [ sec : cabling ] . ) for fixed @xmath3 , the largest value for the upper bound in theorem [ thm : max ] occurs when @xmath23 , giving the following absolute maximum : the maximum bridge number of a knot having a tunnel produced by @xmath3 cabling operations is @xmath24 . in fact , this maximum bridge number is achieved by a sequence of torus knot tunnels , as we will see in proposition [ prop : depth - efficienttorusknots ] . in addition to giving general bounds , the tunnel leveling addendum places very strong restrictions on the possible bridge numbers that can occur : suppose that a knot @xmath25 has a tunnel @xmath26 produced by @xmath27 cabling operations , of which the first @xmath21 produce simple or semisimple tunnels . then @xmath28 is one of the @xmath29 values @xmath30 for @xmath31 . here , @xmath32 is the _ fibonacci function _ of @xmath26 , defined in section [ sec : fibonacci_functions ] . it appears almost certain that all @xmath29 possible values in the bridge number set theorem do occur as bridge numbers . as explained in remark [ rem : bridge_number_set ] , this is easy to see for @xmath23 and @xmath33 , but for the general case we have not been able to verify all the necessary examples . we will also examine the interesting case of the `` middle '' tunnels of torus knots . in our paper @xcite , we calculated the invariants of @xcite for all torus knot tunnels . using that information , we will show that torus knot tunnels achieve the minimum rate of growth of bridge numbers in terms of depth , but not the minimum possible values , while they do achieve the maximum possible bridge numbers in terms of the number of cabling constructions . here is an outline of the sections of the paper . the first two sections constitute a concise review of the material from @xcite that we will need for the present applications . section [ sec : ddd ] introduces the distance and depth invariants , and gives a few results that follow quickly from @xcite and work of other authors . section [ sec : tunnel_leveling ] reviews the tunnel leveling theorem , and section [ sec : efficient ] states and proves the tunnel leveling addendum . fibonacci functions are introduced in section [ sec : fibonacci_functions ] , which also contains the more technical results on bridge number , including the bridge number set theorem . the minimum and maximum bridge number theorems are proved in section [ sec : growth ] , and torus knot tunnels are studied in section [ sec : torus_knots ] . finally , most of the results apply to the case of tunnel number @xmath0 links , and in section [ sec : links ] , we briefly discuss these adaptations .

we use the theory of tunnel number knots introduced in to strengthen the tunnel leveling theorem of goda , scharlemann , and thompson . this yields considerable information about bridge numbers of tunnel number knots . in particular , we calculate the minimum bridge number of a knot as a function of the maximum depth invariant of its tunnels . we also find the maximum bridge number as a function of the number of cabling constructions needed to produce the tunnel , showing in particular that the maximum bridge number of a knot produced by cabling constructions is the fibonacci number . finally , we examine the special case of the `` middle '' tunnels of torus knots .

we use the theory of tunnel number knots introduced in to strengthen the tunnel leveling theorem of goda , scharlemann , and thompson . this yields considerable information about bridge numbers of tunnel number knots . in particular , we calculate the minimum bridge number of a knot as a function of the maximum depth invariant of its tunnels . the growth of this value is on the order of , which improves known estimates of the rate of growth of bridge number as a function of the hempel distance of the associated heegaard splitting . we also find the maximum bridge number as a function of the number of cabling constructions needed to produce the tunnel , showing in particular that the maximum bridge number of a knot produced by cabling constructions is the fibonacci number . finally , we examine the special case of the `` middle '' tunnels of torus knots .

1212.2951

i

hamiltonian eigenvalue problems have a time - honored history , as they arise in numerous applications stemming from fluid mechanics , celestial mechanics , optical and atomic physics among many other disciplines ; see for some recent examples the books @xcite . especially in higher dimensional settings these problems can rapidly become fairly computationally intractable , at least as concerns providing the full diagonalization of the relevant matrix ( e.g. , when it stems from the linearization around two - dimensional vortex structures or three - dimensional vortex - rings @xcite ) . it is therefore highly desirable to be able to reduce the dimensionality of the calculation by providing a technique that can capture the main features of the linearization spectrum through suitable reductions to a finite dimensional eigenvalue problem . it is the aim of the present work to provide a general overview , as well as a systematic set of case examples of such a method . the approach that will be developed will be based on the so - called krein matrix @xcite . the krein matrix is a meromorphic matrix - valued function constructed via a lyapunov - schmidt reduction , and consequently recasts the infinite - dimensional eigenvalues problem as a finite - dimensional one . the construction is such that the eigenvalues are realized as points for which the krein matrix is singular . the computation and visualization of the determinant of this matrix can serve as a tool to identify the eigenvalues of the original problem . when determining the spectrum for the hamiltonian eigenvalue problem , there are two spectral sets to consider : those with positive real part , and those with negative krein index ( signature ) . the latter eigenvalues are purely imaginary ; however , upon collision with eigenvalues of positive krein signature it will generically be the case that a hamiltonian - hopf bifurcation will occur , which leads to an oscillatory instability . while the eigenvalues with positive real part are easy to visually identify , an additional calculation is necessary in order to identify the signature of a purely imaginary eigenvalue . as we will see later in this paper , the krein matrix is constructed in such a manner that the eigenvalues with negative signature can be identified _ graphically_. consequently , all of the ( potentially ) unstable eigenvalues can be identified visually . a related question is : how many ( potentially ) unstable eigenvalues are there to locate ? for a given problem it may be theoretically possible to establish an upper bound on the real part of all eigenvalues ; however , in many problems of interest there is no upper bound on the imaginary part of the eigenvalue . the hamiltonian - krein index , which will be discussed in detail later in this paper , counts the number of eigenvalues with positive real part , as well as the number of purely imaginary eigenvalues with negative krein signature . in the problems presented in this paper this index will be finite , and it will be related to the number of negative directions of the constrained second variation of the energy ( the underlying wave is realized as a critical point of the constrained energy ) . thus , while no bound is present on the imaginary part of all of the eigenvalues , since there are only a finite number of ( potentially ) unstable eigenvalues , there will be an upper bound for this set . a theoretical determination of this bound is probably not possible ; however , it can be determined numerically through the krein matrix . the computation of the krein matrix in this paper will be numerical for each case study . unfortunately , at this point in time we do not know of any examples for which the krein matrix can be explicitly computed . our hope is that for special problems , e.g. , the nonlinear schrdinger equation with the 1-soliton potential , such a calculation may be possible . this will be the topic of future research . we note that there is reason to be optimistic that this will be a fruitful direction for research , in that it is possible in some special cases to explicitly construct the evans function ( another eigenvalue counting tool ) , e.g. , see ( * ? ? ? * chapters 9.3 and 10.4 ) and the references therein . our presentation will be structured as follows . in , we first provide an overview of the hamiltonian - krein index theory for hamiltonian eigenvalue problems . afterwards , we focus on the construction of the krein matrix and provide a summary of its properties . in we consider specific examples stemming from the application of the krein matrix analysis to vortex dynamical states that are of intense recent interest in the field of atomic physics . in particular , we consider single ( unit charge ) vortex states that are presently fairly routine to produce / observe @xcite , but also examine the case of the recently studied vortex dipoles . for the sake of completeness , we also examine in one - dimensional analogs of such vortex states ; namely , multi - dark soliton structures that have been studied theoretically ( see e.g. @xcite and references therein ) and also have been observed experimentally in @xcite . finally , in we summarize our findings and present our conclusions , as well as some potential topics for future study . regarding the states studied in , it is known that the precessional dynamics of a single vortex is connected with the negative krein signature eigenvalues of the corresponding linearization spectrum , see @xcite . the vortex dipoles were produced by dynamical experiments involving flow past an obstacle @xcite , or quenching through the bose - einstein condensation ( bec ) transition @xcite . furthermore , their dynamical properties and structural robustness were studied in considerable length in recent works in the physical literature @xcite . experimental works on this theme - especially , @xcite - were concerned with issues such as : 1 . the equilibrium configuration , which is also explored herein ; 2 . the epicyclic motion around this equilibrium , which was analyzed through the negative krein signature eigenvalues of the dipole s linearization spectrum . it should be noted in passing that the study of spectral stability properties in bec settings ( and particularly for single- and multi - charge vortices ) is a subject rapidly gaining momentum , as evidenced by the recent work of @xcite on the subject . tk gratefully acknowledges the support of the jack and lois kuipers applied mathematics endowment , a calvin research fellowship , and the national science foundation under grant dms-1108783 . pgk and dy gratefully acknowledge support from afosr grant fa9550 - 12 - 1 - 0332 , from nsf - dms grant of number 0806762 , and pgk also from the alexander von humboldt foundation and the binational science foundation , grant number 2010239 .

when finding the nonzero eigenvalues for hamiltonian eigenvalue problems it is especially important to locate not only the unstable eigenvalues ( i.e. , those with positive real part ) , but also those which are purely imaginary but have negative krein signature in particular , we consider one - dimensional settings ( the cigar trap ) possessing real - valued multi - dark - soliton solutions , and two - dimensional settings ( the pancake trap ) admitting complex multi - vortex stationary waveforms .

when finding the nonzero eigenvalues for hamiltonian eigenvalue problems it is especially important to locate not only the unstable eigenvalues ( i.e. , those with positive real part ) , but also those which are purely imaginary but have negative krein signature . these latter eigenvalues have the property that they can become unstable upon collision with other purely imaginary eigenvalues , i.e. , they are a necessary building block in the mechanism leading to the so - called hamiltonian - hopf bifurcation . in this paper we review a general theory for constructing a meromorphic matrix - valued function , the so - called krein matrix , which has the property of not only locating the unstable eigenvalues , but also those with negative krein signature . these eigenvalues are realized as zeros of the determinant . the resulting finite dimensional problem obtained by setting the determinant of the krein matrix to zero presents a valuable simplification . in this paper the usefulness of the technique is illustrated through prototypical examples of spectral analysis of states that have arisen in recent experimental and theoretical studies of atomic bose - einstein condensates . in particular , we consider one - dimensional settings ( the cigar trap ) possessing real - valued multi - dark - soliton solutions , and two - dimensional settings ( the pancake trap ) admitting complex multi - vortex stationary waveforms .

astro-ph0306080

i

classical novae ( cn ) are the result of unstable thermonuclear ignition of freshly accreted hydrogen and helium on a white dwarf ( wd ) in a mass transferring binary . the orbital periods of these binaries presently range from 1.4 to more than 16 hours , with a large number in the 2 - 4 hour range @xcite . these cataclysmic variables ( cvs ; @xcite ) have low - mass stellar companions and spend most of their lives accreting at time averaged rates , @xmath8 ( e.g.howell , nelson , & rappaport 2001 ) . the frequency of cn as a function of orbital period depends on the accumulated mass immediately prior to the explosion , @xmath2 . however , the value of @xmath2 strongly depends on the wd s core temperature , @xmath1 , which is _ a priori _ unknown and must either be calculated or measured . knowledge of the ignition mass is also needed for comparisons to measured ejected masses in cn that would decide whether or not the underlying carbon / oxygen wd is being excavated during the cn . cvs are formed when the wd made during a common envelope event finally comes into contact with its companion as a result of gravitational radiation losses over a few gyr ( e.g. howell et al . the wd will have cooled during this time ; a @xmath9 he wd would have @xmath10 at 4 gyr @xcite , whereas a @xmath11 c / o wd would have @xmath12 in 4 gyr @xcite . these wds would have effective temperatures @xmath13 k. a subset of the cvs , called dwarf novae ( dn ) , contain a wd accreting at low time - averaged rates @xmath14 , where the accretion disk is subject to a thermal instability which causes it to rapidly transfer matter onto the wd ( at @xmath15 ) for roughly a week once every month to year . the @xmath16 onto the wd is low enough between outbursts that the uv emission is dominated by the internal luminosity of the wd , allowing for a measurement of @xmath17 @xcite . this is the best evidence that the wd is hotter than a cooling wd of similar age due to the thermal impact of accretion . @xcite has argued that most of this heating is from gravitational energy released ( i.e. converted to thermal energy ) in the wd interior via material compression . this energy is then transported outward to the stellar surface , and we find that it can similarly heat the core . we will discuss this in great detail , as well as explain the important role of nuclear `` simmering '' . a thorough comparison of our theoretical work to @xmath18 observations and a summary of the implications for cv evolution are in a companion paper @xcite . the gravitational energy released ( @xmath19 ) when a particle falls from a large distance to the stellar surface , sometimes termed the accretion energy , is deposited at , or near , the photosphere and is rapidly radiated away . this energy does not get taken into the star , as the time it takes the fluid to move inward is always much longer than the time it takes for heat to escape . this basically eliminates the outer boundary condition and instead points to the importance of energy released deep in the wd due to both gravitational energy released , via compression , within the star and hydrostatic nuclear burning . that energy takes a long time to exit , will still be visible when accretion has halted , sets @xmath18 , and reheats the wd . we begin in [ sec : accenv ] by explaining the physics of heating within the accreted envelope and how that differs from heating in the deep core ( discussed in appendix a ) . since these wds are accreting at rates low enough so that the accumulated hydrogen burns unstably , we also need to carefully track the accumulated mass of material and account for the additional energy source of slow nuclear `` simmering '' near the base of the accreted layer . this is significant as the layer accumulates and eventually triggers the cn . the calculation of @xmath2 for a fixed @xmath1 is explained in [ sec : ign ] ( closely comparing to the original fujimoto 1982 work ) , where we also exhibit the importance of the @xmath20 content in the accreting material . our method of finding the equilibrium wd core temperature ( townsley & bildsten 2002 ) is explained in [ sec : equil ] and improves on that of @xcite by allowing the accreted envelope mass to change through the cn cycle . we show that early in the cycle , when the mass of the newly accreted layer is small , compressional heating is small , and the wd cools . later in the cycle , the accreted layer becomes thick enough that compressional heating along with nuclear simmering heats the core . so , the core cools at low accumulated masses and is heated prior to unstable ignition . using cn ignition conditions to determine the maximum mass of the overlying freshly accreted shell , we then find the steady - state ( i.e. cooling equals heating throughout the cn cycle ) core temperature , @xmath21 , as a function of @xmath7 and @xmath22 . we close [ sec : equil ] by showing that for @xmath23 yr@xmath24 the wd reaches this equilibrium after accreting an amount of mass less than its own and that in cvs with @xmath25 hours the accretion rate changes slowly enough that the wd should always be near the equilibrium given by @xmath7 and @xmath22 . having found the core temperatures , we then predict the amount of mass that needs to accumulate on the wd in order to unstably ignite the accumulated hydrogen as a function of @xmath7 and @xmath22 . our work is compared to previous calculations in [ sec : res ] , finding very large differences with others due to their lack of knowledge of @xmath1 . we also compare our predictions of @xmath2 to those few measures of the ejected masses in cn of known orbital period . within the confines of this limited comparison , we find that the ejected masses are comparable to the amount accumulated . the equilibrium also yields powerful relations between the wd surface temperature and its accretion rate and mass . these allow for tests of binary evolution models as well as measures of the masses of these wds ; a comparison to the accumulated observations of effective temperatures in the dn systems is being published separately @xcite . we close with a summary and discussion of future work , especially the seismology of these accreting wds .

, the freshly accumulated hydrogen / helium envelope ignites in a thermally unstable manner that results in a classical novae ( cn ) outburst and ejection of material . these accretion rates are most appropriate to wds in cataclysmic variables ( cvs ) of hr , many of which accrete sporadically as dwarf novae . we have includedhe in the accreted material at levels appropriate for cvs and find that it significantly modifies the cn ignition mass .

white dwarfs experience a thermal renaissance when they receive mass from a stellar companion in a binary . for accretion rates , the freshly accumulated hydrogen / helium envelope ignites in a thermally unstable manner that results in a classical novae ( cn ) outburst and ejection of material . we have undertaken a theoretical study of the impact of the accumulating envelope on the thermal state of the underlying white dwarf ( wd ) . this has allowed us to find the equilibrium wd core temperatures ( ) , the classical nova ignition masses ( ) and the thermal luminosities for wds accreting at rates of . these accretion rates are most appropriate to wds in cataclysmic variables ( cvs ) of hr , many of which accrete sporadically as dwarf novae . we have includedhe in the accreted material at levels appropriate for cvs and find that it significantly modifies the cn ignition mass . we compare our results with several others from the cn literature and find that the inclusion ofhe leads to lower for , and that for below this the particular author s assumption concerning , which we calculate consistently , is a determining factor . initial comparisons of our cn ignition masses with measured ejected masses find reasonable agreement and point to ejection of material comparable to that accreted .

1508.01459

i

we consider relay - assisted device - to - device ( d2d ) communication underlaying lte - a cellular networks where d2d user equipments ( ues ) are served by the relay nodes @xcite . when the link condition between two d2d ues is too poor for direct communication , the d2d traffic can be transmitted via a relay node , which performs scheduling and resource allocation for the d2d ues . we refer to this as _ relay - aided d2d communication _ which can be an efficient approach to provide better quality of service ( qos ) for communication between distant d2d ues . for this , we utilize the lte - a layer-3 ( l3 ) relay @xcite . we consider scenarios in which the potential d2d ues are located in the same macrocell ; however , the proximity and link condition may not be favorable for direct communication . therefore , they communicate via relays . the radio resources ( e.g. , resource blocks [ rbs ] and transmission power ) at the relays are shared among the d2d communication links and the two - hop cellular links . we formulate an optimization problem to allocate radio resources at a relay node in a muti - relay multi - user orthogonal frequency - division multiple access ( ofdma ) cellular network ( e.g. , lte - a network ) . due to the np - hardness of the resource allocation problem , we utilize time sharing strategy and provide an asymptotically optimal centralized solution . considering the random nature of wireless channels , we reformulate the resource allocation problem using the worst - case robust optimization theory . the uncertainties in link gains are modeled using ellipsoidal uncertainty sets . each relay node can centrally solve the problem taking channel uncertainty into consideration . however , considering the high ( e.g. , cubic to the number of ues and rbs ) computational overhead at the relay nodes , we provide a _ distributed _ solution based on _ stable matching _ theory which is computationally inexpensive ( e.g. , linear with the number of ues and rbs ) . we also analyze the stability , uniqueness , and optimality of the proposed solution . considering the computational and signalling overheads and lack of scalability of the centralized solutions , game theoretical models have been widely used for wireless resource allocation problems . however , the analytical tractability of equilibrium in such game - theoretical models requires special properties for the objective functions , such as convexity , which may not be satisfied for many practical cases @xcite . in this context , resource allocation using matching theory has several beneficial properties @xcite . for example , the stable matching algorithm terminates for every given preference profile . the outcome of matching provides suitable solutions in terms of stability and optimality , which can accurately reflect different system objectives . besides , with suitable data structures , a pareto optimal stable matching ( e.g. , allocation of resources to the ues ) can be obtained quickly for online implementation . the goal of this work is to design a practical radio resource scheme for relay - aided d2d communication in a multi - user multi - relay ofdma network . as opposed to most of the work in the literature where channel gain information is assumed to be perfect , we capture the dynamics of random and time - varying nature of wireless channels . to this end , we develop a low - complexity distributed solution based on the theory of stable matching and demonstrate how this scheme can be implemented in a practical lte - a system . the major contributions of this work can be summarized as follows : * we model and analyze the radio resource allocation problem for relay - aided d2d communication underlaying an ofdma cellular network considering uncertainties in channel gains . we formulate an optimization problem to maximize system capacity in a two - hop network while satisfying the minimum data rate requirement for each ue and limiting the interference to other receiving nodes . we show that the convexity of the optimization problem is conserved under bounded channel uncertainty in both the useful and interference links . * using the theory of stable matching , we develop a distributed iterative solution , which considers bounded channel uncertainty . the stability , uniqueness , optimality , and complexity of the proposed solution are analyzed . we also present a possible implementation approach of our proposed scheme in an lte - a system . * numerical results show that the proposed distributed solution performs close to the upper bound of the optimal solution obtained in a centralized manner ; however , it incurs a lower ( e.g. , linear compared to cubic ) computational complexity . through simulations , we also compare the performance of the proposed approach with a traditional underlay d2d communication scheme and observe that after a distant margin , relaying of d2d traffic improves network performance . we organize the rest of the paper as follows . we briefly review the related work in section [ sec : related_works ] . section [ sec : system_model ] presents the system model and related assumptions . followed by the formulation of the nominal resource allocation problem in section [ sec : rap_optimization ] , we reformulate the resource allocation problem considering wireless channel gain uncertainties in section [ sec : rap_uncert ] . we develop the stable matching - based distributed resource allocation algorithm in section [ sec : ra_sm ] . theoretical analysis of the proposed solution is presented in section [ sec : analysis_sm ] . in section [ sec : numerical_results ] , we present the performance evaluation results before we conclude the paper in section [ sec : conclusion_sm ] .

wireless device - to - device ( d2d ) communication underlaying cellular network is a promising concept to improve user experience and resource utilization . unlike traditional d2d communication where two mobile devices in the proximity establish a direct local link bypassing the base station , in this work we focus on relay - aided d2d communication . , we provide a centralized solution under bounded channel uncertainty . with a view to reducing the computational burden at relay nodes , we propose a distributed solution approach using stable matching to allocate radio resources in an efficient and computationally inexpensive way . numerical results show that the performance of the proposed method is close to the centralized optimal solution and there is a distance margin beyond which relaying of d2d traffic improves network performance . device - to - device ( d2d ) communication , lte - a l3 relay , uncertain channel state information , distributed resource allocation , stable matching .

wireless device - to - device ( d2d ) communication underlaying cellular network is a promising concept to improve user experience and resource utilization . unlike traditional d2d communication where two mobile devices in the proximity establish a direct local link bypassing the base station , in this work we focus on relay - aided d2d communication . relay - aided transmission could enhance the performance of d2d communication when d2d user equipments ( ues ) are far apart from each other and/or the quality of d2d link is not good enough for direct communication . considering the uncertainties in wireless links , we model and analyze the performance of a relay - aided d2d communication network , where the relay nodes serve both the cellular and d2d users . in particular , we formulate the radio resource allocation problem in a two - hop network to guarantee the data rate of the ues while protecting other receiving nodes from interference . utilizing time sharing strategy , we provide a centralized solution under bounded channel uncertainty . with a view to reducing the computational burden at relay nodes , we propose a distributed solution approach using stable matching to allocate radio resources in an efficient and computationally inexpensive way . numerical results show that the performance of the proposed method is close to the centralized optimal solution and there is a distance margin beyond which relaying of d2d traffic improves network performance . device - to - device ( d2d ) communication , lte - a l3 relay , uncertain channel state information , distributed resource allocation , stable matching .

1205.1990

i

observations of diffuse gas have found a population of massive , fast moving clouds . with line - of - sight speeds between @xmath2 km s@xmath3 and @xmath4 km s@xmath3 @xcite , they are appropriately named high velocity clouds ( hvcs ) . these clouds are plentiful ; neutral hvc material covers @xmath5 of the sky @xcite while intermediately and highly ionized hvc material covers @xmath6 and @xmath7 of the sky , respectively @xcite . although some of the high velocity material is isolated , many of the clouds are grouped into large complexes . complex c , for example , stretches from @xmath8 to @xmath9 , while the magellanic stream runs along @xmath10 from @xmath11 to near the south galactic pole and then resumes again , running along @xmath12 from the south galactic pole to @xmath13 . several clouds are relatively near to the galactic plane . the smith cloud ( also called complex gcp ) , complex a , the cohen stream , which is part of the anticenter complexes , and complex c are between @xmath14 and @xmath15 kpc , 2.5 and 7 kpc , @xmath15 and @xmath16 kpc , and 5 and 10 kpc , respectively , above or below the galactic midplane @xcite . these clouds are near enough to the plane to be interacting with the galaxy s thick disk / halo ( see @xcite and references within ) . cloud - ism interactions may be identified through anticorrelations with galactic h at normal velocities @xcite , high ion ratios @xcite , and x - ray enhancements ( e.g. , @xcite ) . for example , @xcite noted an excess soft x - ray surface brightness near high velocity h gas in draco , a region now considered the southern part of complex c. later , @xcite reported excess 1/4 kev x - rays on the edge of complex m , @xcite noted excess 1/4 kev x - rays in the complex c region , and @xcite reported 1/4 kev excesses for complexes c , d , and gcn . ( see figure [ fig : complexcmap ] for our estimate of the complex c excess . ) generally , diffuse 1/4 kev x - rays are interpreted as tracers of @xmath17 k gas . a slight excess of somewhat more energetic x - rays has been reported for a sight line through the magellanic stream @xcite . although the clouds in the magellanic stream are not interacting with the milky way s disk , they may be interacting with the extended halo or with gas ablated from preceding clouds in the stream . like @xcite , @xcite suggested that the excess x - rays may have been emitted by shock - heated gas . shock heating would be possible if the collision speed were multi - hundred km s@xmath3 and the gas were initially warm or hot . for unmagnetized warm plasmas , the post shock temperature would be @xmath18 k if the collision speed were @xmath19 km s@xmath3 @xcite . such a speed may be achieved by magellanic stream clouds , given that the orbital velocity of the magellanic stream is @xmath20 km s@xmath3 @xcite . as is the case for most hvcs , the impact speed of complex c is unknown . most hvcs have line - of - sight velocities @xmath21 km s@xmath3 , but their total velocities may be much larger than their line - of - sight velocities if the angles between the hvcs velocities and the lines - of - sight are large . this is the case for the smith cloud , whose total velocity has been calculated from the variation in line - of - sight velocity as a function of observing angle and other observables to be @xmath4 km s@xmath3 , while its line - of - sight velocity is only @xmath22 km s@xmath3 @xcite . in addition , an hvc s currently observed velocity may be less than its velocity when it first encountered the galaxy . we examine the x - ray productivity of gas shocked by fast clouds in this paper . turbulent mixing should also be considered . as the cloud passes through the ambient medium , shear instabilities develop at the contact surface . gas on either side of the interface mixes , resulting in a zone of intermediate temperature , intermediate density gas . this logic has been used to explain high ions associated with hvcs @xcite . in this paper , we also consider the possibility that some of the transition zone gas may be hot enough and dense enough to yield observable quantities of x - rays . other potential mechanisms include magnetic reconnection @xcite . as high velocity clouds move through the halo and thick disk , they should deform and compress the magnetic field . @xcite suggest that shear between the cloud and the ambient plasma will turbulently mix the magnetic field in the region very near to the cloud . when these magnetic field lines reconnect , they release energy . @xcite performed analytic and resistive magnetohydrodynamic simulations of the system finding that magnetic reconnections can release enough energy to heat the gas to @xmath23 k. because the magnetic reconnection scenario has already been examined with magnetohydrodynamic simulations , it is not simulated again in this paper . recently , additional ideas have been suggested . noting the x - rays emission that follows after charge exchange reactions in the heliosphere , @xcite suggest that charge exchange may be important at the interfaces between clouds and hot gas , and , noting the possible role of mhd plasma waves in heating the solar corona @xcite suggest that plasma waves instigated by collisions between high velocity clouds and halo gas may also be important . in order to better understand hvcs , their interactions with the galaxy , and the possibility that they may induce x - rays , we perform flash magnetohydrodynamic simulations of the shock heating and turbulent mixing scenarios . our simulations begin with a cloud of similar size and h column density as the lumps in complex c. in our simulations of the shock heating scenario , the cloud initially has a speed of @xmath24 km s@xmath3 relative to the ambient gas . we examine the effect of ambient density , using moderate ( e.g. , @xmath25 atoms @xmath26 ) and lower densities for the ambient gas . the moderately dense ambient medium may represent material ablated from a preceding hvc or a thick disk / halo cloud . we found that when @xmath27 km s@xmath3 clouds interact with moderate density ambient media and radiative cooling is disabled , the shocked , compressed ambient medium yields extremely bright x - rays for @xmath28 myr . if , in contrast , radiative cooling proceeds at the collisional ionizational equilibrium ( cie ) rate , then the gas is only moderately bright and for only @xmath29 myr . in both the adiabatic and the radiatively cooling simulations , greater ambient densities resulted in greater emission intensities . in our turbulent mixing simulations , a cool cloud falls through hot halo gas that is in hydrostatic equilibrium . in the simulations having very hot ambient media ( @xmath30 k ) , the mixed zone contains some @xmath31 k gas , which is hot enough to produce 1/4 kev x - rays in cie calculations . however , the mixed gas falls behind the cloud , into a region where the pressure and density are low . it is the low density that limits the x - ray production of this scenario , causing the surface brightnesses to be too small to be detectable . in section [ sect : technique ] , we describe the modeling algorithms and list the simulational parameters . section [ sect : results ] presents the results . in section [ subsect : cievsnei ] , we compare cie and non - equilibrium ionization ( nei ) calculations , finding that the cie approximation yields similar 1/4 kev x - ray spectra to the nei calculations . in section [ subsect : shockheating ] , we evaluate the ability of fast hvc collisions to shock heat the ambient gas and induce x - ray emission . the predictions include 1/4 kev surface brightnesses , o and o intensities , and o column densities . in section [ subsect : hotism ] , we evaluate the ability of turbulent mixing to create hot , x - ray emissive gas . section [ subsect : obsappearance ] describes how the simulated clouds would appear to observers while section [ subsect : resolution ] discusses higher and lower resolution simulations , concluding that the numerical resolutions used in our earlier simulations are adequate . the results are summarized in section [ sect : discussion ] .

with the goal of understanding why x - rays have been reported near some high velocity clouds , we perform detailed 3 dimensional hydrodynamic and magnetohydrodynamic simulations of clouds interacting with environmental gas like that in the galaxy s thick disk / halo or the magellanic stream . the x - ray productivity depends strongly on the speed of the cloud and the radiative cooling rate . in order to shock - heat environmental gas to temperatures of k , cloud speeds of km if , in contrast , the radiative cooling rate is similar to that of collisional ionizational equilibrium plasma with solar abundances , then the shocked gas is only mildly bright and for only about 1 myr .

with the goal of understanding why x - rays have been reported near some high velocity clouds , we perform detailed 3 dimensional hydrodynamic and magnetohydrodynamic simulations of clouds interacting with environmental gas like that in the galaxy s thick disk / halo or the magellanic stream . we examine 2 scenarios . in the first , clouds travel fast enough to shock - heat warm environmental gas . in this scenario , the x - ray productivity depends strongly on the speed of the cloud and the radiative cooling rate . in order to shock - heat environmental gas to temperatures of k , cloud speeds of km / s are required . if cooling is quenched , then the shock - heated ambient gas is x - ray emissive , producing bright x - rays in the 1/4 kev band and some x - rays in the 3/4 kev band due to o and other ions . if , in contrast , the radiative cooling rate is similar to that of collisional ionizational equilibrium plasma with solar abundances , then the shocked gas is only mildly bright and for only about 1 myr . the predicted count rates for the non - radiative case are bright enough to explain the count rate observed with _ xmm - newton _ toward a magellanic stream cloud and some enhancement in the _ rosat _ 1/4 kev count rate toward complex c , while the predicted count rates for the fully radiative case are not . in the second scenario , the clouds travel through and mix with hot ambient gas . the mixed zone can contain hot gas , but the hot portion of the mixed gas is not as bright as those from the shock - heating scenario .

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in order to evaluate the cie approximation , we compare spectra that we calculate from the nei and cie ionization fractions of silicon and oxygen . the nei ionization fractions , i.e. , the fractions of the atoms at any given ionization level were obtained by having flash track the ionization levels in a time dependent fashion in moderate resolution versions of models br3 , br4 , and br5 . the cie ionization fractions were obtained from the hydrodynamic information for these same models ; specifically , they were calculated by the raymond and smith code using the temperature of the gas as an input . for each of these three models , we calculate the spectra produced by nei silicon , cie silicon , nei oxygen , and cie oxygen for various vertical sight lines through the domain at each epoch , 2 myr , 4 myr , etc . ( although the shocked gas has already radiated way much of its energy by 2 myr , it is still sufficiently emissive for these experiments . ) in order to reduce the quantity of information , we then convolve each silicon spectrum with the _ rosat _ 1/4 kev band response function and each oxygen spectrum with the _ rosat _ 3/4 kev band response function , yielding count rates in these bands . in each case , the cie count rates in the 1/4 kev band are fairly similar to the nei count rates . for example , the _ rosat _ 1/4 kev count rate calculated from the cie and nei silicon spectra produced along the central sight line of the br4 model at 2 myr are within @xmath97 of each other . the relationship between the cie and nei oxygen spectra were not as consistent from model to model and epoch to epoch . for model br4 at 2 myr the cie and nei oxygen spectra are within @xmath98 of each other . the emission line spectra for this case are displayed in figure [ fig : cievsnei ] . sometimes , the o intensities from the models are less consistently aligned with each other than are the silicon intensities and frequently the o quantities ( which are always small ) are poorly aligned , presumably due to delayed ionization and recombination . similarly , the high resolution model br simulations also show poor alignment between the cie and nei o column densities . + theoretically , if the clouds collide with neighboring gas at fast enough speeds , then shocks should develop in both media . the temperature ( @xmath99 ) of the shocked plasma can be estimated from the equation for plane parallel shocks @xcite : @xmath100 [ ( \gamma+1)+(\gamma-1)(m_1 ^ 2 - 1)]}{(\gamma+1)^2 m_1 ^ 2 } , \label{eq : shocktemp}\ ] ] where @xmath101 is the temperature of the unshocked gas , @xmath102 is the mach number calculated from the speed at which the unshocked gas is overrun by the shock , and @xmath103 is the adiabatic constant for monotonic gas ( @xmath104 ) . here , we compare the theoretical post - shock temperature with those of models ba3 and c3 at the first epoch ( @xmath105 myr ) . these models begin with cloud velocities of @xmath106 km s@xmath3 and do not model radiative cooling ( although , in post - processing , we can estimate the x - ray spectra that would be emitted by gas at the simulated temperatures ) . by the first archived epoch at 2 myr of simulated time , the cloud has shock - heated the environmental gas beneath it while a reverse shock has been driven into the lower part of the cloud . in both model ba3 and c3 , the shocked environmental gas was initially warm ( @xmath107 k ) , ionized ism . although the unshocked portion of the cloud still travels with approximately its initial velocity , @xmath106 km s@xmath3 , at this epoch , the shocked portion of the cloud moves downwards at speeds between 240 and 300 km s@xmath3 and the swept up ism moves downwards at speeds up to 240 km s@xmath3 with an average of about 200 km s@xmath3 and moves sideways with speeds exceeding 100 km s@xmath3 . thus , the impacted material does not simply pile up in front of the cloud , as in a shock - tube simulation , but instead partially skirts around the cloud . the shockfront travels downwards at 4/3 of the shocked ism s downwards speed , which is confirmed by the displacement of the shockfront between @xmath105 and 4 myr . thus , @xmath108 . from equation [ eq : shocktemp ] , we find that @xmath99 should be @xmath109 k , which is consistent with the post - shock temperatures in models ba3 and c3 : 0.95 and @xmath109 k , respectively . see figure [ fig : images ] . since the clouds decelerate in our gravity - less simulations , the post - shock velocity decreases with time and thus the post - shock temperature decreases with time as well . this can be seen by comparing the temperatures at 10 myr with those at 2 myr in figure [ fig : images ] . + a reverse shock propagates through the cloud , but due to the density contrast , it propagates slower than the forward shock in the ism . in our simulations of model c3 at 2 myr , the reverse shock moves into the cloud at a speed of @xmath2 km s@xmath3 from the cloud s reference frame . given an initial cloud temperature of @xmath110 k , the reverse shock should be strong and according to equation [ eq : shocktemp ] , it should heat the cloud to @xmath111 k. our simulational results find the temperature to range from the cloud temperature to this value ; see figure [ fig : images ] . while the reverse shock - heated material is far hotter than the unshocked portion of the cloud , it is still not hot enough to produce x - rays . the x - rays that result from this geometry originate in the shock - heated ambient medium . in the following subsections , we explain that their intensity ranges from unobservably dim to significantly bright , depending upon the time since interaction , collision speed , and strength of radiative cooling . + the simulations and theory discussed above did not include the effects of radiative cooling . when it is included in the calculations , the shocked ambient gas quickly cools . this can be seen by comparing the temperature and density distributions in models ba3 and c3 with those from model br3 in figure [ fig : images ] . these are fair comparisons because each model has the same parameters for the cloud and lower ism and , although the ionization fractions of some elements were calculated in a time - dependent manner in model br3 ( but not in the others ) , the nei ionization levels did not affect the hydrodynamics and we replace them with the cie ionization levels for the following spectral calculations . furthermore , we note that the ambient medium in models ba3 and br3 include a layer of hot gas , but this layer contributes only @xmath112 counts s@xmath3 arcmin@xmath48 which is trivially small and is subtracted before we report the results . without radiative cooling , the shock - heated gas is very bright for millions of years . as can be seen in figure [ fig:1/4kevevolution ] , even the moderately fast clouds ( @xmath113 km s@xmath3 ) induce surface brightnesses across their footprints of @xmath114 @xmath115 counts s@xmath3 arcmin@xmath48 in the _ rosat _ r12 band at their peak . faster clouds produce @xmath116 counts s@xmath3 arcmin@xmath48 in this band at their peaks . these models are much brighter than the typical intrinsic intensity of 1/4 kev photons emitted above the galactic disk , which is @xmath117 to @xmath118 counts s@xmath3 arcmin@xmath48 with significant directional variation @xcite . all of these simulated clouds continue to make @xmath119 counts s@xmath3 arcmin@xmath48 until at least 14 myr after the collision . + + when radiative cooling is included in the simulation , the hot gas in front of the cloud sheds most of its energy via radiation , only some of which is in the x - ray band . figures [ fig:1/4kevevolution ] and [ fig : offcentercountrate ] include plots of the resulting 1/4 kev surface brightnesses from the high resolution model br simulations . the average surface brightnesses across footprints that are 200 pc in radius peak around 3 , 500 , and @xmath120 counts s@xmath3 arcmin@xmath48 in the _ rosat _ 1/4 kev band within 1 to 1@xmath121 myr of the collision for the @xmath122 and @xmath123 km s@xmath3 collisions , respectively . the surface brightness profiles of models ba3 and c3 in figure [ fig : offcentercountrate ] show that the surface brightness peaks near each cloud s axis and drops non - monotonically with radius . model br3 s profile is more complicated . the peaks and valleys in the profiles are associated with the density and temperature structure of the off - axis gas . when the gas is very bright , the profile extends beyond the footprint of the cloud . sensitive x - ray observations of the clouds would see extended disks . the shock - heated gas is less conspicuous in the 3/4 kev band than in the 1/4 kev band , in both the radiative cooling and the non - cooling scenarios . for both models ba3 and c3 , the o triplet ( photon energy @xmath124 ev ) intensity across a disk of radius = 200 pc averages to @xmath29 photon s@xmath3 cm@xmath48 sr@xmath3 for the first several million years ( see figure [ fig : ovii_oviii ] ) . it averages to far less than 1 photon s@xmath3 cm@xmath48 sr@xmath3 for model br3 . the former intensity is about @xmath125 of the typical observed intensity on randomly chosen sight lines away from the galactic center @xcite . because the collisions weaken with time , the o intensities fade sooner than the 1/4 kev surface brightnesses . furthermore , none of the @xmath106 km s@xmath3 models produce appreciable o intensities at any time . the average o column density within a footprint of radius 200 pc is @xmath126 cm@xmath48 , for both models ba3 and c3 at 2 myr . it remains near this level for 10 myr , thus outliving the duration of the bright o emission . in model br3 , the average o column density is @xmath127 cm@xmath48 from about 1.3 to about 1.5 myr . the o and o column densities for these and other speeds simulated for model ba and the high resolution versions of model br are plotted in figure [ fig : ovii_oviiicolden ] . the gas in these models is also uv emissive . when we divide the predicted energy spectra into 0.25-dex wide bins , we find that the 10 to 18 ev photon energy range is the most luminous part of the @xmath128 to @xmath129 ev spectrum for models ba3 , br3 , and c3 . model br3 , for example , radiates more than 100 times more power in 10 to 18 ev photons than in 100 to 180 ev photons when it is at its peak 1/4 kev x - ray brightness ( age @xmath1301.3 myr ) . at earlier and later times , the ratio is even larger . with its comparatively large radiative power , the uv plays a more important role in cooling the shock - heated gas than does the x - ray . we have presented results for both radiatively cooling and adiabatic models . in the following subsections , we continue to discuss both cases . while , on the face of it , it appears contradictory to consider the x - ray count rates expected from hot gas whose hydrodynamics were calculated in models that excluded radiative cooling ( models ba and c ) , we note that 1 . ) the true cooling rate is unknown , 2 . ) if the gas phase abundances are between zero and the solar values , then the cooling rate should be between that used in the br suite of models and those used in the ba and c suites , and 3 . ) x - ray emission accounts for very little cooling . because x - ray emission accounts for such a small fraction of the cooling and because the relative contribution to the spectrum made by any given element varies from one energy band to the next , it is possible for variations in gas phase metallicities to preferentially lower the cooling rate compared with those in case ba or raise the x - ray count rate compared with those from case br . iron provides a good example of the effect of the gas - phase metallicity . almost @xmath131 of the energy radiated in 5 to 100 ev photons by a @xmath132 k plasma having @xcite abundances are emitted by iron ions , while slightly less than @xmath133 of the _ rosat _ r12 counts are due to photons emitted by these ions . thus , if the true iron abundance in the shock - heated gas were half that expected by @xcite , then the overall radiative cooling rate would be noticeably affected ( it would be about @xmath134 of the cie rate ) , while the _ rosat _ r12 count rate would be insignificantly affected ( it would be about @xmath135 of cie rate ) . reducing the iron abundance to zero decreases the radiative cooling rate by 3/5 , while reducing the 1/4 kev luminosity by only 1/5 . similar phenomena occur at higher temperatures . silicon provides another example , because it accounts for @xmath136 of the 5 to 100 ev power , but almost @xmath137 of the _ rosat _ r12 count rate . thus , doubling its relative abundance would increase the radiative loss rate by only 1/8 , but increase the 1/4 kev count rate by almost third . here , we are nt suggesting that the halo has supersolar abundances of silicon , but are pointing out that if the ratio of silicon to other elements is larger than in solar abundance gas , the effect would preferentially benefit the x - ray luminosity . the interested reader is referred to @xcite figure 18 for relative cooling rates from various elements . other reasons why the rate of radiative cooling might differ from the cie rate for solar abundances include disequilibrium between electron and ion temperatures and delayed ionization and recombination . + we ran several additional simulations in order to explore the effects of initial velocities . these , plus the simulations already mentioned , create several suites . models ba2 , 3 , 4 , 5 , and 6 have initial cloud velocities of @xmath138 , and @xmath75 km s@xmath3 , respectively . models c3 , 4 , 5 , and 6 have velocities of @xmath139 , and @xmath75 km s@xmath3 , respectively . the faster end of this range is greater than expected for hvcs near our galaxy , but may be of value for studying more energetic collisions . models br2 , 3 , and 4 have velocities of @xmath140 , and @xmath67 km s@xmath3 , respectively . we simulated the model br suite in both moderate and high resolution forms , but for this analysis , we focus on only the high resolution simulations . even the @xmath141 km s@xmath3 cloud induces bright x - rays in the non radiatively cooled simulations and some x - rays in the radiatively cooled simulations . these x - rays are from gas that was shock - heated to @xmath142 k. the faster clouds shock - heat the ism to higher temperatures . as a result , they produce more 1/4 kev x - rays for longer periods of time ( see figure [ fig:1/4kevevolution ] ) . furthermore , the o and o intensities , which are modest in models ba2 and ba3 , become stronger in models ba4 , 5 , and 6 ( see figure [ fig : ovii_oviii ] ) . because the shock heated gas is more highly ionized in the faster models , the column densities of o and o are also larger ( see figure [ fig : ovii_oviiicolden ] ) . + the density of the environmental gas affects the hydrodynamics and production of 1/4 kev x - rays in multiple ways . when the ambient density is greater , then the swept up , shock - heated environmental gas in front of the cloud has greater density and depth , resulting in a higher 1/4 kev surface brightness . in addition , denser gas better decelerates the cloud , resulting in lower post - shock temperatures . the effect of lowering the post - shock temperature , however , can increase or decrease the emissivity , depending upon the circumstances . given that the peak in the theoretical 1/4 kev x - ray emissivity curve is near @xmath143 k for cie plasmas , slowing the cloud increases the 1/4 kev x - ray emissivity in the cases of very fast clouds ( e.g. , those with initial @xmath144 km s@xmath3 ) and decreases it in the cases of only moderately fast clouds ( e.g. , those that have reached @xmath145 km s@xmath3 . ) with each of these factors playing a role , our model c3 is 10 times brighter than its less dense counterpart , model c3d , whose environmental density is 1/10 that of model c3 . our model c6 is 100 times brighter than its less dense counterpart , model c6d , whose environmental density is 1/10 that of model c6 , and our model br3 is @xmath146 times brighter than its less dense counterpart , model br3d , whose environmental density is 1/10 that of model br3 . furthermore , the greater the amount of shock - heated interstellar material that is swept up , the greater the column densities of very high ions . consequently , models c3 and c6 have about 10 times greater o column densities than models c3d and c6d , respectively , while model br3 has roughly twice the o column densities of model br3d . + here , we consider mixing between cool and warm clouds as they travel through hot , rarefied ambient gas . as the cloud passes through the hot gas , kelvin - helmholtz instabilities develop and mixing between the cloud and ambient material creates a zone of intermediate temperature , intermediate density gas @xcite . analytical calculations and computational simulations have already shown that mixed layers are rich in high ions , such as o @xcite . in order to determine whether or not mixing zones between hvcs and very hot gas can also be x - ray productive , we simulate the hydrodynamics of 3 dimensional clouds passing through hot , rarefied gas . this approach differs from the more common approach , which treats the two regions as blocks that slide past each other , but better replicates the effects of the cloud s rounded shape and motion . the names of these simulations begin with a. in order to model the interaction adequately , the simulations must resolve the mixing length scale . interstellar turbulence may exist across a wide range of length scales , but the largest length scale dominates the mixing @xcite . in our case , the largest length scale is the height of the distorted cloud . this height and width are adequately resolved in our model a simulations , which , when fully resolved , use @xmath146 zones to model a 400 pc span ( the nominal height of the interaction zone in figure [ fig : cloudwithears ] ) . + our simulations do not include thermal conduction , but @xcite found that turbulent diffusion is much more effective than thermal conduction at leveling the temperature gradient . thus , our omission of thermal conduction is not problematic . note , also , that radiative cooling has not been allowed in the model a simulations . it was disallowed in order to maintain hydrostatic balance in the background gas . the ramifications of cooling are too complicated for us to simply say that adding cooling would lower the radiation rates of the turbulently mixed gas . this is because radiative cooling would not only allow the @xmath147 k gas to cool to lower temperatures , but it would allow hotter gas to cool to @xmath147 k. model a1 serves as an example of case a simulations and as our reference simulation for comparison with the others . in this simulation , we track the cloud as it falls from its initial height of 12 kpc to near the bottom of our grid ( @xmath36 kpc ) , which takes 32 myr of simulated time . we record the simulation results at 2 myr intervals and here describe the results at two of the sampled epochs . by 16 myr , the cloud has accelerated to @xmath148 km s@xmath3 and fallen to a height of @xmath149 kpc . by 30 myr , it has accelerated to @xmath150 km s@xmath3 and fallen to @xmath151 kpc . we obtain the cloud - induced excess intrinsic count rate in the 1/4 kev band by subtracting the count rate of the undisturbed hot halo from that toward the disturbed gas . vertical sight lines throughout the domain are sampled . at 16 myr , the brightest x - ray excess is @xmath152 counts s@xmath3 arcmin@xmath48 . at 30 myr , it is @xmath153 counts s@xmath3 arcmin@xmath48 . the latter is the brightest rate for model a1 at any time . note that these are intrinsic count rates ; absorption by @xmath154 cm@xmath48 would decrease them by factors of @xmath155 . even without absorption , the small count rate enhancements would be inconspicuous against the diffuse x - ray background . the timescale for the growth of the kelvin - helmholtz instabilities decreases as the cloud falls and the density contrast between the cloud and the ambient gas decreases . for the last @xmath156 myr of the simulation , we estimate that the timescale for the growth of instabilities is @xmath157 myr , from @xcite section 101 , and assuming that instabilities grow on similar timescales in plane parallel geometries as in our geometry . hence , the lack of x - rays due to turbulent mixing in our simulations is unlikely to be due to the instabilities having insufficient time to grow . models that simulate a larger ambient temperature ( models a4 and a11 ) , a greater ambient pressure ( models a5 and a11 ) , faster initial speeds ( models a2 , a8 , a9 , and a10 ) , denser clouds ( model a11 ) , less dense clouds ( models a3 and a10 ) , and nonzero magnetic fields ( models a6 and a7 ) were also simulated . of the slow models ( initial @xmath158 km s@xmath3 ) the greatest x - ray enhancement seen anywhere in the domain at any time during the simulations is @xmath159 counts s@xmath3 arcmin@xmath48 . this occurred in model a11 at 30 myr , just before the cloud crossed the domain s lower boundary . the next brightest model was model a4 , with a peak enhancement of @xmath160 counts s@xmath3 arcmin@xmath48 at 30 myr , also just before the cloud crossed the domain s lower boundary . models a4 and 11 have the largest ambient gas temperature ( @xmath161 k ) and , through most of the domain , have the largest ambient density of all of the case a models . these attributes prime models a4 and 11 to be bright ; the hotter ambient medium produces hotter mixed gas , while the denser ambient and cloud gas produce denser mixed gas than the other models . although model a11 is within a factor of a few of being comparable with x - ray observations , suggesting that further adjustment of the model parameters could result in a sufficiently bright model , the parameters in model a11 are already near reasonable limits . some of the fast models ( initial @xmath162 or 400 km s@xmath3 ) create brighter disturbances . model a9 , for example , has a peak enhancement of @xmath163 counts s@xmath3 arcmin@xmath48 at 8 myr , which is the last epoch before the cloud leaves the domain . the bright region is fairly extended , with a radius of 740 pc ( with the cut off being defined where the count rate exceeds the background by 5@xmath164 ) over which the count rate averages @xmath165 counts s@xmath3 arcmin@xmath48 . while an excess of this magnitude and spatial extent may be observable , it is not due to turbulent mixing . it is due to the shock . likewise , the shock in model a8 created a bright region , whose maximum average brightness was @xmath166 counts s@xmath3 arcmin@xmath48 over a 200 pc radius footprint at 10 myr , the last epoch before the cloud left the grid . again , the x - rays are due to the shock , not the mixed material . here we consider the dynamics of the mixed gas and how they lead to x - ray dimness . although our models develop a mixed zone , as expected , and although the mixed zone contains some hot gas , in several models ( a1 - a3 and a5 - a10 ) too little of the mixed gas was sufficiently hot ( i.e. , @xmath167 nearing @xmath57 k ) to be x - ray emissive and even when the temperature was sufficiently high , as it was in models a4 and a11 , the mixed gas fell behind the clouds into the semi - vacuum created by the cloud s passage . here the density was not sufficient for great emissivity . model a11 provides an example of the varying conditions and low pressure in the ablated material ( see figure [ fig : cloudwithears ] ) . within the trailing stream the temperature and density vary from hot ( @xmath168 k ) but diffuse ( stream density @xmath169 of the density in the undisturbed halo gas at this height ) near the surface of the stream to only mildly hot ( @xmath170 k ) but denser ( stream density @xmath171 of the density in the undisturbed gas ) in the core . the pressures in these example locations are @xmath172 those of the ambient gas . the enhancement due to turbulent mixing by a single cloud is modest when compared with the typical x - ray count rate for high latitude sight lines . scattered clouds may contribute unidentifiably to the soft x - ray background and multiple , aligned clouds could create a non - negligible x - ray surface brightness . however , obtaining bright x - rays from individual clouds requires fast speeds as discussed in the preceding section . like the suites of ba , br , and c models , the suite of a models radiates more prolifically in the uv than in the x - ray . the broadband spectra are several orders of magnitude brighter in the far uv than in the soft x - ray . the ultimate source of this energy is the reservoir of thermal energy in the hot ambient gas . mixing with the ablated cloud material has lowered the temperature and ionization level of the neighboring hot gas such that it has become highly emissive , especially in the uv . + to the observer who looks straight upwards at an incoming hvc , the x - ray bright region would extend for at least 200 pc from the center of the cloud , thus 400 pc in diameter . if the observer is not located directly beneath the cloud , then the bright region would be somewhat displaced from the cloud itself and would subtend a smaller angle in the direction along the cloud s motion . if the clouds were as far away as complex c , which is located @xmath173 kpc from earth , then the 400 pc diameter x - ray bright footprint due to a single cloudlet would subtend only a 2 angle . such a small feature can not be easily examined with _ rosat _ all sky survey ( rass ) data . however , the overlapping footprints of many bright clouds in an ensemble , could create an extended x - ray bright region that should be compared with the rass maps . if complex c is composed of such an ensemble , then we can estimate the average 1/4 kev count rate across the complex . here we examine the cases in which the x - rays result from shock heating by assuming that the individual clouds within complex c are like model ba3 or br3 clouds ; faster models would result in greater x - ray count rates while slower models or more cooling would result in lower count rates . any gas that was ablated from the clouds and mixed with the ambient medium would also be dim . the expected count rate is a product of the count rate of a single cloud when viewed from below ( @xmath174 ) , the number of such clouds ( @xmath175 ) , and a scaling factor ( @xmath176 ) that accounts for the dilution of the surface brightness over the larger area of complex c. for model ba3 , at its brightest epoch , the average 1/4 kev surface brightness , @xmath174 , within a circular extraction region of radius 400 pc ( this is twice as large as the previously mentioned extraction region , in order to capture more of the photons ) is 3600 @xmath115 counts s@xmath3 arcmin@xmath48 in the _ rosat _ r12 band . in model br3 , the emission is dimmer , but more concentrated . the surface brightness in the _ rosat _ r12 band for a 200 pc radius footprint is 560 @xmath115 counts s@xmath3 arcmin@xmath48 . the number of individual clouds is the ratio of complex c s mass ( @xmath177 m@xmath178 , @xcite ) to the initial mass of one model ba3 or br3 cloud ( @xmath179 m@xmath178 ) , thus @xmath175 is @xmath180 . if the area of each model extraction region , @xmath181 pc)@xmath182 for model ba3 and @xmath183 pc)@xmath182 for model br3 , were to be diluted so as to encompass complex c , whose area is @xmath184 kpc @xmath185 15 kpc @xcite , then conservation of luminosity would require the average count rate of each cloud to be reduced by a factor of @xmath186 . not only does this factor account for dilution , but it also accounts for the concentration of the x - rays when the viewing angle results in a foreshortened cross section . combining @xmath174 , @xmath175 , and @xmath176 yields a theoretical intrinsic r12 count rate of @xmath187 counts s@xmath3 arcmin@xmath48 for the case in which the clouds are like those in model ba3 and @xmath188 counts s@xmath3 arcmin@xmath48 when they are like model br3 . attenuation by intervening material will reduce the count rate . assuming that @xmath154 cm@xmath48 , which is the typical column density of galactic gas in the directions toward the brighter parts of complex c , @xmath189 to @xmath190 of the original photons will be absorbed or scattered before reaching the observer . thus , the observer would see an average cloud - induced x - ray surface brightness of @xmath191 counts s@xmath3 arcmin@xmath48 from a complex of model ba3 clouds . this is a significant enhancement , though not as large as that seen along some directions in the region of complex c ( see figure [ fig : complexcmap ] ) . for a complex of model br3 clouds , the predicted count rate is @xmath192 counts s@xmath3 arcmin@xmath48 , which is negligible . irrespective of the cooling rate , faster clouds would result in brighter x - rays . the magellanic stream provides another point of comparison . @xcite report an enhancement of 0.4 to 1.0 kev x - rays on the leading side of the ms30.7 - 81.4 - 118 cloud within the magellanic stream . with the _ xmm - newton _ pn detector , they found an excess of @xmath47 counts ks@xmath3 arcmin@xmath48 . this is a @xmath193 effect . ( @xcite also found an excess in their _ chandra _ data , but at the @xmath194 level . ) the bright region is roughly 6 arcmin across , equating to roughly 90 pc in width . here , we compare with the count rates for 100 pc wide circular footprints from our models ba3 , ba4 , br3 and br4 , which , with velocities of 300 and 400 km s@xmath3 , bracket the stream velocity ( roughly 380 km s@xmath3 , @xcite ) . our non - radiative models , models ba3 and ba4 , produce 0.25 and 3.2 counts ks@xmath3 arcmin@xmath48 at their brightest epochs ( 6 and 4 myr , respectively ) , thus bracketing the observed value . meanwhile , our radiative models , models br3 and br4 produce only @xmath195 and 0.42 counts ks@xmath3 arcmin@xmath48 at their brightest epochs ( 1.16 and 0.92 myr , respectively ) . only the faster non - radiative model is within range of the magellanic stream observations . thus , collisions between fast hvc gas and relatively dense warm gas can account for the observed x - rays , but do so more easily if the radiation rate is quenched and/or the cloud is moving very fast . as shown in figure [ fig : ovii_oviiicolden ] , our faster model ba simulations yield o column densities of @xmath196 cm@xmath48 . this is similar to the median column density for sight lines through the galactic halo ( @xcite , excluding sight lines through the galactic center soft x - ray enhancement ) , but is also of the same order of magnitude as the sight line - to - sight line variation in observed values . thus , in the absence of radiative cooling , hvc - shocked gas might be observable with future , high resolution instrumentation that could distinguish fast - moving from slow - moving ions . again , if the shock - heated gas cooled at the cie rate , then far fewer o ions would result , making the region unobservable . + in order to examine the effects of computational resolution we calculate additional versions of models ba3 , 4 , 5 , and 6 and model br3 using lesser and greater numbers of refinement levels than in the foregoing simulations , i.e. , in flash , we use lrefine@xmath197max = 4 and 6 , for the additional model ba3 , 4 , 5 , and 6 simulations , rather than the value of 5 used in the primary simulations discussed in previous sections of the paper . we follow a similar pattern for comparison with the moderate resolution model br3 simulations , but also use lrefine@xmath197max = 5 and 6 when making simulations for comparison with the high resolution model br3 simulations , which used lrefine@xmath197max = 7 . we find that within this range , the refinement level does not affect the timescale on which the clouds fragment , although it does affect the shapes of the clouds and of the x - ray bright regions . in order to compare the x - ray productivities of the various simulations , we extract the 1/4 kev x - ray count rates within circular regions of radius equal to 400 pc for the case ba simulations and 200 pc for the comparisons with the case br simulations . ( we set the footprints for the case ba simulations to be greater than those used in earlier parts of this paper in order to capture all or nearly all of the downward directed flux . ) we extract these count rates from every epoch in the model ba4-like simulations , every epoch from the model br3-like simulations that were made for comparison with the primary moderate resolution model br3 simulation , every epoch from the simulations that were made for comparison with the high resolution model br2 , 3 , and 4 simulations , and the @xmath198 myr epoch from the model ba3 , 4 , 5 , and 6-like simulations . we then compare our resolution experiment simulations with the control simulations having the same initial cloud velocity . the x - ray count rates vary somewhat between our test simulations , but in almost all cases are within @xmath199 of that of the relevant control simulation . frequently , they are much closer to those of the control simulations . we also examined 2-dimensional cylindrically symmetric simulations using maximum refinement levels of 4 , 5 , 6 , 7 , and 8 . the principle advantage of this configuration is that it allows much smaller zone sizes . the principle disadvantage is that 2-d simulations are not able to track azimuthal instabilities @xcite . lacking azimuthal modulation , the cloud material concentrates along the symmetry axis and resists fragmentation until later times than in the 3-d simulations . in general , the 2-dimensional simulations predict similar x - ray count rates as the 3-dimensional simulations , but with greater variation between runs having different refinement levels .

/ s are required . if cooling is quenched , then the shock - heated ambient gas is x - ray emissive , producing bright x - rays in the 1/4 kev band and some x - rays in the 3/4 kev band due to o and other ions . the predicted count rates for the non - radiative case are bright enough to explain the count rate observed with _ xmm - newton _ toward a magellanic stream cloud and some enhancement in the _ rosat _ 1/4 kev count rate toward complex c , while the predicted count rates for the fully radiative case are not . in the second scenario , the mixed zone can contain hot gas , but the hot portion of the mixed gas is not as bright as those from the shock - heating scenario .

with the goal of understanding why x - rays have been reported near some high velocity clouds , we perform detailed 3 dimensional hydrodynamic and magnetohydrodynamic simulations of clouds interacting with environmental gas like that in the galaxy s thick disk / halo or the magellanic stream . we examine 2 scenarios . in the first , clouds travel fast enough to shock - heat warm environmental gas . in this scenario , the x - ray productivity depends strongly on the speed of the cloud and the radiative cooling rate . in order to shock - heat environmental gas to temperatures of k , cloud speeds of km / s are required . if cooling is quenched , then the shock - heated ambient gas is x - ray emissive , producing bright x - rays in the 1/4 kev band and some x - rays in the 3/4 kev band due to o and other ions . if , in contrast , the radiative cooling rate is similar to that of collisional ionizational equilibrium plasma with solar abundances , then the shocked gas is only mildly bright and for only about 1 myr . the predicted count rates for the non - radiative case are bright enough to explain the count rate observed with _ xmm - newton _ toward a magellanic stream cloud and some enhancement in the _ rosat _ 1/4 kev count rate toward complex c , while the predicted count rates for the fully radiative case are not . in the second scenario , the clouds travel through and mix with hot ambient gas . the mixed zone can contain hot gas , but the hot portion of the mixed gas is not as bright as those from the shock - heating scenario .

1207.0181

i

for investigating the pion - exchange and nucleon fermi - motion effects on the dy process in proton - deuteron(@xmath2 ) reactions , we have derived convolution formula starting with a nuclear model within which the deuteron has @xmath0 and @xmath1 components . the nucleon fermi motion is included by the convolution of pdfs of the nucleon over the nucleon momentum distribution calculated from the @xmath0 component . the contribution from the @xmath1 component is expressed in terms of a convolution of pdfs of the pion over a pion momentum distribution that depends sensitively on the @xmath1 form factor . with a @xmath1 form factor determined by fitting the @xmath3 scattering data up to invariant mass @xmath4 1.3 gev , we find that the pion - exchange and nucleon fermi - motion effects can change significantly the ratios between the proton - deuteron and proton - proton dy cross sections @xmath5 in the region where the partons emitted from the target deuteron are in the bjorken @xmath6 region . the calculated ratios @xmath7 at 800 gev agree with the available data . for analyzing the forthcoming data from fermilab , we also have made predictions at 120 gev . we would like to thank donald geesaman , roy holt , and jen - chieh peng for their very helpful discussions . this work is supported by the u.s . department of energy , office of nuclear physics division , under contract no . de - ac02 - 06ch11357 . hk acknowledges the support by the hpci strategic program ( field 5 `` the origin of matter and the universe '' ) of ministry of education ( japan ) . this research used resources of the national energy research scientific computing center , which is supported by the office of science of the u.s . department of energy under contract no . de - ac02 - 05ch11231 , and resources provided on `` fusion , '' a 320-node computing cluster operated by the laboratory computing resource center at argonne national laboratory .

is expressed in terms of a pion momentum distribution that depends sensitively on the form factor . with a form factor determined by fitting the scattering data up to invariant mass 1.3 gev , we find that the pion - exchange and nucleon fermi - motion effects can change significantly the ratios between the proton - deuteron and proton - proton drell - yan cross sections , , in the region where the partons emitted from the target deuteron are in the bjorken region . the calculated ratios at 800 gev agree with the available data . predictions at 120 gev for analyzing the forthcoming data from fermilab are presented .

within a nuclear model that the deuteron has and components , we derive convolution formula for investigating the drell - yan process in proton - deuteron ( ) reactions . the contribution from the component is expressed in terms of a pion momentum distribution that depends sensitively on the form factor . with a form factor determined by fitting the scattering data up to invariant mass 1.3 gev , we find that the pion - exchange and nucleon fermi - motion effects can change significantly the ratios between the proton - deuteron and proton - proton drell - yan cross sections , , in the region where the partons emitted from the target deuteron are in the bjorken region . the calculated ratios at 800 gev agree with the available data . predictions at 120 gev for analyzing the forthcoming data from fermilab are presented .

1212.1486

i

the power - law temporal decays displayed by the radio , optical , and x - ray fluxes of grb afterglows ( @xmath8 ) have provided strong support for the prediction ( meszaros & rees 1997 ) that afterglows arise from the relativistic blast - wave generated as the grb outflow ejecta interacts with the ambient medium . if the grb outflow is a collimated jet then a break in the smooth power - law decay of the afterglow is expected for both either a conical jet ( panaitescu , meszaros & rees 1998 ) or a sideways - spreading jet ( by rhoads 1999 ) . the breaks found in the flux decay light curves of most of the well - sampled afterglows that were localized by the bepposax satellite seemed to provide solid observational support for the existence of these predicted jet - breaks ( e.g. frail et al 2001 ) . it was also realized early on that there should be a substantial diversity in the steepness of the afterglow flux decay , even when the spectral slope is constant , if the fundamental forward - shock parameters vary as the shock traverses the ambient medium . rees & meszaros ( 1998 ) derived the expected power - law flux decay for the forward - shock synchrotron flux in the case of an outflow whose kinetic energy - per - solid angle @xmath9 is not constant in time , either because the shock s energy increases due to fresh ejecta arriving at the blast - wave or because @xmath9 is anisotropic . two important microphysical parameters ( @xmath10 and @xmath11 ) , which quantify the fraction of the post - shock energy acquired by electrons and magnetic field , also determine the intensity the afterglow synchrotron flux , and their variability could also yield a variety of decay indices @xmath12 . swift measurements of grb x - ray afterglows provide support for that shock parameters vary . the standard forward - shock model with constant energy and shock micro - parameters predicts a closure relation between the temporal decay index @xmath12 and the slope @xmath13 of the x - ray continuum ( @xmath14 ) of the form @xmath15 . the early x - ray flux of some swift afterglows decays slower than expected for the measured spectral slope @xmath13 , which was attributed to a variable kinetic energy of the forward shock ( nousek et al 2006 , panaitescu et al 2006 , zhang et al 2006 ) . moreover , the flux decay indices @xmath12 displayed by swift x - ray afterglows after the slow decay phase are not correlated with the x - ray spectral slope @xmath13 ( panaitescu 2007 ) , as would be expected from the @xmath16 closure relation for the forward - shock emission . when optical light - curves are taken into account , the standard jet model fares even worse , being inconsistent with practically all swift afterglows ( liang et al 2008 ) . while more than half of the well - sampled optical afterglows display coupled optical and x - ray light - curves ( panaitescu & vestrand 2011 ) , exhibiting similar flux decay indices and/or simultaneous light - curve breaks , many other afterglows show a decoupling of their optical and x - ray light - curves , with a light - curve break occurring only in the x - ray . at least four possibilities for this light - curve decoupling , which is not predicted by the standard jet model , have been proposed : @xmath17 ) the x - ray afterglow emission arises occasionally from the same not - yet - understood mechanism which produces the prompt burst emission ( ghisellini et al 2007 ) , @xmath18 ) there is a dominant contribution of the reverse - shock to the afterglow emission ( uhm & beloborodov 2007 ) , @xmath19 ) the forward - shock emission is reprocessed by bulk - scattering and/or inverse - compton scattering outside the forward - shock ( panaitescu 2008 ) , or @xmath20 ) the optical and x - ray afterglow flux arise from different parts of the forward - shock , from different jets ( e.g. racusin et al 2008 ) . in this work , _ we assume that swift x - ray afterglows arise from the forward - shock _ , and attribute the failure of the standard jet model in accounting for the x - ray flux decay indices to the assumption that the forward shock energy is constant . evolving micro - physical parameters ( e.g. ioka et al 2006 ) could , in principle , explain the measured x - ray flux decay indices , but the existence of light - curve breaks requires an unnatural , sudden change in their evolution . for that reason , we maintain in this work the basic assumption of the standard jet model that micro - physical parameters do not evolve . we also assume that the ambient medium with which the post - grb outflow interacts is uniform , without discontinuities that could yield breaks in the afterglow light - curve at a frequency . a notable model thus excluded is that where the afterglow - producing outflow interacts with a prior outflow ( ioka et al 2006 ) whose density increases radially outward up to its termination shock , yielding a slower decay of the afterglow flux than expected for a homogeneous ambient medium , followed by a break to a steeper decay . one reason for relaxing the constant shock energy constraint is the observational evidence for x - ray flares in swift afterglows ( e.g. chincarini et al 2007 ) . the short timescale of those flares indicates that the grb progenitor produces relativistic ejecta after the burst phase , whose arrival at the decelerating forward - shock could increase substantially the blast - wave s energy . our hypothesis is that such an injection of energy in the forward - shock is , in general , a more persistent and continuous process . however , we note that the fluence of x - ray flares is about 10 percent that of the burst ( falcone et al 2007 ) , hence the late outflow powering the flares could carry a dynamically - important energy only if that outflow is much less efficient than the grb outflow in producing x - ray emission . we derive in [ anal ] the closure relations @xmath16 for a continuous energy injection in the forward - shock . for the ease of extracting from observations the required injected power history , we assume that the forward - shock energy increases as a power with observer - time , @xmath21 , which is motivated by that the resulting afterglow flux should be power - law in observer time . this assumption circumvents a calculation of the kinematics for the ejecta forward - shock interaction . in [ swift ] , the closure relations for the forward - shock emission with energy injection are applied to a set of swift afterglows with well sampled light - curves . there , we examine two plausible scenarios for the origin of afterglow x - ray light - curve breaks ( break in energy injection , jet - break ) , three dynamical regimes of the forward - shock ( spherical expansion , conical jet , spreading jet ) , and two radiation processes that may yield the afterglow x - ray flux ( synchrotron , inverse - compton ) .

has been proposed most often to be the reason for the x - ray afterglow complexity . we examine 117 light - curve breaks of 98 swift x - ray afterglows , selected for their high - quality monitoring and well - constrained flux decay rates . thirty percent of afterglows have a break that can be an adiabatic jet - break , in the sense that there is one variant of the forward - shock emission from a collimated outflow model that can account for both the pre- and post - break flux power - law decay indices , given the measured x - ray spectral slope . that anticorrelation can also be seen as bursts with a higher energy output being followed by faster fading x - ray afterglows . to test the above two mechanisms for afterglow light - curve breaks , 8 c 51 52 53 54 ii o radiation mechanisms : non - thermal , relativistic processes , shock waves , gamma - ray bursts , ism : jets and outflows

+ since its launch in 2004 , the swift satellite has monitored the x - ray afterglows of several hundred gamma - ray bursts , and revealed that their x - ray light - curves are more complex than previously thought , exhibiting up to three power - law segments . energy injection into the relativistic blast - wave energizing the burst ambient medium has been proposed most often to be the reason for the x - ray afterglow complexity . we examine 117 light - curve breaks of 98 swift x - ray afterglows , selected for their high - quality monitoring and well - constrained flux decay rates . thirty percent of afterglows have a break that can be an adiabatic jet - break , in the sense that there is one variant of the forward - shock emission from a collimated outflow model that can account for both the pre- and post - break flux power - law decay indices , given the measured x - ray spectral slope . if allowance is made for a steady energy injection into the forward - shock , then another 56 percent of x - ray afterglows have a light - curve break that can be explained with a jet - break . the remaining 12 percent that are not jet - breaks , as well as the existence of two breaks in 19 afterglows ( out of which only one can be a jet - break ) , suggest that some x - ray breaks arise from a sudden change in the rate at which energy is added to the blast - wave , and it may well be that a larger fraction of x - ray light - curve breaks are generated by that mechanism . the fractional increase in the shock energy , inferred from the energy injection required to account for the observed x - ray flux decays , may be anticorrelated with the grb prompt output , whether the x - ray break is a jet - break or an energy - injection break . that anticorrelation can also be seen as bursts with a higher energy output being followed by faster fading x - ray afterglows . to test the above two mechanisms for afterglow light - curve breaks , we derive comprehensive analytical results for the dynamics of outflows undergoing energy injection and for their light - curves , including closure relations for inverse - compton afterglows and for the emission from spreading jets interacting with an wind - like ambient medium . + + 2 3 4 8 c 51 52 53 54 ii o radiation mechanisms : non - thermal , relativistic processes , shock waves , gamma - ray bursts , ism : jets and outflows

1212.1486

c

by comparing the flux decay index ( @xmath12 ) with the spectral slope ( @xmath13 ) measured for a set of 98 well - sampled swift x - ray afterglows with the expectations for the forward - shock model , we find that about a third of those afterglows display a break that could be the traditional ` jet - break ' claimed to have been observed in a dozen pre - swift optical afterglows ( [ adb ] ) . for this test of _ adiabatic _ jet - breaks , we have considered various details of the forward - shock model : homogeneous or wind - like ambient media , spectral cooling frequency higher or lower than the x - rays , synchrotron or inverse - compton as the dominant x - ray process , a collimated conical or spreading outflow . if a steady energy injection into the forward - shock occurs , then the jet - break model may account for 88 percent of the 117 light - curve breaks or , else put , for at least one break in 87 percent of the 98 afterglows selected here ( [ jbei ] ) . this vast improvement over the adiabatic jet model suggests that energy injection could be a prevalent process in grb afterglows . the remaining 12 percent of breaks that can not be explained by a jet - break undergoing a steady energy injection , and the 19 afterglows with two breaks ( only one being , at most , a jet - break ) , indicate that some x - ray breaks may originate from a change in the rate at which energy is added to the forward - shock ( an energy - injection break ) , and it is possible that some ( many ? ) of the identified jet - breaks are also energy - injection breaks ( [ eibr ] ) . it should be recognized that the complete success of the energy - injection break model over the traditional jet - break model could be due mostly to that the latter model is over - constrained ( observations provide two constraints : flux pre- and post - break power - law decay indices for one model parameter : the energy injection power - law exponent ) , while the former model is not . we find a tentative correlation between the grb output and the afterglow x - ray flux decay rate , more energetic bursts being followed by faster decaying afterglows ( [ fag ] ) . if energy injection is a common process in grb afterglows , then the slower decaying afterglows should be identified with a stronger total energy injection . this means that the grb energy afterglow ( x - ray flux ) decay rate correlation should lead to an anticorrelation of the grb output with the increase of the outflow kinetic energy during the afterglow phase , i.e. more energetic bursts should be followed by afterglows with less energy being injected . this anticorrelation is , indeed , observed for both the jet - break and the energy injection break models for x - ray light - curve breaks , and for various model details ( dynamics , x - ray afterglow emission process , radial stratification of the ambient medium ) . if the grb progenitor is a long - lived source of relativistic ejecta , the above anticorrelation implies an anticorrelation of the kinetic energy of the leading outflow ( producing the burst ) with that of the following ejecta ( which inject energy in the blast - wave during the afterglow phase ) , but the total ejecta energy ( burst plus afterglow ) is far from being universal . the energy budget required by most of the possible variants of the forward - shock model ranges from @xmath294 to @xmath295 ergs , and only variants involving inverse - compton emission in the x - rays and a wind - like medium can be excluded on energetic grounds because , in those models , the required jet - energy exceeds @xmath296 erg ( [ jeten ] ) . considering both models for light - curve breaks ( jet - break with steady energy - injection and energy - injection break ) , we find that the most energetically economical model is that of a narrow jet whose jet - break occurs early on ( before first x - ray measurement ) with the light - curve break being an energy - injection break , followed by a model where the x - ray light - curve break is a jet - break , with the most `` wasteful '' model being that of a wide jet whose break occurs late ( after last x - ray measurement ) , the x - ray break being an energy - injection break . however , the average ( over afterglows ) energy ratio among pairs of these three break models is only 23 .

the remaining 12 percent that are not jet - breaks , as well as the existence of two breaks in 19 afterglows ( out of which only one can be a jet - break ) , suggest that some x - ray breaks arise from a sudden change in the rate at which energy is added to the blast - wave , and it may well be that a larger fraction of x - ray light - curve breaks are generated by that mechanism . the fractional increase in the shock energy , inferred from the energy injection required to account for the observed x - ray flux decays , may be anticorrelated with the grb prompt output , whether the x - ray break is a jet - break or an energy - injection break .

+ since its launch in 2004 , the swift satellite has monitored the x - ray afterglows of several hundred gamma - ray bursts , and revealed that their x - ray light - curves are more complex than previously thought , exhibiting up to three power - law segments . energy injection into the relativistic blast - wave energizing the burst ambient medium has been proposed most often to be the reason for the x - ray afterglow complexity . we examine 117 light - curve breaks of 98 swift x - ray afterglows , selected for their high - quality monitoring and well - constrained flux decay rates . thirty percent of afterglows have a break that can be an adiabatic jet - break , in the sense that there is one variant of the forward - shock emission from a collimated outflow model that can account for both the pre- and post - break flux power - law decay indices , given the measured x - ray spectral slope . if allowance is made for a steady energy injection into the forward - shock , then another 56 percent of x - ray afterglows have a light - curve break that can be explained with a jet - break . the remaining 12 percent that are not jet - breaks , as well as the existence of two breaks in 19 afterglows ( out of which only one can be a jet - break ) , suggest that some x - ray breaks arise from a sudden change in the rate at which energy is added to the blast - wave , and it may well be that a larger fraction of x - ray light - curve breaks are generated by that mechanism . the fractional increase in the shock energy , inferred from the energy injection required to account for the observed x - ray flux decays , may be anticorrelated with the grb prompt output , whether the x - ray break is a jet - break or an energy - injection break . that anticorrelation can also be seen as bursts with a higher energy output being followed by faster fading x - ray afterglows . to test the above two mechanisms for afterglow light - curve breaks , we derive comprehensive analytical results for the dynamics of outflows undergoing energy injection and for their light - curves , including closure relations for inverse - compton afterglows and for the emission from spreading jets interacting with an wind - like ambient medium . + + 2 3 4 8 c 51 52 53 54 ii o radiation mechanisms : non - thermal , relativistic processes , shock waves , gamma - ray bursts , ism : jets and outflows

hep-lat0403005

i

a direct calculation of multi - nucleon processes such as @xmath55 is impossible on a euclidean space lattice . as briefly mentioned in the introduction , the obstruction is the maiani - testa theorem @xcite which precludes the calculation of s - matrix elements away from kinematic thresholds in an infinite volume . in principle however , by performing lattice calculations of matrix elements of the relevant electroweak operators at unphysical kinematics in appropriate multi - nucleon states , e.g. , @xmath56 , the undetermined coefficients of the low - energy eft ( modified to accommodate the injection of energy by the lattice ) can be determined , leading to an _ ab initio _ calculation of the low - energy dependence of the process in question . unfortunately , by present day standards , calculation of such five - point correlators is prohibitively expensive in computational terms . in order to do such a calculation , the two - nucleon ( six quark ) sources and sinks and the electroweak current operator must be tied together with quark propagators in all possible ways and the corresponding contributions averaged over the ensemble of gauge configurations . naively , this is one or two orders of magnitude more difficult than computing the nn four - point correlator . clearly , a more cost - effective solution to this problem is desired we will show that calculations of electroweak processes , such as @xmath57 and @xmath58 , will be feasible in the near future . our method is to some extent motivated by the earliest lattice calculations of the magnetic moments of the proton and neutron . modern calculations of these quantities are performed by taking nucleon matrix elements of the electromagnetic current operator . however , in the early days of lattice qcd , calculations of nucleon matrix elements were computationally prohibitive ( just as multi - nucleon matrix elements are today ) and the magnetic moments were first extracted by measuring the shift in the nucleon mass when the lattice is immersed in a background magnetic field @xcite . taking the magnetic field to be constant and aligned along the @xmath59-direction , @xmath60 the nucleon masses are shifted , e.g. the mass of a proton with spin aligned in the direction of the field is @xmath61 however , it is the energy of the nucleon that is measured on the lattice , and when immersed in a background magnetic field the energy eigenstates of the proton in an infinite volume are @xmath62 where @xmath63 is an integer denoting the landau - level occupied by the proton , and @xmath64 is the momentum of the proton parallel to the magnetic field . for weak magnetic fields , the spin - dependent energy - splitting is proportional to the magnetic moment of the proton , @xmath65 , while for stronger fields the magnetic polarizability , @xmath66 becomes significant and measurable @xcite . to be complete we note that by using background electric fields , electric polarizabilities @xcite and the electric dipole moment of the nucleon @xcite have been investigated . to apply a spatially constant background magnetic field aligned in the @xmath59-direction in a lattice simulation , one takes a su(3 ) gauge - configuration and modifies the link fields by @xmath67 with @xmath68 where @xmath69 is proportional to @xmath70 where @xmath71 is the lattice spacing , throughout . ] . a vector potential with periodic boundary conditions in the transverse directions requires that @xmath72 , where @xmath73 is the transverse area of the box . this requirement generates large magnetic fields for present day lattices @xcite , large enough to shift the nucleon mass by @xmath74 , and thus too strong to be described by @xmath4 . not requiring periodic boundary conditions on the vector potential introduces an exceptional plaquette that can be placed wherever it does the least `` harm '' in the single nucleon case @xcite . it remains to be seen if this plaquette can be placed somewhere to have minimal impact on multi - nucleon simulations or if the periodic requirement must be enforced . for the weak interactions , and in particular for an axial - vector interaction , the left- and right - handed quarks need to be immersed in different background fields . one way to implement this is to use domain - wall ( kaplan @xcite ) fermions in the simulation and have the background field vary only in the fifth dimension . a background axial field was used in the first lattice calculation of the axial coupling of the nucleon @xcite . by applying such background electroweak fields to nucleons in a finite volume , the energy - levels become sensitive to the various one- and two - nucleon electroweak current operators that contribute to the deuteron properties and interactions , such as @xmath57 , @xmath58 and other related electroweak processes . it is interesting to note that lattice calculations of the energy - levels relevant to the deuteron magnetic ( or weak ) moment ( isoscalar operator ) will be more difficult than those impacting isovector processes as they require the evaluation of disconnected diagrams ( where the operator does not connect to valence quarks ) which are significantly harder to compute , even in the single nucleon sector @xcite . as we will discuss later , it will be necessary to work with asymmetric volumes of dimensions @xmath75 the energy - levels of two - particles in an asymmetric volume have been discussed recently @xcite and we review this analysis and extend a number of relevant aspects in appendix [ app : one ] . it is straightforward to show that the locations of the low - lying energy - levels of two - nucleons interacting in an s - wave on an asymmetric lattice are given by the solutions of @xcite @xmath76 where @xmath77 uniquely describes the infinite - volume s - wave scattering amplitude below inelastic thresholds . the function @xmath78 is given by @xmath79 where @xmath80 , and the limits of the linearly - divergent , three - dimensional sum are given by the ellipsoid @xmath81 . the energy corresponding to a given value of @xmath82 is @xmath83 given the behavior of two - nucleon energy - levels as a function of the volume , the phase shifts ( or at least the first few parameters of the effective range expansion @xmath84 ) can be recovered . to aid in such recovery , one can find analytic , large volume ( @xmath85 ) expansions for the locations of the energy - eigenstates , as done by lscher for the case of @xmath86 @xcite and done by li and liu @xcite for the lowest continuum level in asymmetric volumes . we detail this construction in appendix [ app : one ] , and give explicit expressions for the large volume locations of the low - lying levels in the two - nucleon sector . a small @xmath87 expansion of eq . ( [ eq : exactee ] ) can also be performed @xcite , though we do not do this here . it is straightforward to extend this analysis of two - nucleon energy - levels to include a background electroweak field . the presence of the background fields can give rise to a number of complications such as landau - levels and mixing of two - nucleon states of differing total spin and isospin . for this reason we shall develop the necessary generalizations of the above formulas as we need them . the hamiltonian of a structure - less point particle of charge @xmath37 , moving in a uniform , time - independent magnetic field in the @xmath59-direction is @xmath88 where @xmath89 , and @xmath90 is the angular momentum operator parallel to the magnetic field . in an infinite volume , the energy - eigenvalues are given by the expression in eq . ( [ eq : epup ] ) . however , in a finite volume the oscillator potential is bounded above , and for small enough lattices the potential arising from the magnetic field can be treated as a perturbation . consequently , for a small magnetic field we can work with momentum eigenstates in the transverse direction . requiring that the energy - shifts due to these magnetic interactions are small compared with the inter - level spacing of the two - nucleon momentum eigenstates in the finite volume gives , @xmath91 where @xmath92 is the size of the transverse dimensions . in what follows we work with momentum eigenstates in the transverse directions , and thus are constrained by eq . ( [ eq : llcon ] ) .

the energies of the lowest - lying states of two nucleons on a finite volume lattice with periodic boundary conditions in the presence of a background magnetic field are sufficient to determine the local four - nucleon operators that contribute to the deuteron magnetic moment and to the threshold cross - section of . similarly , the energy - levels of two nucleons immersed in a background isovector axial weak field can be used to determine the coefficient of the leading local four - nucleon operator contributing to the neutral- and charged - current break - up of the deuteron .

0.5 cm we demonstrate how to make rigorous predictions for electroweak matrix elements in nuclear systems directly from qcd . more precisely , we show how to determine the short - distance contributions to low - momentum transfer electroweak matrix elements in the two - nucleon sector from lattice qcd . in potential model descriptions of multi - nucleon systems , this is equivalent to uniquely determining the meson - exchange currents , while in the context of nuclear effective field theory , this translates into determining the coefficients of local , gauge - invariant , multi - nucleon - electroweak current operators . the energies of the lowest - lying states of two nucleons on a finite volume lattice with periodic boundary conditions in the presence of a background magnetic field are sufficient to determine the local four - nucleon operators that contribute to the deuteron magnetic moment and to the threshold cross - section of . similarly , the energy - levels of two nucleons immersed in a background isovector axial weak field can be used to determine the coefficient of the leading local four - nucleon operator contributing to the neutral- and charged - current break - up of the deuteron . this is required for the extraction of solar neutrino fluxes at sno and future neutrino experiments . 1.0 cm -1.5 cm 0.5 cm

1307.0872

i

the utility maximization is a basic problem in mathematical finance . it was introduced by merton @xcite . using stochastic control methods , he exhibits a closed formula for the value function and the optimal proportion - portfolio when the risky assets follow a geometric brownian motion and the utility function is of crra type . + in the literature , many works assume that the underlying model is exactly known . in this paper we consider a problem of utility maximization under uncertainty . the objective of the investor is to determine the optimal consumption - investment strategy when the model is not exactly known . such problem is known as the robust utility maximization and is formulated as @xmath0 where @xmath1 is the @xmath2-expected utility . the investor has to solve a sup inf problem . he considers the worst scenario by minimizing over a set of probability measures and then he maximizes his utility . in the literature there are two approaches to solve the robust utility maximization problems . the first one relies on duality methods such as quenez @xcite or shied and wu @xcite . they considered a set of probability measures called priors and they minimized over this set . the second approach , which is followed in this paper , is based on the penalization method and the minimization is taken over all possible models such as in anderson , hansen and sargent @xcite . moreover skiadas @xcite followed the same point of view and he gave the dynamics of the control problem via bsde in the markovian context . in our case , the @xmath2-expected utility is the sum of a classical utility function and a penalization term based on a relative entropy . in bordigoni @xcite , they proved the existence of a unique @xmath3 optimal model which minimizes our cost function . they used the stochastic control techniques to study the dynamic value of the minimization problem . in the case of continuous filtration , they showed that the value function is the unique solution of a generalized bsde with a quadratic driver . + in faidi , matoussi and mnif @xcite , they studied the maximization part of the problem in a complete market by using the bsde approach as in duffie and skiadas @xcite and el karoui et al . @xcite . + in our paper , we assume that the portfolio is constrained to take values in a given closed convex non - empty subset @xmath4 of @xmath5 . such problem was studied when the underlying model is known by karatzas , lehoczky , shreve and xu @xcite in the incomplete market case and then by cvitanic and karatzas @xcite for convex constraints on the portfolio . skiadas and schroder @xcite studied the lifetime consumption - portfolio recursive utility problem under convex trading constraints . they used the utility gradient approach . they derived a first order conditions of optimality which take the form of a constrained forward backward stochastic differential equation . wealth was computed in a recursion starting with a time - zero value forward in time , while utility was computed in a recursion starting with a terminal date value backward in time . in our context , we study the robust formulation of the consumption - investment utility problem under convex constraints on the portfolio . using change of measures and optional decomposition under constraints , we give a dual characterization of the admissible consumption investment strategy , then we state an existence result to the optimization problem where the criterion is the solution at time 0 of a quadratic bsde with unbounded terminal condition . to describe the structure of the solution , we use duality arguments . the heart of the dual approach in the classical setting , when the criterion is taken under the historical probability measure , is to find a saddle point for the lagrangian and apply a mini - max theorem in the infinite dimensional case . it is appropriate to use the conjugate function of @xmath6 and @xmath7 . in our case , the criterion is taken under the probability measure modeling the worst scenario and the conjugate function does not appear naturally . we use the duality arguments in a different way . we prove the existence of a probability measure under which the budget constraint is satisfied with equality . then , we derive a maximum principle which gives a necessary and sufficient conditions of optimality . thanks to this result , we give an implicit expression of the optimal terminal wealth and the optimal consumption rate . this later result is a generalization of cvitanic and karatzas @xcite work . + the paper is organized as follows . section 2 describes the model and the stochastic control problem . section 3 is devoted to the existence and the uniqueness of an optimal strategy . in section 4 , we characterize the optimal consumption strategy and the optimal terminal wealth by using duality techniques . in section 5 , we relate the optimal control to the solution of a forward - backward system and we study some examples .

: we study a robust utility maximization problem from terminal wealth and consumption under a convex constraints on the portfolio . we state the existence and the uniqueness of the consumption - investment strategy by studying the associated quadratic backward stochastic differential equation ( bsde in short ) . we characterize the optimal control by using the duality method and deriving a dynamic maximum principle . * key words :* utility maximization , backward stochastic differential equations , recursive utility , model uncertainty , robust control , maximum principle , forward - backward system . * msc classification ( 2000 ) :* 92e20 , 60j60 , 35b50 .

: we study a robust utility maximization problem from terminal wealth and consumption under a convex constraints on the portfolio . we state the existence and the uniqueness of the consumption - investment strategy by studying the associated quadratic backward stochastic differential equation ( bsde in short ) . we characterize the optimal control by using the duality method and deriving a dynamic maximum principle . * key words :* utility maximization , backward stochastic differential equations , recursive utility , model uncertainty , robust control , maximum principle , forward - backward system . * msc classification ( 2000 ) :* 92e20 , 60j60 , 35b50 .

0802.3682

i

during the last years , the field of ultracold few - body confined systems has progressed remarkably . by employing optical dipole traps @xcite and atom chips @xcite it is possible to fabricate mesoscopic structures in which the atoms are freezed to occupy a single or a few lowest quantum states of a confining potential such that in one or more dimensions the characteristic length possesses the order of the atomic debroglie wavelength . these configurations can be well described by effective one - dimensional systems . well - known examples are quantum wires and atom waveguides or quasi two - dimensional systems such as 2d electronic gases . the quantum dynamics of such systems is strongly influenced by the geometry of the confinement . to control the coherent propagation of particle beams through 1d or 2d traps it is crucial to very well understand the impact of the confinement on the collisional properties ( see refs . @xcite and refs.therein ) . free - space scattering theory is no longer valid in such systems and a new theory is needed . this stimulated the development of quantum scattering theory in low dimensions . for a sufficiently dilute gas under a strong transverse confinement , one may expect both the chemical potential and the thermal energy @xmath1 being less than the transverse level spacing . with this assumption , the dynamics of ultracold atoms in low dimensional structures e.g. tight wave guides has been studied using the simplification that the atoms occupy only the ground state of the transverse confining potential . nevertheless , the virtual transverse excitations in the course of the collision process can play a crucial role in the scattering leading to the so - called confinement - induced resonances ( cirs ) , predicted by olshanii @xcite . s - wave zero - energy scattering of bosons is mapped to an effective longitudinal zero - range pseudopotential @xmath2 approximating the 1d atom - atom interaction in a transverse harmonic confinement . it was shown@xcite that cirs appear if the binding energy of the pseudopotential , approximating the two - atom molecular state in the presence of the confinement , coincides with the energy spacing between the levels of the transverse harmonic potential . in the vicinity of the cir the coupling constant @xmath3 can be tuned from @xmath4 to @xmath5 by varying the strength of the confining potential over a small range . this can result in a total atom - atom reflection , thereby creating a gas of impenetrable bosons . cirs have also been studied for the three - body @xcite and the four - body @xcite scattering under confining potential , as well as for a pure p - wave scattering of fermions @xcite . experimental evidence for the cirs for bosons @xcite and fermions @xcite has recently been reported . a general analytical treatment of low - energy scattering under action of a general cylindrical confinement involving all partial waves and their coupling , was first provided in ref.@xcite for a spherically symmetric short - range potential . the effect of the c.m . motion on the s - wave collision of two distinguishable atoms ( i.e. a two - species mixture ) in a harmonic confinement as well as for two identical atoms in a non - parabolic confining potential has been investigated in ref.@xcite in the zero - energy limit neglecting the s and p wave mixing . a detailed study including the effect of the c.m . nonseparability and taking into account the s and p wave mixing for harmonic confinement was performed in the single - mode regime in ref . recently a so - called dual - cir was discovered @xcite , which is characterized by a complete transmission ( suppression of quantum scattering ) in the waveguide due to destructive interference of s and p waves although the corresponding collisions in free space involve strong interactions . the problem of atomic pair collisions under the action of a harmonic trap in the multi - mode regime when the energy of the atoms exceeds the level spacing of the transverse trapping potential is much more intricate than the single - mode regime due to several open transverse channels . it demands the development of a multi - channel scattering theory accounting for the possible transitions between the levels of the confining potential . using as a starting point the formalism for scattering in restricted geometries suggested in refs . @xcite , the multi - channel scattering problem for bosons in a harmonic confining potential has been analyzed analytically by olshanii el al . @xcite in the s - wave pseudopotential approximation and the zero - energy limit . without detailization of the interatomic interaction but using only two input parameters - the s - wave two - body scattering length in free space and the trap frequency - they have derived an approximate formula for the scattering amplitude describing two boson collisions confined by transverse harmonic trap in the multi - mode regime . in the present work we develop a general grid method for multi - channel scattering of identical as well as distinguishable atoms confined by a transverse harmonic trap . the method applies to arbitrary atomic interactions , permitting a rich spectral structure where several different partial waves are participating in the scattering process or even the case of an anisotropy of the interaction . the only limitation is that we consider harmonic traps with a single frequency for every atom causing a separation of the c.m . and relative motion . with our approach we analyze transverse excitations / deexcitations in the course of the collisional process ( distinguishable or identical atoms ) including all important partial waves and their couplings due to the broken spherical symmetry . special attention is paid to the analysis of the cirs in the multi - mode regimes for non - zero collision energies , i.e. , to suggest a non - trivial extension of the cirs theory developed so far only for the single - mode regime and zero - energy limit . in detail we proceed as follows . section ii contains the derivation of the hamiltonian , definitions of the interatomic interaction and the scattering asymptotics in the confined geometry , and a discussion of the scattering parameters and the transition probabilities characterizing the two - body collisions in the trap . our computational method is outlined in sec . iii , important technical details are given in the appendix . in section iv our results are presented and analyzed . a summary and conclusions are given in sec .

[ txt : abstract ] we develop a grid method for multi - channel scattering of atoms in a waveguide with harmonic confinement . collisions of identical bosonic and fermionic as well as distinguishable atoms in harmonic traps with a single frequency permitting the center - of - mass ( c.m . ) separation are explored in depth . in the zero - energy limit and single mode regime

[ txt : abstract ] we develop a grid method for multi - channel scattering of atoms in a waveguide with harmonic confinement . this approach is employed to extensively analyze the transverse excitations and deexcitations as well as resonant scattering processes . collisions of identical bosonic and fermionic as well as distinguishable atoms in harmonic traps with a single frequency permitting the center - of - mass ( c.m . ) separation are explored in depth . in the zero - energy limit and single mode regime we reproduce the well - known confinement - induced resonances ( cirs ) for bosonic , fermionic and heteronuclear collisions . in case of the multi - mode regime up to four open transverse channels are considered . previously obtained analytical results are extended significantly here . series of feshbach resonances in the transmission behaviour are identified and analyzed . the behaviour of the transmission with varying energy and scattering lengths is discussed in detail . the dual cir leading to a complete quantum suppression of atomic scattering is revealed in multi - channel scattering processes . possible applications include , e.g. , cold and ultracold atom - atom collisions in atomic waveguides and electron - impurity scattering in quantum wires .

0802.3682

r

with the above - described method being implemented we have analyzed the two - body scattering under the transverse harmonic confinement for both cases of identical and distinguishable colliding atoms . for confined scattering of identical atoms one has to distinguish the bosonic and fermionic cases . in the case of two colliding bosons the two - body wave function must be symmetric and only even scattering amplitude provides us with a nonzero contribution . first , we show that our result for the special case @xmath159 of a single - channel scattering is in agreement at @xmath160 with the s - wave pseudopotential approach @xcite , and , particularly , reproduces s - wave cir predicted and analyzed in refs . @xcite for bosons . then we extend our consideration to the multi - channel scattering @xmath161 . we demonstrate that our results are in a good agreement in the limit of a long - wavelength trap @xmath162 with the analytical expression given in @xcite which has been obtained in the s - wave pseudopotential approach for the zero - energy limit . the range of validity of the analytical investigation in ref . @xcite is explored . next we present results for multi - channel scattering of two fermions under transverse harmonic confinement . for a fermionic collision the two - body wave function is antisymmetric , i.e. only the odd scattering amplitude is nonzero . in the special case of single - channel scattering we reproduce the p - wave cir for fermions @xcite . these results are also in agreement with our previous investigations in refs.@xcite performed within a wave - packet propagation method @xcite . finally we consider the confined multi - channel scattering of two distinguishable atoms . in this case both even and odd amplitudes contribute to the scattering process . @xmath163{1.jpg}\\ \end{array}$ ] for modeling different interatomic interactions in the subsequent sections we vary the depth @xmath31 of the potential ( [ potential ] ) in the wide range @xmath164 for a fixed width @xmath40 . in free space , this potential being superimposed with the centrifugal term @xmath165 makes an effective potential which may support some _ even _ or _ odd _ bound states depending on the value of the quantum number @xmath166 and the parameter @xmath31 . for @xmath167 there might be also some _ shape resonances _ for certain relative energies . these _ shape resonances _ may enhance strongly the contribution of @xmath167 partial waves in the energy domain where one would have expected a pure @xmath168 scattering . it is known that in the zero - energy limit , when the scattering process does not depend on the details of the potential , the collision can be described by a single parameter : the s - wave scattering length @xmath169 for @xmath168 ( bosonic collision ) and the p - wave scattering volume @xmath170 for @xmath171 ( fermionic collision ) . for sufficiently low collision energy the contribution of the partial waves with larger @xmath166 can be neglected . in fig.[fig1 ] we have plotted @xmath172 and @xmath173 in the region @xmath164 . fig.[fig1 ] demonstrates the rich spectral structure of the chosen form of the interatomic interaction : the scattering parameters @xmath172 and @xmath173 can be positive or negative and they diverge for the values of @xmath31 corresponding to the appearance of new bound states . in the case of p - wave scattering the increase of the depth @xmath31 of the potential first leads to a shape resonance which approaches zero energy and finally transforms to a p - wave bound state . for two bosons colliding in a transverse harmonic confinement the scattering wave function is symmetric with respect to the exchange @xmath174 , i.e. @xmath175 in eq.([full asymptotic wave ] ) . we consider multi - channel scattering with the dimensionless energy @xmath176 ( [ wave vector k ] ) permitting the collisional transverse excitations / deexcitations @xmath177 up to four open channels ( four - mode regime ) . for comparison with analytical results @xcite obtained in the s - wave pseudopotential approach , we have extracted the effective quasi-1d coupling constant @xmath178 as well as the transmission coefficient @xmath179([transmission ] ) and the scattering amplitude @xmath180([full asymptotic wave ] ) , as a function of the scattering length @xmath172 in the single - mode regime ( @xmath181 ) . the calculated parameters are presented along with the analytical results in fig.[fig2 ] for @xmath182 and the longitudinal relative energy @xmath183 . fig.[fig2](a ) shows the coupling constant @xmath3 as a function of the scattering length @xmath172 . our numerical result clearly exhibit a singularity at @xmath184 with @xmath185 , which corresponds to the well - known s - wave cir @xcite . in fig.[fig2](b ) we present the transmission coefficient @xmath156 versus @xmath172 . the transmission coefficient @xmath156 goes to unity ( total transmission ) when @xmath172 tends to zero ( i.e. no interaction between the atoms ) , while at the cir position , it exhibits the well - known minimum ( blocking of the atomic current by the cir ) . fig.[fig2](c ) shows the scattering amplitude @xmath180 as a function of @xmath172 . the amplitude approaches zero at @xmath186 and @xmath187 at the cir position , which results in total transmission and total reflection respectively . in general the presented values of @xmath180 are in very good agreement with the analytical results . @xmath188{2a.jpg } & \includegraphics[height=6cm , width=8cm]{2b.jpg}\\ \includegraphics[height=6cm , width=8cm]{2c.jpg } \\ \end{array}$ ] in the multi - mode regime our results are in good agreement with the analytical ones obtained within the s - wave pseudopotential approach in the zero - energy limit@xcite for long - wavelength traps ( tight confinement : @xmath162 ) . in fig.[fig3 ] we present our scattering amplitude @xmath180 along with the analytical results as a function of the dimensionless energy @xmath58 for @xmath189 and @xmath190 . apart from energies close to the channel thresholds , the real and imaginary part of the scattering amplitude @xmath180 show a monotonous behaviour : @xmath191 is monotonically increasing and approaching zero asymptotically whereas @xmath192 decays monotonically and also approaches zero for large values of @xmath58 . the peak structure located at integer values of @xmath58 is due to the resonant scattering once a new previously closed channel opens with increasing energy . there is a good agreement between our results and the analytical ones given by eq.(6.9 ) in ref . @xcite for the complete range @xmath193 . however , we encounter major deviations with increasing @xmath0 except for narrow regions close to the channel thresholds ( as @xmath58 approaches integer values ) for the real parts of the scattering amplitudes ( see fig.[fig4 ] ) . these deviations are most presumably due to the energy dependence of the s - wave scattering length which is neglected in ref.@xcite . @xmath188{3a.jpg}&\includegraphics[height=6cm , width=8cm]{3b.jpg}\\ \end{array}$ ] @xmath188{4a.jpg } \includegraphics[height=6cm , width=8cm]{4b.jpg}\\ \end{array}$ ] for the multi - channel regime ( @xmath161 ) we find a strong dependence of the total transmission coefficient @xmath156 on the population of the initial state @xmath50 , except for the case @xmath194 of noninteracting bosons in free space . fig.[fig5 ] shows the calculated transmission coefficients([transmission ] ) as a function of @xmath195 for @xmath196 for the ( a ) two - mode regime with @xmath197 and ( b ) the three - mode regime with @xmath198 . note , that all these cases correspond to near - threshold collision energies if the maximal integer is subracted from @xmath58 . similar to the single - mode regime , @xmath156 goes to unity ( total transmission ) when @xmath172 tends to zero . we also encounter a minimum . however , the value of the transmission at the minimum is not zero anymore in the multi - mode regime , the larger the number of open channels , the position of the minima will be more shifted to the left . for a fixed value of the ratio @xmath199 , a lower initially populated transverse level @xmath50 , leads to a larger total transmission . @xmath188{5a.jpg } \includegraphics[height=6cm , width=8cm]{5b.jpg}\\ \end{array}$ ] in fig.[fig6 ] we present the transmission as a function of the dimensionless energy @xmath58 for the two cases of the system being initially in the ground @xmath200 ( a ) or first excited @xmath201 ( b ) transverse states , for different values of the ratio @xmath202 . with increasing collision energy the transmission coefficient exhibits a nonmonotonic behaviour : we observe a sequence of minima and peaks . for @xmath203 the value of @xmath156 at the minimum is zero . as the number of open channels increases with increasing collision energy @xmath204 , the transmission values at the corresponding minima increase strongly . the corresponding transmission peaks @xmath205 are located at the channel thresholds . the shape of the transmission valleys in between two integer values of @xmath58 as well as the positions of the minima strongly depend on the ratio @xmath202 which can be changed by varying the strength of the interatomic interaction @xmath31 or the trap frequency @xmath0 . both , changing @xmath31 and/or @xmath0 leads to energetical shifts of the bound states ( in particular for the excited transversal channels ) of the atoms in the presence of the confinement . if the collision energy coincides with a bound state of the corresponding closed channel we encounter an occupation of the closed channel in the course of the scattering process , i.e. a feshbach - resonance occurs . the interpretation of the minimum of the transmission @xmath156 in terms of a feshbach - resonance at the point @xmath206 for the zero - energy limit was provided in refs . @xcite , where it was shown that the origin of the cir is an intermediate occupation of a bound state belonging to an excited transverse ( closed ) channel . to demonstrate that the above - discussed behaviour ( minima ) of the transmission coefficient @xmath207 in certain regions of @xmath58 is due to feshbach resonances we have analyzed the probability density of the scattering wave function of the atoms in the trap . in the single - mode regime and in the zero - energy limit we encounter the well - known cir : fig.[fig6e ] shows the corresponding probability density @xmath208 for an initial transverse ground state @xmath200 and @xmath209 as well as @xmath210 . for small @xmath211 one observes additional two pronounced peaks along the transverse ( @xmath125- ) direction corresponding to the occupation of the bound state ( with the binding energy @xmath212 ) in the first excited closed channel of the transverse potential . the probability density tends to zero as @xmath213 . this leads to a zero of the transmission @xmath207 for @xmath160 ( see fig.[fig6](a ) ) corresponding to the zero - energy cir . in fig.[fige6 ] we show the probability densities @xmath208 at @xmath214 for several values of the dimensionless energy @xmath58 for ( a ) the single- and ( b ) two - mode regimes for collisions with initial transverse state @xmath200 . the corresponding probability density exhibits for small values of @xmath211 additional two ( for the single - mode regime ) and four ( for the two - mode regime ) pronounced peaks with respect to the transverse ( @xmath125-)direction as @xmath58 approaches the cir - position . this demonstrates the occupation of bound states of higher , namely first excited ( with binding energy @xmath215 ) and second excited ( with binding energy @xmath216 ) channels in the course of the scattering process . the corresponding transmission values are also indicated in fig.[fige6 ] . zero transmission is observed also for @xmath214 and @xmath217 with no probability density being present for large positive values of @xmath47 , see fig.[fige6](a ) . @xmath188{6a.jpg}\includegraphics[height=6cm , width=8cm]{6b.jpg}\\ \end{array}$ ] @xmath188{6ea.jpg}\includegraphics[height=6cm , width=8cm]{6ed.jpg}\\ \includegraphics[height=6cm , width=8cm]{6eb.jpg}\includegraphics[height=6cm , width=8cm]{6ee.jpg}\\ \includegraphics[height=6cm , width=8cm]{6ec.jpg}\includegraphics[height=6cm , width=8cm]{6ef.jpg}\\ \end{array}$ ] the energy of the bound state @xmath215 , that leads to a minimal transmission due to a resonant scattering process , changes with varying @xmath202 as follows . it is below @xmath218 for @xmath219 and consequently no minimum is encountered for @xmath207 in the range @xmath220 ( see fig . [ fig6 ] ) . at the position of the zero - energy cir it is located just above the threshold @xmath221 leading to a zero transmission for @xmath222 . for @xmath223 the bound state energy is somewhere in between the channel thresholds @xmath221 and @xmath224 whereas for @xmath225 it is below but close to @xmath224 leading again to a corresponding minimum of @xmath156 . for both cases , @xmath225 and @xmath223 , an increase of @xmath195 leads to a narrow transmission well and the corresponding transmission minimum is shifted towards the next higher channel threshold . the dependence of @xmath215 on the parameter @xmath202 is in agreement with the pseudopotential analysis given in ref.@xcite ( see fig . 2 of this ref . ) . in fig.[fig7](a ) we show the transition probabilities @xmath77 as a function of @xmath195 for @xmath196 and @xmath226 corresponding to four open channels . we observe that the probability of remaining at the same initial state , @xmath227 ( i.e. elastic scattering ) is in the complete range of the ratio @xmath202 much larger than the probability of a transition into a different state , @xmath77 ( i.e. inelastic scattering ) . with increasing @xmath50 or @xmath68 the inelastic transition probabilities @xmath77 increase but the elastic probabilities @xmath227 decrease . in an inelastic ( elastic ) collision @xmath77 ( @xmath227 ) goes to zero ( unity ) as @xmath172 tends to zero . @xmath77 ( @xmath227 ) possess a maximum ( minimum ) at the resonance position @xmath228 consistent with the minimum of @xmath207 at @xmath226 . it is instructive to see how the distribution of the initial flux among the open channels changes due to pair collisions as a function of the collision energy . fig.[fig7](b ) shows the transition probabilities @xmath77 as a function of the dimensionless energy up to four open channels . the probability of elastic scattering remains larger than that of inelastic scattering in the complete range of the energy . for two open channels the elastic collision probability @xmath227 is independent of the initial state ( @xmath229 ) . for a higher number of open channels @xmath227 is decreasing with increasing initial value of @xmath50 . near the thresholds , the probabilities of the inelastic ( elastic ) transitions @xmath77 ( @xmath227 ) go to zero ( unity ) . @xmath188{7a.jpg}\includegraphics[height=6cm , width=8cm]{7b.jpg}\\ \end{array}$ ] in this section we focus on fermionic collisions in harmonic traps . in this case the interatomic wave function is anti - symmetric with respect to the interchange of the two fermions and the even amplitude @xmath66 in eqs.([full asymptotic wave ] ) is zero . we have analyzed the multi - channel scattering of fermions up to four open transverse channels for different interatomic interactions , by varying the potential strength @xmath31 in the vicinity of the value @xmath230 ( see fig.1 ) generating a resonant p - wave state in free space . fig . [ fig8 ] shows corresponding results for the single - mode regime . [ fig8](a ) shows the _ mapped coupling constant _ @xmath231 @xcite as a function of the p - wave scattering length @xmath232{v_p}$ ] . the _ mapped coupling constant _ @xmath233 goes to zero at the position of the mapped cir @xcite , which for @xmath182 and @xmath234 is equal to @xmath235 . the position of the mapped cir obviously depends on the values of @xmath0 and @xmath58 . in fig.[fig8](b ) we have plotted the transmission coefficient @xmath156 as a function of @xmath236 . the transmission coefficient exhibits a minimum and an accompanying well ( i.e. the blocking due to the resonance ) at the position of the cir , and tends to unity ( i.e. total transmission ) for @xmath236 far from the cir - position . for larger @xmath0 the well becomes wider , and its minimum is shifted to the left , see also ref.@xcite . [ fig8](c ) shows the scattering amplitude @xmath237 as a function of @xmath236 for @xmath238 and @xmath239 . the amplitude approaches zero far from the cir position and @xmath187 at the cir position , which results in total transmission , @xmath240 ( i.e. the fermions do not scatter each other ) and total reflection , @xmath241 ( i.e. strongly interacting and impenetrable fermions ) , respectively . @xmath163{8a.jpg}\\ \includegraphics[height=6cm , width=8cm]{8b.jpg}\\ \includegraphics[height=6cm , width=8cm]{8c.jpg}\\ \end{array}$ ] in fig.[fig9 ] we present the total transmission coefficient as a function of @xmath236 in the two - mode regime for @xmath242 ( a ) and three - mode regime for @xmath243 ( b ) for @xmath196 . similar to the single - mode regime , @xmath156 exhibits a minimum and accompanying well , however the position of the minimum is shifted to the right and the value at the minimum is nonzero . for the lower degree of transversal excitation , we observe a deeper and narrower transmission well . with increasing energy the transmission well becomes wider and more shallow and its position is shifted to larger values of @xmath244 . this is also demonstrated in fig.[fig10 ] , where the transmission coefficient is plotted as a function of @xmath58 for several values of @xmath244 for the two cases of being initially in the ground @xmath200 ( a ) and the first excited @xmath201 ( b ) transverse states for @xmath182 . we observe that for any number of open channels , @xmath156 exhibits a minimum for some value of @xmath244 . with increasing @xmath244 the transmission well becomes more shallow ( except for the single - mode regime ) and wider . in contrast to the bosonic case , there is no specific threshold behaviour . this is a consequence of the fact that the relative motion does not feel the interatomic interaction in the closed channels which are strongly screened by the centrifugal repulsion playing a dominant role for near - threshold collision energies or in other words : we encounter a weak coupling of the different scattering channels . @xmath188{9a.jpg}\includegraphics[height=6cm , width=8cm]{9b.jpg}\\ \end{array}$ ] @xmath188{10a.jpg}\includegraphics[height=6cm , width=8cm]{10b.jpg}\\ \end{array}$ ] in fig.[fig11 ] we show the transition probabilities @xmath77 as a function of @xmath244 for four open channels . we see that the probability of an elastic scattering process ( i.e. to remain in the same transversal state ) is much larger than that of an inelastic collision ( i.e. the transition to a different transversal state ) . for an elastic collision the probability @xmath227 shows a minimum and corresponding well which becomes wider and more shallow with increasing initial quantum number @xmath50 ( i.e. , with the population of a higher excited initial transversal state ) . for an inelastic collision @xmath77 ( @xmath245 ) exhibits a peak which becomes less pronounced as the quantum numbers @xmath50 or @xmath68 increase . @xmath163{11.jpg}\\ \end{array}$ ] in this section we analyze the multi - channel scattering of two distinguishable particles in a harmonic trap with the same trap frequency @xmath246 allowing the separation of the c.m . such a case corresponds to the different atomic species confined by the same potential as it is the case e.g. for two different isotopes in the same optical dipole trap . the two - body scattering wave - function of the distinguishable atoms does not possess a well - defined symmetry with respect to the reflection @xmath174 , i.e. both s- and p - state contributions ( @xmath247 and @xmath248 ) must be taken into account for the scattering amplitude . fig.[fig12 ] shows our results for the transmission coefficient @xmath156 in the single - mode regime ( @xmath249 ) , which is plotted as a function of the tuning parameter @xmath250 of the interparticle interaction . in general the scattering process can not be described by a single scattering length @xmath172 or @xmath236 for this case . in regions with a negligible p - wave contribution ( see the regions in fig.[fig1 ] with @xmath251 ) , @xmath156 exhibits a behavior similar to bosonic scattering . we observe the well - known s - wave cirs which lead to zeros of the transmission @xmath156 at the positions @xmath252 and tend to unity when @xmath172 goes to zero ( together with @xmath236 ) . in regions , where @xmath172 and @xmath236 are comparable we observe the effect reported in ref . @xcite : remarkable peaks of the transmission @xmath253 i.e. almost complete transmission in spite of the strong interatomic interaction in free space . this is the so - called dual cir : quantum suppression of scattering in the presence of confinement due to destructive interference of odd and even scattering amplitudes . equally minima of @xmath254 due to the interference of even and odd scattering amplitudes under the action of the transverse confinement can occur ( see fig.[fig12 ] ) . complete transmission corresponds to @xmath255 while total reflection corresponds to @xmath256 . fig.[fig13 ] shows the corresponding amplitudes @xmath257 as a function of @xmath250 . @xmath163{12.jpg}\\ \end{array}$ ] @xmath163{13.jpg}\\ \end{array}$ ] fig.[fig14 ] shows the total transmission coefficient versus @xmath250 in the three - mode regime for @xmath182 and @xmath243 . similar to the single - mode regime , when @xmath236 is negligible compared to @xmath172 , @xmath156 behaves analogously to the case of a bosonic collision , and tends to unity ( complete transmission ) when @xmath172 tends to zero , while at the s - wave cir position , it exhibits a minimum with a nonzero value . for a lower degree of transversal excitation of the initial state , we encounter a larger transmission coefficient . for the same reasons as in the single - mode regime , we observe in the regions of @xmath31 where the p - wave scattering length @xmath236 is comparable to @xmath172 , sharp peaks of @xmath156 . however in contrast to the single - mode regime we do not observe complete transmission i.e. @xmath258 ( see e.g. @xmath156 at @xmath259 in fig.[fig14 ] ) . @xmath163{14.jpg}\\ \end{array}$ ] fig.[fig15 ] presents the transmission coefficients as a function of the dimensionless energy @xmath58 for @xmath182 . fig.[fig15](a ) shows the results for several ratios of @xmath202 if @xmath260 is small compare to @xmath261 . here the system is initially in the transversal ground state . the behaviour of the transmission coefficient is similiar to the case of two - boson scattering ( see [ fig6]-a ) . fig.[fig15](b ) shows the transmission for the scattering of two distinguishable atoms together with the results for bosonic- ( blue ) and fermionic- ( black ) collisions , for @xmath262 when both scattering length @xmath172 and @xmath236 are large . in the limit @xmath222 the behaviour of the transmission for the distinguishable and the bosonic case are very similar while in the vicinity of the energy of the p - wave shape - resonance @xmath263 , apart from a small shift to larger energies , we can find a complete coincidence of the transmission behaviour for the case of distinguishable and fermionic scattering . at the threshold energy @xmath224 the latter two transmission curves cross . fig.[fig15](c ) shows the transmission coefficient versus @xmath58 for @xmath262 initially occupying the ground state @xmath200 ( blue ) , the first excited state @xmath201 ( black ) , the second excited state @xmath264 ( red ) and the third excited state @xmath265 ( green ) . in the limit @xmath266 , @xmath156 drops rapidly to zero . apart from the single mode regime , it is for @xmath267 approximately constant with @xmath268 . in fig.[fig16 ] we present the transition probabilities @xmath77 as a function of @xmath250 for four open channels . for the regions of @xmath31 where @xmath236 is negligible compared to @xmath172 , a very good agreement of the transmission behaviour for distinguishable and bosonic atoms is observed . in regions where @xmath172 and @xmath236 are comparable , similar to the fermionic case , we observe narrow and deep wells ( for elastic collision ) and narrow as well as strongly pronounced peaks ( for inelastic collision ) . @xmath163{15a.jpg}\\\includegraphics[height=6cm , width=8cm]{15b.jpg}\\\includegraphics[height=6cm , width=8cm]{15c.jpg}\\ \end{array}$ ] @xmath163{16.jpg}\\ \end{array}$ ]

this approach is employed to extensively analyze the transverse excitations and deexcitations as well as resonant scattering processes . to four open transverse channels are considered . previously obtained analytical results are extended significantly here . series of feshbach resonances in the transmission behaviour are identified and analyzed . the behaviour of the transmission with varying energy and scattering lengths is discussed in detail . the dual cir leading to a complete quantum suppression of atomic scattering is revealed in multi - channel scattering processes .

[ txt : abstract ] we develop a grid method for multi - channel scattering of atoms in a waveguide with harmonic confinement . this approach is employed to extensively analyze the transverse excitations and deexcitations as well as resonant scattering processes . collisions of identical bosonic and fermionic as well as distinguishable atoms in harmonic traps with a single frequency permitting the center - of - mass ( c.m . ) separation are explored in depth . in the zero - energy limit and single mode regime we reproduce the well - known confinement - induced resonances ( cirs ) for bosonic , fermionic and heteronuclear collisions . in case of the multi - mode regime up to four open transverse channels are considered . previously obtained analytical results are extended significantly here . series of feshbach resonances in the transmission behaviour are identified and analyzed . the behaviour of the transmission with varying energy and scattering lengths is discussed in detail . the dual cir leading to a complete quantum suppression of atomic scattering is revealed in multi - channel scattering processes . possible applications include , e.g. , cold and ultracold atom - atom collisions in atomic waveguides and electron - impurity scattering in quantum wires .

0802.3682

i

we have analyzed atomic multi - channel scattering in a 2d harmonic confinement . identical bosonic and fermionic scattering as well as scattering of distinguishable atoms in traps with the same frequency for the different species have been explored . equal frequencies allows us to separate the c.m . and relative motion . firstly we reproduced the well - known s - wave cir for bosonic collision in the single - mode regime@xcite . next bosonic collisions in the multi - channel regime including elastic and inelastic processes i.e. transverse excitations and deexcitations have been investigated . transmission coefficients as well as transition probabilities for energies covering up to four open channels are reported on . it is shown that the transmission coefficient as a function of the scattering length exhibits a minimum at the cir position . except for @xmath269 in the first channel , the transmission curves show , with varying energy , a minimum and accompanying well . for a single open channel the value of the minimum of the transmission is zero . increasing the degree of transverse excitation leads to an increase of the transmission minima . a distinct threshold behaviour is observed at every @xmath270 . for @xmath271 the accompanying transmission well is more pronounced compared to the case @xmath272 and it is also deeper in the case of several open channels . the position of the minimum is closer to the upper threshold again when compared to the case @xmath272 . with increasing ratio @xmath202 for either @xmath272 or @xmath271 , the corresponding transmission well becomes also more pronounced i.e. we encounter a deeper and narrower well for more open channels and the energetical position of the minimum moves to the neighboring upper threshold . our results for the transition probabilities @xmath77 show that the probability of remaining in the same state ( elastic collision ) is larger than transitions into a different transversal state ( inelastic collision ) . in the case of elastic collisions ( inelastic collisions ) it has to go to unity ( zero ) as @xmath172 tends to zero . the inelastic transition probability @xmath77 increases as the numbers @xmath50 or @xmath68 increase while the elastic transition probability @xmath77 decreases . our next focus has been the multi - channel scattering of fermions addressing up to four open channels in the waveguide . in the regime of a single open channel we reproduced the well - known p - wave mapped cir in the zero - energy limit @xcite . we have analyzed the p - wave cir dependence on the collision energy @xmath204 and the trapping frequency @xmath0 . consequently the multi - mode regime has been explored by determining the behaviour of the transmission as well as the transition probabilities . the dependence of the transmission on the p - wave scattering length exhibits a minimum with zero transmission and an accompanying well for the single - mode regime . increasing the energy , this well becomes more shallow ( except for the single - mode regime),wider and its position is shifted to the region of higher energies . in the multi - mode regime the transmission well depends also on the degree of the initial transverse excitation . increasing the degree of initial transverse excitation the transmission well becomes shallower and wider and the transmission is overall increased . for a fixed number of open channels the transmission exhibits as a function of the energy a minimum for some value of the p - wave scattering length . increasing @xmath273 leads to a shift of the transmission minimum to higher energies and an increasingly shallower well . this holds except for the single mode regime in which the minimal value is zero . in contrast to the bosonic case , we do not observe a distinct threshold behavior . the transition probabilities @xmath77 for fermionic collisions show that elastic collisions are more probable than inelastic ones . the probability @xmath227 for an elastic process shows a well which becomes wider and shallower as the initial population of the excited states @xmath50 increases , while for an inelastic collision it exhibits a peak which becomes smaller as the channel numbers @xmath50 or @xmath68 increase . by varying the potential parameter @xmath31 in the viccinity of the value @xmath230 , we found a set of shape - resonances . finally we analyzed the multi - channel-1d scattering of distinguishable atoms in the trap . here both s- and p - wave contributions have been taken into account . we have studied the transmission coefficient in the single - mode regime and reproduced the cir @xcite as well as the dual - cir @xcite corresponding to total reflection and transmission , respectively . in the multi - mode regime the transmission versus @xmath250 shows except for the regions where @xmath236 is comparable with @xmath172 a behaviour analogous to the situation of bosonic scattering . we encounter @xmath274 for @xmath275 . at the position of the cir , @xmath156 exhibits a minimum with a nonzero value . the lower is the transverse excitation of the initial state , the larger is the transmission coefficient . in regions of @xmath31 where the p - wave scattering length @xmath236 is comparable to @xmath172 , @xmath156 exhibits sharp peaks or dips near the dual - cirs due to comparable contributions of both s- and p - waves . in contrast to the single - mode regime there is no a complete transmission at the dual cir points . our results for the transmission coefficient versus energy show that in the limit of zero longitudinal relative energy the distinguishable atoms behave like bosons , while in the vicinity of the position of a shape - resonance , they behave like fermions . for larger energies @xmath276 @xmath156 is close to unity . finally we have analyzed the transition probability as a function of @xmath250 . for values of @xmath31 where @xmath236 is negligible compared to @xmath172 we find an excellent agreement with the results for bosonic collisions . in regions where these two scattering parameters are comparable , we observe , similar to the fermionic case , sharp downward- ( for elastic collision ) and upward- ( for inelastic collision ) peaks but with different values . we conclude with the general statement that our multi - channel scattering results in waveguides are of immediate relevance to cold or ultracold atomic collisions in atomic waveguides or impurity scattering in quantum wires .

we reproduce the well - known confinement - induced resonances ( cirs ) for bosonic , fermionic and heteronuclear collisions . in case of the multi - mode regime up possible applications include , e.g. , cold and ultracold atom - atom collisions in atomic waveguides and electron - impurity scattering in quantum wires .

[ txt : abstract ] we develop a grid method for multi - channel scattering of atoms in a waveguide with harmonic confinement . this approach is employed to extensively analyze the transverse excitations and deexcitations as well as resonant scattering processes . collisions of identical bosonic and fermionic as well as distinguishable atoms in harmonic traps with a single frequency permitting the center - of - mass ( c.m . ) separation are explored in depth . in the zero - energy limit and single mode regime we reproduce the well - known confinement - induced resonances ( cirs ) for bosonic , fermionic and heteronuclear collisions . in case of the multi - mode regime up to four open transverse channels are considered . previously obtained analytical results are extended significantly here . series of feshbach resonances in the transmission behaviour are identified and analyzed . the behaviour of the transmission with varying energy and scattering lengths is discussed in detail . the dual cir leading to a complete quantum suppression of atomic scattering is revealed in multi - channel scattering processes . possible applications include , e.g. , cold and ultracold atom - atom collisions in atomic waveguides and electron - impurity scattering in quantum wires .

1312.4971

i

let @xmath3 be a finite , undirected graph without loops or multiple edges . for @xmath4 , the _ distance _ from @xmath5 to @xmath2 is the least number of edges in a path from @xmath5 to @xmath2 , and is denoted @xmath6 ( or simply @xmath7 if @xmath0 is clear from the context ) . a _ resolving set _ for a graph @xmath3 is a set of vertices @xmath8 such that for each vertex @xmath9 , the list of distances @xmath10 uniquely determines @xmath11 . equivalently , @xmath12 is a resolving set for @xmath0 if , for any pair of vertices @xmath13 , there exists @xmath14 such that @xmath15 ; we say that @xmath16 _ resolves _ @xmath5 and @xmath11 . the _ metric dimension _ of @xmath0 is the smallest size of a resolving set for @xmath0 . this concept was introduced to the graph theory literature in the 1970s by harary and melter @xcite and , independently , slater @xcite ; however , in the context of arbitrary metric spaces , the concept dates back at least as far as the 1950s ( see blumenthal @xcite , for instance ) . for further details , the reader is referred to the survey paper @xcite . when studying metric dimension , distance - regular graphs are a natural class of graphs to consider . a graph @xmath0 with diameter @xmath17 is _ distance - regular _ if , for all @xmath18 with @xmath19 and any vertices @xmath20 with @xmath21 , the number of neighbours of @xmath2 at distances @xmath22 , @xmath18 and @xmath23 from @xmath5 depend only on the distance @xmath18 , and not on the choices of @xmath5 and @xmath2 . these numbers are denoted by @xmath24 , @xmath25 and @xmath26 respectively , and are known as the _ parameters _ of @xmath0 . it is easy to see that @xmath27 , @xmath28 are undefined , @xmath29 , @xmath30 and @xmath31 ( where @xmath32 is the valency of @xmath0 ) . we put the parameters into an array , called the _ intersection array _ of @xmath0 , @xmath33 in the case where @xmath0 has diameter @xmath34 , we have a _ strongly regular _ graph , and the intersection array may be determined from the number of vertices @xmath35 , valency @xmath32 , and the parameters @xmath36 and @xmath37 ; in this case , we say @xmath38 are the parameters of the strongly regular graph . another important special case of distance - regular graphs are the _ distance - transitive _ graphs , i.e. those graphs @xmath0 with the property that for any vertices @xmath39 such that @xmath40 , there exists an automorphism @xmath41 such that @xmath42 and @xmath43 . for more information about distance - regular graphs , see the book of brouwer , cohen and neumaier @xcite and the forthcoming survey paper by van dam , koolen and tanaka @xcite . in recent years , a number of papers have been written on the subject of the metric dimension of distance - regular graphs ( and on the related problem of class dimension of association schemes ) , by the present author and others : see @xcite , for instance . in this paper , we shall focus on various classes of _ imprimitive _ distance - regular graphs , which are explained below . a distance regular graph @xmath0 with diameter @xmath17 is _ primitive _ if and only if each of its distance-@xmath18 graphs ( for @xmath44 ) is connected , and is _ imprimitive _ otherwise . for @xmath45 , i.e. strongly regular graphs , the only imprimitive examples are the complete multipartite graphs @xmath46 ( with @xmath47 parts of size @xmath48 ) . for valency @xmath49 , a result known as _ smith s theorem _ ( after d. h. smith , who proved it for the distance - transitive case @xcite ) states that there are two ways for a distance - regular graph to be imprimitive : either the graph is bipartite , or is _ antipodal_. the latter case arises when the distance-@xmath17 graph consists of a disjoint union of cliques , so that the relation of being at distance @xmath50 or @xmath17 in @xmath0 is an equivalence relation on the vertex set . the vertices of these cliques are referred to as _ antipodal classes _ ; if the antipodal classes have size @xmath48 , then we say @xmath0 is _ @xmath48-antipodal_. it is possible for a graph to be both bipartite and antipodal , with the hypercubes providing straightforward examples . if @xmath0 is a bipartite distance - regular graph , the distance-@xmath34 graph has two connected components ; these components are called the _ halved graphs _ of @xmath0 . if @xmath0 is @xmath48-antipodal , the _ folded graph _ , denoted @xmath51 , of @xmath0 is defined as having the antipodal classes of @xmath0 as vertices , with two classes being adjacent in @xmath51 if and only if they contain adjacent vertices in @xmath0 . the folded graph @xmath51 is also known as an _ antipodal quotient _ of @xmath0 ; conversely , @xmath0 is an _ antipodal @xmath48-cover _ of @xmath51 . we note that @xmath0 and @xmath51 have equal valency ; a result of gardiner ( * ? ? ? * corollary 4.4 ) shows that @xmath48 is at most this valency . the operations of halving and folding may be used to reduce imprimitive graphs to primitive ones : see ( * ? ? ? * 4.2a ) for details . in particular , an imprimitive distance - regular graph with valency @xmath49 may be reduced to a primitive one by halving at most once and folding at most once . also , the intersection arrays of the halved and/or folded graphs of @xmath0 may be obtained from that of @xmath0 . in a 2006 paper of alfuraidan and hall ( * ? ? * theorem 2.9 ) , a refinement of smith s theorem is obtained which will be especially useful to us . we summarize their result below . [ thm : ah ] let @xmath0 be a connected distance - regular graph with @xmath35 vertices , diameter @xmath17 and valency @xmath32 . then one of the following occurs : 1 . @xmath0 is primitive , with @xmath52 and @xmath49 ; 2 . @xmath53 , and @xmath0 is a cycle @xmath54 ; 3 . @xmath55 , and @xmath0 is a complete graph @xmath56 ; 4 . @xmath45 , and @xmath0 is a complete multipartite graph @xmath46 ( where @xmath57 ; 5 . @xmath58 , @xmath0 is both bipartite and @xmath34-antipodal , @xmath59 , and @xmath0 is @xmath60(a complete bipartite graph with a perfect matching deleted ) ; 6 . @xmath58 , @xmath0 is bipartite but not antipodal , @xmath59 , and @xmath0 is the incidence graph of a symmetric design with @xmath2 points and block size @xmath61 ; 7 . @xmath58 , @xmath0 is antipodal but not bipartite , and @xmath0 is an antipodal cover of a complete graph @xmath62 ; 8 . @xmath63 , @xmath0 is both bipartite and antipodal , @xmath0 is an antipodal cover of a complete bipartite graph @xmath64 , and the halved graph is complete multipartite ; 9 . @xmath65 , @xmath0 is both bipartite and antipodal , the halved graphs are antipodal of diameter @xmath66 , and the folded graph is bipartite of diameter @xmath66 ; 10 . @xmath67 , @xmath0 is antipodal but not bipartite , and the folded graph is primitive with diameter @xmath68 and valency @xmath49 ; 11 . @xmath67 , @xmath0 is bipartite but not antipodal , and the halved graphs are primitive with diameter @xmath68 and valency at least @xmath66 ; 12 . @xmath17 is odd and @xmath69 , @xmath0 is bipartite and @xmath34-antipodal , the folded graph is primitive with diameter @xmath70 and valency @xmath49 , and the halved graphs are primitive with diameter @xmath70 and valency at least @xmath66 ; 13 . @xmath17 is even and @xmath71 , @xmath0 is bipartite and antipodal , and the graphs obtained by successive halving and folding are primitive with diameter @xmath72 and valency at least @xmath66 . we shall refer to these classes as ah1ah13 . the numbering is not exactly the same as that given in @xcite . we have separated the case of @xmath60 from the other imprimitive graphs of diameter @xmath66 ( cf . * corollary 2.10 ) ) ; as we shall see , it is something of a special case . apart from @xmath73 and @xmath74 , no graph appears in more than one class . one of main aims of this paper is to consider the asymptotic behaviour of the metric dimension of imprimitive distance - regular graphs . we use knuth s convention for asymptotic notation ( from @xcite ; see also ( * ? ? ? * 9.2 ) ) : for @xmath35 sufficiently large , we say that @xmath75 if there is a constant @xmath76 such that @xmath77 , that @xmath78 if there is a constant @xmath79 with @xmath80 , and @xmath81 if both of these happen . for any graph with @xmath35 vertices and diameter @xmath17 , it is straightforward to see that the metric dimension @xmath82 must satisfy the inequality @xmath83 ( see ( * ? ? ? * proposition 3.6 ) ) ; when considering families of fixed diameter ( such as strongly regular graphs ) , this gives a lower bound on @xmath82 of @xmath84 . like alfuraidan and hall @xcite , we regard class ah1 as the `` generic '' class of distance - regular graphs . for graphs in this class , namely primitive distance - regular graphs of diameter @xmath52 and valency @xmath49 , the pioneering work of babai @xcite in the early 1980s ( in a different context : see @xcite for details ) yields the following . [ thm : babai ] suppose that @xmath0 is a primitive distance - regular graph with @xmath35 vertices , valency @xmath49 and diameter @xmath52 . then : * @xmath85 ; * if @xmath45 ( i.e. @xmath0 is strongly regular ) , we have ( a ) @xmath86 and ( b ) @xmath87 ( where @xmath88 ) ; * if @xmath89 is the maximum size of a set of vertices at a given distance from any vertex of @xmath0 , we have @xmath90 some remarks about theorem [ thm : babai ] are in order . while the bound ( b ) in part ( ii ) appears weaker than ( a ) , if @xmath35 and @xmath32 have a linear relationship ( for example , in the case of paley graphs where @xmath91 ) this may be combined with the lower bound above to obtain @xmath92 . on the other hand , the strongly regular johnson and kneser graphs @xmath93 and @xmath94 have metric dimension @xmath95 ( see ( * ? ? ? * corollary 3.33 ) ) , so the @xmath96 factor can not be eliminated in general . in part ( iii ) the value of @xmath97 may be calculated from the intersection array ; for families where @xmath17 is fixed we may also obtain an improvement on the @xmath98 upper bound . for classes ah2ah4 , the metric dimension is easy to determine exactly , as we summarise below . [ prop : easy ] for the graphs in families ah2ah4 , we have @xmath99 , @xmath100 and @xmath101 . for cycles and complete graphs , this is trivial ; for complete multipartite graphs , it is straightforward ( see ( * ? ? ? * proposition 1 ) ) . asymptotically , for both complete graphs and complete multipartite graphs on @xmath35 vertices , we have @xmath102 . however , we suggest that classes ah2ah4 are pathological cases which should be disregarded as atypical . for the remaining classes ah5ah13 , much more work is required .

a _ resolving set _ for a graph is a collection of vertices , chosen so that for each vertex , the list of distances from to the members of uniquely specifies . the _ dimension _ of is the smallest size of a resolving set for . much attention has been paid to the metric dimension of distance - regular graphs .

a _ resolving set _ for a graph is a collection of vertices , chosen so that for each vertex , the list of distances from to the members of uniquely specifies . the _ dimension _ of is the smallest size of a resolving set for . much attention has been paid to the metric dimension of distance - regular graphs . work of babai from the early 1980s yields general bounds on the metric dimension of primitive distance - regular graphs in terms of their parameters . we show how the metric dimension of an imprimitive distance - regular graph can be related to that of its halved and folded graphs , but also consider infinite families ( including taylor graphs and the incidence graphs of symmetric designs ) where more precise results are possible .

1312.4971

r

given that imprimitive distance - regular graphs may be reduced to primitive graphs by the operations of halving and folding , it is desirable to obtain relationships between resolving sets and metric dimension for imprimitive graphs and their halved and/or folded graphs . in this section , we obtain such relationships . first , we consider the halving operation when @xmath0 is bipartite . our first result does not assume that @xmath0 is distance - regular . [ prop : halving ] let @xmath3 be a connected bipartite graph with bipartition @xmath103 , and let @xmath104 and @xmath105 be its halved graphs . then @xmath106 . let @xmath107 and @xmath108 be resolving sets for @xmath109 and @xmath110 , respectively . we will show that @xmath111 is a resolving set for @xmath0 . let @xmath112 . if one of these is in @xmath113 and the other in @xmath114 , then for any vertex @xmath115 , we must have that one of @xmath116 and @xmath117 is odd and the other is even , and thus @xmath118 , i.e. @xmath11 resolves @xmath119 and @xmath120 . in particular , we are free to choose @xmath121 . so we must consider the case where @xmath119 and @xmath120 are both in the same bipartite half . if @xmath122 , then there exists @xmath123 such that @xmath124 , and thus @xmath125 i.e. @xmath11 resolves @xmath119 and @xmath120 ( in @xmath0 ) . the case where @xmath126 is similar . hence @xmath12 is a resolving set for @xmath0 , and thus @xmath106 . a simple application of this theorem is when @xmath127 , so @xmath128 ; clearly @xmath129 and the bound holds with equality . even in the case of distance - regular graphs , the halved graphs need not be isomorphic ( although they must have the same parameters ) , so we can not assume that @xmath130 and @xmath131 should be equal . indeed , a counterexample is provided by the incidence graph of the unique ( up to duality ) generalized quadrangle @xmath132 : its halved graphs ( i.e. the point graphs of the @xmath132 and its dual ) have metric dimension @xmath133 and @xmath134 respectively ( see ( * ? ? ? * table 11 ) ) ; the incidence graph itself has metric dimension @xmath135 ( see ( * ? ? ? * table 4 ) ) . this also shows that the upper bound in proposition [ prop : halving ] need not be met with equality . obtaining bounds on the metric dimension of an antipodal distance - regular graph @xmath0 in terms of its folded graph @xmath51 is less straightforward . suppose @xmath3 is @xmath48-antipodal , with @xmath136 partitioned into @xmath137 antipodal classes @xmath138 . we define a _ @xmath48-antipodal partition _ to be a partition of @xmath136 into transversals of @xmath138 . ( note that some authors use the term `` antipodal partition '' to refer to the partition of @xmath136 into antipodal classes , so care is required here . ) we remark that a @xmath48-antipodal graph has many @xmath48-antipodal partitions , although in certain cases there natural partition arising from how the graph is constructed . we note that in an antipodal distance - regular graph @xmath0 with diameter @xmath17 , for @xmath4 with @xmath139 we have @xmath140 for any @xmath141 , and the diameter of @xmath51 is @xmath142 . [ prop : folding ] let @xmath3 be an @xmath143-antipodal distance - regular graph with diameter @xmath17 , and let @xmath144 be an @xmath143-antipodal partition of @xmath136 . suppose @xmath145 is a resolving set for the folded graph @xmath146 whose diameter is @xmath147 . for @xmath148 , let @xmath149 be its inverse image in @xmath136 with @xmath150 for each @xmath151 . let @xmath152 . * if @xmath153 with @xmath154 , @xmath155 and @xmath156 , then there exists @xmath157 with @xmath158 and @xmath159 such that @xmath160 ( i.e. @xmath161 resolves @xmath162 and @xmath163 ) . * if @xmath164 is odd , or for every @xmath165 there exists @xmath166 such that @xmath167 , then @xmath12 is a resolving set for @xmath0 . in particular , @xmath168 . * if @xmath169 is even and there exists @xmath165 such that @xmath170 for all @xmath121 , then @xmath171 is a resolving set for @xmath0 . in particular , @xmath172 . we start by proving part ( i ) of the theorem . suppose that @xmath153 with @xmath154 , @xmath155 and @xmath156 . since @xmath145 is a resolving set for @xmath51 , there exists @xmath166 such that @xmath173 . consequently , there exist indices @xmath174 such that @xmath175 we wish to find some @xmath157 that resolves @xmath162 and @xmath163 ; we consider the following cases . 1 . if @xmath176 , let @xmath177 , so @xmath157 and @xmath178 . 2 . if @xmath179 , we have @xmath180 and similarly @xmath181 by the properties of antipodal vertices in @xmath0 . in particular , we have @xmath182 , so @xmath183 and resolves @xmath162 and @xmath163 . otherwise , we have @xmath184 . at most one of @xmath174 can be @xmath50 ; without loss of generality we suppose that @xmath185 , and so @xmath186 . for a contradiction , suppose that @xmath187 does not resolve @xmath188 and @xmath163 , i.e. @xmath189 . since @xmath190 , we then have @xmath191 @xmath192 in particular , this implies that @xmath193 , a contradiction . thus @xmath187 resolves @xmath188 and @xmath163 . to prove parts ( ii ) and ( iii ) , we must construct a resolving set for @xmath0 . by part ( i ) , we know that for vertices @xmath194 , if @xmath156 then there is a vertex in @xmath12 which resolves them . it remains to consider the case where @xmath195 and @xmath196 , i.e. @xmath162 and @xmath163 are antipodal vertices in @xmath0 . first , we suppose that there exists @xmath158 such that @xmath197 . then if @xmath196 , for any @xmath198 , we must have that @xmath199 since @xmath200 and @xmath201 , we have @xmath202 , and thus @xmath161 resolves @xmath162 and @xmath203 . combined with part ( i ) , this shows that @xmath12 is a resolving set for @xmath0 of size @xmath204 , and thus ( ii ) holds . otherwise , we must have that @xmath170 for all @xmath158 . since @xmath145 is a resolving set for @xmath51 , there can be at most one vertex of @xmath51 with this property . if @xmath164 is odd , for any @xmath198 , we must have that @xmath205 and so @xmath161 resolves @xmath162 and @xmath203 . thus @xmath12 is a resolving set for @xmath0 of size @xmath204 , and again ( ii ) holds . if @xmath169 is even , we have @xmath206 for all @xmath207 , and thus @xmath208 are not resolved by any @xmath161 . however , by taking all but one of @xmath209 along with @xmath12 , we have that @xmath171 is a resolving set for @xmath0 of size @xmath210 , and thus ( iii ) holds . this completes the proof . straightforward examples are provided by the complete multipartite graphs @xmath46 : these are @xmath48-antipodal covers of the complete graph @xmath211 , and have diameter @xmath34 . since any resolving set @xmath145 for @xmath212 contains @xmath213 vertices , the remaining vertex is adjacent to all of @xmath145 , so case ( iii ) of proposition [ prop : folding ] applies . this gives @xmath214 , which we know from proposition [ prop : easy ] to be the exact value , so the upper bound is achieved . further such cases are discussed in section [ subsection:2antipodal ] below . some examples of where the bounds in proposition [ prop : folding ] are not achieved can be found in the tables in @xcite . first , the conway smith graph @xmath215 on @xmath216 vertices and with diameter @xmath217 is a @xmath66-antipodal cover of the kneser graph @xmath218 ; from ( * ? ? ? * table 10 ) we have @xmath219 and @xmath220 , so @xmath221 . second , the foster graph @xmath222 on @xmath223 vertices and with diameter @xmath134 is a @xmath66-antipodal cover of tutte s @xmath134-cage @xmath224 ; from ( * ? ? ? * table 3 ) we have @xmath225 and @xmath226 , so @xmath227 . in fact , in this latter case the covering graph has smaller metric dimension than its folded graph . when considering the classification of theorem [ thm : ah ] , the most immediate applications of propositions [ prop : halving ] and [ prop : folding ] are to graphs when halving and/or folding yields a primitive graph with diameter at least @xmath34 ; these are precisely the graphs in classes ah10ah13 . combined with babai s theorem [ thm : babai ] , we can obtain upper bounds on the metric dimension of any graph in those classes in terms of its parameters . first , we have the following result for bipartite graphs in classes ah1113 . [ cor : bipartite - babai ] suppose @xmath0 is a bipartite distance - regular graph of diameter @xmath67 whose halved graphs are primitive and have diameter at least @xmath34 . then we have : * @xmath228 ; * @xmath229 ( where @xmath89 is the maximum size of a set of vertices at a given distance from any vertex of @xmath0 ) . using proposition [ prop : halving ] , we know that @xmath230 . since the halved graphs are primitive distance - regular graphs with diameter @xmath68 , we can apply theorem [ thm : babai ] to them . we note that the distance classes of @xmath109 and @xmath110 are formed from the distance classes of @xmath0 , so we have @xmath231 . in case ah10 , we have that @xmath0 is antipodal but not bipartite , so we need to apply proposition [ prop : folding ] instead . [ cor : antipodal - babai ] suppose @xmath0 is a @xmath48-antipodal distance - regular graph of diameter @xmath67 whose folded graph @xmath51 is primitive and has diameter at least @xmath34 . then we have : * @xmath232 ; * @xmath233 ( where @xmath234 is the maximum size of a set of vertices at a given distance from any vertex of @xmath51 ) . for graphs in classes ah5ah9 , halving and/or folding yields either a complete or complete bipartite graph , and so we obtain upper bounds on the metric dimension of such graphs which are linear in the number of vertices . much of the remainder of this paper is devoted to improving upon this . however , we shall first consider some properties of @xmath34-antipodal graphs . in the case where @xmath0 is @xmath34-antipodal with diameter @xmath17 and folded graph @xmath51 , proposition [ prop : folding ] shows that @xmath235 if @xmath17 is odd , and @xmath236 if @xmath17 is even . however , we can obtain more detailed results in this case : the following lemma will be especially useful . for any vertex @xmath2 of @xmath0 , we denote by @xmath237 the set of vertices of @xmath0 that are at distance @xmath18 from @xmath2 . [ lemma : plusminus ] suppose that @xmath0 is a @xmath34-antipodal distance regular graph of diameter @xmath17 , whose vertex set has a @xmath34-antipodal partition @xmath238 . then , without loss of generality , a resolving set for @xmath0 can be chosen just from vertices in @xmath113 . we claim that if @xmath12 is any resolving set for @xmath0 and @xmath239 , then @xmath240 is also a resolving set . to show this , suppose that @xmath241 are resolved by @xmath242 , i.e. @xmath243 . suppose that @xmath244 , i.e. @xmath245 . since @xmath0 is distance - regular , there exists a path of length @xmath246 to some vertex in @xmath247 ; however , as @xmath242 is the unique vertex in @xmath247 , it follows that @xmath248 , and so @xmath249 . therefore , @xmath250 , and hence @xmath251 also resolves @xmath241 . by repeating the above process as required , an arbitrary resolving set for @xmath0 may be transformed into a resolving set consisting only of vertices in @xmath113 , and the result follows . if @xmath0 is bipartite as well as antipodal , and has odd diameter @xmath252 , then it is necessarily @xmath34-antipodal ( otherwise , it would contain an odd cycle of length @xmath253 ) ; such graphs form classes ah5 and ah12 . we have the following theorem . [ thm : bip_2ant_odd ] let @xmath3 be a bipartite , @xmath34-antipodal distance - regular graph with odd diameter @xmath254 , with folded graph @xmath146 of diameter @xmath255 . then @xmath256 . by proposition [ prop : folding ] we have @xmath235 . to show the converse , we consider the bipartition @xmath103 , which is also a @xmath34-antipodal partition , so for any @xmath148 , its preimages in @xmath136 are @xmath257 and @xmath258 . by lemma [ lemma : plusminus ] , there exists a resolving set @xmath259 for @xmath0 with @xmath107 . let @xmath260 . for all @xmath261 , there exists @xmath262 with @xmath263 . if these distances both lie in the interval @xmath264 , we must have @xmath265 similarly , if these distances both lie in the interval we have @xmath266 otherwise , we have ( without loss of generality ) that and @xmath267 , which implies that @xmath268 is even and @xmath269 is odd . therefore , @xmath11 resolves @xmath270 , and thus @xmath145 is a resolving set for @xmath51 . hence @xmath271 . this completes the proof . immediately , we have the following corollary about the graphs in class ah5 . [ cor : doubledclique ] the metric dimension of the graph @xmath60 , i.e. a complete bipartite graph with a @xmath272-factor removed , is @xmath273 . we have that @xmath60 is a bipartite , @xmath34-antipodal distance - regular graph with diameter @xmath58 , and its folded graph is the complete graph @xmath274 which has metric dimension @xmath273 . then we apply theorem [ thm : bip_2ant_odd ] . in terms of the asymptotic behaviour of metric dimension , this tells us that for graphs in class ah5 , namely @xmath275 with @xmath59 , we have @xmath102 , in common with classes ah3 and ah4 . so we may regard this class as another pathological case . for graphs in class ah12 , we have no change in the asymptotics from what we saw in the previous subsection , although we can be more precise . the following definition gives us an alternative interpretation of theorem [ thm : bip_2ant_odd ] . [ defn : bipdouble ] let @xmath3 be a graph . then the _ bipartite double _ ( or _ bipartite cover _ ) of @xmath0 is the bipartite graph @xmath276 whose vertex set consists of two disjoint copies of @xmath136 , labelled @xmath113 and @xmath114 , and where @xmath277 and @xmath278 are adjacent in @xmath276 if and only if @xmath5 and @xmath11 are adjacent in @xmath0 . for example , the bipartite double of a complete graph @xmath279 is the graph @xmath60 from corollary [ cor : doubledclique ] above . more generally , if @xmath0 is distance - regular with diameter @xmath17 and odd girth @xmath280 , then @xmath276 is distance - regular with diameter @xmath280 , and is an antipodal @xmath34-cover of @xmath0 . furthermore , any distance - regular graph of odd diameter which is both bipartite and antipodal must arise this way ( see ( * ? ? ? * 4.2d ) ) , and the bipartition @xmath238 is also a @xmath34-antipodal partition . thus theorem [ thm : bip_2ant_odd ] may be rephrased as follows . [ thm : bipdouble ] suppose that @xmath0 is a distance - regular graph of diameter @xmath17 with odd girth @xmath280 . then the metric dimension of its bipartite double @xmath276 is equal to the metric dimension of @xmath0 . as an example of its applications , theorem [ thm : bipdouble ] may be applied to the following infinite family . the _ odd graph _ @xmath281 has as its vertex set the collection of all @xmath282-subsets of a @xmath283-set , with two vertices adjacent if and only if the corresponding @xmath282-sets are disjoint . ( the odd graph @xmath284 is the petersen graph . ) this graph is distance - regular , has diameter @xmath285 and odd girth @xmath286 , so therefore satisfies the conditions of theorem [ thm : bipdouble ] ; its bipartite double is known as the _ doubled odd graph_. ( see ( * ? ? ? * 9.1d ) for further details . ) consequently , we have another corollary . [ cor : doubledodd ] the odd graph @xmath281 and doubled odd graph @xmath287 have equal metric dimension , which is at most @xmath288 . it follows from ( * ? ? ? * theorem 6 ) that the odd graph @xmath281 has metric dimension at most @xmath288 . since this graph satisfies the hypotheses of theorem [ thm : bipdouble ] , the result follows . this latter corollary provides a slight improvement on theorem 3.1 of guo , wang and li @xcite , who showed that @xmath289 . however , it removes the requirement to consider the doubled odd graph separately from the odd graph .

work of babai from the early 1980s yields general bounds on the metric dimension of primitive distance - regular graphs in terms of their parameters . we show how the metric dimension of an imprimitive distance - regular graph can be related to that of its halved and folded graphs , but also consider infinite families ( including taylor graphs and the incidence graphs of symmetric designs ) where more precise results are possible .

a _ resolving set _ for a graph is a collection of vertices , chosen so that for each vertex , the list of distances from to the members of uniquely specifies . the _ dimension _ of is the smallest size of a resolving set for . much attention has been paid to the metric dimension of distance - regular graphs . work of babai from the early 1980s yields general bounds on the metric dimension of primitive distance - regular graphs in terms of their parameters . we show how the metric dimension of an imprimitive distance - regular graph can be related to that of its halved and folded graphs , but also consider infinite families ( including taylor graphs and the incidence graphs of symmetric designs ) where more precise results are possible .

1411.4530

i

in the field of ion storage rings dedicated to molecular and atomic physics experiments , the electrostatic cryogenic storage ring ( csr ) @xcite of the max planck institute for nuclear physics ( mpik ) in heidelberg , germany , bridges the gap between traditional medium - energy magnetic heavy - ion synchrotrons , like tsr @xcite , astrid @xcite or cryring @xcite , and smaller low - energy electrostatic storage rings . most of the latter are off - springs of the elisa facility @xcite and target very low ion energies around 20 kev @xcite . the most advanced designs , like the recently commissioned desiree facility in stockholm @xcite , the future riken storage ring in saitama @xcite , and also the above mentioned csr , feature beam guiding vacuum systems that can be cooled to deeply cryogenic temperatures , which results in very low residual gas density and very long storage times@xcite . at a maximum kinetic energy of 300 kev per unit charge , ions stored in the csr are still low energetic compared to traditional magnetic storage rings . nevertheless , ions with charge - to - mass ratios up to 1/160 e / u will have storage velocities high enough to allow phase - space cooling using an electron cooler @xcite . consequently , csr will be the first electrostatic storage ring to enable ion - neutral , ion - photon , and ion - electron collision experiments at high precision using cooled , low - emittance stored beams . collision experiments with stored ions generally produce daughter beams of different ion - optical rigidity compared to their parent , which leave the closed orbit of the storage ring at the next bending element @xcite . the daughter particles can e.g. be charge - changed products from electron collisions of highly - charged atomic ions , neutral products from recombination of singly charged cations , or fragments from dissociation of stored molecular or cluster ions . in the case of low - emittance ion beams as stored in an electron cooler ring , movable , single - particle counting detectors of narrow aperture are a well - established way to selectively and sensitively measure the production rates of specific daughters @xcite . the bending elements of the storage ring then act as mass spectrometers that separate different product beams according to their charge - to - mass ratio @xmath1 and , thereby , allow to determine the corresponding reaction cross - sections . in the case of csr , such a detector has to meet additional technical criteria imposed by the design of the storage ring . a first limitation arises from the characteristic storage energy of csr . among its prime experimental targets are singly - charged molecular and weakly - charged atomic cations . given the maximum kinetic energy of 300 kev per unit charge , limited by the deflection fields of the csr bending electrodes , the specific kinetic energies of stored ions and of daughter beams produced in collision experiments can thus be as low as a few kev / u . this can easily result in penetration depths in solids as short as 100 nm @xcite and , hence , excludes any detection principle that requires the particles to traverse significant layers of passive material before reaching the detection volume , as is notably the case for surface - barrier semiconductor counters . second , the detector has to operate in the rather harsh csr environment . for the above mentioned advantage of extremely good vacuum conditions , but also in order to enable experiments on rotationally - ground - state molecular ions @xcite , csr is an all - cryogenic storage ring , where the beam - guiding vacuum chamber as well as all ion beam optics are cooled to @xmath0 k by a superfluid helium circuit @xcite . both , the detection principle and the mechanics enabling free positioning of the detector at the output of a csr bending element , must work reliably at this low temperature . in addition , in order to achieve uhv vacuum conditions ( @xmath2 mbar ) also in room or intermediate temperature operation , the beam pipe and all beam - facing experimental equipment are required to be bakeable to 250@xmath3c . in cryogenic mode , a room - temperature equivalent pressure of @xmath4 mbar is then achieved @xcite . last , in order to enable the csr to store ions of very low rigidity , e.g. low - energetic protons or light molecular ions like h@xmath5 or h@xmath6 , disturbances of the ion trajectories induced by stray magnetic fields must be kept at a minimum . all materials used for equipment installed in vicinity of the stored - beam orbit are therefore required to be of very low relative magnetic permeability @xmath7 . in this paper , we present a movable single - particle detector developed at mpik for counting of reaction products from ion collision experiments at csr . in sect . [ design ] we discuss the technical design of the set - up , consisting of the actual particle sensor and the cryogenic translation mechanism . in sect . [ tests ] we characterise the detector with regard to its counting efficiency and reliability of operation in a cryogenic vacuum environment . in sect . [ commissioning ] we report the the first operational test at csr in room temperature mode . section [ summary ] provides a summary and outlook onto possible future upgrades of the set - up .

a compact , highly efficient single - particle counting detector for ions of kev / u kinetic energy , movable by a long - stroke mechanical translation stage , has been developed at the max - planck - institut fr kernphysik ( max planck institute for nuclear physics , mpik ) . both , we present a series of functional tests that demonstrate full suitability for this application and characterise the set - up with regard to its particle detection efficiency .

a compact , highly efficient single - particle counting detector for ions of kev / u kinetic energy , movable by a long - stroke mechanical translation stage , has been developed at the max - planck - institut fr kernphysik ( max planck institute for nuclear physics , mpik ) . both , detector and translation mechanics , can operate at ambient temperatures down to k and consist fully of ultra - high vacuum ( uhv ) compatible , high - temperature bakeable and non - magnetic materials . the set - up is designed to meet the technical demands of mpik s cryogenic storage ring ( csr ) . we present a series of functional tests that demonstrate full suitability for this application and characterise the set - up with regard to its particle detection efficiency .

1502.01074

i

consensus algorithms have been recognized as an important step in a variety of decentralized and distributed algorithms , such as the rendezvous problem , distributed convex optimization or distributed sensing . we pose and solve in this paper what we term the _ weighted consensus _ problem over a directed graph . specifically , given a set of positive weights assigned to the agents , we say that the agents reach a weighted consensus if they converge to the weighted average of their initial conditions a formal definition to be given shortly . as is commonly done , we assume that the information flow in the system is described by a directed graph . our goal is to determine which weighted averages can be computed for a given information flow . furthermore , we describe how the agents can communicate over the graph to _ design _ the dynamical system whose evolution reaches the desired weighted consensus . computing a weighted average rather than a simple average is a natural one when the agents in the system are not all on equal footing . for example , think of a rendezvous problem where the rendezvous position depends on the initial positions of only a small group of agents ; of distributed sensing , where the weighting can be proportional to the accuracy of the sensing device , or of opinion dynamics , where participants may have different levels of influence on the decision process . because of their broad relevance , a fair amount is already known about consensus algorithms . indeed , questions concerning sufficient and/or necessary conditions for agents to reach consensus ( @xcite ) , questions concerning time delay ( @xcite , @xcite ) , consensus with quantized measurements ( @xcite , @xcite ) , consensus with time varying network topologies ( @xcite ) , and questions about convergence rate ( @xcite ) , robustness ( @xcite,@xcite ) in the presence of an adversary have all been treated to some degree . broadly speaking , the problem we address in this paper is one of _ feasibility of an objective given decentralization constraints_. similar questions , but involving controllability of linear systems @xcite , stability of linear systems @xcite and formation control @xcite have also been investigated . while the general problem of feasibility of an objective under decentralization constraints is far from being completely understood , we shall see that a fairly complete characterization can be obtained in the present case , in the cases of both discrete- and continuous - time dynamics . however , still open questions remain , such as : how to handle negative weights ? how to handle time - varying information flow graphs ? how to make sure that no - agent can game the system " and increase or decrease its assigned weight ? we next describe the model precisely . we assume that there are @xmath0 agents @xmath1 evolving in @xmath2 , and that the underlying network topology is specified by a directed graph ( or simply _ digraph _ ) @xmath3 , with @xmath4 the set of vertices and @xmath5 the set of edges . we let @xmath6 be a subset of @xmath7 comprised of the outgoing neighbors of vertex @xmath8 , i.e. , @xmath9 and we assume in this paper that each agent @xmath10 can only observe its outgoing neighbors . the equations of motion for the @xmath0 agents @xmath11 are then given by @xmath12 with each @xmath13 a non - negative real number , which we call the interaction weight . the objective of the system is characterized by positive real numbers @xmath14 . we define the _ objective function _ @xmath15 as : @xmath16 the feasibility question we ask is the following : given a digraph @xmath17 , and a weight vector @xmath18 in @xmath19 , does there exist a set of non - negative interaction weights @xmath20 such that for any initial condition @xmath21 in @xmath2 , all agents will converge to the same point in @xmath2 specified by the objective map , i.e. , @xmath22 for all @xmath23 . in other words , we require that all the agents not only reach consensus , but also converge to a specific point which is a weighted sum of the initial positions of the agents . in the following section , we will convert this problem to one of asking whether there exists a sparse , infinitesimal stochastic matrix @xmath24 with a fixed zero pattern ( specified by the digraph ) such that @xmath24 has a simple zero eigenvalue with the vector @xmath25 being the corresponding left eigenvector . in the paper , we will provide a complete answer to the question of weighted consensus within model . in particular , we will characterize not only the set of objective maps which are feasible by choices of interaction weights , but also the set of interaction weights for a feasible objective map . note that the problem of evaluating averages in a _ distributed _ manner has also been handled using discrete - time dynamics @xcite . the paper is organized as follows . in section [ defthm ] , we introduce some definitions and state the main results of the paper . precisely , the main theorem characterizes the set of objective maps that can be realized over a given network topology . section iii is devoted to the proof of the main theorem . in section vi , we present a decentralized algorithm for finding a set of interaction weights associated with a feasible objective map . in particular , we relate the set of interaction weights to solutions of graph balancing . we provide conclusions in the last section . the paper ends with an appendix .

a consensus system is a linear multi - agent system in which agents communicate to reach a so - called consensus state , defined as the average of the initial states of the agents . consider a more generalized situation in which each agent is given a positive weight and the consensus state is defined as the weighted average of the initial conditions . we characterize in this paper the weighted averages that can be evaluated in a decentralized way by agents communicating over a directed graph . specifically , we introduce a linear function , called the objective map , that defines the desired final state as a function of the initial states of the agents . we then provide a complete answer to the question of whether there is a decentralized consensus dynamics over a given digraph which converges to the final state specified by an objective map . in particular , we characterize not only the set of objective maps that are feasible for a given digraph , but also the consensus dynamics that implements the objective map .

a consensus system is a linear multi - agent system in which agents communicate to reach a so - called consensus state , defined as the average of the initial states of the agents . consider a more generalized situation in which each agent is given a positive weight and the consensus state is defined as the weighted average of the initial conditions . we characterize in this paper the weighted averages that can be evaluated in a decentralized way by agents communicating over a directed graph . specifically , we introduce a linear function , called the objective map , that defines the desired final state as a function of the initial states of the agents . we then provide a complete answer to the question of whether there is a decentralized consensus dynamics over a given digraph which converges to the final state specified by an objective map . in particular , we characterize not only the set of objective maps that are feasible for a given digraph , but also the consensus dynamics that implements the objective map . in addition , we present a decentralized algorithm to design the consensus dynamics .

math-ph0505081

i

one of the possible applications of quantum deformations of groups and algebras @xcite is the construction of classical and quantum integrable systems with an arbitrary number of degrees of freedom which was presented in @xcite . in this context , poisson coalgebras ( poisson algebras endowed with a compatible coproduct structure ) have been shown to generate in a systematic way certain ( super)integrable classical hamiltonian systems . in this construction , once a symplectic realization of the algebra is given , the generators of the poisson coalgebra play the role of dynamical symmetries of the hamiltonian , while the coproduct is used to ` propagate ' the integrability to arbitrary dimension . from this coalgebra approach , several well - known classical ( super)integrable systems have been recovered and some integrable deformations for them , as well as new integrable systems , have also been obtained @xcite . recently , this integrability - preserving deformation procedure has been used to introduce both superintegrable and integrable free motions on two - dimensional ( 2d ) spaces with curvature , either constant or variable , respectively @xcite . therefore one could expect that potential terms can also be considered , in such a way that the coalgebra approach should provide ( super)integrable potentials on curved spaces . the aim of the present paper is to prove this assertion through the construction of some relevant hamiltonians . in order to make these ideas more explicit , let us consider the non - standard quantum deformation of @xmath0 @xcite written as a poisson coalgebra @xmath7 with ( deformed ) poisson brackets , coproduct and casimir given by \{,}=2 z \{,}=-2\{,}=4 [ ba ] _ _ z(j_i)=j_i ^z + e^-z j_i i=+,3 [ bb ] _ z= -^2 [ bc ] where @xmath1 is a real deformation parameter . a two - particle symplectic realization of ( [ ba ] ) in terms of two canonical pairs of coordinates @xmath8 and momenta @xmath9 with respect to the usual poisson bracket \{f , g}=_i=1 ^ 2 ( - ) , [ ag ] and that depends on two real parameters @xmath10 , reads @xcite l + . [ be ] by substituting ( [ be ] ) in ( [ bc ] ) we obtain the two - particle casimir & & c_z = ( q_1p_2 - q_2p_1)^2 e^-z q_1 ^ 2e^z q_2 ^ 2 + ( _ 1 e^2z q_2 ^ 2 + _ 2 e^-2z q_1 ^ 2 ) & & + ( _ 1 + _ 2 ) e^-z q_1 ^ 2e^z q_2 ^ 2 [ bf ] which poisson - commutes with the generators ( [ be ] ) . the limit @xmath11 of such deformed generators leads to the well - known symplectic realization of @xmath0 : l . [ beeb ] the coalgebra approach @xcite ensures that _ any _ smooth function @xmath12 defined on ( [ be ] ) provides an integrable hamiltonian , for which @xmath13 is the constant of the motion . in this paper we shall study some choices for @xmath14 that lead to hamiltonians which are quadratic in the momenta and belong to the family _ z=12 f ( z ) + ( z ) [ ahaa ] where @xmath15 and @xmath16 are arbitrary smooth functions such that the @xmath17 is well defined and @xmath18 . therefore integrable deformations of the free motion of a particle on the 2d euclidean space are obtained from ( [ ahaa ] ) by setting @xmath19 and @xmath20 . two main representative cases appear @xcite : * the simplest _ hamiltonian + l h_z^i=12 + [ freei ] which defines the geodesic motion on a 2d riemannian space with metric s^2= e^-z q_2 ^ 2 q_1 ^ 2 + e^z q_1 ^ 2 q_2 ^ 2 [ cc ] and whose non - constant gaussian curvature @xmath21 is given by k(q_1,q_2)=- z ( z(q_1 ^ 2+q_2 ^ 2 ) ) . [ cd ] * the _ superintegrable _ hamiltonian + l h_z^s=12 e^ z + [ frees ] that leads to a riemannian metric of constant curvature which coincides with the deformation parameter , @xmath22 , namely s^2= e^-z q_1 ^ 2e^-2 z q_2 ^ 2 q_1 ^ 2 + e^-z q_2 ^ 2 q_2 ^ 2 . [ ec ] consequently , the ` classical ' limit @xmath2 corresponds to a zero - curvature limit . section 2 is devoted to the explicit solution of the geodesic flows on all these spaces , that complete the preliminary description given in @xcite and include deformations of the 2d sphere and hyperbolic spaces as well as of the @xmath23d ( anti-)de sitter spacetimes . the introduction of integrable potentials with coalgebra symmetry is then analysed by making use of the function @xmath16 and taking both parameters @xmath24 arbitrary . in fact , any @xmath16 such that @xmath25 can be interpreted as a deformation of the well - known 2d smorodinsky winternitz ( sw ) system @xcite formed by an isotropic harmonic oscillator with angular frequency @xmath26 plus two ` centrifugal terms ' governed by @xmath27 : ^sw = 12 ( p_1 ^ 2 + p_2 ^ 2 ) + + + _ 0 ( q_1 ^ 2+q_2 ^ 2 ) . [ ai ] on the other hand , analogues of the kepler coulomb ( kc ) potential can be obtained by considering any @xmath16 such that @xmath28 ( @xmath29 is another real constant ) : ^kc = 12 ( p_1 ^ 2 + p_2 ^ 2 ) + + - . [ aai ] in section 3 we shall propose the following _ integrable _ sw and kc systems , @xmath30 and @xmath31 , on the spaces of non - constant curvature previously defined through @xmath32 ( [ freei ] ) : & & h^_z=12 + _ 0 [ ahad ] + & & h^_z=12 - e^2 z . [ ahat ] the sw potential on the spaces of constant curvature with free motion given by @xmath33 ( [ frees ] ) will be introduced by means of the following choice for the hamiltonian ^_z=12 ^ z + _ 0 e^ z ^_z e^ z . [ bh ] we already know @xcite that this gives rise , under ( [ be ] ) , to a stckel - type system @xcite and so determines a _ superintegrable _ deformation of ( [ ai ] ) since , besides ( [ bf ] ) , there exists an additional constant of the motion given by _ z= e^z q_1 ^ 2 p_1 ^ 2 + e^z q_1 ^ 2+e^2 z q_1 ^ 2 . [ bjj ] note that this extra integral is _ not _ obtained from the coalgebra symmetry of the hamiltonian . parameters must vanishes and both the specific additional ` laplace - runge - lenz ' integral and the appropriate @xmath16 compatible with it should be previously obtained . ] section 4 is fully devoted to the study of @xmath34 , which is shown to provide a superintegrable system containing a ( curved ) harmonic oscillator together with two more potential terms ( either oscillators or centrifugal barriers ) on the usual sphere , hyperbolic and ( anti-)de sitter spaces . the explicit potentials are analysed in detail for each particular space . we stress that we recover known results on the riemannian spaces @xcite but also we obtain new ones on the relativistic spacetimes . finally , some remarks and comments close the paper .

a family of classical integrable systems defined on a deformation of the two - dimensional sphere , hyperbolic and ( anti-)de sitter spaces is constructed through hamiltonians defined on the non - standard quantum deformation of a poisson coalgebra . all these spaces have a non - constant curvature that depends on the deformation parameter . as particular cases , the analogues of the harmonic oscillator and kepler coulomb potentials on such spaces are proposed . another deformed hamiltonian is also shown to provide superintegrable systems on the usual sphere , hyperbolic and ( anti-)de sitter spaces with a constant curvature that exactly coincides with . according to each specific space , the resulting potential is interpreted as the superposition of a central harmonic oscillator with either two more oscillators or centrifugal barriers . + e-09001 burgos , spain _ + e - mail : [email protected] , [email protected] _dipartimento di fisica , universit di roma tre and instituto nazionale di fisica nucleare sezione di roma tre , via vasca navale 84 , + i-00146 roma , italy _ + e - mail : [email protected] pacs : 02.30.lk 02.20.uw

a family of classical integrable systems defined on a deformation of the two - dimensional sphere , hyperbolic and ( anti-)de sitter spaces is constructed through hamiltonians defined on the non - standard quantum deformation of a poisson coalgebra . all these spaces have a non - constant curvature that depends on the deformation parameter . as particular cases , the analogues of the harmonic oscillator and kepler coulomb potentials on such spaces are proposed . another deformed hamiltonian is also shown to provide superintegrable systems on the usual sphere , hyperbolic and ( anti-)de sitter spaces with a constant curvature that exactly coincides with . according to each specific space , the resulting potential is interpreted as the superposition of a central harmonic oscillator with either two more oscillators or centrifugal barriers . the non - deformed limit of all these hamiltonians can then be regarded as the zero - curvature limit ( contraction ) which leads to the corresponding ( super)integrable systems on the flat euclidean and minkowskian spaces . angel ballesteros , francisco j. herranz and orlando ragnisco _departamento de fsica , universidad de burgos , pza.misael bauelos s.n . , + e-09001 burgos , spain _ + e - mail : [email protected] , [email protected] _dipartimento di fisica , universit di roma tre and instituto nazionale di fisica nucleare sezione di roma tre , via vasca navale 84 , + i-00146 roma , italy _ + e - mail : [email protected] pacs : 02.30.lk 02.20.uw

1502.04212

i

let us consider a non - convex higher order variational problem in the one - dimensional case , which is the obstacle problem for the energy as proposed in @xcite : @xmath1=\varepsilon^2 \int \kappa^2 ds + \int ds - \int_{\{u=\psi\ } } ( 1-\alpha)\ ds.\end{aligned}\ ] ] here a smooth function @xmath2\rightarrow\mathbb{r}$ ] called an _ obstacle _ ( function ) , a constant coefficient @xmath3 , and a continuous function @xmath4\rightarrow(0,1)$ ] are given . the function @xmath5 is an admissible function constrained above the obstacle , and @xmath6 , @xmath7 denote the curvature and the arclength of the graph of @xmath5 respectively . the first term of the energy is called _ bending energy _ , the second term _ tension _ , the third term _ adhesion energy _ , and @xmath8 is called _ adhesion coefficient_. the multiple constant of the tension is normalized to one . the adhesion coefficient @xmath8 can be inhomogeneous so that it may depend on a space variable . according to @xcite , this problem is motivated to determine the shape of membranes , interfaces or filaments on rippled surfaces ( as figure [ membranes ] ) in certain mesoscopic or nearly mesoscopic settings . the coefficients @xmath9 and @xmath8 and the obstacle function @xmath10 depend on the setting of materials , scaling and so on . in this case the graph of @xmath5 is a membrane . in this paper we consider the one dimensional model so when one considers a membrane it depends on only one direction and invariant in other direction in our setting . in addition , we regard the bending energy which is a higher order term as a perturbation , that is , only consider for sufficiently small @xmath3 . cc , width=188 ] , width=188 ] a characteristic point of this energy is to contain the adhesion energy . by this energy , surfaces shall reasonably adhere to the obstacle in order to decrease the energy . accordingly , there may occur patterns as drawn in figure [ membranes ] in this model . however that law is complicated . one of physical and mathematical concerns is to perceive such pattern formation . we shall first take the simplest approximation @xmath11 in order to consider the case @xmath9 is sufficiently small . this approximation simplifies the problem ( [ problem1 ] ) thus we can obtain many fine properties for minimizers ( this is one of the important results of this paper , see theorem [ regezero ] ) . it is rigorously stated in theorem [ regezero ] , but roughly speaking the shape of any minimizer of @xmath12 is as drawn in figure [ membrane ] . there occur `` edge '' singularities at the free boundary and their angles are determined by the adhesion coefficient at the place of the free boundary , symbolically @xmath13 ( young s equation ) . this condition has been formally given in @xcite . however , even if @xmath11 , the energy is not convex and may admit that there exist multiple minimizers lacking consistency in their shape . that is to say , for instance , either of two different states as drawn in figure [ membrane ] might be a minimizer for the same energy . since this minimizing problem is considered to be a physical model , this non - uniqueness may be due to some small effect , perhaps , of higher order terms . therefore , restoring the effect of the bending energy , it is expected to ameliorate the approximation . cc [ membrane],width=188 ] [ membrane],width=188 ] the main goal of this paper is a formulation of a singular perturbation by the bending energy , that is , to characterize the limit of minimizers of @xmath14 as @xmath15 rigorously . to this end we utilize the notion of @xmath0-convergence established by de giorgi @xcite in the 70 s ( more precisely , see @xcite , @xcite , @xcite , @xcite ) which is a convergence of energy functionals for minimizing problems . the idea of this convergence is to identify the first nontrivial term in an asymptotic expansion for the energy of perturbed problems . our main singular limit result is rigorously stated in theorem [ gammathm ] , but roughly speaking as follows : [ mainthm1 ] if we define the singular limit energy @xmath16 by @xmath17:=\int_{\partial\{u>\psi\}}4(\sqrt{2}-\sqrt{1+\alpha})\ d\mathcal{h}^0,\ ] ] then the @xmath0-convergence holds with respect to @xmath18-norm : @xmath19 where @xmath20 is a certain space of admissible functions @xmath21 . from this theorem , the following asymptotic expansion is also valid for our problem in some sense ( see @xcite , @xcite ) : @xmath22 thus it means that @xmath16 is the main effect of the bending energy and its quantity only depends on the @xmath23-measure ( the number ) of the free boundary and the adhesion coefficient there . since the adhesion coefficient at the free boundary determines the contact angle there ( @xmath13 ) as mentioned above , it also means that the effect is determined by the number of `` edge '' singularities and their angles . thanks to our singular limit result and geometrical intuition for the minimizing problem of @xmath16 , we can easily find a key effect of the bending energy . for example , if @xmath24 and there are multiple minimizers of @xmath12 then the one which has less number of edges shall be a minimizer of @xmath14 when @xmath3 is sufficiently small . more precisely , by theorem [ mainthm1 ] and the fundamental theorem of @xmath0-convergence , we obtain the following : [ limitcoro ] if @xmath25 in @xmath18 and any @xmath26 is a minimizer of @xmath14 in ( [ problem1 ] ) , then @xmath5 minimizes @xmath16 among minimizers of @xmath12 in ( [ problem1 ] ) . it turns out that we can characterize the limit of minimizers of @xmath27 as @xmath15 by our theorem . an important point of our proof of theorem [ mainthm1 ] is to prove the liminf condition of @xmath0-convergence ( see definition [ gammaconv ] ) . the proof is mainly separated into two parts . the first part is to prove that it suffices to consider more regular sequences which are `` close '' to a minimizer of @xmath12 in some sense . to state it rigorously , we introduce a notion called _ @xmath28-associate _ which explains closeness of functions . especially , the part regarding how to coincide with @xmath10 is a key point because adhering or detaching leads to a discontinuous transition in our energy . we replace a general sequence by @xmath28-associate of @xmath29-regularity converging to a minimizer of @xmath12 so that all quantities in the energy are well - defined with no increase of the energy . the second part is to obtain a lower estimate for functions @xmath28-associated with a minimizer of @xmath12 . by this procedure , we are able to handle the energy geometrically and establish a modica - mortola type inequality to prove the liminf condition . now let us briefly survey some mathematical problems related to our problem from two viewpoints . in the non - adhesive case @xmath30 , the energy in ( [ problem1 ] ) is consisting of the total squared curvature functional and the length functional : @xmath31 so - called _ euler s elastic energy_. the critical points of the energy are called _ elastica _ ( usually under boundary conditions and the length constraint for a curve @xmath32 ) . this problem is first considered by euler in 1744 @xcite . numerous authors have considered this variational problem or related problems under various constraints in order to analyze the configuration of elastic bodies ( see @xcite , @xcite , or @xcite including a very well - written summary of the history of elastic problems by one section ) . however , there are still many unclear points in this problem because of difficulties of a higher order problem . our problem is the variational problem for the euler s elastic energy with the adhesion term under an obstacle - type constraint , thus it seems to have similar difficulties . to circumvent such difficulties , we regard the bending energy as a perturbation in this paper . obstacle problems , which are variational problems under obstacle - type constraints , are motivating problems invoking free boundaries and have been studied for a long time ( @xcite , @xcite , @xcite , @xcite ) . a typical model is for the area functional ( or the dirichlet energy , the linearized version ) : @xmath33 under a boundary condition . here @xmath5 is a function on a bounded smooth domain @xmath34 . this is so - called the unilateral plateaux problem . this problem invokes the free boundary @xmath35 and in the non - coincidence set @xmath36 the graph of a solution @xmath5 is a minimal surface ( or harmonic ) . generally , if an energy is convex , bounded and coercive in a sense as ( [ problem3 ] ) then the classical variational inequality approach can work . thus we can obtain many fine properties of solutions ( at least in the linearized case ) , for instance the uniquely existence , further the regularity of solution and of its free boundary @xcite . the problem ( [ problem3 ] ) corresponds to the case no bending @xmath11 and no adhesion @xmath30 in our problem ( [ problem1 ] ) . in the problem ( [ problem3 ] ) , we only obtain a natural singular limit even if the energy is perturbed by bending ( * ? ? ? * theorem 9.5 ) . therefore , in the non - adhesive case , it seems that higher order terms can be neglected when @xmath37 unlike our problem . our problem is closely related to the alt - caffarelli type variational problem @xcite which is a model of cavitation : @xmath38 under a boundary condition , where @xmath39 is a certain function . this is not an obstacle problem explicitly but the solutions are automatically constrained above zero , thus it is equivalent to the problem with the constraint @xmath40 ( flat obstacle problem ) . this problem is one of important interface models and has been generalized variously ( for example , see @xcite generalizing the first term , @xcite the second term , or their references ) . especially , yamaura @xcite considered a non - linearized case , namely the case that the first term is replaced to the area functional . our problem is a generalization of the ( one - dimensional ) non - linearized alt - caffarelli problem regarding obstacle . indeed , if @xmath11 and @xmath41 in ( [ problem1 ] ) then it is equivalent to @xmath42 since @xmath43 in @xmath44 . thus the result in this paper is particularly valid for ( [ problem4 ] ) with area functional instead of the dirichlet energy and with continuous @xmath45\rightarrow(0,1)$ ] . in view of singular perturbation by @xmath0-convergence for variational problems , there are some related results especially in phase transition models . one of the most celebrated results is , owing to modica - mortola @xcite ( and @xcite , @xcite ) , for the energy arising from the van der waals - cahn - hilliard theory of fluid - fluid phase transitions : @xmath46 where @xmath47 satisfying a volume constraint and @xmath48 is a double - well potential function , usually it is taken as @xmath49 ( @xmath50 ) . they proved that the singular limit ( @xmath0-limit ) of the energy is proportional to the area of a transition layer . these works are generalized to the vector - valued case , anisotropic cases and multi - well potential cases ( see @xcite and references cited there ) . furthernore , there are several higher order version results for the following energy : @xmath51 one of the earliest studies is for the functional arising from the theory of smectic liquid crystals introduced by aviles - giga @xcite . the authors considered the case that @xmath52 satisfies certain boundary conditions and @xmath48 is a `` single - circle - well '' potential @xmath53 ( @xmath54 ) . the energy ( [ problem5 ] ) or ( [ problem6 ] ) or similar one also arises from , for example the theory of solid - solid phase transitions , thin - films and magnetism . there are several singular limit results for them ( @xcite , @xcite , @xcite , @xcite , @xcite ) . however , the number of results of higher order singular perturbations are limited compared with the first order cases . our result is one of the higher order singular perturbations and means that the problem ( [ problem1 ] ) can be regarded as a phase transition model as above . the cost of transition between the phase @xmath55 and @xmath36 is determined by the place of a transition layer . as mentioned above , a key point in our proof of the liminf condition of @xmath0-convergence is to reduce a general sequence to a sequence which is easy to handle . we mention that this concept resembles the `` slicing '' technique used in @xcite . this paper is organized as follows : in [ presec ] we prepare some notations and definitions . in [ ezerosec ] we first consider the case @xmath11 and derive some properties of minimizers of @xmath12 . they are useful to prove our singular limit result . in [ gammaconvsec ] we state our main singular limit theorem ( theorem [ gammathm ] ) , and we prove it in [ liminfsec ] and [ limsupsec ] .

a free boundary problem arising from materials science is studied in the one - dimensional case . the problem studied here is an obstacle problem for the non - convex energy consisting of a bending energy , tension and an adhesion energy . if the bending energy , which is a higher order term , is deleted then `` edge '' singularities of the solutions ( surfaces ) may occur at the free boundary as alt - caffarelli type variational problems . the main result of this paper is to give a singular limit of the energy utilizing the notion of-convergence , when the bending energy can be regarded as a perturbation . this singular limit energy only depends on the state of surfaces at the free boundary as seen in singular perturbations for phase transition models .

a free boundary problem arising from materials science is studied in the one - dimensional case . the problem studied here is an obstacle problem for the non - convex energy consisting of a bending energy , tension and an adhesion energy . if the bending energy , which is a higher order term , is deleted then `` edge '' singularities of the solutions ( surfaces ) may occur at the free boundary as alt - caffarelli type variational problems . the main result of this paper is to give a singular limit of the energy utilizing the notion of-convergence , when the bending energy can be regarded as a perturbation . this singular limit energy only depends on the state of surfaces at the free boundary as seen in singular perturbations for phase transition models .

astro-ph0506152

i

proper motion catalogs have historically been the primary sources for the identification of stellar systems in the vicinity of the sun . while star distances are ultimately determined from measurements of annual parallactic motions , these require a substantial investment of time and effort . parallax programs are thus most successful when they rely on input lists of objects already suspected to be nearby . since a large proper motion is an indicator of proximity , high proper motion ( hpm ) stars have always been prime targets for parallax programs . it is a historical fact that the vast majority of the stars now known to be in the `` solar neighborhood '' ( @xmath5 pc ) , and recorded in compendiums such as the _ third catalog of nearby stars _ @xcite hereafter the cns3 , or the nasa _ nstars database _ , have first been identified as hpm stars . perhaps the most important feature of the nearby star census is the fact that it is dominated by low - luminosity red dwarfs , with absolute magnitudes @xmath6 . the vast majority of the `` solar neighborhood '' red dwarfs are therefore not listed in the hipparcos catalog @xcite which has a limiting magnitude @xmath7 . on the other hand , most nearby red dwarfs are expected to be detected on the photographic plates of the large schmidt telescope surveys ( e.g. poss - i , poss - ii , ses , aao ) which typically reach @xmath8 . because nearby red dwarfs have optical colors similar to those of distant giants or dust - reddened stars , they are most easily and reliably identified by their large proper motions . in fact , the main strength of proper motion surveys is that they can locate nearby stars independently of their physical appearance ( color , luminosity ) . one caveat is that a high proper motion is neither a necessary nor a sufficient condition for a star to be nearby . nearby stars can have small proper motions if their motion vector is pointing toward , or away from the sun @xcite . conversely , distant stars can have large proper motions if their transverse motion relative to the sun is also large , such as is typically the case for stars on galactic halo orbits . hence the dilemma : the completeness of a nearby star census based on proper motion surveys increases as the proper motion limit is set to smaller values , but decreasing the proper motion limit also greatly increases the number of distant stars that make it into the survey , which can be viewed as `` contaminants '' for parallax programs aimed at finding the nearest stars . the earlier proper motion catalogs of @xcite and @xcite had relatively high proper motion limits ( @xmath9 yr@xmath1 - 0.5@xmath10 yr@xmath1 ) and together contained a little over 2500 stars , a manageable size for parallax programs . however , later catalogs became increasingly larger , bringing the number of known high proper motion stars to sizes difficult to manage . the catalogs by @xcite and @xcite contain 11,000 + stars with @xmath11 yr@xmath1 , while the famous `` nltt catalog '' of @xcite , the main reference in the field for 25 years , contains over 58,000 stars with @xmath12 yr@xmath1 , down to a magnitude @xmath13 . these large catalogs provide several times more targets than can be handled by existing ground - based parallax programs @xcite . to illustrate this , one need only consider the yale catalog of trigonometric parallaxes @xcite , which compiles all published ground - based parallax measurements prior to 1995 , and which contains data for only 1501 stars fainter than @xmath14 . given these limitations , most efforts at finding nearby stars have focused on a subsample of the nltt , the `` lhs catalog '' @xcite , which basically lists the 4470 nltt stars with the largest proper motions ( @xmath15 yr@xmath1 ) . it is however possible to mine large proper motion catalogs for nearby stars , by using secondary distance estimators such as photometric or spectroscopic distance moduli . photometry and spectroscopy are more readily obtained for large samples of objects than parallax measurements , although they provide much less reliable distance estimates . but even approximate distance moduli can be used to trim a large proper motion sample down to a more manageable list of probable nearby stars . luyten himself devoted substantial efforts to obtaining photographic magnitudes and colors for all the stars in his catalogs , though these were sometimes only approximate . while his @xmath16,@xmath17 photographic magnitude system was used to identify some nearby objects @xcite , its usefulness in estimating distance moduli for the ubiquitous red dwarfs was found to be very limited in practice @xcite . more photometric / spectroscopic data was needed , and the follow - up vri photometric survey of @xmath18 nltt stars with @xmath19 yr@xmath1 @xcite proved successful in identifying 295 new solar neighborhood candidates . a major advance came with the availability of accurate infra - red jhk@xmath20 photometry from the 2 micron all - sky survey ( 2mass ) . in a series of papers ( `` meeting the cool neighbors . i .- ix . '' ) , i. n. reid and colleagues used data from the 2mass _ second incremental release _ to systematically mine the nltt for nearby stars . in the first paper of their series , a combination of luyten s estimated photographic red magnitude ( @xmath17 ) with accurate @xmath21 magnitudes from the _ 2mass second incremental release _ was succesfully used to identify a subsample of candidate red dwarfs within 20 pc of the sun @xcite . distance moduli were calculated based on the 2mass magnitudes and follow - up bvri photometry @xcite , and spectroscopy @xcite of the nltt candidates . unfortunately , positions quoted in the nltt catalog often contain large errors @xcite ; this proved a major impediment , as 2mass counterparts of nltt stars sometimes could not be found , or were mismatched . these problems were mitigated by the use of the _ revised nltt _ ( or rnltt ) catalog of @xcite , which provide re - estimates of nltt positions , and through the use of additional selection criteria ( e.g. color - color cuts ) to identify and reject mismatches @xcite . with these successes , the nearby star census appears now to be only limited by the nltt catalog itself . apart from the issues of the accuracy of its photometry and astrometry , the nltt has long been known to be significantly incomplete in some parts of the sky @xcite . the nearby star census would benefit from a more complete proper motion survey , but also from an expansion to fainter magnitudes , and especially from an expansion to smaller proper motions , the nltt itself being limited to stars with @xmath22 yr@xmath1 . this is why the new lspm - north catalog , as a replacement of the old nltt , promises to improve significantly on nearby stars surveys . the lspm - north catalog @xcite is the product of a massive data mining of the digitized sky surveys ( dss ) with a specialized software ( superblink ) that uses image subtraction algorithms to identify moving and variable objects . the lspm - north lists 61,976 stars with proper motions @xmath23 down to v=21.0 , and is estimated to be @xmath24 complete down to @xmath25 . besides being marginally deeper , and significantly more complete than the nltt , the lspm is also much more accurate , with positions within @xmath26 at the 2000.0 epoch , and optical photographic magnitudes to @xmath27mags obtained from the usno - b1.0 catalog of @xcite . the lspm - north catalog also provides counterparts from the 2mass _ all sky point source catalog _ @xcite when they exist . by being deeper , more accurate , and more complete , the lspm - north catalog supersedes the nltt in all respects ( though only at northern declinations for now ) . the use of the 2mass _ all sky point source catalog _ also offers the opportunity to expand significantly upon the reid _ analysis , which was restricted to the fraction of the sky covered by the 2mass _ second incremental release_. the first paper of this series presents our initial efforts at identifying nearby stars in the lspm - north catalog , specifically the identification of new candidate main - sequence dwarfs within 33pc of the sun . data are found in the literature for all lspm stars that have published trigonometric parallaxes or photometric / spectroscopic distance moduli . a calibration of the @xmath28 $ ] relationship in the @xmath29 system of the lspm - north catalog provides the identification of 1672 new candidate nearby stars with distances estimated to be within 33pc of the sun . identification of nearby white dwarfs from the lspm - north catalog will be detailed in the second paper of this series , while a subsequent paper will address the problem of identifying nearby metal - pool subdwarfs ( lpine , _ in preparation _ ) . this paper is organized as follows : 2 describes the calibration of the @xmath30 color magnitude relationship for main sequence dwarfs , which is used to estimate photometric distance moduli of lspm stars . 3 gives complete lists of nearby dwarfs listed in the lspm catalog for which there exists published trigonometric parallaxes or photometric / spectroscopic distance moduli , and presents the selection of new candidate stars within 33pc . 4 analyzes the current completeness level of the nearby star census in terms of limiting magnitude and proper motion selection . the main results are summarized in the conclusion ( 5 ) .

trigonometric parallax measurements are found in the literature for 1,676 of the stars in the sample ; photometric and spectroscopic distance moduli are found for another 783 objects . the remaining 1,672 objects are reported here as nearby star candidates for the first time . the list of new candidates includes 539 stars which are suspected to be within 25 parsecs of the sun , including 63 stars estimated to be within only 15 parsecs . the current completeness of the census of nearby stars in the northern sky is discussed in light of the new candidates presented here .

a list of 4,131 dwarfs , subgiants , and giants located , or suspected to be located , within 33 parsecs of the sun is presented . all the stars are drawn from the new lspm - north catalog of 61,976 stars with annual proper motions larger than yr . trigonometric parallax measurements are found in the literature for 1,676 of the stars in the sample ; photometric and spectroscopic distance moduli are found for another 783 objects . the remaining 1,672 objects are reported here as nearby star candidates for the first time . photometric distance moduli are calculated for the new stars based on the ( m,v - j ) relationship , calibrated with the subsample of stars which have trigonometric parallaxes . the list of new candidates includes 539 stars which are suspected to be within 25 parsecs of the sun , including 63 stars estimated to be within only 15 parsecs . the current completeness of the census of nearby stars in the northern sky is discussed in light of the new candidates presented here . it is estimated that ( ) of nuclear burning stars within 33 parsecs ( 25 parsecs ) of the sun remain to be located . the missing systems are expected to have proper motions below the yr limit of the lspm catalog .

astro-ph0506152

c

this paper has presented a list of nearby and candidate nearby main sequence stars , subgiants , and giants within 33 pc of the sun . the list is based on an analysis of the lspm - north catalog of stars with proper motions @xmath105 yr@xmath1 . the census contains a total of 4221 stars in the half of the sky north of the j2000 celestial equator . the list includes 1676 previously known nearby stars with measured trigonometric parallaxes , 783 previously suspected nearby objects , and 1762 new candidate nearby stars . a relationship is determined between the absolute v magnitude ( @xmath42 ) and the @xmath44 color index . this relationship can be used to calculate photometric distance moduli @xmath179 in the @xmath135 magnitude system . this is convenient for estimating distances of all the stars in the lspm - north ( for which @xmath43 and @xmath180 magnitude estimates exist ) to the extent that the relationship is applied to main sequence(h - burning ) stars of near - solar metallicity . for single stars , the relationship is accurate to @xmath181 mag , which means that it provides distance estimates accurate to @xmath182 . the relationship breaks down for white dwarfs and subdwarfs , whose cases will be addressed in upcoming papers of this series . it is found , however , that the sample of main sequence dwarfs selected based on the color - magnitude relationship should not be significantly contaminated by mis - identified white dwarfs and subdwarfs , as long as the search is limited to stars within 33 pc of the sun . the main purpose of the present list of candidate objects is to provide targets for upcoming parallax programs . a fraction of the 783 previously suspected nearby ms stars are probably already on parallax programs . the list of 1762 new candidate nearby stars should be examined to sort out the most promising candidates to be added to the parallax programs . note that current distance estimates based on photometry are only approximate , and should be used with caution . a large spectroscopic follow - up program is under way , which will soon provide spectral types and radial velocities for most of the new candidate nearby stars presented here . results will be presented in upcoming papers in this series . while these will also yield spectroscopic distance moduli , these are not expected to be significantly more accurate than the photometric distance moduli presented here . accurate distances will ultimately come from parallax measurements . the census of nuclear - burning stars within 33 pc of the sun , based on the present study , appears to be only @xmath172 for the northern sky . the census of nuclear - burning stars within 25 pc , the traditional confines of the so - called `` solar neighborhood '' is estimated to be @xmath175 complete . it is revealed that the main source of incompleteness lies in the low proper motion limit ( @xmath105 yr@xmath1 ) of the lspm - north catalog . expanding our survey to reach a smaller proper motion limit appears to be the best way to significantly increase the completeness of the nearby star census . an extension of the superblink survey down to a proper motion limit of @xmath183 yr@xmath1 is now being completed , and a second extension down to @xmath184 yr@xmath1 is being planned . an analysis of the @xmath184 yr@xmath1 catalog should ultimately yield the identification of @xmath185 of the nuclear burning stars up to and at a distance of 25 pc . this work has been made possible by the generous support of hilary lifsitz and of the american museum of natural history . the author is indebted to michael m. shara ( amnh ) and r. michael rich ( ucla ) for their constant support and encouragement . cutri , r. m. , _ et al . _ 2003 , the 2mass all - sky catalog of point sources university of massachusetts and infrared processing and analysis center ( ipac / california institute of technology _ cds - vizier catalog number ii/246 _ ) giclas , h. l. , burnham , r. , & thomas , n. g. 1971 , lowell proper motion survey northern hemisphere . the g numbered stars . 8991 stars fainter than magnitude 8 with motions @xmath186 0".26/year , flagstaff , arizona : lowell observatory _ cds - vizier catalog number i/79 _ ) hog e. , fabricius c. , makarov v.v . , urban s. , corbin t. , wycoff g. , bastian u. , schwekendiek p. , & wicenec a. 2000 , the tycho-2 catalogue of the 2.5 million brightest stars , , 355 , 27 ( _ cds - vizier catalog number i/259 _ ) perryman , m. a. c. 1997 , the hipparcos and tycho catalogues . astrometric and photometric star catalogues derived from the esa hipparcos space astrometry mission , publisher : noordwijk , netherlands : esa publication ( _ cds - vizier catalog number i/239 _ ) reid , i. n. , cruz , k. l. , laurie , s. p. , liebert , j. , dahn , c. c. , harris , h. c. , guetter , h. h. , stone , r. c. , canzian , b. , luginbuhl , c. b. , levine , s. e. , monet , a. k. b. , monet , d. g. 2003b , , 125 , 354 llrrrrrrrrrr g 129 - 55 & lspm j0000 + 1659 & 0.200457 & 16.988232 & -0.069 & -0.305 & 8.80 & 1.85 & [email protected] & hip & & 31.4@xmath136 1.2 + lhs 101 & lspm j0002 + 2704 & 0.542444 & 27.082132 & 0.830 & -0.989 & 5.77 & 1.07 & [email protected] & hip & & 12.4@xmath136 0.5 + g 130 - 40 & lspm j0004 + 2316 & 1.234669 & 23.269632 & 0.382 & -0.007 & 7.82 & 1.42 & [email protected] & hip & & 25.6@xmath136 0.6 + lhs 1014 & lspm j0005 + 4547 & 1.295397 & 45.786568 & 0.870 & -0.151 & 10.05 & 3.35 & [email protected] & hip & [email protected] & 11.5@xmath136 0.2 + lhs 1016 & lspm j0005 + 4548s & 1.420823 & 45.810383 & 0.839 & -0.162 & 8.97 & 2.83 & [email protected] & hip & [email protected] & 11.8@xmath136 0.4 + lhs 1017 & lspm j0005 + 4548n & 1.420888 & 45.812080 & 0.879 & -0.154 & 8.83 & 2.73 & [email protected] & hip & [email protected] & 11.8@xmath136 0.4 + ltt 10023 & lspm j0006 + 2901 & 1.653266 & 29.021517 & 0.381 & -0.178 & 6.07 & 1.34 & [email protected] & hip & & 13.7@xmath136 0.1 + g 243 - 13 & lspm j0006 + 5826 & 1.565996 & 58.436764 & 0.271 & 0.030 & 6.36 & 1.49 & [email protected] & hip & & 20.3@xmath136 0.4 + lhs 1022 & lspm j0007 + 0800 & 1.996295 & 8.005391 & -0.349 & -0.413 & 13.33 & 3.94 & [email protected] & ypc & [email protected] & 22.7@xmath136 3.8 + v * alf and & lspm j0008 + 2905 & 2.096912 & 29.090433 & 0.136 & -0.162 & 2.05 & -0.08 & [email protected] & hip & & 29.8@xmath136 0.7 + v * v740 cas & lspm j0008 + 6627 & 2.238476 & 66.456650 & 0.178 & 0.002 & 8.62 & 1.59 & [email protected] & hip & & 31.9@xmath136 2.3 + lhs 1027 & lspm j0009 + 5908 & 2.294539 & 59.149780 & 0.527 & -0.180 & 2.27 & 0.56 & [email protected] & hip & & 16.7@xmath136 0.2 + ross 310 & lspm j0011 + 5820 & 2.838105 & 58.349915 & 0.235 & 0.020 & 9.48 & 2.29 & [email protected] & hip & & 28.0@xmath136 4.7 + ccdm j00126 + 214 & lspm j0012 + 2142n & 3.139525 & 21.713451 & 0.183 & -0.289 & 11.91 & 3.07 & [email protected] & hip & [email protected] & [email protected] + lp 348 - 42 & lspm j0012 + 2142s & 3.143580 & 21.706341 & 0.187 & -0.294 & 13.65 & 3.99 & [email protected] & hid & [email protected] & [email protected] llrrrrrrrrrrrrr lp 404 - 33 & lspm j0008 + 2050 & 2.224675 & 20.840403 & -0.061 & -0.255 & 13.90 & 5.03 & [email protected] & cns & & & [email protected] & [email protected] + lp 191 - 43 & lspm j0008 + 4918 & 2.229864 & 49.315651 & 0.347 & 0.205 & 16.53 & 5.67 & & & [email protected] & r03 & [email protected] & [email protected] + & lspm j0011 + 2259 & 2.970996 & 22.984573 & 0.146 & -0.229 & 11.98 & 3.12 & & & [email protected] & r03 & [email protected] & [email protected] + lhs 1037 & lspm j0011 + 3303 & 2.985193 & 33.054703 & -0.544 & -0.395 & 12.98 & 3.91 & [email protected] & r04 & & & [email protected] & [email protected] + lp 149 - 35 & lspm j0012 + 5059 & 3.238347 & 50.988163 & 0.295 & 0.032 & 17.24 & 5.83 & & & [email protected] & r03 & [email protected] & [email protected] + lp 404 - 66 & lspm j0016 + 2003 & 4.236689 & 20.065327 & 0.228 & 0.024 & 14.11 & 4.43 & [email protected] & cns & & & [email protected] & [email protected] + lp 404 - 80 & lspm j0017 + 2057w & 4.494271 & 20.955217 & -0.272 & -0.384 & 12.16 & 3.47 & [email protected] & r04 & & & [email protected] & [email protected] + lp 404 - 81 & lspm j0017 + 2057e & 4.496541 & 20.956783 & -0.272 & -0.384 & 10.72 & 2.47 & [email protected] & r04 & & & & [email protected] + & lspm j0017 + 3028 & 4.491442 & 30.469551 & 0.287 & 0.052 & 16.28 & 4.61 & & & [email protected] & r04 & [email protected] & [email protected] + lp 292 - 66 & lspm j0018 + 2748 & 4.723306 & 27.813824 & 0.387 & -0.101 & 13.80 & 4.27 & [email protected] & cns & & & [email protected] & [email protected] + lhs 1060 & lspm j0021 + 1843 & 5.318830 & 18.732157 & 0.682 & -0.084 & 17.17 & 5.85 & & & [email protected] & r03 & [email protected] & [email protected] + lp 149 - 56 & lspm j0021 + 4912 & 5.490994 & 49.210533 & 0.204 & -0.031 & 12.74 & 3.60 & [email protected] & cns & & & [email protected] & [email protected] + lhs 1073 & lspm j0025 + 2253 & 6.335831 & 22.886417 & -0.241 & -0.457 & 14.71 & 4.99 & [email protected] & cns & & & [email protected] & [email protected] + lp 193 - 488 & lspm j0026 + 3947 & 6.510745 & 39.789875 & 0.224 & 0.021 & 16.33 & 5.34 & & & [email protected] & r03 & [email protected] & [email protected] + lp 349 - 25 & lspm j0027 + 2219 & 6.983301 & 22.325680 & 0.408 & -0.174 & 17.40 & 6.79 & & & [email protected] & r03 & [email protected] & [email protected]

a list of 4,131 dwarfs , subgiants , and giants located , or suspected to be located , within 33 parsecs of the sun is presented . all the stars are drawn from the new lspm - north catalog of 61,976 stars with annual proper motions larger than yr . it is estimated that ( ) of nuclear burning stars within 33 parsecs ( 25 parsecs ) of the sun remain to be located .

a list of 4,131 dwarfs , subgiants , and giants located , or suspected to be located , within 33 parsecs of the sun is presented . all the stars are drawn from the new lspm - north catalog of 61,976 stars with annual proper motions larger than yr . trigonometric parallax measurements are found in the literature for 1,676 of the stars in the sample ; photometric and spectroscopic distance moduli are found for another 783 objects . the remaining 1,672 objects are reported here as nearby star candidates for the first time . photometric distance moduli are calculated for the new stars based on the ( m,v - j ) relationship , calibrated with the subsample of stars which have trigonometric parallaxes . the list of new candidates includes 539 stars which are suspected to be within 25 parsecs of the sun , including 63 stars estimated to be within only 15 parsecs . the current completeness of the census of nearby stars in the northern sky is discussed in light of the new candidates presented here . it is estimated that ( ) of nuclear burning stars within 33 parsecs ( 25 parsecs ) of the sun remain to be located . the missing systems are expected to have proper motions below the yr limit of the lspm catalog .

nucl-th0212025

c

the dressed rpa equations have been extended to account for the coupling of two ph phonons in forming the excited states of a many - body system . the coupling among ph and multi - phonon configurations is conceptually similar to the interacting boson model of ref . @xcite but limited , in this application , to only two - phonon admixtures . nevertheless , the present approach has the added advantage of taking into account both the effects of nuclear fragmentation and the rpa - like correlations , as generated by two - phonon fluctuations in the ground state . the resulting extended rpa formalism has been applied to study the excitation spectrum of @xmath0 . the results suggests a sizable mixing of ph and two - phonon configurations for the case of the @xmath61 quadrupole resonance at 20.7 mev . other solutions , carrying quantum numbers that can not be generated by the simple drpa , are obtained with this method , among which a few isoscalar negative parity states and a triplet with @xmath83=@xmath4 , @xmath61 and @xmath62 near 12 mev , in accord with experiment . in particular , the states in the triplet were seen to be almost pure two - phonon configurations obtained by coupling two @xmath7 phonons . this feature confirms the 2p2h character of these states . the results are less satisfying for the low - lying positive parity states , which are known to require a proper description of 4p4h excitations . the present approach predicts the lowest solution for the isoscalar @xmath4 channel to be at 11.3 mev , considerably above the first experimental excited state . a sizable component of this solution is seen to be generated by the coupling of two of the lowest @xmath4 phonon themselves . this suggests that important contribution of 4p4h excitation may be included already at the two - phonon level in a self - consistent fashion . other correlations beyond the 2p2h level are partially included in the present calculation through the dressing of the propagators and the rpa approach . as expected , though , the present implementation is not sufficient to obtain a complete description of the low - lying excitation spectrum of @xmath0 . the results obtained in this work show that an interaction between multi - phonon configuration is still missing . this can be achieved by including pp and hh correlation between different ph phonons . also the inclusion of up to four - phonon states is expected to be relevant for this system . finally , the stability of the present results has been tested with respect to the truncation of the model space and to the number of two - phonon configurations accounted for . it was found that the effects of nuclear fragmentation acts to ` renormalize ' the sp propagator , making the solutions of the erpa fairly independent of higher energy configurations . as discussed in sec . [ sec : trunc ] , this feature generates stable solutions with respect to the size of the model space and the corresponding @xmath8-matrix interaction used in this work . the four - phonon calculation of refs . @xcite give a very good description of the excitation spectrum of @xmath0 . those findings and the effects of fragmentation discussed in this paper suggest that the present erpa formalism can be suitably extended to generate a satisfactory description of this nucleus , within the framework of scgf . such extensions are presently under consideration . such a calculation may also significantly reduce the discrepancy between the measured and the theoretical sp spectral function for this nucleus @xcite . this work was supported in part by the u.s . national science foundation under grants no . phy-9900713 and phy-0140316 and in part by the natural sciences and engineering research council of canada ( nserc ) .

the resulting formalism is applied to study the low - lying excitation spectrum of . the stability of the present calculation is tested vs. the truncation of model space . it is demonstrated that when single - particle strength fragmentation is properly considered , the present formalism exhibits convergence with respect to the chosen model space within the confines of the chosen approximation scheme .

a microscopic formalism is developed that includes the coupling to two particle - hole phonons in the particle - hole propagator by extending the dressed random phase approximation ( drpa ) equation for a finite system . the resulting formalism is applied to study the low - lying excitation spectrum of . it is observed that the coupling to two - phonon states at low energy generates excited states with quantum numbers that can not be obtained in the drpa approach . nevertheless , the two - phonon states mix weakly with particle - hole configurations and participate only partially in the formation of the lowest - lying positive - parity excited states . the stability of the present calculation is tested vs. the truncation of model space . it is demonstrated that when single - particle strength fragmentation is properly considered , the present formalism exhibits convergence with respect to the chosen model space within the confines of the chosen approximation scheme .

0901.1050

i

about 1960 , a change in education and evaluation of general phenomenological thermodynamics was observed . before 1960 , it was mainly based on arguments by carnot , kelvin and clausius . after 1960 , it was mainly based on the gibbs distribution of statistical mechanics . this gibbs rational thermodynamics has the following priors for a system of interacting structureless particles : 1 . the only general entities are the particles ; the rational is obtained from the thermodynamic limit : number of particles @xmath11 under the condition of finite density ( @xmath12 given ) , 2 . there is a large heat reservoir that feeds the temperature @xmath13 as an equivalence - class index into the system , 3 . the non - fluctuation of the reservoir temperature , @xmath14 , is transferred into the definition of the general temperature ( to justify the sharp @xmath15 denominator in the boltzmann factor for energy in the gibbs distribution ) . these priors are tried and tested in systems where the spatial infinities , sufficiently separated from the particles , are contained inside the system itself , quasi as an internal heat reservoir . examples are the infinite lattice in a solid or an infinite vacuum of vacuum elements in a gas with isolated particles imbedded . we ask , whether these priors can be applied to liquids , especially to liquid dynamics , where such separated infinities are not obvious . the existence of two experimentally well - tried particularities could be useful for cosmology by starting the universe from an initial liquid ( initial liquid hypothesis ) . smaller ones ( glarum levy defects for dynamic heterogeneity of the dynamic glass transition , @xmath0 defect as a new entity ) could be the seeds for the later galaxies @xmath7 we use now the symbol @xmath16 for their number in the universe @xmath7 , and a larger one ( fischer speckle ) could be the largest causal region in the initial liquid , wherefrom the increasing diameter @xmath17 of the expanding universe results . in the dispersion zone of the dynamic glass transition of a classical molecular liquid , the @xmath0 defects must dynamically be described by a levy distribution with a levy exponent @xmath18 , @xmath19 for relaxation ( frequency @xmath20rad / s ) . this follows from the representativeness theorem ( section 3.1 ) . the difference @xmath21 is called tilt and is later related to the tilt @xmath22 of the spectral index @xmath23 in cosmic density fluctuations . the preponderant component of the levy sum for @xmath24 corresponds to a levy diffusion step of a molecule through the cage door of its nearest neighbor particles . a relation between the small @xmath0 defects and the large @xmath1 speckle is obtained via an analytic continuation of the diffusion steps . if the application to the cosmological initial liquid is reliable , a relation results between the number of galaxies @xmath16 in the universe of diameter @xmath3 and the tilt @xmath22 . all this is worded by the phrase shaping power of levy distribution . the thermodynamic entity is the key concept of this second paper second part . this entity is defined dynamically by a representative containing one @xmath0 defect which is formally labeled by one boltzmann constant @xmath25 from an internal quantum mechanical experiment of nyquist ( 1928 ) , cf . the remark of section 3.1 . the internal experiment is a self - experiment in the liquid @xmath7 without any reservoir and without any conscious observer @xmath7 that is thermodynamically described by the fluctuation dissipation theorem ( fdt ) . this self - experiment may be understood as a common filter construction of the hidden charge model @xcite , common in relation to several particles , or to quantums in a nyquist transmission line . in the model , a common filter construction from several eigensolutions must be allowed for the construction of e.g. a baryon : from a 1-class lepton , a 2-class prebaryon and a 3-class confinon eigensolution . the entity is , so to speak , a common thermodynamic culminating event of the model . the term defect diffusion was introduced by glarum @xcite . an experimental retardation function that could later be identified with the characteristic function of the symmetric levy distribution was detected by kohlrausch @xcite in 1847 . many experimental hints of the connection of glass relaxation data with an underlying levy distribution where collected , e.g. by ngai @xcite . a theoretical review was e.g. by shlesinger @xcite . the fischer dispersion zone @xcite and his speckles @xcite are reviewed by himself . the levy character of the defects was further developed in the book @xcite containing also the representativeness theorem . the fdt as an equation for thermodynamic self - experiments was developed on the base of the nyquist model @xcite , first in 1982 @xcite and later sophisticated in @xcite . glass transition arguments were used in cosmology e.g. in the paper of she @xcite . the hidden charge model is discussed in part 1 @xcite .

a new thermodynamics for liquids related to von laue s approach ( 1917 ) substitutes some particle priors of gibb s rational thermodynamics . this allows the definition of a new dynamic entity ( defect ) whose diffusion properties also claim a largest causal region ( speckle ) . in the frame of the hidden charge model it is discussed , whether this new thermodynamics can be applied to an initial liquid for cosmology , where the defects lead to the later galaxies and the speckles to a finite expanding universe of diameter . far below a * keywords : * 1 . inflation 2 .

a new thermodynamics for liquids related to von laue s approach ( 1917 ) substitutes some particle priors of gibb s rational thermodynamics . this allows the definition of a new dynamic entity ( defect ) whose diffusion properties also claim a largest causal region ( speckle ) . in the frame of the hidden charge model it is discussed , whether this new thermodynamics can be applied to an initial liquid for cosmology , where the defects lead to the later galaxies and the speckles to a finite expanding universe of diameter . far below a hadronic compton wave length of order 1 fermi , , there is no room left for too small filter elements , that would , however , be necessary for a filter convergence to an isolated cold quantum mechanical point particle . when the expansion of the universe comes to , i.e. for , then many hadrons are created . the related negative pressure gets large amounts and leads to an intense hadronic cosmological inflation . the defects are formed by the shaping power of levy distribution ( preponderant component , hierarchy , damping factor ) . a relation between the number of galaxies , the tilt in the density fluctuation , and the temperature amplitude of the cmb is obtained . for ( much vacuum ) , the electromagnetic tangent objects are large and flat . this allows a geometric interpretation of the stony dark energy as flatness on the golden side of the einstein equation , . * keywords : * 1 . inflation 2 . power spectrum 3 . dark energy theory 4 . gravity