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1111.4959	i	we have shown that the physics of systems with heavy fermions is determined by the extended quasiparticle paradigm . in contrast to the paradigm that the quasiparticle effective mass is a constant , within the extended quasiparticle paradigm the effective mass of new quasiparticles strongly depends on the temperature , magnetic field , pressure , and other parameters . the quasiparticles are well defined and can be used to describe the scaling behavior of the thermodynamic hf metals in a wide range of both temperatures @xmath3 and magnetic fields @xmath5 . it was demonstrated that the phase diagram of systems located near the fermion condensation quantum phase transition are strongly influenced by control parameters such as chemical pressure , pressure , the number density or magnetic field . analyzing the phase diagram of @xmath36 , we have found that under the application of the chemical pressure ( positive / negative ) qcp is destroyed or converted into the quantum critical line , correspondingly . we have analyzed the thermodynamic properties of @xmath36 in both the low and the high magnetic fields . our calculations allow us to conclude that in magnetic field the hf system of @xmath36 evolves continuously without a metamagnetic transition and possible localization of heavy @xmath307 electrons . at low temperatures and under the application of magnetic field the hf system demonstrates the lfl behavior , at elevated temperatures the system enters the transition region followed by the nfl behavior . our observations are in good agreement with experimental facts and show that the fermion condensation quantum phase transition is indeed responsible for the observed nfl behavior and quasiparticles survive both high temperatures and high magnetic fields .	in contrast to the landau paradigm stating that the quasiparticle effective mass is a constant , the effective mass of new quasiparticles strongly depends on temperature , magnetic field , pressure , and other parameters . our observations are in good agreement with experimental facts and show that fcqpt is responsible for the observed nfl behavior and quasiparticles survive both high temperatures and high magnetic fields .	strongly correlated fermi systems are among the most intriguing , best experimentally studied and fundamental systems in physics . there is , however , lack of theoretical understanding in this field of physics . the ideas based on the concepts like kondo lattice and involving quantum and thermal fluctuations at a quantum critical point have been used to explain the unusual physics . alas , being suggested to describe one property , these approaches fail to explain the others . this means a real crisis in theory suggesting that there is a hidden fundamental law of nature . it turns out that the hidden fundamental law is well forgotten old one directly related to the landau migdal quasiparticles , while the basic properties and the scaling behavior of the strongly correlated systems can be described within the framework of the fermion condensation quantum phase transition ( fcqpt ) . the phase transition comprises the extended quasiparticle paradigm that allows us to explain the non - fermi liquid ( nfl ) behavior observed in these systems . in contrast to the landau paradigm stating that the quasiparticle effective mass is a constant , the effective mass of new quasiparticles strongly depends on temperature , magnetic field , pressure , and other parameters . our observations are in good agreement with experimental facts and show that fcqpt is responsible for the observed nfl behavior and quasiparticles survive both high temperatures and high magnetic fields .
1407.2757	r	figure [ fig - sp ] shows spectra of the supermaser observed in 18 epochs of the regular astrometry observations from 2011 to 2012 , and figure [ fig - time ] shows time variations of the flux density , velocity width , and peak velocity for all the observed epochs including both 18 epochs of the regular astrometry and 53 epochs of the spectral line monitoring observations . first , these parameters are determined by fitting a single gaussian to the observed profile . however , there are two distinct velocity components at @xmath46.9 km s@xmath5 and @xmath47.5 km s@xmath5 as reported in @xcite . these components can be clearly seen in spectral profiles such as the double - peaked structure on 2011/121 and 2011/137 and red - shifted shoulder on 2011/208 ( figure [ fig - sp ] ) . this results in a significant deviation from the observed line profile in the fitting . thus , we next fit two gaussians to the observed profiles for these epochs . although these line parameters show slightly larger error bars as shown in figure [ fig - time ] , we can see time variations of flux density , velocity width , and peak velocity for the @xmath47.5 km s@xmath5 component continuously changing even during this phase . in contrast , the velocity component that appeared later at @xmath46.9 km s@xmath5 shows a different time variation . according to characteristics of the time variation in figure [ fig - time ] , we can divide the monitoring period of the current h@xmath0o maser burst into four phases ; a moderately active phase in 2009 followed by a relatively quiescent phase in 2010 , a start of the burst with rapid variation in 2011 , the maximum phase in 2012 , and a quiescent / possible initial phase of the next burst in 2013 . in 2009 , there is a moderately active phase slowly increasing and decreasing in the flux density both in total power and cross power spectra . timescales of both rising and falling phases , which are defined as periods from minimum to maximum and maximum to minimum flux densities , respectively , are almost equal , 10 months and 11 months , respectively ( figure [ fig - flux](a ) ) . during this phase , the peak velocity is also slightly changing from 7.4 to 7.3 km s@xmath5 while the velocity width , @xmath40.8 km s@xmath5 , is almost stable with time . after this moderately active phase in 2009 , the maser activity becomes a quiescent phase , whereas the total and correlated flux densities are as high as 2400 jy and 500 jy , respectively , at the minimum phase on 2010/227 . toward this minimum phase , the velocity width of the total - power spectrum gradually increases although that of the cross - power spectrum shows a decreasing trend . at the minimum phase on 2010/227 , the velocity width and peak velocity change drastically . furthermore , these parameters show significant differences between total - power and cross - power spectra but with larger uncertainties than other epochs . this could be caused by other velocity components as their contributions become more and more significant relative to that of the 7.5 km s@xmath5 component . before and after this minimum phase , there were breaks of monitoring observations each for 100 days due to the maintenance of the vera antennas , and hence , we could not trace time variations in this quiescent phase . the h@xmath0o maser burst has started in the end of 2010 or the beginning of 2011 @xcite . the flux density of the total - power spectrum at @xmath47.5 km s@xmath5 has started to increase since 2010/350 while that of the cross power spectrum is temporarily halted on 2010/360 followed by the brightening from 2011/023 . although there is a lack of maser images , this might reflect a variation in the spatial structure of the emitting region . at the beginning of the current burst phase in 2011 , there are two maximum phases on 2011/60 - 2011/121 and 2011/296 - 2011/311 with the total flux density of about 50000 jy ( figure [ fig - time ] ) . the timescales of rising and falling phases are 7 months and 3 months , respectively , for the maximum phase of 2011/60 - 2011/121 ( figure [ fig - flux](b ) ) , although the flux density in this phase shows a variability rather than a monotonic increase or decrease . the timescales for the subsequent maximum phase of 2011/296 - 2011/311 ( figure [ fig - flux](c ) ) are 2 months for both rising and falling phases . apart from the different timescales , the behaviors in rising and falling phases seem to be symmetric as seen in the active phase in 2009 ( figure [ fig - flux ] ) . as discussed above , the burst appears to occur in two different velocity components at 6.9 km s@xmath5 and 7.5 km s@xmath5 @xcite as seen in figures [ fig - time](b ) and ( c ) . the burst activity is temporarily stopped at the end of 2011 , but more active burst has started in early 2012 . the maximum total flux density of 135000 jy is recorded on 2012/154 at the peak velocity of 7.4 km s@xmath5 . in this most active phase , the flux density monotonically increases with the timescale of 5 months . the velocity width is about 0.60 - 0.75 km s@xmath5 , which is the narrowest value observed in our monitoring as shown in figure [ fig - time](b ) . on 2012/123 , the derived velocity widths show the minimum values of [email protected] km s@xmath5 and [email protected] km s@xmath5 for the total - power and cross - power spectra , respectively . only in this epoch , the velocity widths are significantly narrower than those observed just before and after this epoch ( 2012/107 and 2012/145 ) . due to the lack of maser images on 2012/123 , we do not discuss what is the true reason for these narrower velocity widths only at this epoch . the flux density of the maser decreases with the timescale of 4 months after this maximum phase . it should be noted that the time variations in rising and falling phases again seem to be symmetric as seen in figure [ fig - flux](d ) . at the end of the burst phase in 2012/265 and 2012/269 , the peak velocities of cross - power spectra show significant differences from those of the total - power spectra . they are thought to be the results of significant contributions from other velocity components and/or effects of structure changes in maser features . this effect is seen particularly in less active phases such as in 2010 . finally , the burst activity seems to end around 2012/269 while it again appears to be brightening from 2013/138 . it is most likely an ignition of a newly occurred burst event . we will continue monitoring observations with vera of the time variation of the supermaser in orion kl . still , the activity of the 22 ghz h@xmath0o maser burst in 2011 - 2012 is relatively lower by a factor of 10 in comparison with the previous bursts in which the peak flux densities reached 10@xmath6 jy . we note that the fluxes reported in figures [ fig - time ] and [ fig - flux ] are those integrated over the whole region including both the supermaser and other features . we investigate possible contribution from other maser features at almost the same velocity with the supermaser feature in the 18 epochs of our vlbi imaging . although it is difficult to make full channel maps with a wide field of view of an order of 10 , we search for positions of the maser features detected by @xcite . as a result , we detect one maser feature around the position offset of ( @xmath43.175 , @xmath4 - 1.850 ) in right ascension and declination , respectively , with respect to the supermaser feature . @xcite detected two maser features near this position at the velocities of 6.3 km s@xmath5 and 7.6 km s@xmath5 with the flux densities of 21.0 jy and 897.7 jy , respectively . figure [ fig - se ] shows the flux density of this maser feature ( we call this feature `` se feature '' ) and the flux density ratio relative to the supermaser feature . the flux density of the se feature increases with time and the maximum phase is observed on 2012/244 . it is about 2 months after the maximum phase of the supermaser . even around the maximum phase of the se feature , a possible contribution to the total flux density is as large as 8% as shown in figure [ fig - se ] ( b ) . therefore , we conclude that the contamination from other maser features including the se features are not significant in figures [ fig - time ] and [ fig - flux ] . the time variation of the linewidth of the supermaser implies an anti - correlation with the flux density as shown in figure [ fig - dv ] . according to model calculations , the line profile of the maser first tends to be narrower as its intensity increases as long as the maser is unsaturated @xcite . then the maser line starts to rebroaden when it becomes saturated @xcite . under the condition of an unsaturated maser , the logarithm of the flux density of the maser line , @xmath12 , is predicted to be proportional to the inverse square of the linewidth , @xmath13 . in figure [ fig - dv ] , we also show best - fit results ; @xmath14 our results may suggest that the supermaser in the current burst phase is still unsaturated . it is consistent with the observed narrow linewidths , 0.40 - 0.48 km s@xmath5 , of the supermaser in 1998 - 1999 possibly attributed to the line narrowing for an unsaturated maser @xcite . in contrast , no clear relationship between the flux density and linewidth is found in the burst in 1979 - 1985 @xcite , suggesting a saturated maser emission . the difference in the degree of saturation could be attributed to the lower flux density , @xmath410@xmath15 jy in the current burst phase than those in the previous bursts , @xmath310@xmath6 jy @xcite . we note that the line narrowing is predicted to occur even for a saturated maser if a stimulated emission rate is not large compared with the cross - relaxation rate @xcite . this means that the above relation holds when the maser flux density is not enough large regardless of saturated or unsaturated cases . thus , we can not firmly estimate the degree of saturation of the supermaser by judging from the linewidth - flux density relation only . figure [ fig - map ] represents channel maps of the phase - referenced images of the supermaser in 2011/137 . three spatially distinct components are found in the initial phase of the burst from 2011/068 to 2011/137 as reported previously @xcite . it is well known that the 22 ghz h@xmath0o line ( 6@xmath16 - 5@xmath17 ) has a hyperfine structure with 3 main components and that the @xmath18=7 - 6 and 5 - 4 components appear with the separation of + 0.45 km s@xmath5 and -0.58 km s@xmath5 with respect to the central component , @xmath18=6 - 5 @xcite . the velocity separation of -0.58 km s@xmath5 is consistent with that observed for two bursting features . however , our results suggest that the two velocity components observed at 6.9 km s@xmath5 and 7.5 km s@xmath5 in the supermaser are not emitted from the same masing gas clump . thus , these two velocity components are unlikely due to the hyperfine structure but they corresponds to distinct masing gas clumps with different positions and velocities . we conduct two - dimensional gaussian fittings on the phase - referenced images to measure the absolute position of each maser spot . hereafter , we define a `` spot '' as a maser emission identified in a single velocity channel and a `` feature '' as a group of spots that are spatially coincident in two or more consecutive velocity channels . by using these results , we derive the absolute proper motions of the detected spots as summarized in table [ tab - proper ] and figure [ fig - position ] . we find that the northern feature , feature 1 ( or spots 1 , 3 , and 5 ) , is detectable only until 2011/296 ( table [ tab - proper ] ) . the lifetime of the northern feature 1 is about 8 months . given the typical monitoring interval and detection criterion , in which a spot is regarded as real when it is detected for more than three contiguous epochs , we might miss a short - term variation of a maser spot on phase - referenced images within a lifetime of less than @xmath42 months . according to the absolute proper motion measurements , the supermaser features are apparently moving toward south and southwest directions as shown in the gray arrows in figure [ fig - map ] . the derived proper motions are consistent but are more reliable than those previously obtained @xcite because we have continued the proper motion measurements in a longer observing period . when we subtract a modulation of an annual parallax of 2.39 mas @xcite and the absolute proper motion of a possible powering source of the low - velocity outflow , source i ( @xmath19 , @xmath20)=(6.3 mas yr@xmath5 , -4.2 mas yr@xmath5 ) , measured by astrometric observations with the very large array ( vla ) @xcite , the derived proper motion vectors with respect to source i point toward west and southwest directions as drawn in the black arrows in figure [ fig - map ] . the magnitude of the proper motions range from 2.7 to 11.4 mas yr@xmath5 or from 5 to 23 km s@xmath5 ( table [ tab - proper ] ) . similar to the previous reports @xcite the supermaser features are elongated along the northwest - southeast direction perpendicular to the low - velocity outflow @xcite . observed proper motions with respect to source i are almost perpendicular to the major axis of each feature . the size of the maser spot at the peak channel on the maximum epoch , 2012/164 , is [email protected] [email protected]@xmath110.006 mas ( 0.95 [email protected] au ) obtained from a gaussian fitting on the self - calibrated image . the peak flux density is ( [email protected])@xmath22 jy , corresponding to the brightness temperature of 1.2@xmath23 k. the isotropic luminosity is estimated to be 2.4@xmath2110@xmath24 by assuming a linewidth of 0.6 km s@xmath5 . to study physical and chemical properties of the supermaser , we utilize alma cycle 0 data to make images of submillimeter continuum emissions and molecular lines at band 7 . first , we have searched for any 321.225656 ghz h@xmath0o line signal toward the compact ridge where the supermaser resides for the 321.20 - 321.25 ghz range , as shown in figure [ fig - alma ] . several spectral lines are seen , but they are identified as the hcooch@xmath1 lines . if the 321 ghz h@xmath0o line is excited by the maser action like that at 22 ghz , it should be much more compact than those of other molecular lines . with this in mind , we then investigate spectra of the h@xmath0o lines by using the visibility data with the baseline length longer than 100 k@xmath25 , corresponding to the angular size of the emission region of @xmath22 . as a result , we can resolve out all of the lines in the compact ridge while a significant fraction of the 321 ghz h@xmath0o line . in contrast , the broad 321 ghz h@xmath0o line is clearly seen in source i with a double peaked profile @xcite . the 321 ghz h@xmath0o line remains in source i even with the baselines longer than 200 k@xmath25 suggesting a compact structure @xcite . thus , we conclude that no clear evidence of the 321 ghz h@xmath0o maser is detected at the position of the supermaser in spite of the extraordinary strong emission of the 22 ghz h@xmath0o maser . we note that in the observed spectral range a vibrationally excited ( @xmath26=1 , 5@xmath27 - 6@xmath28 ) h@xmath0o line at 336.227931 ghz is not detected in the compact ridge . non - detection of the 321 ghz and 336 ghz h@xmath0o lines implies that the physical conditions around the compact ridge are certainly different from those in source i @xcite . we next compare the distribution of the molecular gas in the compact ridge which hosts the supermaser . for this purpose , we employ the hcooch@xmath1 line at 321.22338 ghz ( @xmath29=0 , 28@xmath30 - 27@xmath31 a ) , which is close to the frequency of the 321 ghz h@xmath0o line ( figure [ fig - alma ] ) , as a tracer of the dense molecular gas in the compact ridge @xcite . the 321.223 ghz hcooch@xmath1 line is not blended with other hcooch@xmath1 transitions unlike those at 321.229 ghz ( @xmath29=1 ) lines , and hence , it is more suitable to analyze the velocity structure of the molecular gas . figure [ fig - moment](a ) shows the moment 0 ( integrated intensity ) map of the 321.223 ghz hcooch@xmath1 line superposed on the alma band 7 continuum emission . the supermaser is located at 8 southwest of source i and is coincident with the compact ridge . the position of the supermaser is close to the hcooch@xmath1 peak but is rather located at the edge of the hcooch@xmath1 condensation . as can be seen in the moment 1 ( peak velocity ) map in figure [ fig - moment ] ( b ) , the velocity of the supermaser @xmath46.9 - 7.5 km s@xmath5 is slightly blue - shifted compared with that of the hcooch@xmath1 line . furthermore , the moment 2 ( velocity width ) map in figure [ fig - moment ] ( c ) implies that the linewidth of the hcooch@xmath1 line tends to be broader around the supermaser . we stress that the velocity structure seems to change abruptly around the supermaser . these apparent velocity structures are caused by two different velocity components of the molecular gas traced by the hcooch@xmath1 line . in figure [ fig - pv ] , we can see detailed velocity structures in the compact ridge by the position - velocity diagram along the x and y axes as indicated in figure [ fig - moment ] ( a ) . it is clear that there exist two different velocity components at 7.5 km s@xmath5 and 9.0 km s@xmath5 . these two components were identified in the previous observations @xcite , but we can resolve both the velocity and spatial structures by higher spectral and spatial resolutions with alma . the supermaser is thought to be associated with one of them at 7.5 km s@xmath5 . interestingly , the velocity of the weak emission from the hcooch@xmath1 line in figure [ fig - pv ] ranges from @xmath46 to 12 km s@xmath5 , although the linewidths of the hcooch@xmath1 lines are only about 1 km s@xmath5 as shown in figure [ fig - alma ] . the velocity range of the weak hcooch@xmath1 emission is significantly broader at x=0 and y=0 , corresponding to the position of the supermaser ( see figure [ fig - pv ] ) . this is probably an evidence of a shock front at the position close to the supermaser . indeed , possible effects of shocks in the compact ridge have been suggested by the enhancement of organic molecules such as hcooh @xcite , hcooch@xmath1 @xcite , and ch@xmath1och@xmath1 @xcite . figure [ fig - cont ] shows a close - up view of distributions of the alma band 7 continuum emission superposed on the integrated intensity map of the 321.223 ghz hcooch@xmath1 line ( figure [ fig - moment](a ) ) . positions of the 22 ghz h@xmath0o masers @xcite including that of the supermaser are also indicated . we detect the compact continuum emission both at alma bands 6 and 7 @xcite . the accurate position of the supermaser is significantly shifted from the continuum peak by 0.3 southeast . we also indicate positions of other possible counterparts observed previously . their relationship will be discussed in the next section .	the supermaser is located close to the methylformate ( hcooch ) line and continuum emission peaks in the orion compact ridge detected by alma , atacama large millimeter / submillimeter array . the broader velocity range of the weak hcooch emission at the supermaser position would be an evidence of a shock front . on the other hand , the 321 ghz ho line is not detected at the position of the supermaser .	the 22 ghz ho maser in orion kl has shown extraordinary burst events in 1979 - 1985 and 1998 - 1999 , sometimes called supermaser . we have conducted monitoring observations of the supermaser in orion kl using vera , vlbi exploration of radio astrometry , in the current third burst since 2011 march . three flux maxima are detected in 2011 and 2012 with rising and falling timescales of 2 - 7 months . time variations of the supermaser seem symmetric for all of the active phases . the maximum total flux density of 135000 jy is observed in 2012 june while it is still one order of magnitude lower than those in previous bursts . the supermaser consists of two spatially different components at different velocities . they are elongated along a northwest - southeast direction perpendicular to the low - velocity outflow driven by source i. proper motions of the supermaser features with respect to source i are measured toward west and southwest directions , almost parallel to the low - velocity outflow . the flux density and linewidth show an anti - correlation as expected for an unsaturated maser emission . the supermaser is located close to the methylformate ( hcooch ) line and continuum emission peaks in the orion compact ridge detected by alma , atacama large millimeter / submillimeter array . the broader velocity range of the weak hcooch emission at the supermaser position would be an evidence of a shock front . on the other hand , the 321 ghz ho line is not detected at the position of the supermaser . it can be explained qualitatively by one of the theoretical ho excitation models without extraordinary conditions . our results support a scenario that the supermaser is excited in the dense gas interacting with the low - velocity outflow in the compact ridge . the extremely high flux density and its symmetric time variation for rising and falling phases could be explained by a beaming effect during the amplification process rather than changes in physical conditions .
1407.2757	c	in this paper , we report results of continued monitoring observations of the supermaser with vera for more than 5 years . we also acquire follow - up observational data with alma of submillimeter continuum emissions and h@xmath0o lines at 321 ghz to reveal characteristics of the supermaser and their environments . in this section , we will address following issues related to the supermaser : what is the powering source of the supermaser and what makes the 6.9 and 7.5 km s@xmath5 features in the compact ridge only such a special burst event ? why there is no bursting h@xmath0o maser feature at 321 ghz despite the extraordinary high flux density in the 22 ghz h@xmath0o maser ? how the drastic burst of the h@xmath0o maser can be explained ? is there a periodicity of the burst event ? according to the absolute position of the supermaser derived from our vera observations , we propose that the supermaser would be excited in the shocked molecular gas interacting between the low - velocity outflow driven by source i and ambient dense gas in the compact ridge @xcite . proper motions and elongations of the supermaser features ( figure [ fig - map ] ) and the broader hcooch@xmath1 line at the position of the supermaser ( figure [ fig - pv ] ) support this scenario . it has also been suggested by the fact that the h@xmath0o maser tends to be distributed in the interface of the shocked molecular gas in the compact ridge traced by hcooh @xcite and hcooch@xmath1 @xcite lines . furthermore , @xcite point out a possible relation between the compact ridge and an explosive outflow traced by the co lines @xcite . indeed , the supermaser is found to be located at the edge of the low - velocity bipolar molecular outflow traced by the thermal sio lines @xcite as well as the explosive outflow @xcite . the latter one is thought to be the result of a recent close encounter of source i and bn object @xcite , although a relationship between these two outflows is still unclear . note that an infrared source irc 5 is located at 1 southeast of the supermaser . the position of irc 5 corresponds to a nearby 3 mm continuum peak , c29 @xcite , and an hcooch@xmath1 peak , mf14 @xcite and hence , it is more closely related to these sources . since irc 5 is thought to be a shocked molecular gas heated externally @xcite , it would not be directly related to the excitation of the supermaser . alternatively , both of them are thought to be heated by the common outflow . as discussed previously @xcite , however , it has been still unknown why only the 6.9 km s@xmath5 and 7.5 km s@xmath5 features show such an extraordinary burst phenomenon . one of the possible explanations is a special physical or geometrical condition of the maser excitation in this region . an anomalous amplification of the h@xmath0o maser burst might need a long path length . such a condition could be achieved only in the systemic velocity component . because it can supply plenty of ambient molecular gas within a narrow velocity range , maser emission would be efficiently amplified only close to the systemic velocity @xcite . millimeter and submillimeter continuum emissions are detected by @xcite , smm1 in @xcite and cb1 in @xcite with spatial resolution of @xmath40.8 - 3 . the mass of the submillimeter core in the compact ridge is estimated to be 4@xmath32 @xcite , and hence , they could provide the dense gas required to form new stars . a similar conclusion is obtained from the alma science verification continuum data that have been analyzed by @xcite . to account for a necessary condition for the supermaser , it is also suggested that the maser burst could occur as a result of an interaction with outflows and a pre - existing yso in the compact ridge @xcite . as discussed in detail by @xcite , there are possible candidate sources physically associated with the supermaser ; a radio continuum source labeled r detected with vla @xcite , 3 mm continuum emission sources detected with the combined array for research in millimeter - wave astronomy ( carma ) @xcite , molecular peaks traced by hcooch@xmath1 lines with the iram plateau de bure interferometer ( pdbi ) @xcite , and optical source parenago 1822 , which is also identified from millimeter , near infrared , optical and x - ray ( see simbad ) , in the compact ridge ( figure [ fig - cont ] ) . @xcite detect a compact 1.3 mm continuum source named hc 438 in the compact ridge with a flux density of [email protected] mjy by using carma . we also detect a compact continuum source at alma band 7 ( see contours in the middle of figure [ fig - cont ] ) which is also detected at band 6 @xcite . these observations achieve much higher spatial resolution of @xmath40.5 than those reported above @xcite . the flux density at alma bands 6 and 7 are 57@xmath115 mjy and 129@xmath1114 mjy , respectively @xcite . the alma band 6 result is consistent with that of the carma 230 ghz observation @xcite . the supermaser is located within the submillimeter core detected by alma but is shifted by 0.3 from the peak position . taking into account positional uncertainties , they are identical to hc 438 @xcite , the 3 mm continuum source c32 @xcite and hcooch@xmath1 peak mf1 @xcite . the circumstellar mass of hc 438 is derived to be 0.085 @xmath32 with the assumed dust temperature of 20 k @xcite . if we assume a higher temperature of 100 k derived from the hcooch@xmath1 data @xcite , the smaller mass of 0.01@xmath32 is obtained . these mass estimates would be a lower limit of the dust continuum source possibly associated with the supermaser because most of the flux is filtered out by alma and carma with extended configurations . we speculate that an embedded yso associated with jet / outflow / disk @xcite would play an important role to realize special conditions required for the supermaser . we notice that the h@xmath0o maser features near the supermaser detected with vla @xcite are distributed around the submillimeter continuum peak as seen in figure [ fig - cont ] . it may imply an expanding shell ejected by an embedded yso , which are sometimes seen in massive ysos @xcite . as discussed in section [ sec - vera ] , we tried to search for other maser features in orion kl region previously detected with vla @xcite . we made channel maps of the h@xmath0o maser features with vera within an 1@xmath211 field of view around the supermaser in the compact ridge . however , we found no maser emission because of the limited dynamic range seriously affected by the extremely strong supermaser . further observations of continuum emission and h@xmath0o masers with higher dynamic range will unveil the exact location of the embedded yso in the compact ridge . it is proposed that the pumping mechanism of the h@xmath0o maser is dominated by collisional excitation @xcite . the burst of the h@xmath0o maser in orion kl is proposed as the result of collisional pumping in the magnetohydrodynamic shock wave caused by the outflow @xcite . on the other hand , alternative mechanisms are also considered to account for the extraordinary h@xmath0o maser burst , such as overlapping of two maser gas clumps @xcite and accidental beaming of radiation toward the earth rather than a change in excitation @xcite . to constrain the physical properties of the supermaser , we have carried out observations of the submillimeter h@xmath0o lines which could be masing @xcite by using alma . among a number of h@xmath0o lines , we employ the 10@xmath33 - 9@xmath34 transition at 321 ghz which is proposed to be a good indicator of some key parameters including temperature , density , and h@xmath0o abundance in the masing gas clump @xcite . however , there is no significant emission of the 321 ghz h@xmath0o line at the position around the supermaser . the upper limit of the flux density of the 321 ghz h@xmath0o line is @xmath40.1 jy . if we assume physical properties of the masing gas are common for both the 22 ghz and 321 ghz lines , then a photon luminosity ratio , @xmath35(22 ghz)/@xmath35(321 ghz ) , is identical to the observed flux density ratio , @xmath18(22 ghz)/@xmath18(321 ghz ) . then , an upper limit of @xmath35(22 ghz)/@xmath35(321 ghz)@xmath310@xmath6 is obtained from the flux density of the 22 ghz maser of @xmath310@xmath15 jy . when the beaming angle of the 22 ghz maser is also the same as that of 321 ghz , an emissivity ratio @xmath36(22 ghz)/@xmath37(321 ghz ) @xcite is also equal to the photon luminosity ratio and flux density ratio , @xmath38 . as demonstrated in the model calculations @xcite , the lower limit of @xmath38 can be achieved when the temperature is @xmath4200 - 400 k or the parameter @xmath39 is @xmath40.4 - 1.8 depending on the temperature within the calculated range below 2000 k ( see their figure 3 ) . the parameter @xmath40 is defined as @xmath41(h@xmath0o ) @xmath42/@xmath43 , in which @xmath44(h@xmath0o ) , @xmath45 , and @xmath43 are a fractional abundance of h@xmath0o relative to hydrogen nuclei in units of 10@xmath46 , a number density of hydrogen nuclei in units of 10@xmath47 @xmath48 , and a velocity gradient in units of 10@xmath49 cm s@xmath5 cm@xmath5 @xcite . we note that the model employed here is calculated under the assumption of a saturated maser @xcite and hence , the estimated parameters may be different from an unsaturated case as adopted for the supermaser . furthermore , the model calculation only considers collisional pumping of h@xmath0o molecules ignoring infrared pumping . in addition , the collision rates used in these works are now superseded by newer calculations @xcite . despite these uncertainties , we use the model of @xcite to roughly interpret the supermaser burst at 22 ghz and the non - detection of the 321 ghz line . as a result , we find the supermaser burst at 22 ghz and the non - detection at 321 ghz could still be explained by the theoretical model @xcite without extraordinary physical conditions . thus , under the condition of the unsaturated 22 ghz h@xmath0o maser , the lower temperature and larger value of @xmath40 would also be expected according to a qualitative consideration . to explain the non - detection of the 321 ghz maser line ( high value of @xmath51 ) , either high h@xmath0o abundance , high h@xmath0 density , small velocity gradient , or low temperature of 200 - 400 k would be required . the h@xmath0o abundance in the compact ridge is estimated from the herschel data to be 2.6@xmath2110@xmath52 with the source size of 6 @xcite . if a local abundance enhancement occurs around the supermaser , the higher h@xmath0o abundance up to 6.5@xmath2110@xmath46 as observed in the hot core region @xcite may be possible . the average h@xmath0 number density of the dust continuum source in the compact ridge is estimated to be ( 0.5 - 5)@xmath2110@xmath47 @xmath48 assuming a diameter ( fwhm ) of 0.43 or 90 au @xcite and a total mass of 0.01 - 0.1 @xmath32 @xcite . if we assume a velocity width of 0.6 km s@xmath5 and a path length of 1 au as obtained from a gaussian fitting for a bursting maser spot , the velocity gradient @xmath43 is calculated to be 0.4 . although the above results contain large uncertainties by a factor of 10 or more , these parameters seem reasonable to explain estimated range of @xmath39 of 0.4 - 1.8 unless the h@xmath0o abundance is the lowest estimate of @xmath44(h@xmath0o)=0.026 @xcite . it is also conceivable that the supermaser is the result of strong beaming effects @xcite . if only the 22 ghz maser emission has a smaller beaming angle compared with that of the 321 ghz line , the emissivity ratio @xmath53 is proportional to the flux density ratio , @xmath18(22 ghz)/@xmath18(321 ghz ) , and the ratio of beaming angles , @xmath54(22 ghz)/@xmath54(321 ghz ) , which reduces the upper limit of @xmath53 estimated from the observed flux density ratio . the smaller beaming angle of the 22 ghz maser line than that of 321 ghz by a factor of @xmath4100 would enable a large @xmath54(22 ghz)/@xmath54(321 ghz ) value of @xmath410000 . this may result in the lower @xmath53 value by a factor of 10000 which can be achieved under wider range of physical conditions as seen in figure 3 of @xcite . in spite of the presence or absence of a beaming effect , the condition for the h@xmath0o maser burst only at the 22 ghz transition , @xmath38 , does not require extreme physical properties but rather those typical in hot molecular cores @xcite . we suggest that the symmetric time variation in the flux density ( figure [ fig - flux ] ) could be explained by a change in the beaming angle of the maser rather than changes in the physical properties such as h@xmath0o abundance , h@xmath0 density , and/or temperature . on the other hand , a change in a velocity gradient caused by a length of the maser cloud and/or velocity structure might happen such as those in the overlapping maser model @xcite . nevertheless , it is still uncertain how such an accidental overlapping and/or a beaming effect could occur in two spatially distinct clouds for several times during our monitoring period of @xmath45 years . comparing the basic properties such as the peak lsr velocity , the spatial structure of each feature , and the location coincident with the compact ridge , all of the burst events in 1979 - 1985 , 1998 - 1999 , and 2011 - 2012 could have a common origin . it is also suggested that the h@xmath0o maser burst may have periodicity of 13 years @xcite . however , the current burst shows less activities in terms of the maximum flux density . furthermore , no such burst event is reported in 1973 @xcite , in which the burst event is expected if 13 year - periodicity is valid ( i.e. 1972 - 1973 , 1979 - 1985 , 1998 - 1999 , and 2011 - 2012 ) . in 1973 july , the observed flux density of the h@xmath0o maser at 7.4 km s@xmath5 was only about 100 jy and was weaker than the 11.0 km s@xmath5 component @xcite . this component was probably identical to the second brightest component in the current burst phase ( figure [ fig - sp ] ) . the position of the 7.4 km s@xmath5 component was measured to be r.a.=05h35m14.22s and [email protected] ( j2000 ) and was consistent with that of the current bursting feature located in the compact ridge . in 1975 - 1976 , the h@xmath0o maser feature at 7.6 km s@xmath5 was detected at the position of r.a.=05h35m14.07s and [email protected] ( j2000 ) . the position of this feature was again in good agreement with that of the current h@xmath0o maser burst , whereas it was rather weak ( much less than 1000 jy ) compared with another strong feature at 10.8 km s@xmath5 . although the h@xmath0o maser feature at @xmath47.5 km s@xmath5 could be excited by a common origin in the compact ridge , it is not very likely that the maser burst occurs regularly at a period of 13 years . more archive data of past observations will be helpful to investigate a long - term variability of the h@xmath0o maser activities since early 1970s . the flux increase started in 2013 is now on - going and hence , further monitoring will also provide some hints to understand a possible relation with previous bursts . along with the 22 ghz h@xmath0o maser lines , it could be useful to continue monitoring observations of the 321 ghz h@xmath0o lines in orion kl with alma in order to see whether the compact ridge and source i , which is a powering source of the outflow interacting with the compact ridge , behave in the same way . figures [ fig - sp]-[fig - flux ] imply that the current burst in 2011 and 2012 sometimes shows variations in the flux density and velocity structure with the timescales of 2 - 7 months . it is comparable to those of typical h@xmath0o masers in orion kl @xcite . although the spectral component of the supermaser seems to survive for more than 5 - 10 years @xcite , a spatial structure of each bursting feature is found to be changing within a timescale of a few months to @xmath22 years at the longest lifetime ( table [ tab - proper ] ) . thus , it is unlikely that the bulk of the bursting maser gas is identical for longer than @xmath42 years .	three flux maxima are detected in 2011 and 2012 with rising and falling timescales of 2 - 7 months . it can be explained qualitatively by one of the theoretical ho excitation models without extraordinary conditions . our results support a scenario that the supermaser is excited in the dense gas interacting with the low - velocity outflow in the compact ridge . the extremely high flux density and its symmetric time variation for rising and falling phases could be explained by a beaming effect during the amplification process rather than changes in physical conditions .	the 22 ghz ho maser in orion kl has shown extraordinary burst events in 1979 - 1985 and 1998 - 1999 , sometimes called supermaser . we have conducted monitoring observations of the supermaser in orion kl using vera , vlbi exploration of radio astrometry , in the current third burst since 2011 march . three flux maxima are detected in 2011 and 2012 with rising and falling timescales of 2 - 7 months . time variations of the supermaser seem symmetric for all of the active phases . the maximum total flux density of 135000 jy is observed in 2012 june while it is still one order of magnitude lower than those in previous bursts . the supermaser consists of two spatially different components at different velocities . they are elongated along a northwest - southeast direction perpendicular to the low - velocity outflow driven by source i. proper motions of the supermaser features with respect to source i are measured toward west and southwest directions , almost parallel to the low - velocity outflow . the flux density and linewidth show an anti - correlation as expected for an unsaturated maser emission . the supermaser is located close to the methylformate ( hcooch ) line and continuum emission peaks in the orion compact ridge detected by alma , atacama large millimeter / submillimeter array . the broader velocity range of the weak hcooch emission at the supermaser position would be an evidence of a shock front . on the other hand , the 321 ghz ho line is not detected at the position of the supermaser . it can be explained qualitatively by one of the theoretical ho excitation models without extraordinary conditions . our results support a scenario that the supermaser is excited in the dense gas interacting with the low - velocity outflow in the compact ridge . the extremely high flux density and its symmetric time variation for rising and falling phases could be explained by a beaming effect during the amplification process rather than changes in physical conditions .
1407.2757	i	we have carried out astrometric monitoring observations of the bursting 22 ghz h@xmath0o maser feature , called supermaser , in orion kl using vera since 2011 march . combined with spectral line data obtained as a fringe - finder , we reveal a time variation of the supermaser for more than 5 years . in addition , we utilize alma cycle 0 data at band 7 ( 320 - 330 ghz ) for both spectral lines and continuum emissions to investigate physical and chemical properties of the supermaser . the main findings are summarized as follows : 1 . within the monitoring period in 2011 and 2012 , we detect three active phases with rising and falling timescales ranging from 2 to 7 months . we also find a smaller burst in 2009 with a slightly longer rising and falling timescales of @xmath410 months . the flux variations of the supermaser seem to be symmetric in time for all of the active phases . 2 . the maximum phase of the current burst is observed on 2012/154 with the total flux density of 135000 jy , which is one order of magnitude lower than those in previous bursts . although the burst events may occur with a possible periodicity of 13 years , ( i.e. 1979 - 1985 , 1998 - 1999 , and 2011 - 2012 ) , a lower flux density by a factor of 10 in the current burst , as well as no significant burst event in 1973 @xcite would make the claimed periodicity of 13 years still unconvincing . the outburst of the maser emission can be seen in two velocity components at @xmath46.9 km s@xmath5 and @xmath47.5 km s@xmath5 as reported in @xcite and @xcite . the 6.9 km s@xmath5 feature is alive only in 2011 with the lifetime of @xmath48 months . note that we detect two spatially distinct features at 6.9 km s@xmath5 and 7.5 km s@xmath5 , and hence , these two velocity components are unlikely due to the hyperfine structure of the h@xmath0o molecule . 4 . the flux density and linewidth show an anti - correlation as expected for an unsaturated maser emission @xcite , in which the logarithm of the flux density of the maser line , @xmath12 , is proportional to the inverse square of the linewidth , @xmath13 . however , we can not rule out a possibility of a saturated maser case because such a line narrowing is also predicted to occur even for a saturated maser if a stimulated emission rate is not large compared with that of the cross - relaxation @xcite . as reported in previous papers @xcite the bursting maser features are elongated along the northwest - southeast direction perpendicular to the low - velocity outflow driven by source i. absolute proper motions of the bursting maser features are measured based on a longer monitoring period than that in the previous paper @xcite . their proper motions with respect to a powering source of the low - velocity outflow , source i , are almost perpendicular to the elongation of the maser features , suggesting that they are related to the low - velocity outflow . the size of the maser spot at the peak channel on the maximum epoch , 2012/164 , is 2.265 [email protected] mas , and the total flux density is 1.029@xmath2110@xmath15 jy . these values correspond to the brightness temperature and the isotropic luminosity of 1.2@xmath23 k and 2.4@xmath2110@xmath24 , respectively . the supermaser is located at the compact ridge region in orion kl . continuum peaks detected by alma bands 6 and 7 are located 0.3 northwest of the supermaser . as suggested by @xcite , there are a radio continuum source labeled r @xcite , 3 mm continuum source c32 @xcite , hcooch@xmath1 core mf1 @xcite , and optical source parenago 1822 , which are probably identical or closely related to the compact continuum sources detected by alma and the supermaser . the position of the supermaser is coincident with the dense gas traced by the hcooch@xmath1 line . the velocity of the supermaser agrees well with one of the two velocity components of the hcooch@xmath1 line detected by alma and pdbi @xcite . a slightly broader velocity range of the weak hcooch@xmath1 emission would imply a shock front at the position of the supermaser . the 321 ghz h@xmath0o line is not detected around the 22 ghz supermaser features , although the strong maser emission is found to be associated with source i @xcite . given the high emissivity ratio , the maser burst at 22 ghz could occur under conditions of the temperature of @xmath2200 - 400 k and/or the parameter @xmath56 , suggesting a high abundance of h@xmath0o , a high number density of h@xmath0 , and/or a small velocity gradient . meanwhile , these physical properties are not extraordinary values but are very similar to typical hot molecular cloud cores . thus , the supermaser burst at 22 ghz with non - detection of the 321 ghz maser emission could be explained by the theoretical model qualitatively @xcite . further detailed calculations would be required to interpret the observed flux ratios of the masers @xcite . alternatively , the supermaser may be caused by an accidental beaming only for the 22 ghz h@xmath0o maser @xcite . the symmetric time variation in the flux density is consistent with a result of the beaming rather than changes in physical properties of the masing gas . however , it still remains a matter of debate how accidental overlapping and/or beaming occur repetitively for more than @xmath430 years since the discovery of the supermaser . we are grateful to alain baudry for useful comments , which is essential to improve our scientific discussion . we thank the staff of the vera stations and alma observatory to support our project . this paper makes use of the following alma data : ads / jao.alma#2011.0.00199.s . alma is a partnership of eso ( representing its member states ) , nsf ( usa ) and nins ( japan ) , together with nrc ( canada ) and nsc and asiaa ( taiwan ) , in cooperation with the republic of chile . the joint alma observatory is operated by eso , aui / nrao and naoj . this research has made use of the simbad database , operated at cds , strasbourg , france . t.h . is supported by the mext / jsps kakenhi grant numbers 21224002 , 24684011 , and 25108005 , and the alma japan research grant of naoj chile observatory , naoj - 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burgk , j. , loinard , l. , menten , k. m. , & curiel , s. 2012 , apj , 754 , l17 zapata , l. a.,schmid - burgk , j. , ho , p. t. p. , rodrguez , l. f. , menten , k. m. 2009 , apj , 704 , l45 zapata , l. a. , schmid - burgk , j. , & menten , k. m. 2011 , a&a , 529 , a24 cccccc feature & spot & @xmath58 & @xmath19 & @xmath20 & + id@xmath59 & id@xmath60 & [ km s@xmath5 ] & [ mas yr@xmath5 ] & [ mas yr@xmath5 ] & epoch + 1 & 1 & 6.74 & -2.0(0.4 ) & -1.8(0.4 ) & 2011/068 - 2011/296 + 1 & 3 & 6.95 & -2.2(0.5 ) & -1.7(0.6 ) & 2011/068 - 2011/296 + 1 & 5 & 7.16 & -2.7(1.2 ) & -1.0(1.4 ) & 2011/068 - 2011/250 + 2 & 2 & 6.74 & 5.2(0.9 ) & -10.2(0.8 ) & 2011/296 - 2012/164 + 2 & 4 & 6.95 & 4.8(0.6 ) & -9.7(0.5 ) & 2011/250 - 2012/207 + 2 & 6 & 7.16 & 4.0(0.3 ) & -9.0(0.2 ) & 2011/068 - 2012/207 + 2 & 7 & 7.37 & 4.0(0.2 ) & -9.1(0.2 ) & 2011/068 - 2012/207 + 2 & 8 & 7.58 & 4.0(0.2 ) & -9.1(0.2 ) & 2011/068 - 2012/269 + 2 & 10 & 7.79 & 4.0(0.2 ) & -9.0(0.2 ) & 2011/068 - 2012/269 + 3 & 9 & 7.58 & -2.6(9.2 ) & -4.1(8.3 ) & 2011/121 - 2011/208 + 3 & 11 & 7.79 & 0.6(3.7 ) & -5.5(3.7 ) & 2011/121 - 2011/208 + + +	we have conducted monitoring observations of the supermaser in orion kl using vera , vlbi exploration of radio astrometry , in the current third burst since 2011 march . time variations of the supermaser seem symmetric for all of the active phases . the maximum total flux density of 135000 jy is observed in 2012 june while it is still one order of magnitude lower than those in previous bursts . they are elongated along a northwest - southeast direction perpendicular to the low - velocity outflow driven by source i. proper motions of the supermaser features with respect to source i are measured toward west and southwest directions , almost parallel to the low - velocity outflow . the flux density and linewidth show an anti - correlation as expected for an unsaturated maser emission .	the 22 ghz ho maser in orion kl has shown extraordinary burst events in 1979 - 1985 and 1998 - 1999 , sometimes called supermaser . we have conducted monitoring observations of the supermaser in orion kl using vera , vlbi exploration of radio astrometry , in the current third burst since 2011 march . three flux maxima are detected in 2011 and 2012 with rising and falling timescales of 2 - 7 months . time variations of the supermaser seem symmetric for all of the active phases . the maximum total flux density of 135000 jy is observed in 2012 june while it is still one order of magnitude lower than those in previous bursts . the supermaser consists of two spatially different components at different velocities . they are elongated along a northwest - southeast direction perpendicular to the low - velocity outflow driven by source i. proper motions of the supermaser features with respect to source i are measured toward west and southwest directions , almost parallel to the low - velocity outflow . the flux density and linewidth show an anti - correlation as expected for an unsaturated maser emission . the supermaser is located close to the methylformate ( hcooch ) line and continuum emission peaks in the orion compact ridge detected by alma , atacama large millimeter / submillimeter array . the broader velocity range of the weak hcooch emission at the supermaser position would be an evidence of a shock front . on the other hand , the 321 ghz ho line is not detected at the position of the supermaser . it can be explained qualitatively by one of the theoretical ho excitation models without extraordinary conditions . our results support a scenario that the supermaser is excited in the dense gas interacting with the low - velocity outflow in the compact ridge . the extremely high flux density and its symmetric time variation for rising and falling phases could be explained by a beaming effect during the amplification process rather than changes in physical conditions .
1504.04567	i	[ intro ] in the present work we continue our theoretical studies @xcite of multicharged tungsten ions . the spectroscopic parameters of systems with the open 4d - shell are investigated . extensive interest in highly - charged tungsten ions @xcite is caused by its unique physical properties . metallic tungsten is widely exploited in high - temperature devices , including fusion reactors @xcite . although tungsten is difficult to melt and vaporize , its highly - charged ions emerge in fusion plasma and decrease its temperature . therefore one needs to control the concentration of these ions by monitoring their spectra . unfortunately , the experimental data for the multicharged tungsten ions are very sparse . this fact is very evident from the recent compilation @xcite of the experimental and semi - empirical data for the tungsten ions . it is absolutely clear from that review that the tungsten ions from the rubidium - like to the palladium - like systems , which have an open 4d - shell , are investigated very seldom . for the most ions , only a few levels from the ground @xmath6 configuration are determined . moreover , very few energy levels of the first excited @xmath7 and @xmath8 configurations are determined for some tungsten ions . this situation has encouraged us to perform the theoretical investigation of the spectroscopic parameters for these ions . the calculated data can substantially facilitate experimental studies of the corresponding spectra ; on the other hand , these data can be adopted directly for plasma spectra modelling . the w@xmath0 ion energy spectrum of the @xmath3 , @xmath4 and @xmath5 configurations consists of significantly larger number of energy levels , and the range of possible transition wavelengths is wider compared to the previously studied w@xmath9 @xcite and w@xmath10 @xcite ions . in order to keep the current paper concise , we present only the energy spectra and the characteristics of levels . the remaining spectroscopic parameters will be available from the database adamant ( applicable data of many - electron atom energies and transitions ) which is currently under development . likewise for the ions mentioned above ions , we employ a quasirelativistic ( qr ) approach @xcite with an extensive inclusion of correlation effects to investigate the w@xmath0 ion spectroscopic properties . since application of this approach has produced high - accuracy results for the w@xmath9 and w@xmath10 ions , there is no doubt about its applicability to the tungsten ion of slightly lower ionization degree . in section [ calc ] we provide a description of the adopted calculation method . since this approximation ultimately matches the one applied for the investigation of the w@xmath9 and w@xmath10 spectroscopic data in @xcite , here we provide only a brief summary of our method . produced results are discussed in section [ result ] .	the _ ab initio _ quasirelativistic hartree - fock method developed specifically for the calculation of spectroscopic parameters of heavy atoms and highly charged ions was used to derive spectral data for the multicharged tungsten ion w . the energy level spectra , radiative lifetimes , lande-factors are calculated for the , and configurations of the w ion .	the _ ab initio _ quasirelativistic hartree - fock method developed specifically for the calculation of spectroscopic parameters of heavy atoms and highly charged ions was used to derive spectral data for the multicharged tungsten ion w . the configuration interaction method was applied to include the electron - correlation effects . the relativistic effects were taken into account in the breit - pauli approximation for quasirelativistic hartree - fock radial orbitals . the energy level spectra , radiative lifetimes , lande-factors are calculated for the , and configurations of the w ion .
1111.1603	c	motivated by the fact that our current understanding on the abundances of alkali elements in a - type stars is considerably insufficient , we conducted a comprehensive non - lte analysis to establish the photospheric abundances of na , li , and k for 24 selected sharp - lined a - type stars ( @xmath0 km s@xmath1 , 7000 k @xmath2 10000 k ) , many of which are am stars showing different degree of chemical peculiarity . for this purpose , we primarily invoked the spectra of moderately high - dispersion ( @xmath24 ) and high s / n ratio ( typically a few hundreds ) obtained with boes at boao / korea , though spectra of much higher quality ( @xmath28 and s / n @xmath114 ) secured with hides at oao / japan were additionally used for 7 apparently bright stars ( mostly of early a - type ) . we first carried out spectrum fitting analyses applied to the 61466163 @xmath16 region and derived @xmath18 , @xmath23 , @xmath3(o ) , and @xmath3(fe ) , from which the degree of am characteristics for each star could be confirmed . the abundances of sodium , which were determined by the spectrum fitting method applied to the region comprising na i 5682/5688 lines , revealed a significant trend that @xmath3(na ) tightly scales with @xmath3(fe ) , which means that na becomes enriched similarly to fe in accordance with the degree of am phenomenon . this result should be regarded as important because it seriously contradicts the prediction from the atomic diffusion theory . regarding lithium , @xmath3(li ) derived from the weak li i line at 6708 @xmath16 showed a tendency of @xmath4-dependence for late a - type stars in the sense that @xmath3(li ) gradually decreases from @xmath94 ( @xmath95 k ) to @xmath96 ( @xmath97 k ) , while @xmath3(li ) for early a - type stars ( @xmath14 k ) tends to be around the solar system abundance of @xmath94 . however , several stars apparently deviating from this general trend and showing marked underabundances do exist , though what triggers such a li deficiency is not clear . the abundances of potassium derived from the k i 7699 line revealed a tendency somewhat similar to the case of lithium : an apparent @xmath4-dependence ( and possibly with a weak anti - correlation with am peculiarity ) exists for late - a stars where @xmath3(k ) tend to be mildly subsolar systematically decreasing from @xmath8 ( @xmath9 k ) to @xmath10 ( @xmath11 k ) , whereas those for most early - a stars remain near - solar around @xmath12 5.05.2 . when these observational facts are compared with the theoretical prediction of richer et al . ( 2000 ) or talon et al . ( 2006 ) based on their atomic diffusion calculations , a serious discrepancy is found for na ( almost no anomaly or slightly subsolar tendency is predicted , while an enrichment of na just like fe is suggested from our analysis ) , though the simulated results appear to qualitatively reproduce the general trends observed for li and k. further improvement and development on the theoretical side would be desirably awaited to explain the results concluded in this study , which may serve as important constraints for any theory aiming to account for the origin of chemical anomalies in am stars . this research has made use of the simbad database , operated by cds , strasbourg , france . i. han acknowledges the financial support for this study by kicos through korea ukraine joint research grant ( grant 07 - 179 ) . lee acknowledges the astrophysical research center for the structure and evolution of the cosmos ( arsec , sejong university ) of the korea science and engineering foundation ( kosef ) through the science research center ( src ) program . adelman , s. j. 1996 , mnras , 280 , 130 adelman , s. j. 1988 , mnras , 230 , 671 adelman , s. , & philip , a. g. d. 1996 , mnras , 282 , 1181 anders , e. , & grevesse , n. 1989 , geochim . acta , 53 , 197 burkhart , c. , & coupry , m. f. 1991a , a&a , 249 , 205 burkhart , c. , & coupry , m. f. 1991b , mem . soc . astron . it . , 62 , 91 burkhart , c. , & coupry , m. f. 1995 , mem . astron . it . , 66 , 357 burkhart , c. , & coupry , m. f. 2000 , a&a , 354 , 216 burkhart , c. , coupry , m. f. , faraggiana , r. , & gerbaldi , m. 2005 , a&a , 429 , 1043 caliskan , h. , & adelman , s. j. 1997 , mnras , 288 , 501 coupry , m. f. , & burkhart , c. 1992 , a&as , 95 , 41 esa 1997 , the hipparcos and tycho catalogues , esa sp-1200 , available from nasa - adc or cds in a machine - readable form ( file name : hip_main.dat ) flower , p. j. 1996 , apj , 469 , 355 fossati , l. , bagnulo , s. , landstreet , j. , wade , g. , kochukhov , o. , monier , r. , weiss , w. , & gebran , m. 2008 , a&a , 483 , 891 fossati , l. , bagnulo , s. , monier , r. , khan , s. a. , kochukhov , o. , landstreet , j. , wade , g. , & weiss , w. 2007 , a&a , 476 , 911 fossati , l. , ryabchikova , t. , bagnulo , s. , alecian , e. , grunhut , j. , kochukhov , o. , & wade , g. 2009 , a&a , 503 , 945 gebran , m. , & monier , r. 2007 , in convection in astrophysics , ed . f. kupka , i. w. roxburgh , & k. l. chan , proc . 239 ( cambridge : cambridge university press ) , 160 gebran , m. , & monier , r. 2008 , a&a , 483 , 567 gebran , m. , monier , r. , & richard , o. 2008 , a&a , 479 , 189 gebran , m. , vick , m. , monier , r. , & fossati , l. 2010 , a&a , 523 , 71 girardi , l. , bressan , a. , bertelli , g. , & chiosi , c. 2000 , a&as , 141 , 371 gray , d. f. 2005 , the observation and analysis of stellar photospheres , 3rd ed . 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star puzzle , proc . 224 , eds . j. zverko , j. @xmath115i@xmath116@xmath117ovsk@xmath118 , s.j . adelman , w.w . weiss ( cambridge : cambridge university press ) , p.443 paunzen , e. , iliev , i. kh . , kamp , i. , & barzova , i. s. 2002 , mnras , 336 , 1030 richer , j. , michaud , g. , & turcotte , s. 2000 , apj , 529 , 338 sadakane , k. 2006 , pasj , 58 , 1023 sadakane , k. , & okyudo , m. 1990 , pasj , 42 , 317 smith , v. v. , lambert , d. l. , & nissen , p. e. 1998 , apj , 506 , 405 takeda , y. 1995 , pasj , 47 , 287 takeda , y. 2008 , mnras , 388 , 913 ( paper i ) takeda , y. , han , i. , kang , d .- i . , lee , b .- , & kim , k .- 2008a , jkas , 41 , 83 takeda , y. , kambe , e. , sadakane , k. , & masuda , s. 2010 . pasj , 62 , 1239 takeda , y. , kang , d .- , han , i. , lee , b .- , & kim , k .- m . 2009 , pasj , 61 , 1165 ( paper ii ) takeda , y. , kato , k. , watanabe , y. , & sadakane , k. 1996 , pasj , 48 , 511 takeda , y. , & kawanomoto , s. 2005 , pasj , 57 , 45 takeda , y. , kawanomoto , s. , & ohishi , n. 2007 , pasj , 59 , 245 takeda , y. , ohkubo , m. , & sadakane , k. 2002 , pasj , 54 , 451 takeda , y. , & sadakane , k. 1997 , pasj , 49 , 367 takeda , y. , sato , b. , & murata , d. 2008b , pasj , 60 , 781 takeda , y. , & takada - hidai , m. 1994 , pasj , 46 , 395 talon , s. , richard , o. , & michaud , g. 2006 , apj , 645 , 634 van leeuwen , f. 2007 , hipparcos , the new reduction of the raw data ( berlin : springer ) varenne , o. , & monier , r. 1999 , a&a , 351 , 247 rrccccrrrrccclhd # & hr # & name & sp.type & @xmath4 & @xmath31 & @xmath18 & @xmath23 & @xmath119 & @xmath120 & @xmath121 & @xmath122 & @xmath123 & remark + + 195725 & 7850 & @xmath124 cep & a7iii & 7816 & 3.74 & 4.45 & 52.0 & 7.60 & 8.47 & 3.27 & 6.35 & 4.81 & + 95418 & 4295 & @xmath35 uma & a1v & 9489 & 3.85 & @xmath1252.50 & 46.8 & 7.73 & 8.45 & ( @xmath1264.34 ) & 6.45 & ( @xmath1265.47 ) & + 27819 & 1380 & @xmath127tau & a7v & 8047 & 3.95 & 3.93 & 46.5 & 7.45 & 8.78 & 3.35 & 6.23 & 4.88 & h + 43378 & 2238 & 2 lyn & a2vs & 9210 & 4.09 & @xmath1252.10 & 45.4 & 7.34 & 8.70 & ( @xmath1264.07 ) & 6.13 & ( @xmath1265.18 ) & + 218396 & 8799 & @xmath128 & a5v & 7091 & 4.06 & @xmath1253.00 & 41.4 & 6.90 & 8.88 & 2.82 & 5.83 & 5.01 & vega - like star + 84107 & 3861 & 15 leo & a2iv & 8665 & 4.31 & 3.57 & 38.1 & 7.50 & 8.62 & ( @xmath1263.44 ) & 6.21 & 4.93 & + 33204 & 1670 & @xmath128 & a5 m & 7530 & 4.06 & 4.14 & 36.4 & 7.76 & 8.46 & 3.11 & 6.47 & 4.72 & h + 204188 & 8210 & @xmath128 & a8 m & 7622 & 4.21 & @xmath1253.90 & 35.3 & 7.50 & 8.74 & ( @xmath1262.77 ) & 6.24 & 4.75 & + 141795 & 5892 & @xmath54 ser & a2vm & 8367 & 4.24 & 4.04 & 34.4 & 7.72 & 8.17 & ( @xmath1263.16 ) & 6.46 & 5.02 & + 173648 & 7056 & @xmath129lyr & a4 m & 8004 & 3.90 & 4.73 & 32.4 & 7.74 & 8.31 & 3.21 & 6.47 & 4.82 & + 27628 & 1368 & 60 tau & a3 m & 7218 & 4.05 & 4.74 & 32.3 & 7.74 & 8.43 & 3.03 & 6.46 & 4.75 & h + 28546 & 1428 & 81 tau & a5 m & 7640 & 4.17 & 3.63 & 28.1 & 7.74 & 8.58 & 3.11 & 6.47 & 4.86 & h + 172167 & 7001 & @xmath25 lyr & a0va & 9435 & 3.99 & 1.85 & 21.9 & 6.96 & 8.63 & ( @xmath1263.84 ) & 6.00 & ( @xmath1265.38 ) & vega - like star + 60179 & 2891 & @xmath25 gem & a1v & 9122 & 3.88 & 2.33 & 19.7 & 7.52 & 8.42 & ( @xmath1263.71 ) & 6.15 & 5.10 & + 95608 & 4300 & 60 leo & a1 m & 8972 & 4.20 & 2.93 & 17.2 & 7.84 & 8.19 & ( @xmath1263.43 ) & 6.46 & 5.32 & + 48915 & 2491 & @xmath25 cma & a1vm & 9938 & 4.31 & @xmath1252.53 & 16.5 & 7.89 & 8.41 & ( @xmath1264.01 ) & 6.52 & ( @xmath1265.19 ) & + 27749 & 1376 & 63 tau & a1 m & 7448 & 4.21 & 3.90 & 12.7 & 7.97 & 8.25 & 3.09 & 6.56 & 4.50 & h + 33254 & 1672 & 16 ori & a2 m & 7747 & 4.14 & 3.07 & 12.2 & 7.99 & 8.18 & ( @xmath1262.53 ) & 6.60 & 4.66 & h + 72037 & 3354 & 2 uma & a2 m & 7918 & 4.16 & 2.48 & 11.6 & 7.89 & 7.98 & ( @xmath1262.55 ) & 6.53 & 4.66 & + 47105 & 2421 & @xmath26 gem & a0iv & 9115 & 3.49 & 1.81 & 10.9 & 7.55 & 8.76 & ( @xmath1263.50 ) & 6.35 & 4.90 & + 27962 & 1389 & 68 tau & a2iv & 8923 & 3.94 & 3.44 & 10.4 & 7.73 & 8.54 & ( @xmath1263.23 ) & 6.46 & 5.22 & h + + 182564 & 7371 & @xmath15 dra & a2iiis & 9125 & 3.80 & 3.43 & 27.3 & 7.83 & 8.48 & 3.47 & 6.65 & 4.98 & + 172167 & 7001 & @xmath25 lyr & a0va & 9435 & 3.99 & 1.90 & 21.9 & 6.97 & 8.63 & 3.21 & 6.05 & 5.13 & vega - like star + 48915 & 2491 & @xmath25 cma & a1vm & 9938 & 4.31 & 2.53 & 16.6 & 7.89 & 8.42 & ( @xmath1263.18 ) & 6.59 & 5.15 & + 47105 & 2421 & @xmath26 gem & a0iv & 9115 & 3.49 & 2.49 & 11.1 & 7.48 & 8.74 & 3.17 & 6.33 & 5.19 & + 189849 & 7653 & 15 vul & a4iii & 7870 & 3.62 & 5.16 & 10.7 & 7.34 & 8.65 & 3.03 & 6.31 & 4.60 & + 27962 & 1389 & 68 tau & a2iv & 8923 & 3.94 & 3.99 & 10.5 & 7.69 & 8.54 & 3.17 & 6.46 & 5.10 & h + 214994 & 8641 & @xmath21 peg & a1iv & 9453 & 3.64 & 3.07 & 6.0 & 7.63 & 8.52 & ( @xmath1262.94 ) & 6.46 & 4.74 & + note . + in columns 1 through 6 are given the hd number , hr number , star name ( with constellation ) , spectral type ( taken from hoffleit 1982 ) , effective temperature ( in k ) , and logarithmic surface gravity ( in cm s@xmath130 ) . columns 7 through 10 show the results derived from 61466163 @xmath16 region fitting : the microturbulent velocity ( in km s@xmath1 ) , projected rotational velocity ( in km s@xmath1 ) , ( lte ) abundance of fe , and ( non - lte ) abundance of o. the non - lte abundances of li , na , and k finally resulting from this investigation are presented in columns 1113 . all abundance results are expressed in the usual normalization of @xmath3(h ) = 12.00 . in each of the boao ans oao samples , the objects are arranged in the descending order of @xmath131 . in the remark in column 14 , hyades cluster stars are denoted with `` h '' . + @xmath125regarding these @xmath18 values , literature values were adopted unlike the others , because the @xmath18-determination from the 61466163 @xmath16 region fitting did not work successfully . see subsection 2.3 for more details . cclrldesig . & species & @xmath132 & @xmath133 ( ev ) & @xmath134 + li 6708 & li i & 6707.756 & 0.00 & @xmath135 + & li i & 6707.768 & 0.00 & @xmath136 + & li i & 6707.907 & 0.00 & @xmath137 + & li i & 6707.908 & 0.00 & @xmath138 + & li i & 6707.919 & 0.00 & @xmath139 + & li i & 6707.920 & 0.00 & @xmath137 + o 6156 & o i & 6155.961 & 10.74 & @xmath140 + & o i & 6155.971 & 10.74 & @xmath141 + & o i & 6155.989 & 10.74 & @xmath138 + o 6157 & o i & 6156.737 & 10.74 & @xmath142 + & o i & 6156.755 & 10.74 & @xmath137 + & o i & 6156.778 & 10.74 & @xmath143 + o 6158 & o i & 6158.149 & 10.74 & @xmath144 + & o i & 6158.172 & 10.74 & @xmath145 + & o i & 6158.187 & 10.74 & @xmath146 + na 5682 & na i & 5682.633 & 2.10 & @xmath147 + na 5688 & na i & @xmath148 & 2.10 & @xmath149 + na 6154 & na i & 6154.226 & 2.10 & @xmath150 + na 6160 & na i & 6160.747 & 2.10 & @xmath151 + si 5684 & si i & 5684.484 & 4.95 & @xmath152 + si 5688 & si ii & 5688.817 & 14.19 & + 0.40 + si 6155 & si i & 6155.134 & 5.62 & @xmath153 + s 7696 & s i & 7696.758 & 7.87 & @xmath154 + k 7699 & k i & 7698.974 & 0.00 & @xmath155 + ca 6162 & ca i & 6162.173 & 1.90 & + 0.10 + sc 5684 & sc ii & 5684.202 & 1.51 & @xmath141 + fe 5686 & fe i & 5686.524 & 4.55 & @xmath156 + fe 6147 & fe ii & 6147.741 & 3.89 & @xmath157 + fe 6149 & fe ii & 6149.258 & 3.89 & @xmath157 + fe 6150 & fe ii & 6150.098 & 11.45 & @xmath158 + fe 6157 & fe i & 6157.725 & 4.08 & @xmath151 + fe 6705 & fe i & 6705.101 & 4.61 & @xmath159 + fe 6708 & fe ii & 6708.885 & 10.91 & @xmath160 + ni 5682 & ni i & 5682.198 & 4.11 & @xmath161 + note . + all data are were taken from kurucz & bell s ( 1995 ) compilation , except for those of li i which were adopted from smith et al . ( 1998 ) as in takeda and kawanomoto ( 2005 ) . + @xmath125since this line comprises two close components of stronger @xmath162 ( at 5688.205 @xmath16 ) and weaker @xmath163 ( at 5688.194 @xmath16 ) , we adopted @xmath164 as the sum of these two . regarding the li i lines , we considered only the lines of @xmath165li , since we neglected @xmath166li in our analysis .	the abundances of alkali elements ( li , na , and k ) were determined from the li i 6708 , na i 5682/5688 , and k i 7699 lines by taking into account the non - lte effect for 24 sharp - lined a - type stars ( km s , 7000 k 10000 k , many showing am peculiarities to different degrees ) , based on high - dispersion and high - s / n spectral data secured at boao ( korea ) and oao ( japan ) . we found a significant trend that(na ) tightly scales with(fe ) irrespective of , which means that na becomes enriched similarly to fe in accordance with the degree of am peculiarity . the abundances of potassium also revealed an apparent-dependence in the sense that(k ) in late - a stars tends to be mildly subsolar ( possibly with a weak anti - correlation with(fe ) ) systematically decreasing from ( k ) to ( k ) , while those for early - a stars remain near - solar around 5.05.2 . these observational facts may serve as important constraints for any theory aiming to explain chemical anomalies of a - type stars .	the abundances of alkali elements ( li , na , and k ) were determined from the li i 6708 , na i 5682/5688 , and k i 7699 lines by taking into account the non - lte effect for 24 sharp - lined a - type stars ( km s , 7000 k 10000 k , many showing am peculiarities to different degrees ) , based on high - dispersion and high - s / n spectral data secured at boao ( korea ) and oao ( japan ) . we found a significant trend that(na ) tightly scales with(fe ) irrespective of , which means that na becomes enriched similarly to fe in accordance with the degree of am peculiarity . regarding lithium ,(li ) mostly ranges between and ( i.e. , almost the same as or slightly less than the solar system abundance of 3.3 ) with a weak decreasing tendency with a lowering of at k , though several stars exceptionally show distinctly larger depletion . the abundances of potassium also revealed an apparent-dependence in the sense that(k ) in late - a stars tends to be mildly subsolar ( possibly with a weak anti - correlation with(fe ) ) systematically decreasing from ( k ) to ( k ) , while those for early - a stars remain near - solar around 5.05.2 . these observational facts may serve as important constraints for any theory aiming to explain chemical anomalies of a - type stars .
1305.3174	i	let @xmath6 be a @xmath7-dimensional closed , connected , oriented manifold with an effective @xmath8-dimensional ( i.e. , half - dimensional ) torus @xmath9-action . we call @xmath6 ( or @xmath10 ) a _ torus manifold _ if @xmath11 ( see @xcite ) , where @xmath12 is the set of fixed points . a toric manifold ( i.e. , a non - singular , complete toric variety viewed as a complex analytic space ) with the restricted @xmath9-action is a typical example of torus manifolds . recall that a toric manifold is a complex @xmath13-manifold with the dense orbit ( see @xcite , @xcite ) , and @xmath9 is the maximal compact subgroup of @xmath13 . a fundamental result of toric geometry tells us that there is a one - to - one correspondence between toric manifolds and combinatorial objects called fans . thus , topological ( more precisely , geometric ) invariants of toric manifolds can be described in terms of combinatorial invarinats of fans , such as equivariant cohomology rings , equivariant characteristic classes and other topological invariants . in 2003 , hattori - masuda introduced a torus manifold as the topological generalization of a toric manifold in @xcite . they also introduced the combinatorial objects , called multi - fans ( see @xcite , @xcite ) , and computed topological invariants ( such as equivariant characteristic classes or todd genus for unitary torus manifolds ) in terms of multi - fans . however , unlike toric geometry , a multi - fan does not contain enough information to determine some topological invariants of torus manifolds ( e.g. equivariant cohomology ) . so , in 2007 , maeda - masuda - panov introduced another combinatorial objects , called torus graphs motivated by gkm graphs introduced by guillemin - zara in @xcite . the combinatorial information of torus graphs can completely determine the equivariant cohomology rings of torus manifolds with vanishing odd degree cohomology , i.e. , @xmath14 ( in this paper , we only consider the integer coefficient ) , see @xcite , @xcite ( and also see section [ sect3 ] in this paper about torus graphs ) . however , in general , there is no one - to - one correspondence between torus manifolds with @xmath2 and torus graphs . so , we are naturally led to ask the following two questions : ( 1 ) which subclasses of torus manifolds are completely determined by combinatorial objects ( like multi - fans or torus graphs ) ; ( 2 ) if we find such a subclass of torus manifolds , how we can classify such torus manifolds . several mathematicians have answered to the 1st question ; for example , davis - januszkiewicz @xcite for the subclass called _ quasitoric manifolds _ ( see @xcite or section [ sect4.3 ] in this paper ) , ishida - fukukawa - masuda @xcite for the subclass called _ topological toric manifolds _ , and wiemeler for the class of simply connected @xmath0-dimensional torus manifolds with @xmath2 in @xcite ( see theorem [ wi2 ] ) . the aim of this paper is to answer to the 2nd question for the class of simply connected @xmath0-dimensional torus manifolds with @xmath2 by using torus graphs . let us briefly recall the classification results for torus manifolds with lower dimensions . if @xmath15 acts on a compact @xmath16-dimensional manifold @xmath6 , then @xmath6 is the @xmath16-dimensional sphere @xmath5 , the @xmath16-dimensional real projectiove space @xmath17 or the @xmath16-dimensional torus @xmath18 . because @xmath11 and @xmath6 is oriented , @xmath6 must be equivariantly diffeomorphic to @xmath5 with @xmath15-action ( also see @xcite ) . when @xmath19 . by orlik - raymond s theorem in @xcite , we have the following fact : [ or - thm ] let @xmath6 be a @xmath20-dimensional simply connected torus manifold . then , @xmath6 is equivariantly diffeomorphic to the @xmath20-sphere @xmath21 or an equivariant connected sum of copies of complex projective spaces @xmath22 , @xmath23 ( reversed orientation ) or hirzebruch surfaces @xmath24 . here , in theorem [ or - thm ] , a hirzebruch surface @xmath24 ( @xmath25 ) is a manifold which is defined by the projectivization of the complex @xmath16-dimensional vector bundle @xmath26 over @xmath27 , where @xmath28 is the tautological and @xmath29 is the trivial complex line bundles over @xmath27 . in this paper , we prove that an orlik - raymond type theorem in theorem [ or - thm ] also holds for simply connected @xmath0-dimensional torus manifolds with @xmath2 . before we state our main results , we introduce the result for non - simply connected torus manifolds . as one of the consequences of masuda - panov s theorem ( see theorem [ 2-equiv ] in section [ sect2.2 ] ) , we have the following proposition ( also see @xcite ) : [ wiemeler ] let @xmath30 be a @xmath0-dimensional torus manifold with @xmath31 ( might not be simply connected ) . then , there are a simply connected , @xmath0-dimensional torus manifold @xmath6 with @xmath2 and a homology @xmath1-sphere @xmath32 such that @xmath33 up to equivariantly diffeomorphism . here , in proposition [ wiemeler ] , the product manifold @xmath34 is the product of @xmath32 and the @xmath1-dimensional torus @xmath35 with the free @xmath36-action on the @xmath16nd factor , and the symbol @xmath37 represents the equivariant gluing along two free orbits of @xmath6 and @xmath34 . because the fundamental groups @xmath38 and @xmath39 are isomorphic in proposition [ wiemeler ] , @xmath30 is simply connected if and only if @xmath32 is simply connected , i.e. , the standard sphere . our main theorem is a classification of simply connected torus manifolds appeared in proposition [ wiemeler ] . [ main1 ] let @xmath6 be a simply connected @xmath0-dimensional torus manifold with @xmath2 . then , @xmath6 is equivariantly diffeomorphic to the @xmath0-sphere @xmath40 or obtained by an equivariant connected sum of copies of @xmath0-dimensional quasitoric manifolds or @xmath21-bundles over @xmath41 equipped with the structure of a torus manifold . this type of classification , i.e. , classification by equivariant connected sum , may be regarded as the @xmath0-dimensional analogue of orlik - raymond s classification in theorem [ or - thm ] . so , in this paper , we call this theorem an _ orlik - raymond type classification _ ( also see the papers @xcite and @xcite ) . in the paper @xcite , izmestiev proves an orlik - raymond type classification for some class of @xmath1-dimensional small covers ( i.e. , the real analogue of quasitoric manifolds , see section [ sect4.2 ] ) , called a linear model . the organization of this paper is as follows . in section [ sect2 ] , we recall the basic facts about torus manifolds . in section [ sect3 ] , we recall a torus graph . in particular , corollary [ key2 ] is the key fact to prove theorem [ main1 ] . in section [ sect4 ] , we introduce the torus graphs of @xmath3 , quasitoric manifolds and @xmath4-bundles over @xmath5 . these torus graphs will be the basic graphs to classify simply connected @xmath0-dimensional torus manifolds with @xmath2 . in section [ sect5 ] , we introduce the `` oriented '' torus graphs and translate the equivariant connected sum around fixed points of torus manifolds to the connected sum around vertices of oriented torus graphs . in section [ sect6 ] and [ sect7 ] , we prove theorem [ main1 ] . the brief outline of the proof is as follows . due to corollary [ key2 ] , there is a one - to - one corresponds between @xmath0-dimensional simply connected torus manifolds with @xmath2 and @xmath1-valent torus graphs . therefore , in order to prove theorem [ main1 ] , it is enough to prove that an ( oriented ) torus graph can be decomposed into basic torus graphs in section [ sect4 ] by the connected sum . we prove this by using combinatorial arguments .	the aim of this paper is to classify simply connected-dimensional torus manifolds with vanishing odd degree cohomology . it is shown that there is a one - to - one correspondence between equivariant diffeomorphism types of these manifolds and-valent labelled graphs , called torus graphs introduced by maeda - masuda - panov . using this correspondence and combinatorial arguments , we prove that a simply connected-dimensional torus manifold with is equivariantly diffeomorphic to the-dimensional sphere or an equivariant connected sum of copies of-dimensional quasitoric manifolds or-bundles over .	the aim of this paper is to classify simply connected-dimensional torus manifolds with vanishing odd degree cohomology . it is shown that there is a one - to - one correspondence between equivariant diffeomorphism types of these manifolds and-valent labelled graphs , called torus graphs introduced by maeda - masuda - panov . using this correspondence and combinatorial arguments , we prove that a simply connected-dimensional torus manifold with is equivariantly diffeomorphic to the-dimensional sphere or an equivariant connected sum of copies of-dimensional quasitoric manifolds or-bundles over .
nucl-th0505007	r	for the wave functions of @xmath2b that form the basis of the cdcc expansion of the three - body system we make the following assumptions . we assume that the ground state wave function of @xmath2b , with the @xmath128-component @xmath143 of the total spin @xmath222 of it , is given by @xmath223_{2m_0 } + w_2 \left[i y_1(\hat{\bf r } ) \otimes \zeta_2 \right]_{2m_0 } \ } \nonumber \\ & & \times f_{\rm r}^{(0)}(r ) \nonumber \\ & \equiv&\ ; w_1 f_{1,m_0}^{(0)}({\bf r})+ w_2 f_{2,m_0}^{(0)}({\bf r } ) \label{f0}\end{aligned}\ ] ] in the channel spin representation , neglecting the @xmath224 components . the values of the coefficients @xmath225 and @xmath226 are obtained from the result of the microscopic calculation @xcite of @xmath2b , @xmath227 , where @xmath228 ( @xmath229 ) is the anc in the proton spin - orbit coupling representation corresponding to the @xmath230 ( 3/2 ) state . we further assume the effective @xmath7-@xmath0be interaction for the ground state of @xmath2b , @xmath231 , to be independent of @xmath125 , hence the same radial dependence @xmath232 of the @xmath233 and @xmath234 components in eq . ( [ f0 ] ) . this assumption is valid since only the tail region , @xmath235 , of @xmath103 contributes to the @xmath2b breakup process concerned . the wave function of the @xmath7-@xmath0be scattering state with outgoing scattered waves is given by @xmath236 where @xmath237 is the incident wave with definite channel spin @xmath125 and its @xmath128-component @xmath238 , @xmath239 is the incident energy in the c.m . frame of the @xmath7-@xmath0be system , and @xmath240 is the incident momentum . the wave function with incoming scattered waves @xmath241 corresponding to @xmath242 used below is defined by @xmath243 . we assume that @xmath244 has no tensor force component . we consider the breakup of @xmath2b to its scattering states at low @xmath239 , and truncate the modelspace by @xmath245 mev . in the experiment we analyze , however , the cross section is measured for @xmath246 in the range of 500 kev @xmath247 kev , and it turns out that only coupling of those states with @xmath239 much lower than 10mev need be taken into account as described in sec . [ ress17 ] , for which only s - waves are affected by the nuclear part of @xmath244 . all the higher partial waves have negligible amplitude inside its range because of the coulomb and centrifugal barriers and there have no coupling with the s - waves . therefore , all the angular momenta @xmath124 , @xmath125 and @xmath126 are conserved in @xmath248 . the channel spin @xmath125 is conserved also in s - waves since @xmath249 that is a good quantum number . thus , one sees that @xmath242 is the pure state of @xmath125 , while @xmath124 and @xmath126 are mixed as in the incident wave @xmath250 . it should be noted , however , that @xmath251 for the s - waves depends on @xmath125 as is evident from the large @xmath125-dependence of the s - wave @xmath7-@xmath0be scattering lengths : @xmath252 fm and @xmath253 fm @xcite . furthermore , it turns out that the spin - dependent part of the @xmath7-@xmath4pb optical potential has no effect on the resulting elastic cross section at forward angles . thus , the channel spin @xmath125 is conserved during the breakup process of @xmath2b by the @xmath4pb target @xcite . under these circumstances , the @xmath125-dependent 3-body @xmath28-matrix element in actual cdcc calculation , @xmath254 , is given by @xmath255 where @xmath256 is the wave matrix given in eq . ( [ wavematrix ] ) . the unpolarized @xmath2b breakup cross section calculated by cdcc , @xmath257 , is given by @xmath258 where @xmath259 ( @xmath260 ) is the @xmath128-component of the spin of @xmath7 ( @xmath0be ) and the orthonormality of the clebsch - gordan coefficient is used . we compare @xmath257 with the unpolarized cross sections measured by riken experiment @xcite . in the calculation of @xmath261 and @xmath262 , we use an @xmath126-independent @xmath7-@xmath0be effective interaction @xmath263 as mentioned above . then , the states of @xmath2b with fixed @xmath125 and @xmath124 and different values of @xmath126 are degenerate , which greatly simplifies numerical calculation . the value of @xmath119 in eq . ( [ s170 ] ) corresponding to the spin - dependent anc analysis is @xcite @xmath264 fm . for @xmath231 , the single - particle potential of esbensen and bertsch ( eb ) @xcite is used , except that we neglect the spin - orbit part of the potential and adjust the depth of the central potential to reproduce the separation energy of @xmath7 , 137 kev . the scattering states for the p - waves are also calculated with this @xmath231 . for d- and f - states with both @xmath233 and @xmath234 , we use the potential of barker @xcite . for the s - state in the @xmath234 channel , we use the potential of barker that gives the s - wave @xmath7-@xmath0be scattering length @xmath265 of @xmath266 fm . for the s - state with @xmath233 , we change the depth of the potential of barker to 25.7 mev so that the resulting scattering length @xmath267 is 25 fm . as for the distorting potential between @xmath7 ( @xmath0be ) and @xmath4pb we adopt the global optical potential by koning and delaroche @xcite ( cook @xcite ) . we neglect the spin - orbit parts of the @xmath7-@xmath4pb potential . the multipoles for nuclear and coulomb coupling - potentials are included up to @xmath268 . the discretized - continuum states of @xmath2b are constructed by the average method @xcite . the maximum excitation energy of @xmath2b is 10 mev and 10 , 20 , 10 , and 5 discretized - continuum states are taken for the @xmath269 , 0 , 2 , and 3 states , respectively . the resulting number of scattering - channels is 138 . the maximum values of @xmath49 , @xmath46 , and @xmath27 are , respectively , 200 fm , 1000 fm , and 12000 . the modelspace described above turns out to give good convergence of the resulting breakup cross sections . b breakup cross section integrated over @xmath239 in the range of 500750 kev , as a function of @xmath65 . the dotted , dash - dotted , and solid lines represent the results of the hybrid calculation of cdcc and e - cdcc with @xmath270 , 1000 , and 1500 , respectively . the result of e - cdcc , i.e. @xmath271 , is also shown by the dashed line . , scaledwidth=45.0% ] figure 2 shows the convergence of the hybrid calculation with cdcc and e - cdcc for the breakup cross section of @xmath2b by @xmath4pb at 52 mev / nucleon . the cross section integrated over the excitation energy of @xmath2b measured from the @xmath7+@xmath0be threshold energy , @xmath239 , from 500 kev to 750 kev is plotted as a function of @xmath65 . the dashed line is the result of the e - cdcc calculation ( @xmath271 ) and the dotted , dash - dotted , and solid lines correspond to the hybrid calculation with @xmath270 , 1000 , and 1500 , respectively . the figure shows that the hybrid calculation converges with @xmath272 . the difference between the dash - dotted and solid lines is only less than about 1% in magnitude . thus , we regard the hybrid calculation of cdcc and e - cdcc with @xmath272 as the fully quantum - mechanical cdcc calculation . b breakup cross sections with ( solid line ) and without ( dashed line ) the resolution and efficiency of the measurement @xcite taken into account . the experimental data are taken from ref . ( b ) decomposition of the smeared @xmath2b breakup cross section into the s- ( dashed line ) , p- ( dotted line ) , d- ( dash - dotted line ) , and f - state ( dash - two - dotted line ) breakup components . , scaledwidth=45.0% ] one sees in fig . 2 the oscillation of the cross section at forward angles around 2@xmath273 , which turns out to be due to the interference between nuclear and coulomb breakup - amplitudes . therefore , it can be concluded that nuclear interactions affect the breakup cross section even at very forward angles . however , as one sees below , this oscillation is not observed in actual experimental data because of the limit of the resolution of @xmath65 in the measurement . figure 3 shows the comparison between cdcc calculation and the experimental data for the @xmath2b breakup . in order to take account of the experimental resolution and efficiency , the theoretical result has been smeared out by using the filtering table @xcite provided by the authors of ref . the upper panel shows the filtering effect on the cross section calculated with cdcc , where the solid and dashed lines represent the results obtained with and without the smearing procedure . in the lower panel , the smeared total breakup cross section is decomposed into the s- ( dashed line ) , p- ( dotted line ) , d- ( dash - dotted line ) , and f - state ( dash - two - dotted line ) breakup components of @xmath2b . one sees the smeared result of cdcc well agrees with the experimental data at forward angles ( @xmath120 ) , while it underestimates the data at backward angles . the lower panel shows the importance of the p - state breakup for @xmath274 , which implies that nuclear breakup is significant in this angular region . thus , careful description of the p - state @xmath2b wave function , the resonance structures of it in particular , will be necessary to reproduce the experimental data at backward angles . the underestimation there may be due also to dynamical roles played by the excited - core component in @xmath2b , @xmath0be(1/2@xmath275)@xmath276(3/2@xmath275 ) , that is neglected in the present work as discussed in sec . although further study in this line will be very interesting , it is beyond the scope of the present paper . additionally , the filtering table used was made with assuming the s - state breakup of @xmath2b . thus , quantitative comparison between the calculation and the experimental data , to extract @xmath3 with high accuracy , can only be done in the region where the s - state breakup cross section is dominant . therefore , below we use the data for @xmath277 to determine @xmath278 by @xmath279 where @xmath257 is given by eq . ( [ sigcal ] ) and @xmath280 is the corresponding experimental data . -fit of the breakup cross section calculated with the @xmath2b single - particle potential of esbensen and bertsch ( eb ) @xcite . the solid line is the same as that in each panel in fig . 3 but multiplied by the spectroscopic factor @xmath281 . the result with @xmath282 is also shown by the dashed line for comparison . for the eight data points below @xmath64 , which are used in the fitting procedure , we have put the horizontal bar that represents the resolution of @xmath65 @xcite of the measurement . , scaledwidth=45.0% ] figure 4 shows the result of the @xmath283-fit of the theoretical calculation to the experimental data . the solid line is the same as that in each panel in fig . 3 but multiplied by the spectroscopic factor @xmath281 . the dashed line represents the result before being fitted , i.e. with @xmath282 . each horizontal bar put on the eight data points below @xmath64 does not represent a statistical error but it shows the range of @xmath65 in which the breakup cross sections contribute to each data point @xcite . the value of @xmath283 per datum obtained is 8.5 . although the quality of the fit is not good , it should be noted that estimation of error - propagation in the present case , i.e. comparison between smeared experimental data and a smeared numerical result , is very complicated ; the value of @xmath283 per datum shown above takes account of no error with respect to @xmath65 . the value of @xmath110 in eq . ( [ alpha ] ) for the eb @xmath2b wave - function is 0.704 @xmath284 . with the values of @xmath102 and @xmath110 , the anc @xmath39 is obtained from eq . ( [ c ] ) as @xmath285 @xmath284 . one can then determine @xmath3 by inserting this result into eq . ( [ s170 ] ) , together with @xmath286 fm , i.e. @xmath287 ev b. in the next subsection we quantitatively evaluate uncertainties of the extracted @xmath3 . first , we evaluate the uncertainty of @xmath3 that comes from the use of the anc method , just in the same way as in refs . we show in fig . 5 the result of cdcc calculation with the p - state single - particle potential of @xmath2b by kim _ et al . @xcite ( the dashed line ) and that multiplied by @xmath288 ( the solid line ) ; the latter agrees with the result shown in fig . 4 within 1% . one sees that @xmath102 indeed depends on the p - state potential . b ; the spectroscopic factor @xmath102 obtained is 0.867 . the result with kim s potential before @xmath283-fitting , namely with @xmath282 , is also shown by the dashed line for comparison . , scaledwidth=45.0% ] actually , @xmath110 in eq . ( [ alpha ] ) for kim s potential is 0.796 @xmath284 , which is quite different from the value for the eb potential , 0.704 @xmath284 , because of the difference in the geometry of the two potentials of about 20% . on the contrary , the value of @xmath39 in eq . ( [ c ] ) calculated with kim s potential is 0.741 @xmath284 that agrees very well with the result obtained with the eb potential shown in sec . [ ress17 ] . this result shows that the anc method works with very high accuracy in the present analysis , i.e. the error of the anc method is negligible . second , we estimate the effect of ambiguity of the distorting potentials used in the cdcc calculation on the obtained @xmath3 . for this purpose we use alternative optical potentials for @xmath7-@xmath4pb and @xmath0be-@xmath4pb . for the @xmath7-@xmath4pb potential , we modify the parameter set of koning and delaroche so that the calculated elastic cross section without spin - orbit terms reproduces the one obtained with the full components of the optical potential . the parameter set thus obtained is @xmath289 mev , @xmath290 mev , and @xmath291 mev , with the same notation as in ref . @xcite ; all other parameters are not changed . for the @xmath0be-@xmath4pb potential , we use a single - folding model with the nucleon-@xmath4pb potential of koning and delaroche , neglecting the spin - orbit terms . the density distribution of @xmath0be is assumed to be of the gaussian form with the range that reproduces the rms matter radius of @xmath0be of 2.48 fm @xcite . the difference between the results calculated with the original and alternative optical potentials is found to be negligibly small ( not shown ) . we conclude , therefore , that the error of @xmath3 that comes from the ambiguity of the distorting potentials in the present case is negligibly small . b breakup cross section on the s - state single - particle potentials of @xmath2b for the @xmath233 and @xmath234 channels . the solid line represents the result with the choice of the potentials that corresponds to the s - wave @xmath7-@xmath0be scattering lengths @xmath292 . the dashed ( dotted ) line shows the result with the s - state potentials corresponding to @xmath293 ( @xmath294 ) . , scaledwidth=45.0% ] finally , we estimate the uncertainty of @xmath3 due to the ambiguity of the s - state single - particle potentials of @xmath2b for the @xmath233 and @xmath234 channels by changing the depth of the potential for the @xmath233 ( @xmath234 ) channel ranging from 23.3 mev ( 52.8 mev ) to 30.5 mev ( 57.6 mev ) , which gives the range of the resulting s - wave @xmath7-@xmath0be scattering length @xmath267 ( @xmath265 ) from @xmath295 fm ( @xmath296 fm ) to @xmath297 fm ( @xmath298 fm ) ; these values of @xmath267 and @xmath265 are within the range of errors of the experimental values of them @xcite . in fig . 6 the solid , dashed , and dotted lines represent the results with the s - state potentials corresponding to @xmath299 , @xmath300 , and @xmath301 , respectively . one sees the breakup cross section slightly depends on the choice of the s - state potentials of @xmath2b ; the resulting @xmath3 is found to vary from 20.3 ev b to 21.9 ev b. thus , we evaluate the error of @xmath3 to be @xmath302/@xmath303 . summarizing the discussion given above , the result of the present paper is as follows . the central value of @xmath3 is 20.9 ev b. the theoretical error of the extracted @xmath3 concerned with the s - wave @xmath7-@xmath0be scattering length is @xmath302/@xmath303 . after including the 8.4% systematic experimental error , we obtain @xmath304 the main result of the present paper is @xmath305 ( theo ) @xmath306 ( expt ) ev b derived from @xmath4pb(@xmath2b , @xmath5be)@xmath4pb at 52 mev / nucleon . this value is significantly larger than @xmath23 ev b @xcite obtained in the previous analysis of the same experiment with the first - order perturbation theory . in order to clarify the reason for the difference , we discuss roles of nuclear interaction , e2 transitions , and higher - order processes . in fig . 7 the solid line is the same as in the upper panel in fig . 3 that shows the result of full cdcc . the dashed line corresponds to the calculation without breakup components of nuclear coupling potentials . it should be noted that their diagonal components are included in the calculation to take account of the absorption of the flux of the incident particle by the target nucleus . one sees that the dashed line agrees with the solid line below @xmath307 but deviates from it for @xmath308 . as a result , the value of @xmath3 obtained , @xmath309 ev b , is smaller than @xmath305 ( theo ) @xmath306 ( expt ) ev b obtained with the full cdcc calculation mentioned above . the dash - dotted line in fig . 7 represents the result of first - order iterative solutions of cdcc , designated as one - step cdcc , without nuclear breakup , including only @xmath310 ( e1 ) component of the coulomb interaction ; this calculation is essentially the same as the first - order perturbation theory ( virtual photon theory ) used in the previous analysis of the experimental data @xcite . it overestimates the solid line above 1.5@xmath273 and the resulting value of @xmath3 is @xmath311 ev b , which agrees well with the value @xmath8 ev b obtained in ref . @xcite . if one includes the @xmath312 ( e2 ) component in the one - step cdcc calculation of coulomb breakup , the dotted line in fig . 7 is obtained ; the coupling potentials with @xmath312 are artificially multiplied by 0.7 , following the analysis of the msu data @xcite . one sees from fig . 7 that inclusion of the reduced e2 component somewhat increases the breakup cross section , which results in further decrease of @xmath3 to @xmath313 ev b. this result is consistent with the conclusion of ref . @xcite , in which @xmath314 ev b was derived with first - order perturbation theory including both e1 and the reduced e2 components . if the e2 component is not scaled , the resulting value of @xmath3 is 16.7 ev b. this value is about 20% less than the result of full cdcc , 20.9 ev b. the difference is due to the nuclear and higher - order coulomb processes since the coupling potentials with @xmath315 are found to have little effect on the total breakup - cross - section at @xmath277 . thus , description of @xmath2b breakup process with nuclear and coulomb breakup processes of both the e1 and e2 transitions and higher - order processes is a key to solve a puzzle recognized so far of the discrepancy between the values of @xmath3 extracted from direct @xmath7-capture reactions , @xmath10 ( expt ) @xmath11 ( theo ) ev b , and indirect @xmath2b dissociation experiments . in order to clarify the role of these components in @xmath2b breakup reaction in general , it is necessary to carry out analyses to wider range of data , such as those measured at msu @xcite and gsi @xcite , including the data on other quantities than that dealt with in the present work . analysis of parallel momentum ( @xmath316 ) distribution of @xmath0be - fragment after breakup of @xmath2b is particularly important , since the role of e2 component was determined from it @xcite . in the analysis in ref . @xcite the result of first - order perturbation theory with an adjustable parameter was compared with cdcc calculation that is essentially the same as in the present paper . because of the agreement of the two results , it was concluded that higher order processes were unimportant without quantitative evaluation of the nuclear and higher - order coulomb processes as done in the present work . actually , the contribution is about 20% of the total as already described . a cdcc analysis of the @xmath316 distribution has been done by mortimer _ et al . _ @xcite , where the dependence of the calculated result on the strength of the coulomb @xmath312 ( e2 ) coupling potentials was discussed . they found that the e2 potentials must be multiplied by 1.6 to reproduce the experimental data , although the origin of the enhancement was not clear . therefore , further investigation of the accuracy of the enhancement factor 1.6 seems necessary . unfortunately , filtering table for the msu experiment is not available to the present authors . at this stage , therefore , we can quantitatively extract @xmath3 with cdcc and the anc method only from the @xmath2b breakup experiment done at riken . nevertheless , comparison of our pure theoretical result with that shown in ref . @xcite is very interesting , which will be a subject of our future work . in this subsection we report on our application of the anc method to the @xmath7-capture reaction , @xmath0be(@xmath1)@xmath2b , at energies of 116362 kev @xcite . we assume direct capture of @xmath7 by @xmath0be to the ground state of @xmath2b by a pure e1 transition . a simple potential - model is assumed for the bound and the scattering states of the @xmath7+@xmath0be system , using the single - particle potential of sec . [ input ] . the s- and d - state components in the initial scattering - state wave - function are taken into account , and the intrinsic spins of @xmath7 and @xmath0be are included in the channel spin representation described in sec . [ input ] . in fig . 8 the solid line shows the calculated @xmath317 as a function of the incident energy @xmath318 of the reaction in the c.m . frame of the @xmath7-@xmath0be system . the plotted @xmath21 has been multiplied by the spectroscopic factor @xmath319 obtained by the @xmath283-fit to the data below 362 kev . as a function of the incident energy @xmath318 of the reaction in the c.m . frame of the @xmath7-@xmath0be system . the solid line is the result of the calculation with a simple potential model , multiplied by @xmath319 . the experimental data are taken from ref . @xcite . , scaledwidth=43.0% ] the calculated @xmath21 is not reliable at high energies , say @xmath320 kev , since the inner part of the @xmath2b wave function plays an important role . at low energies , however , the anc method works very well and a reliable value of the anc @xmath39 , and consequently @xmath3 , can be derived from the @xmath283-fitting procedure . the value of @xmath3 thus obtained is 21.7 ev b. uncertainties of the @xmath3 are evaluated in the same way as in sec . [ errors17 ] and found to be @xmath321/@xmath322 ev b , almost all of which is due to the ambiguity of the s - state potentials for the @xmath233 and @xmath234 channels of the @xmath7-@xmath0be system . including the 2.3% systematic experimental error , we obtain the following result : @xmath323 ( theo ) @xmath324 ( expt ) ev b. this result is consistent with both the value extracted from @xmath2b dissociation , @xmath305 ( theo ) @xmath306 ( expt ) ev b , described in the previous subsections , and the result obtained in ref . @xcite , @xmath10 ( expt ) @xmath11 ( theo ) ev b , although no evaluation of the ambiguity due to the uncertainty of the s - wave @xmath7-@xmath0be scattering lengths , as the one described in sec . [ errors17 ] , is made in ref .	the main result of the present paper is ev b. the error consists of 8.4% experimental systematic error and the error due to the ambiguity in the s - wave-be scattering length . this value of differs from the one extracted with the first - order perturbation theory including coulomb breakup by dipole transitions : ev b. it turns out that the difference is due to the inclusion of the nuclear and coulomb - quadrupole transitions and multi - step processes of all - order in the present work . thus , the agreement between the values of obtained from directbe()b and indirectb - breakup measurements is significantly improved .	the astrophysical factor forbe()b at zero energy , , is determined from an analysis ofpb(b ,be)pb at 52 mev / nucleon by means of the method of continuum - discretized coupled - channels ( cdcc ) taking account of all nuclear and coulomb breakup processes . the asymptotic normalization coefficient ( anc ) method is used to extract from the calculated breakup cross section . the main result of the present paper is ev b. the error consists of 8.4% experimental systematic error and the error due to the ambiguity in the s - wave-be scattering length . this value of differs from the one extracted with the first - order perturbation theory including coulomb breakup by dipole transitions : ev b. it turns out that the difference is due to the inclusion of the nuclear and coulomb - quadrupole transitions and multi - step processes of all - order in the present work . the p-be interaction potential used in the cdcc calculation is also used in the anc analysis ofbe()b . the value of ev b obtained is consistent with the previous one obtained from a precise measurement of the-capture reaction cross section extrapolated to zero incident energy , ( expt ) ( theo ) ev b , where ( theo ) stands for the error in the extrapolation . thus , the agreement between the values of obtained from directbe()b and indirectb - breakup measurements is significantly improved .
nucl-th0505007	i	the principal result of the present paper is the value of @xmath3 of @xmath325 ( theo ) @xmath306 ( expt ) ev b obtained by an analysis of the cross section of the @xmath2b breakup reaction @xmath4pb(@xmath2b , @xmath5be)@xmath4pb at 52 mev / nucleon measured at riken @xcite by means of the method of continuum - discretized coupled - channels @xcite ( cdcc ) combined with the asymptotic normalization coefficient ( anc ) method @xcite . the value is consistent with the one extracted from the precise measurement of the cross section of direct capture @xmath0be(@xmath1)@xmath2b , @xmath10 ( expt ) @xmath11 ( theo ) ev b @xcite . the cdcc calculation is based on the three - body model of @xmath7 , @xmath0be , and the target @xmath4pb nucleus , with @xmath0be staying in the ground state throughout the reaction process . this model is shown to be adequate in the breakup reaction in which the fragments @xmath7 and @xmath0be are ejected in very forward angles , less than 4@xmath273 , which is the case for the experimental data analyzed in this work . nuclear and coulomb e1 and e2 transitions and multi - step processes of all - order are included in the calculation . the calculated cross section is shown to be proportional to the squared asymptotic amplitude of the overlap of the ground state wave functions of @xmath0be and @xmath2b , which is a necessary condition for the applicability of the anc method . the cdcc calculation is made efficient by the use of the eikonal cdcc method @xcite ( e - cdcc ) for large angular momentum partial waves . improvements of e - cdcc are made to cope with the coulomb distortions of the incident and scattered waves of relative motion and intrinsic spins of the projectile and the ejectiles . the main source of the error in the obtained @xmath3 is the ambiguity of the s - wave @xmath7-@xmath0be interaction potentials for the channel spin @xmath326 and @xmath327 states . the errors associated with the use of the anc method and the ambiguity of the distorting potentials are both negligible . extracted by the anc method are shown by open symbols : the circles are obtained from three - types of cdcc analysis of @xmath2b breakup and the triangle is the result of analysis of @xmath0be(@xmath1)@xmath2b with a simple potential model . the error of each result is obtained by adding the theoretical and experimental errors in quadrature . the results are compared with @xmath3 extracted from the precise measurement of direct capture @xmath328 cross section @xcite ( closed triangle ) and those obtained from @xmath2b dissociation with first - order perturbation theory ( closed circles ) . , scaledwidth=48.0% ] calculations of @xmath3 with some simplified assumptions are summarized in fig . the results of first - order iterative solutions of cdcc , designated as one - step cdcc , correspond to and agree with those of first - order perturbation theory in the previous work @xcite . the inclusion of the coulomb quadrupole ( e2 ) transitions , scaled by 0.7 , in the one - step calculation decreases @xmath3 by about 6% , and multistep processes increase it by about 20% . this shows the crucial importance of accurate description of the @xmath2b breakup process by cdcc including nuclear and coulomb e1 and e2 transitions and all higher - order processes . it will be interesting to apply the method of the present paper to analyses of wider range of experiments such as those in refs . it may , however , be that the three - body cdcc used in the present paper is not valid in general and the use of cdcc with four - body model such as the one in ref . @xcite becomes necessary .	the astrophysical factor forbe()b at zero energy , , is determined from an analysis ofpb(b ,be)pb at 52 mev / nucleon by means of the method of continuum - discretized coupled - channels ( cdcc ) taking account of all nuclear and coulomb breakup processes . the value of ev b obtained is consistent with the previous one obtained from a precise measurement of the-capture reaction cross section extrapolated to zero incident energy , ( expt ) ( theo ) ev b , where ( theo ) stands for the error in the extrapolation .	the astrophysical factor forbe()b at zero energy , , is determined from an analysis ofpb(b ,be)pb at 52 mev / nucleon by means of the method of continuum - discretized coupled - channels ( cdcc ) taking account of all nuclear and coulomb breakup processes . the asymptotic normalization coefficient ( anc ) method is used to extract from the calculated breakup cross section . the main result of the present paper is ev b. the error consists of 8.4% experimental systematic error and the error due to the ambiguity in the s - wave-be scattering length . this value of differs from the one extracted with the first - order perturbation theory including coulomb breakup by dipole transitions : ev b. it turns out that the difference is due to the inclusion of the nuclear and coulomb - quadrupole transitions and multi - step processes of all - order in the present work . the p-be interaction potential used in the cdcc calculation is also used in the anc analysis ofbe()b . the value of ev b obtained is consistent with the previous one obtained from a precise measurement of the-capture reaction cross section extrapolated to zero incident energy , ( expt ) ( theo ) ev b , where ( theo ) stands for the error in the extrapolation . thus , the agreement between the values of obtained from directbe()b and indirectb - breakup measurements is significantly improved .
1202.0134	i	historically , radio source counts has been a key observational probe of cosmology , more specifically of the geometry of the universe . in a euclidean universe the volume scales with distance as @xmath7 whereas the flux density scales as @xmath8 , which means that the integral number of sources ( for a population of non - evolving sources with constant comoving number density ) above any flux density scales as @xmath9 . departures from this expectation was key evidence for non - euclidean geometry . more recently , the geometry of the cosmos has been established with precision , and source counts represent a measure of cosmological evolution in radio source populations . the behavior of counts at sub - mjy flux density , the nature and evolution of these sources and the question of whether they constitute a new population are unclear . at flux densities of @xmath10 mjy a ` flattening ' of normalized differential source counts has been widely reported in literature ( windhorst et al . 1985 ( wmo85 henceforth ) , @xcite , @xcite and references therein ) . the rms noise level in the latter studies are : @xmath11jy for wmo85 , varying between @xmath12 to about @xmath13jy for hopkins et al . ( 2003 ) ( see fig.9 from hopkins et al . ( 2003 ) ) and approximately @xmath14jy for huynh et al . the flattenning is observed as an apparent change of slope from @xmath15 at @xmath16 mjy to about @xmath17 in the @xmath18 mjy range . wmo85 examined the optical identifications of faint radio sources and found that the sub - mjy radio source population is dominated by blue spiral galaxies . later studies , however , have arrived at discordant results and identify the sub - mjy sources with different populations : starburst galaxies ( @xcite , @xcite , @xcite ) , early type galaxies @xcite , low ( radio ) luminosity active galactic nuclei ( agns ) @xcite or a mixture of these . since spectroscopically complete samples of sub - mjy sources are not available , the exact nature of the population observed as sub - mjy radio sources remains uncertain ; however , it is widely agreed that flattening below @xmath19 mjy requires an evolving population that is different from those that dominate counts at higher flux densities . it may be noted here that the literature is not consistent in observing a flattening in counts at sub - mjy flux density ; for example , the counts in @xcite and @xcite are consistent with a continuation in the slope of the differential counts below mjy flux density . potential causes for the discrepancy are that deep radio surveys often suffer from inadequate sky coverage that is necessary to average over clustering , wide - field surveys often do not go sufficiently deep and so biases arising from the proximity of the detection threshold to the image noise may distort measured counts . additional uncertainly arises from lack of understanding of the radio structures in sub - mjy radio sources , which may lead to biases related to the ability of the survey to catalog sources from detections of source components . the atlbs is a moderately wide - field radio survey , covering @xmath20 square degrees in the southern sky at @xmath21 ghz . the survey has been carried out using the australia telescope compact array ( atca ) , which is a fourier imaging interferometer array . the radio observations for the low - brightness survey were designed for complete u - v coverage up to @xmath22 m ( for details of these observations , see @xcite ) . the work presented herein is based on the combination of the initial low resolution survey and more recent radio observations with the atca in multiple expanded array configurations that extended the u - v coverage to @xmath23 km , giving a synthesized beam with fwhm of @xmath0 and images with rms noise @xmath24jy beam@xmath2 . the high resolution observations are critical in better estimation of the source structures and for removing the effects of blending(source confusion ) in the low resolution survey . see @xcite for details on a sample of extended sources and classification of sources from the atlbs survey , which has been carried out using both the high resolution and low resolution images . the improved imaging of the atlbs survey regions has been used to revisit the 1.4 ghz source counts : the survey has sufficient sensitivity to probe the sub - mjy regime , and the relatively large sky coverage avoids clustering related uncertainties . a specific improvement in this work is the care taken to identify sources with low surface brightness by making use of low resolution images , and using multiple indicators to identify components of sources . the low resolution images were used to make initial identifications so that the sources which might be resolved into multiple components at higher resolution are identified correctly . the blending issues inherent in using low resolution images have been avoided using higher resolution images to identify blends . in addition , the use of low resolution images ( beam fwhm = @xmath6 ) almost completely removes effects of resolution bias ( for a detailed discussion , see section . [ section_resolution_bias ] ) . these strategies , together with use of optical imagesto locate candidate galaxy hosts and a careful visual examination of resolved and complex sources instead of automated classification ensures that the atlbs catalog is a ` source catalog ' as opposed to a ` component catalog ' . the distinction between ` sources ' ( which are single sources ) as opposed to components ( which may be parts of a single source or unrelated sources which are close to each other due to projection effects ) is crucial in estimating the true source counts . the organization of the paper is as follows . in the next section , we give details of the new high resolution radio observations of the atlbs survey regions . in section ( [ section_source_detection ] ) we give details of the procedure adopted for source detection and the estimation of source flux densities . in section ( [ section_source_counts ] ) we present the source counts along with the corrections necessary to derive the true counts from the observations . next , in section ( [ section_comparison ] ) , we compare the atlbs source counts with previous work . finally , in section ( [ section_conclusions ] ) , the conclusions are presented .	the australia telescope low - brightness survey ( atlbs ; ) regions have been mosaic imaged at a radio frequency of 1.4 ghz with angular resolution and 72 jy beam rms noise . , they do not require any changes in the radio source population down to the limit of the survey .	the australia telescope low - brightness survey ( atlbs ; ) regions have been mosaic imaged at a radio frequency of 1.4 ghz with angular resolution and 72 jy beam rms noise . the images ( centered at ra : , dec : and ra : , dec : ( j2000 epoch ) ) cover 8.42 square degrees sky area and have no artifacts or imaging errors above the image thermal noise . multi - resolution radio and optical r - band images ( made using the 4-m ctio blanco telescope ) were used to recognize multi - component sources and prepare a source list ; the detection threshold was 0.38 mjy in a low resolution radio image made with beam fwhm of . radio source counts in the flux density range 0.4 - 8.7 mjy are estimated , with corrections applied for noise bias , effective area correction and resolution bias . the resolution bias is mitigated using low resolution radio images , while effects of source confusion are removed by using high resolution images for identifying blended sources . below 1 mjy the atlbs counts are systematically lower than the previous estimates . showing no evidence for an upturn down to 0.4 mjy , they do not require any changes in the radio source population down to the limit of the survey . the work suggests that automated image analysis for counts may be dependent on the ability of the imaging to reproduce connecting emission with low surface brightness and on the ability of the algorithm to recognize sources , which may require that source finding algorithms effectively work with multi - resolution and multi - wavelength data . the work underscores the importance of using source lists as opposed to component lists and correcting for the noise bias in order to precisely estimate counts close to the image noise and determine the upturn at sub - mjy flux density .
1202.0134	i	high - resolution radio images of the atlbs survey regions are presented , with beam fwhm of @xmath0 . the wide field mosaic images covering @xmath20 square degrees sky area with rms noise @xmath24jy beam@xmath2 are of exceptional quality in that there are no imaging errors or artifacts above the thermal noise over the entire field of view . the images have excellent surface brightness sensitivity - the visibility coverage is complete out to 750 m and hence provides good representation of extended emission components associated with radio sources . the images are , therefore , an excellent resource for examining with automated algorithms for source finding , parameter fitting , and morphological classification , and as a resource for testing such algorithms that would be used on upcoming all - sky continuum surveys with the lofar and askap . we make the high - resolution atlbs images available at the website www.rri.res.in/ atlbs . we have generated a source list from the atlbs images . this is a carefully made source list as opposed to a component list . the images were initially examined using automated algorithms , which used representations with different resolutions , to identify sources and distinguish unresolved and single component sources and complex sources . all complex sources were carefully examined by eye to recognize blends and classify appropriately . optical surveys of the atlbs fields were also examined for candidate host galaxies to aid in the classification of complex sources . the integrated flux densities of the sources were derived in a variety of methods - the method appropriate for the source structural classification was adopted in each case . we emphasize the use of multi - resolution images , which may complement each other , as well as the need to use data from other wavebands such as optical , infrared etc . the source list is also presented online along with the integrated flux densities and classification . the source list was used to estimate the radio source counts down to 0.4 mjy . the counts have been corrected for noise bias , resolution bias , and effective area . it may be noted that considerable care has been taken to ensure that the counts correspond to sources and not components . the counts presented in fig . [ submil_source_counts_new ] and table ( [ submil_counts_table_new ] ) above have been self - calibrated for the noise bias in that the counts derived in a first iteration have been used to derive the noise bias correction . comparing the counts with previous work - the athdfs and pds counts - shows that the atlbs counts are systematically lower . this is attributed to our counts representing sources as opposed to components , as well as corrections for noise bias . we have demonstrated the substantial difference in counts that results from using component catalogs as opposed to source catalogs : at 1 mjy flux density component counts may be as much as 50% above true source counts . this implies that automated image analysis for counts may be dependent on the ability of the imaging to reproduce connecting emission with low surface brightness and on the ability of the algorithm to recognize sources , which may require that source finding algorithms effectively work with multi - resolution and multi - wavelength data . the work presented herein underscores the importance of noise bias correction , in particular for deriving counts close to the limit of the survey sensitivity and for correctly estimating the faint end slope and upturn in the source counts at sub - mjy flux density . finally , the lack of an upturn in the source counts at faint flux densities implies that down to the faintest flux densities we have probed ( approximately 0.4 mjy ) there is no evidence for any new population . the upturn reported in the literature may be due to a combination of small survey areas and identification of radio sources as opposed to components , as well as effects of noise bias close to the detection limit . the atca is part of the australia telescope , which is funded by the commonwealth of australia for operation as a national facility managed by csiro . we thank anant tanna for his assistance with the initial processing of the visibility data . becker , r. h. , white , r. l. , & helfand , d. j. 1994 , aspc , 61 , 165 benn , c. r. , rowan - robinson , m. , mcmahon , r. g. , broadhurst , t. j. , & lawrence , a. 1993 , mnras , 263 , 98 bondi , m. , ciliegi , p. , schinnerer , e. , et al . 2008 , astrophys . j. , 681 , 1129 clark , b.g . 1980 a&a , vol . 89 , no . 3 , 377 - 378 condon , j. j. , 1989 , apj , 338 , 13 condon , j. j. , cotton , w. d. , greisen , e. w. , yin , q. f. , perley , r. a. , taylor , g. b. , and broderick , j. j. 1998 , aj , 115 , 1693 eddington , a. , 1913 , mnras , 73 , 359 gruppioni , c. , mignoli , m. , & zamorani , g. 1999 , mnras , 304 , 199 hopkins , a. m. , afonso , j. , chan , b. , et al . 2003 , aj , 125 , 465 huynh , m. t. , jackson , c. a. , norris , r. p. , & prandoni , i. 2005 , aj , 130 , 1373 huynh , m. t. , jackson , c. a. , norris , r. p. , & fernandez - soto , a. 2008 , aj , 135 , 2470 jauncey , d. l. , 1968 , apj , 152 , 647 mitchell , k. j. , condon , j. j. 1985 , aj , 90 , 1957 murdoch , h.s.,crawford , d.f . , jauncey , r.l . , 1917 , apj.,118,1 prandoni , i. , gregorini , l. , parma , p. , de ruiter , h. r. , vettolani , g. , wieringa , m. h. , ekers , r. d. , 2001 , a&a , 365 , 392 - 399 richards , e.a . , 2000 , aj , 533 , 611 saripalli , l. , subrahmanyan , r. , thorat , k. , ekers , r.d . , hunstead , r.w . , johnston , h.m . , sadler , e.m . , 2011 , apj . , in press sault , r.j . , tueben , p. j. and wright , m. c. h. 1995 , astronomical data analysis software and systems iv , asp conference series , vol . shaw , h.e . payne , and j.j.e . hayes , 433 sault , r.j . & wieringa , m.h . 1994 a&as , 108 , 585 subrahmanyan , r. , ekers , r. d. , saripalli , l. , sadler , e. m. , 2010 , mnras , 402 , 2792 thorat , k. , saripalli , l. , subrahmanyan , r. , 2012 , in preparation . windhorst , r. a. , van heerde , g. m. , & katgert , p. , 1984 , a&as , 58 , 1 windhorst , r.a . , miley , g.k . , owen , f.n . , kron , r.g . and koo , d.c.,1985 , aj , 289 , 494 windhorst , r.a . , mathis , d. , neuschaefer , l.,1990 , pasp , vol . 10 , evolution of the universe of galaxies , ed . kron , r.j . , 389 - 403	the images ( centered at ra : , dec : and ra : , dec : ( j2000 epoch ) ) cover 8.42 square degrees sky area and have no artifacts or imaging errors above the image thermal noise . the work suggests that automated image analysis for counts may be dependent on the ability of the imaging to reproduce connecting emission with low surface brightness and on the ability of the algorithm to recognize sources , which may require that source finding algorithms effectively work with multi - resolution and multi - wavelength data . the work underscores the importance of using source lists as opposed to component lists and correcting for the noise bias in order to precisely estimate counts close to the image noise and determine the upturn at sub - mjy flux density .	the australia telescope low - brightness survey ( atlbs ; ) regions have been mosaic imaged at a radio frequency of 1.4 ghz with angular resolution and 72 jy beam rms noise . the images ( centered at ra : , dec : and ra : , dec : ( j2000 epoch ) ) cover 8.42 square degrees sky area and have no artifacts or imaging errors above the image thermal noise . multi - resolution radio and optical r - band images ( made using the 4-m ctio blanco telescope ) were used to recognize multi - component sources and prepare a source list ; the detection threshold was 0.38 mjy in a low resolution radio image made with beam fwhm of . radio source counts in the flux density range 0.4 - 8.7 mjy are estimated , with corrections applied for noise bias , effective area correction and resolution bias . the resolution bias is mitigated using low resolution radio images , while effects of source confusion are removed by using high resolution images for identifying blended sources . below 1 mjy the atlbs counts are systematically lower than the previous estimates . showing no evidence for an upturn down to 0.4 mjy , they do not require any changes in the radio source population down to the limit of the survey . the work suggests that automated image analysis for counts may be dependent on the ability of the imaging to reproduce connecting emission with low surface brightness and on the ability of the algorithm to recognize sources , which may require that source finding algorithms effectively work with multi - resolution and multi - wavelength data . the work underscores the importance of using source lists as opposed to component lists and correcting for the noise bias in order to precisely estimate counts close to the image noise and determine the upturn at sub - mjy flux density .
1502.02524	i	it is generally believed that there is a supermassive black hole ( bh ) at the center of an active galactic nucleus ( agn ) ; the gravitational potential of the bh is the ultimate energy source of the agn . the accreted matter of a bh forms an accretion disk and loses angular momentum through viscous or turbulent processes ( rees 1984 ) . broad emission lines are one of the dominant features of many agn spectra , which are produced in a ` broad line region ' ( blr ) nearby the bh . the blr is widely acknowledged to be photoionized by the continuum from the accretion disk ( e.g. , kwan & krolik 1981 ; ferland et al . 1992 ) . in order to explain the special radiation properties of bl lac objects ( bl lacs ) , blandford & rees ( 1978 ) proposed that there are relativistic jet structures in these sources . the jet launching is reported to be connected with the central bh , accretion disk , and corona in a source ( armitage & natarajan 1999 ; merloni & fabian 2002 ; wang et al . 2004 ; cao 2004 , 2014 ; yuan & narayan 2014 ; wilkins & gallo 2015 ; chen et al . the jets may be powered via the blandford@xmath5payne ( bp ; blandford & payne 1982 ) process by releasing the gravitational energy of accreting matter that moves toward the bh , and/or via blandford@xmath5znajek ( bz ; blandford & znajek 1977 ) mechanism by extracting the rotational energy of bh . so far , most confirmed extragalactic gev - tev emitters are blazars , a sub - sample of radio - loud agns with relativistic jets . blazars are divided into bl lacs and flat spectrum radio quasars ( fsrqs ) according to their emission line features . generally , the broadband spectral energy distributions ( seds ) of bl lacs can be well explained with the synchrotron radiation and the synchrotron self - compton ( ssc ) scattering of the relativistic electrons in jets ( maraschi et al . 1992 ; ghisellini et al . 1996 , 2010 ; zhang et al . 2012 ; liao et al . 2014 ; yan et al . 2014 ) ; however , fsrqs need a black body spectrum component and a component from inverse compton ( ic ) scattering of the external photons to fit their broadband seds ( e.g. , sikora et al . 1994 ; ghisellini et al . 1996 , 2010 ; zhang et al . 2014 ; cao & wang 2013 ; chen et al . 2010 , 2012 ) . compared with bl lacs , fsrqs have prominent emission lines in their spectra , and sometimes there are significant blue bumps at @xmath7 hz in their observed broadband seds , which is believed to be the thermal emission of accretion disk . however , often no significant blue bump is observed in the seds since the nonthermal radiation from jet overwhelms the thermal mission from accretion disk , especially when the sources are in the high state ( e.g. , for 3c 454.3 , jorstad et al . hence , the gev fsrqs in which the broadband seds are dominated by the jet emission and the significant blue bumps of the thermal emission from accretion disk are observed in their seds , are the good candidates for investigating the correlations among their jet power , accretion disk radiation , and blr luminosity . the flux ratios of emission lines from blr are suggested to be approximately constant among different agns ( francis et al . 1991 ; vanden berk et al . 2001 ) . if setting the emission line luminosity of ly@xmath8 to 100 , the relative luminosities of h@xmath9 , h@xmath8 , mg ii , and c iv lines are 22 , 77 , 34 , and 63 , respectively , and then the total emission line luminosity is 555.8 ( francis et al . 1991 ; celotti et al . therefore , the luminosity of blr can be roughly estimated with the luminosities of one or some emission lines . using the continuum luminosity and the emission line luminosity in shen et al . ( 2011 ) , calderone et al . ( 2013 ) calculated @xmath1 and @xmath2 , respectively , and reported that @xmath10 , i.e. , the covering factor of blr is probably equal to 10 percent ; therefore , the value of @xmath11 is always used as a proxy to the accretion disk luminosity ( @xmath1 ) . sometimes @xmath12 is also used to estimate the luminosity of blr in blazars when authors have obtained @xmath1 and want to calculate the energy density of blr ( e.g. , ghisellini et al . 2010 ; zhang et al . however , so far it has not be examined whether the @xmath13 relation is still valid for blazars , especially for the gev tev blazars . in this paper , a sample of seds for gev fsrqs is compiled to study their jet and accretion disk relations and their covering factors of blrs . the sample selection and data are presented in section 2 . the models and results of sed fitting are described in section 3 . the study of the covering factors of blrs is in section 4 . the possible connection between the jet and accretion disk is shown in section 5 . further investigation to the correlations among the jet , blr , and accretion disk is described in section 6 . a simple discussion on the anisotropic radiation of accretion disk , the jet formation mechanism for gev agns , and the implications of unification for radio loud agns is given in section 7 . a summary for our results is in section 8 . throughout , @xmath14=73 km s@xmath15 mpc@xmath15 , @xmath16 and @xmath17 are adopted .	the broadband spectral energy distributions ( seds ) of 18 gev flat spectrum radio quasars ( fsrqs ) are collected and compiled from literature , in which both the jet emission and the accretion disk radiation can be observed , in order to investigate the correlations among their jet power ( ) , accretion disk luminosity ( ) , and luminosity of broad line region ( blr , ) . on the basis of the sed fits with the jet radiation and accretion disk radiation models , we calculate and .	the broadband spectral energy distributions ( seds ) of 18 gev flat spectrum radio quasars ( fsrqs ) are collected and compiled from literature , in which both the jet emission and the accretion disk radiation can be observed , in order to investigate the correlations among their jet power ( ) , accretion disk luminosity ( ) , and luminosity of broad line region ( blr , ) . on the basis of the sed fits with the jet radiation and accretion disk radiation models , we calculate and . no correlation between with either or is found . with a sub - sample of for 13 gev fsrqs , it is observed that is strongly correlated with their . we also study the blr covering factors ( ) of the gev fsrqs in our sample , averagely which are smaller than that of the large samples of radio - loud and radio - quiet quasars . of some gev fsrqs is higher than , but of all the gev fsrqs is lower than the accretion power of black hole ( bh ) , which is estimated by , indicating that the total accretion power of bh is sufficient to drive the jets in these sources ; however the uncorrelation between and of the gev fsrqs may suggest that their jets are launched by the blandfordznajek process via extracting the rotational energy of bh . using the relation of the gev fsrqs , we estimate of a bl lac sample with their . a comparison of and eddington ratio ( ) among bl lacs , very radio - loud nls1 galaxies , and fsrqs is also presented . it is found that along with the bl lac nls1fsrq sequence and increase , which may correspond to the change of the accretion disk structure and the transformation of the dominant mechanism for jet launching . this is also consistent with the division of their parent populations , i.e. , low - excitation radio galaxies and high - excitation radio galaxies .
1502.02524	i	a sed sample of 18 gev - fsrqs , in which the significant blue bumps from the accretion disk radiation are observed and the blr luminosities ( @xmath2 ) of 13 gev - fsrqs are available , is collected and compiled from literature . on the basis of the sed fits with the jet radiation and accretion disk radiation models , we calculate the jet power ( @xmath0 ) and the accretion disk luminosity ( @xmath1 ) , investigate the correlations of the jet power and disk luminosity as well as the blr luminosity , and also make a comparison of the blr covering factor ( @xmath3 ) with the large rlq and rqq samples from shen et al . our results are summarized below . * @xmath2 of the 13 gev - fsrqs is strongly correlated with @xmath1 , and thus @xmath2 can be used to estimate @xmath1 when the radiation of accretion disk is overwhelmed by the jet emission . the mean of @xmath3 for the 13 gev - fsrqs is 0.043 , which is smaller than that of the rlqs ( @xmath330.082 ) and rqqs ( @xmath330.076 ) in shen et al . ( 2011 ) . considering the inclination effect and anisotropic radiation of accretion disk , the @xmath3 distribution of the 13 gev - fsrqs would be same as that of rlqs and rqqs in shen et al . ( 2011 ) . * no correlation between @xmath0 with @xmath1 and @xmath2 is found for the gev fsrqs . @xmath0 for most of the gev fsrqs is lower than @xmath1 and all of them are lower than the accretion power of bh ( @xmath4 ) , indicating that the total accretion power of bh is sufficient to drive the jets in these sources , but the uncorrelation between @xmath1 and @xmath0 of the gev fsrqs in our sample may suggest that their jets are launched by the bz process via extracting the rotational energy of bh . * using the @xmath2@xmath1 relation of the 13 gev - fsrqs , we estimate @xmath1 of a bl lac sample with their @xmath2 ; a very rl nls1 galaxy sample from yuan et al . ( 2008 ) is also taken into account . it is found that along with the bl lac nls1fsrq sequence @xmath2 and the eddington ratio ( @xmath6 ) increase , which may correspond to the change of the accretion disk structure and the transformation of the dominant mechanism for jet launching . this is also consistent with the division of their parent populations , i.e. , bl lacs / lergs and fsrqs / hergs . we thank the anonymous referee for his / her valuable suggestions . we appreciate helpful discussion with yuan liu , wei cui , bi - fang liu , wei - min yuan , er - lin qiao . this work is supported by the national basic research program ( 973 programme ) of china ( grant 2014cb845800 ) , the national natural science foundation of china ( grants 11373036 , 11133002 , 11025313 ) , the strategic priority research program the emergence of cosmological structures " of the chinese academy of sciences ( grant xdb09000000 ) , the guangxi science foundation ( 2013gxnsffa019001 ) , and the young researcher grant of national astronomical observatories , chinese academic of science . shuang - nan zhang acknowledges support from the qianren start - up grant 292012312d1117210 .	no correlation between with either or is found . with a sub - sample of for 13 gev fsrqs of some gev fsrqs is higher than , but of all the gev fsrqs is lower than the accretion power of black hole ( bh ) , which is estimated by , indicating that the total accretion power of bh is sufficient to drive the jets in these sources ; however the uncorrelation between and of the gev fsrqs may suggest that their jets are launched by the blandfordznajek process via extracting the rotational energy of bh . using the relation of the gev fsrqs , we estimate of a bl lac sample with their . a comparison of and eddington ratio ( ) among bl lacs , very radio - loud nls1 galaxies , and fsrqs is also presented . it is found that along with the bl lac nls1fsrq sequence and increase , which may correspond to the change of the accretion disk structure and the transformation of the dominant mechanism for jet launching . this is also consistent with the division of their parent populations , i.e. , low - excitation radio galaxies and high - excitation radio galaxies .	the broadband spectral energy distributions ( seds ) of 18 gev flat spectrum radio quasars ( fsrqs ) are collected and compiled from literature , in which both the jet emission and the accretion disk radiation can be observed , in order to investigate the correlations among their jet power ( ) , accretion disk luminosity ( ) , and luminosity of broad line region ( blr , ) . on the basis of the sed fits with the jet radiation and accretion disk radiation models , we calculate and . no correlation between with either or is found . with a sub - sample of for 13 gev fsrqs , it is observed that is strongly correlated with their . we also study the blr covering factors ( ) of the gev fsrqs in our sample , averagely which are smaller than that of the large samples of radio - loud and radio - quiet quasars . of some gev fsrqs is higher than , but of all the gev fsrqs is lower than the accretion power of black hole ( bh ) , which is estimated by , indicating that the total accretion power of bh is sufficient to drive the jets in these sources ; however the uncorrelation between and of the gev fsrqs may suggest that their jets are launched by the blandfordznajek process via extracting the rotational energy of bh . using the relation of the gev fsrqs , we estimate of a bl lac sample with their . a comparison of and eddington ratio ( ) among bl lacs , very radio - loud nls1 galaxies , and fsrqs is also presented . it is found that along with the bl lac nls1fsrq sequence and increase , which may correspond to the change of the accretion disk structure and the transformation of the dominant mechanism for jet launching . this is also consistent with the division of their parent populations , i.e. , low - excitation radio galaxies and high - excitation radio galaxies .
1402.1425	i	leaf powers are a family of graph classes that has been introduced by nishimura etal . @xcite to model the problem of reconstructing phylogenetic trees . in particular , a given finite simple graph @xmath2 is called the @xmath1-leaf power of a tree @xmath3 for some @xmath17 , if @xmath4 is the set of leaves in @xmath3 and any two distinct vertices @xmath18 are adjacent , that is @xmath5 , if and only if the distance of @xmath6 and @xmath7 in @xmath3 is at most @xmath1 . for all @xmath17 , the class of graphs that are a @xmath1-leaf power of some tree , is simply called @xmath1-leaf powers and denoted by @xmath0 . the general problem , from a graph theoretic point of view , is to structurally characterize @xmath0 for all fixed @xmath17 and to provide efficient recognition algorithms . obviously , a graph @xmath14 is a @xmath8-leaf power , if and only if it is the disjoint union of cliques , that is , @xmath14 does not contain a chordless path of length @xmath8 . dom etal . @xcite prove that @xmath9-leaf powers are exactly the graphs that do not contain an induced bull , dart , or gem . brandstdt etal . @xcite contribute to the characterization of @xmath9-leaf powers by showing that they are exactly the graphs that result from substituting cliques into the nodes of a tree . moreover , they give a linear time algorithm to recognize @xmath9-leaf powers building on their characterization . a characterization of @xmath10-leaf powers in terms of forbidden subgraphs is yet unknown . however , basic @xmath10-leaf powers , the @xmath10-leaf powers without true twins , are characterized by eight forbidden subgraphs @xcite . the structure of basic @xmath10-leaf powers has further been analyzed by brandstdt etal . @xcite , who provide a nice characterization of the two - connected components of basic @xmath10-leaf powers that leads to a linear time recognition algorithm even for @xmath10-leaf powers . for @xmath11-leaf powers , a polynomial time recognition was given in @xcite . however , no structural characterization is known , even for basic @xmath11-leaf powers . only for distance - hereditary basic @xmath11-leaf powers a characterization in terms of @xmath19 forbidden induced subgraphs has been discovered @xcite . except from the result in @xcite that @xmath20 is not true for every @xmath1 , there have not been any more essential advances in determining the structure of @xmath1-leaf powers for @xmath21 since 2007 . instead , research has focused on generalizations of leaf powers @xcite , which also turned into dead ends , very soon . on the other hand , if we push @xmath1 to infinity , then it turns out that not every graph is a @xmath1-leaf power for some @xmath17 . in particular , a @xmath1-leaf power is , by definition , the subgraph of the @xmath1-th power of a tree @xmath3 induced by the leaves of @xmath3 . since trees are sun - free chordal and as taking powers and induced subgraphs do not destroy this property , it follows trivially that every @xmath1-leaf power , despite the value of @xmath1 , is strongly chordal @xcite . but even not every strongly chordal graph is a @xmath1-leaf power for some @xmath17 . in fact , we are aware of exactly one counter example , which has been found by bibelnieks etal . @xcite and is shown as @xmath22 in figure [ fig : counterexamples ] . insofar , it is reasonable to ask for a precise characterization of the graphs that are not a @xmath1-leaf power for any @xmath17 . this problem can equivalently be formulated as to describe the graphs in the class @xmath23 , which we call leaf powers , for short . interestingly , brandstdt etal . @xcite show that @xmath16 coincides with the class of fixed tolerance nest ( neighborhood subtree tolerance ) graphs , a well - known graph class with an absolutely different motivation given by bibelnieks etal . @xcite . naturally , characterizations and an efficient recognition algorithms for this class are also open questions today . however , by brandstdt etal . @xcite , it is know that @xmath16 is a superclass of ptolemaic graphs , that is , gem - free chordal graphs @xcite , and even a superclass of directed rooted path graphs , introduced by gavril @xcite . recently , we introduced the clique arrangement in @xcite , a new data structure that is especially valuable for the analysis of strongly chordal graphs . the clique arrangement @xmath24 of a chordal graph @xmath14 is a directed acyclic graph that has certain vertex subsets of @xmath14 as a node set and describes the mutual inclusion of these sets by arcs . in particular , for every set @xmath25 of maximal cliques of @xmath14 there is a node in @xmath26 for @xmath27 and two nodes @xmath28 are joined by an arc @xmath29 , if @xmath30 and there is no @xmath31 with @xmath32 . in @xcite , we give a new characterization of strongly chordal graphs in terms of a forbidden cyclic substructure in the clique arrangement , called bad @xmath1-cycles for @xmath33 , and we show how to construct the clique arrangement of a strongly chordal graph in nearly linear time . it is known that the clique arrangements of ptolemaic graphs are even directed trees @xcite . since all ptolemaic graphs are leaf powers and all leaf powers are strongly chordal , it appears likely that the degree of acyclicity in clique arrangements of leaf powers is between forbidden bad @xmath1-cycles , @xmath34 , and the complete absence of cycles . this paper describes a cyclic substructure that is forbidden in the clique arrangement of leaf powers . for convenience , we call these substructures bad @xmath8-cycles , although they are not the obvious continuation of the concept of bad @xmath1-cycles for @xmath34 . as the main result of this paper , we show that bad @xmath8-cycles occur in @xmath13 , if and only if @xmath14 contains at least one of seven induced subgraphs @xmath35 depicted in figure [ fig : counterexamples ] . we leave it as an open question , if these seven graphs are sufficient to characterize @xmath16 in terms of forbidden subgraphs . however , we conjecture that this is the case . this would imply a polynomial time recognition algorithm for @xmath16 , by using the possibility of efficiently recognizing strongly chordal graphs and checking the containment of a finite number of forbidden induced subgraphs .	the class of-leaf powers consists of graphs that have a-leaf root , that is , a tree with leaf set , where , if and only if the-distance between and is at most . structure and linear time recognition algorithms have been found for- ,- ,- , and , to some extent ,-leaf powers , and it is known that the union of all-leaf powers , that is , the graph class , forms a proper subclass of strongly chordal graphs . despite from that , no essential progress has been made lately . in this paper , we use the new notion of clique arrangements to suggest that leaf powers are a natural special case of strongly chordal graphs . the clique arrangement of a chordal graph is a directed graph that represents the intersections between maximal cliques of by nodes and the mutual inclusion of these vertex subsets by arcs . recently , strongly chordal graphs have been characterized as the graphs that have a clique arrangement without bad-cycles for . we show that the clique arrangement of every graph of is free of bad-cycles . the question whether this characterizes the class exactly remains open .	the class of-leaf powers consists of graphs that have a-leaf root , that is , a tree with leaf set , where , if and only if the-distance between and is at most . structure and linear time recognition algorithms have been found for- ,- ,- , and , to some extent ,-leaf powers , and it is known that the union of all-leaf powers , that is , the graph class , forms a proper subclass of strongly chordal graphs . despite from that , no essential progress has been made lately . in this paper , we use the new notion of clique arrangements to suggest that leaf powers are a natural special case of strongly chordal graphs . the clique arrangement of a chordal graph is a directed graph that represents the intersections between maximal cliques of by nodes and the mutual inclusion of these vertex subsets by arcs . recently , strongly chordal graphs have been characterized as the graphs that have a clique arrangement without bad-cycles for . we show that the clique arrangement of every graph of is free of bad-cycles . the question whether this characterizes the class exactly remains open .
astro-ph0007262	i	in paper i ( wielen et al . 1999b ) , we have shown that the combination of the data of the hipparcos astrometric satellite ( esa 1997 ) with ground - based results ( such as the fk5 ) is able to provide for many stars individual proper motions which are significantly more accurate than the hipparcos proper motions themselves . the method has been already successfully applied in the construction of the fk6 , the sixth catalogue of fundamental stars ( part i of the fk6 : wielen et al . 1999d , part iii of the fk6 : wielen et al . 2000a ) . the method of combination presented in paper i is , however , strictly valid for single stars only . in the fk6 , we call this procedure therefore the ` single - star mode ' . in reality most of the stars are members of binaries or of multiple systems . if the duplicity of an individual object is already definitely known , either from ground - based investigations or from hipparcos observations , then the method of combination has to be changed properly in order to obtain meaningful results . we call such procedures ` special solutions ' . paper iii of this series of papers will discuss the special solutions for visual binaries and other types of double stars . the present paper ( paper ii ) describes an appropriate method of the combination of hipparcos results with ground - based observations for ` apparently single stars ' . even if we have removed from such a sample of apparently single stars all the objects with known duplicity , there remains beside the truly single - stars a large number of hitherto undetected astrometric binaries . the measured photo - center of an unresolved astrometric binary moves on the sky on a wavy curve , in contrast to the linear motion of single stars ( fig . 1 ) . in such a case , an ` instantaneously ' measured proper motion deviates from a ` mean ' proper motion , averaged over a long interval of time . the proper motions provided by hipparcos ( esa 1997 ) are essentially such instantaneously measured quantities , since they are derived from positional measurements spread over about three years only . in contrast , the proper motions given in the fk5 ( fricke et al . 1988 , 1991 ) are long - term averages over up to about 200 years . we have called the difference between the instantaneous proper - motion and the mean one the ` cosmic error ' of the instantaneous proper motion ( wielen 1995a , b , 1997 , wielen et al . 1997 ) . in some cases , the individual cosmic error is so large that the duplicity of an apparently single star is strongly indicated by this fact . we have called such objects ` @xmath2 binaries ' ( wielen et al . 1999a ) . in most cases , however , the cosmic error in the hipparcos proper motion of a hitherto undetected astrometric binary is not _ individually _ significant , but can be shown to exist only _ statistically _ in a larger sample of apparently single stars . nevertheless , an appropriate combination method should not neglect the statistical consequences of these cosmic errors . our comparison of hipparcos proper motions with ground - based results has shown that , at least for brighter stars , the average cosmic error in a hipparcos proper motion is often larger than the hipparcos measuring error , typically by a factor of three ( wielen 1995a , b , wielen et al . 1997 , 1998 , 1999c ) . wielen ( 1997 , henceforth called paper wpsa ) has developed a coherent scheme of ` statistical astrometry ' for handling the effects of cosmic errors in high - precision astrometry . in the following sections , we shall apply the concepts of statistical astrometry to the problem of combining the hipparcos results with ground - based measurements for a sample of apparently single stars . the main results will be solutions which we call the ` long - term prediction mode ( ltp ) ' and the ` short - term prediction mode ( stp ) ' . our results have already been applied for the ltp and stp solutions given in part i and part iii of the fk6 ( wielen et al . 1999d , 2000a ) . it is clear that in principle the most desirable solution for our problem would be to treat each star individually and fully correctly . this would mean ( 1 ) for truly single stars : to use the ` single - star mode ( si ) ' described in paper i , and ( 2 ) for binaries : to apply individual orbital corrections , as e.g. done for polaris by wielen et al . . however , since for ` apparently single stars ' the true nature ( single or double ) of the individual objects is unknown , we _ have _ to rely on statistical methods in order to handle such a sample of stars properly . the treatment of a sample of apparently single stars by our statistical procedures gives _ on average _ the best astrometric prediction , and it provides the most realistic error budget for such a sample . in this sense , our statistical treatment is certainly much more appropriate than to ignore the binary nature of a large fraction of a sample of apparently single stars altogether . in paper i , we have already pointed out that the older observations carry a high weight in the combination of ground - based measurements with hipparcos data , and that therefore the gc ( boss et al . 1937 ) should be also considered here because of its high number of rather well - measured stars . we call the result of the combination of the gc with hipparcos the combination catalogue gc+hip .	the combination of ground - based astrometric compilation catalogues , such as the fk5 or the gc , with the results of the esa astrometric satellite hipparcos produces for many thousands of stars proper motions which are significantly more accurate than the proper motions derived from the hipparcos observations alone . in paper i ( wielen et al . 1999 , a&a 347 , 1046 ) we have presented a method of combination for single stars ( si mode ) .	the combination of ground - based astrometric compilation catalogues , such as the fk5 or the gc , with the results of the esa astrometric satellite hipparcos produces for many thousands of stars proper motions which are significantly more accurate than the proper motions derived from the hipparcos observations alone . in paper i ( wielen et al . 1999 , a&a 347 , 1046 ) we have presented a method of combination for single stars ( si mode ) . the present paper ii derives a combination method which is appropriate for an ensemble of ` apparently single - stars ' which contains undetected astrometric binaries . in this case the quasi - instantaneously measured hipparcos proper motions and positions are affected by ` cosmic errors ' , caused by the orbital motions of the photo - centers of the undetected binaries with respect to their center - of - mass . in contrast , the ground - based data are ` mean values ' obtained from a long period of observation . we derive a linear ` long - term prediction ' ( ltp mode ) for epochs far from the hipparcos epoch , and a linear ` short - term prediction ' ( stp mode ) for epochs close to . the most accurate prediction for a position at an arbitrary epoch is provided by a smooth , non - linear transition from the stp solution to the ltp solution . we present an example for the application of our method , and we discuss the error budget of our method for the fk6 ( a combination of the fk5 with hipparcos ) and for the combination catalogue gc+hip . for the basic fundamental stars , the accuracy of the fk6 proper motions in the ltp mode is better than that of the hipparcos proper motions ( taking here the cosmic errors into account ) by a factor of more than 4 .
math0702892	i	let @xmath3 be a convex body in @xmath7 . the _ covariogram _ @xmath5 of @xmath3 is the function @xmath8 where @xmath9 and @xmath10 denotes volume in @xmath7 . this functional , which was introduced by matheron in his book @xcite on random sets , is also sometimes called the _ set covariance _ , and it coincides with the _ autocorrelation _ of the characteristic function of @xmath3 : @xmath11 the covariogram @xmath5 is clearly unchanged by a translation or a reflection of @xmath3 . ( the term _ reflection _ will always means reflection in a point . ) matheron @xcite and , independently , adler and pyke @xcite asked the following question . does the covariogram determine a convex body , among all convex bodies , up to translations and reflections ? matheron conjectured a positive answer for the case @xmath12 but this conjecture has not been completely settled . matheron @xcite observed that , for @xmath13 and for all @xmath14 , the derivatives @xmath15 give the distribution of the lengths of the chords of @xmath3 parallel to @xmath16 . such information is common in _ stereology , _ _ statistical shape recognition _ and _ image analysis , _ when properties of an unknown body are to be inferred from chord length measurements ; see @xcite , @xcite and @xcite , for example . blaschke ( cf . @xcite ) asked whether the distribution of the lengths of chords ( in all directions ) of a convex body characterizes the body , up to rigid motions , but mallows and clark @xcite proved that this is false even for convex polygons . in fact ( see @xcite ) the covariogram problem is equivalent to the problem of determining a convex body from all its separate chord length distributions , one for each direction @xmath13 . adler and pyke @xcite asked matheron s question in probabilistic terms . does the distribution of the difference @xmath17 of independent random variables @xmath18 and @xmath19 uniformly distributed over @xmath3 determine @xmath3 , up to translations and reflections ? since the convolution in is , up to a multiplicative factor , the probability density of @xmath17 , this problem is equivalent to the covariogram one . matheron s problem is also relevant in _ x - ray crystallography , _ where the atomic structure of a _ crystal _ ( or _ quasicrystal _ ) is to be found from _ diffraction images . _ a convenient way of describing many important examples of quasicrystals is via the _ cut and project scheme_. here to the atomic structure , represented by a discrete set @xmath20 contained in a space @xmath21 , is associated a _ lattice _ @xmath22 in a higher dimensional space @xmath23 and a _ window _ @xmath24 ( which in many cases is a convex set ) . in this setting @xmath20 coincides with the projection on @xmath21 of the points of the lattice @xmath22 which belong to @xmath25 . in many examples the lattice @xmath22 can be determined by the diffraction image . to determine @xmath20 it is however necessary to know @xmath26 : the covariogram problem enters at this point , since the covariogram of @xmath26 can be obtained by the diffraction image ; see @xcite . enns and ehlers @xcite express in terms of the covariogram the distributions of random line segments in a convex body , under different types of randomness with which they are generated . the monograph @xcite contains an extensive discussion of retrieval problems for convex bodies , while the survey @xcite deals with algorithmic aspects of reconstruction problems in convex geometry . the first contribution to matheron s question was made in 1993 by nagel @xcite , who gave a positive answer when @xmath3 is a planar convex polygon ; see also schmitt @xcite . matheron s conjecture is still unsettled for general planar convex bodies , but it has been confirmed for @xmath27 convex bodies , non - strictly convex bodies , and convex bodies that are not @xmath28 ; see @xcite . it has been recently shown that every convex polytope in @xmath29 is determined by its covariogram , up to translations and reflections ( cf . @xcite ) . for @xmath30 there exist examples of convex polytopes that are not determined by their covariogram ( cf . however @xcite proves that , if @xmath31 is a @xmath32-dimensional simplicial convex polytope in general relative position with respect to @xmath33 , the determination by the covariogram data is unique for every @xmath34 ( see next section for all unexplained definitions ) . the paper @xcite discusses various open retrieval problems related to the covariogram . one of the purposes of this paper is to sharpen some of the known results on matheron s conjecture , indicating how much of the covariogram information is needed to get the uniqueness of determination . we indicate some subsets of the support of the covariogram , with arbitrarily small lebesgue measure , such that the covariogram , restricted to those subsets , identifies certain geometric properties of the body . these results are more precise in the planar case , but some of them , both positive and negative ones , are proved for bodies of any dimension . moreover some results regard _ most _ convex bodies , in the _ baire category sense . _ another purpose is to extend the class of convex bodies for which matheron s conjecture is confirmed by including all planar convex bodies possessing two non - degenerate boundary arcs being reflections of each other . given two convex bodies @xmath3 and @xmath35 in @xmath7 and a closed set @xmath36 we introduce the following property involving @xmath37 and @xmath38 @xmath39 is a shorthand notation standing for `` covariogram coincidence '' ( where covariogram is traditionally referred to by the letter @xmath40 ) . @xmath41 : : the equality @xmath42 holds for all @xmath43 in some neighbourhood of @xmath44 the following theorem presents two choices of the set @xmath18 for which @xmath41 implies the coincidence of @xmath3 and @xmath35 up to translations and reflections , under the assumption @xmath45 before stating the theorem we need to introduce the notion of local symmetry and give some related explanations . a pair of closed boundary arcs of a planar convex body @xmath3 is said to be a _ local symmetry _ of @xmath3 if they are reflections of each other in a point , have disjoint and nonempty relative interiors , and they are not properly contained in a pair of boundary arcs with the same properties . a planar convex body @xmath3 is called _ locally symmetric _ if it possesses a local symmetry . planar convex bodies without local symmetries are called _ globally non - symmetric . _ it is known that the support of @xmath5 is the _ difference body _ of @xmath3 , @xmath46 , and that @xmath47 is @xmath48-symmetric . if @xmath49 and @xmath50 are arcs of @xmath51 which compose a local symmetry , then the set @xmath52 , translated in such a way to be @xmath48-symmetric , is the union of two arcs @xmath53 and @xmath54 of @xmath55 . we say that these arcs of @xmath55 correspond to the local symmetry @xmath56 ( see figs . [ 06.05.23,21:46 ] and [ 05.12.19,11:36 ] ) . a convex body @xmath3 is said to belong to the class @xmath57 if its boundary is a two - times continuously differentiable manifold and all its principal curvatures are non - zero ( for detailed information see ( * ? ? ? * section 2.5 ) ) . [ 05.08.10,15:35 ] let @xmath3 and @xmath35 be planar convex bodies and let @xmath3 be @xmath57 regular . let @xmath58 be the collection of all the arcs of @xmath55 which correspond to local symmetries of @xmath3 . by @xmath59 we denote the midpoint of the segment joining the endpoints of the arc @xmath60 let @xmath61 and let @xmath62 or @xmath63 ( see figs . [ 06.05.23,21:46 ] and [ 05.12.19,11:36 ] ) . then @xmath41 implies the coincidence of @xmath3 and @xmath64 up to translations and reflections . @xmath65 cc ( 40,30 ) ( 12,8 ) ( 11,20)@xmath3 & ( 40,30 ) ( 4,4 ) ( 21,16)@xmath48 ( 3,25)@xmath47 + & we remark that the two choices of @xmath18 defined in the statement of theorem [ 05.08.10,15:35 ] are in some sense minimal for the assertion of the theorem to hold ( for further details see remark [ 06.05.16,16:17 ] below ) . moreover the set @xmath66 depends only on @xmath5 and not on @xmath3 , in the sense that if @xmath35 and @xmath3 satisfy @xmath67 or @xmath68 then the same set @xmath66 corresponds to @xmath35 and @xmath3 . this is the content of the second part of theorem [ 06.05.16,15:21 ] . the following corollary is a direct consequence of theorem [ 05.08.10,15:35 ] . [ 06.05.16,17:58 ] let @xmath3 and @xmath35 be planar convex bodies and let @xmath3 be @xmath57 regular . then the following statements hold . a. there exists a closed and at most countable subset @xmath18 of @xmath69 with no accumulation points in @xmath70 such that @xmath71 implies the coincidence of @xmath3 and @xmath64 up to translations and reflections . furthermore , @xmath18 can be chosen lying on a strictly convex curve . b. if @xmath3 is globally non - symmetric and @xmath18 is either @xmath72 or @xmath73 then @xmath41 implies the coincidence of @xmath3 and @xmath64 up to translations and reflections . @xmath65 it is an open question whether part ii of the above theorem holds for all strictly convex @xmath3 not necessarily @xmath74 the positive answer to this question would imply the confirmation of matheron s conjecture for all planar convex bodies . the following theorem presents determination results involving locally symmetric and symmetric convex bodies . [ 06.05.16,15:21 ] let @xmath3 and @xmath35 be planar convex bodies with @xmath3 strictly convex . then the following statements hold true a. if @xmath3 is @xmath48-symmetric and @xmath53 is a closed simple curve in @xmath70 bounding an open region in @xmath47 that contains the origin , then the conditions @xmath75 and @xmath76 imply the coincidence of @xmath3 and @xmath64 up to translations and reflections . b. if @xmath18 is either @xmath72 or @xmath73 then @xmath41 implies the coincidence of all local symmetries of @xmath3 and @xmath64 up to translations . @xmath65 the statement of the following corollary follows directly from the second part of theorem [ 06.05.16,15:21 ] and two results from ( * ? ? ? * theorem 1.1 and proposition 1.4 ) . [ 06.05.24,09:59 ] every locally symmetric convex body in @xmath77 is determined uniquely , up to translations and reflections , by its covariogram function . @xmath65 let @xmath78 denote the closed unit ball in @xmath7 centered at the origin . further on , we introduce the condition @xmath79 a relaxation of @xmath80 and the `` local coincidence '' condition @xmath81 @xmath82 : : the equality @xmath83 holds for all @xmath43 in some neighbourhood of @xmath18 and a suitable constant @xmath84 @xmath85 : : for every boundary point @xmath86 of @xmath3 there exists a boundary point @xmath87 of @xmath35 such that for some @xmath88 the bodies @xmath89 and @xmath90 coincide , up to translations and reflections ; the same statement also holds with the roles of @xmath3 and @xmath35 interchanged . in the following theorem the relationship between the conditions @xmath91 @xmath92 @xmath93 and @xmath85 is discussed . [ 06.05.15,12:36 ] let @xmath3 and @xmath35 be convex bodies in @xmath94 then the following statements hold true . a. if @xmath3 is strictly convex , then @xmath85 implies @xmath95 b. if @xmath96 and @xmath3 is @xmath97 then @xmath85 is equivalent to @xmath95 c. if @xmath96 and @xmath3 is strictly convex , then @xmath98 is equivalent to @xmath95 d. there exist planar convex bodies @xmath3 and @xmath35 belonging to the class @xmath57 such that @xmath67 holds , while @xmath99 does not . e. there exist @xmath3 and @xmath64 which are convex @xmath32-polytopes , such that the conditions @xmath75 and @xmath99 hold , while @xmath67 does not . @xmath65 it is an open problem whether for @xmath57 convex bodies in @xmath100 @xmath101 the condition @xmath67 implies @xmath81 the space @xmath102 endowed with the hausdorff metric is locally compact and by this a baire space ( see @xcite and @xcite ) . thus , we may speak about statements that hold for most convex bodies , i.e. , for all convex bodies with at most a meager set of exceptions . we recall that a set is said to be _ meager _ if it is a countable union of nowhere dense sets and _ residual _ if it is a complement of a meager set . trivially , a finite intersection of residuals is a again a residual . furthermore , every set possessing a residual subset is also a residual . [ 06.05.08,17:28 ] in the baire category sense , for most convex bodies @xmath3 and all convex bodies @xmath35 in @xmath7 the following statements hold true . a. if @xmath3 and @xmath35 satisfy @xmath93 then @xmath3 and @xmath35 coincide , up to translations and reflections . b. if @xmath96 and @xmath3 and @xmath35 satisfy @xmath91 then @xmath3 and @xmath35 coincide , up to translations and reflections . furthermore , the above two statements can not be extended to all pairs of convex bodies @xmath3 and @xmath64 since there exist bodies @xmath3 and @xmath35 not coinciding , up to translations and reflections , and such that @xmath103 holds . in addition , the bodies @xmath3 and @xmath35 satisfying the above conditions can be chosen belonging to the class @xmath74 @xmath65 it is an open question whether part ii of the statement can be carried over to convex bodies of higher dimensions . the previous theorem is related to ( * ? ? ? * theorem 2 ) and ( * ? ? ? * theorem 6.2 ) . theorem 2 from @xcite states that most convex bodies @xmath3 in @xmath7 , for any @xmath6 , are determined by the combined knowledge of the _ width _ of @xmath3 in direction @xmath16 and of the @xmath104-dimensional volume of @xmath105 , for each @xmath13 . here @xmath106 denotes the orthogonal complement to @xmath107 and @xmath105 stands for the orthogonal projection of @xmath3 onto the hyperplane @xmath108 ( see also @xcite , where `` local versions '' of some results from @xcite are obtained , as well as ( * ? ? ? * theorems 3.3.17 and 3.3.18 ) . ) the relation with the covariogram comes from the fact that knowing its support @xmath109 is equivalent to knowing the width of @xmath3 in all directions , and that the knowledge of @xmath5 in a neighbourhood of @xmath48 gives the volumes of all @xmath110-dimensional projections of @xmath3 . this follows from the formula @xmath111 proved in @xcite and @xcite . here @xmath112 stands for right derivative . theorem 6.2 from @xcite is another result related to theorem [ 06.05.08,17:28 ] , which states that most convex planar bodies are determined by the covariogram function over its entire support . in section 3 we prove theorem [ 06.05.15,12:36 ] . sections 4 and 5 are independent of each other and present proofs of theorem [ 05.08.10,15:35 ] and theorem [ 06.05.16,15:21 ] , respectively . in section 6 we prove theorem [ 06.05.08,17:28 ] .	positive answers to matheron s question have been obtained for large classes of planar convex bodies , while for there are both positive and negative results . one of the purposes of this paper is to sharpen some of the known results on matheron s conjecture indicating how much of the covariogram information is needed to get the uniqueness of determination . we indicate some subsets of the support of the covariogram , with arbitrarily small lebesgue measure , such that the covariogram , restricted to those subsets , identifies certain geometric properties of the body . these results are more precise in the planar case , but some of them , both positive and negative ones , are proved for bodies of any dimension . moreover some results regard most convex bodies , in the baire category sense . another purpose is to extend the class of convex bodies for which matheron s conjecture is confirmed by including all planar convex bodies possessing two non - degenerate boundary arcs being reflections of each other . 52a20 , 52a22 , 52a38 , 60d05 .	the covariogram of a convex body is the function which associates to each the volume of the intersection of with matheron asked whether determines , up to translations and reflections in a point . positive answers to matheron s question have been obtained for large classes of planar convex bodies , while for there are both positive and negative results . one of the purposes of this paper is to sharpen some of the known results on matheron s conjecture indicating how much of the covariogram information is needed to get the uniqueness of determination . we indicate some subsets of the support of the covariogram , with arbitrarily small lebesgue measure , such that the covariogram , restricted to those subsets , identifies certain geometric properties of the body . these results are more precise in the planar case , but some of them , both positive and negative ones , are proved for bodies of any dimension . moreover some results regard most convex bodies , in the baire category sense . another purpose is to extend the class of convex bodies for which matheron s conjecture is confirmed by including all planar convex bodies possessing two non - degenerate boundary arcs being reflections of each other . 52a20 , 52a22 , 52a38 , 60d05 . convex body , convex polytope , covariogram , genericity result , geometric tomography , set covariance , quasicrystal .
0704.2706	i	in this paper , we present a number of results concerning a dynamical version of coalescing random walks , which was recently introduced in @xcite . our results concern times of hausdorff dimension less than one where the system of coalescing walks behaves exceptionally . the results are analogous to and were motivated by the model of dynamical percolation and its exceptional times @xcite . in this section , we define the basic model treated in this paper , which we call the dynamical discrete web ( ddw ) , recall some facts about dynamical percolation , and then briefly describe our main results . the justification for calling this model a discrete web is that there is a natural scaling limit , which is one of our main motivations for analyzing the discrete web ( as it is in @xcite ) ; we also discuss in this section that scaling limit , which is a dynamical version of the brownian web ( see @xcite ) . a paper is in preparation @xcite on the construction of that model , which is closely related to the brownian net of sun and swart @xcite . we note that conjectures conerning ways to construct scaling limits of dynamical percolation ( in two - dimensional space ) appear in @xcite . we further note that exceptional times for dynamical versions of random walks in various spatial dimensions have been studied in @xcite and elsewhere , but these are quite different from the random walks of the ddw , as we note in subsection [ mainresults ] below . let @xmath4 for @xmath5 denote a simple symmetric random walk on @xmath6 starting at @xmath7 , i.e. at @xmath8 at @xmath9 . ( for real @xmath10 , we set @xmath11)$ ] , where @xmath12 $ ] denotes the integer part of @xmath13 . ) if we also consider other simple symmetric random walks starting from arbitrary points on the even space - time sublattice @xmath14 , which are independent of each other except that they coalesce when they meet , that is the system of ( one - dimensional ) coalescing random walks that is closely related to the one - dimensional ( discrete time ) voter model ( see @xcite ) and may be thought of as a one plus one dimensional directed percolation model . the percolation structure is highlighted by defining @xmath15 for @xmath16 to be the increment between times @xmath17 and @xmath18 of the random walker at location @xmath19 at time @xmath17 . these bernoulli variables are symmetric and independent and the paths of all the coalescing random walks can be reconstructed by assigning to any point @xmath20 an arrow pointing from @xmath20 to @xmath21 and considering all the paths starting from arbitrary points in @xmath22 and following the arrows . we note that there is also a set of dual ( or backward ) paths defined by the same @xmath15 s with arrows from @xmath23 to @xmath24 . the collection of all dual paths is a system of backward ( in time ) coalescing random walks that do not cross any of the forward paths . the ddw is a very simple stochastic process @xmath25 in a new dynamical time parameter @xmath0 whose distribution at any deterministic @xmath0 is exactly that of the static coalescing random walk model just described . specifically , let @xmath26 be a family of independent continuous time cadlag markov processes with state space @xmath27 and rate @xmath28 for changing state in either direction , with the initial condition that @xmath29 is a family of independent bernoulli random variables with @xmath30 . although this dynamical version of coalescing random walks sounds quite trivial at first hearing , it turns out that it can have interesting behavior at exceptional values of the dynamical time parameter s. this is a feature that it shares in common with dynamical percolation . static percolation models are defined also in terms of independent bernoulli variables @xmath31 , indexed by points @xmath32 in some @xmath33-dimensional lattice , which in general are asymmetric with parameter @xmath34 . there is a critical value @xmath35 when the system has a transition from having infinite clusters ( connected components ) with probability zero to having them with probability one . it is expected that at @xmath36 there are no infinite clusters and this is proved for @xmath37 and for high @xmath33 ( see , e.g. , @xcite ) . in dynamical percolation one extends @xmath31 to time varying functions @xmath38 , as in the case of coalescing walks , except that the transition rates for the jump processes @xmath38 are chosen to have the critical asymmetric @xmath39 distribution to be invariant . the question raised in @xcite was whether there were exceptional times when an infinite cluster ( say , one containing the origin ) occurs , even though this does not occur at deterministic times . this was answered negatively in @xcite for large @xmath33 and , more remarkably , was answered positively by schramm and steiff for @xmath37 in @xcite , where they further obtained upper and lower bounds on the hausdorff dimension ( as a subset of the dynamical time axis ) of these exceptional times . we apply in this paper the approaches used for dynamical percolation to the dynamical discrete web . although we restrict attention to one - dimensional random walks whose paths are in two - dimensional space - time and hence analogous to @xmath37 dynamical percolation , by considering different possible exceptional phenomena , we use both the high @xmath33 and @xmath37 approaches of @xcite . a natural initial question was whether there might be exceptional dynamical times @xmath0 for which the walk from the origin @xmath40 is transient ( say to @xmath41 ) . our first main result ( see theorem [ th1 ] in section [ tameness ] below ) , modeled after the high-@xmath33 dynamical percolation results , is that there are no such exceptional times . as we explain in remark [ remtame ] in section [ tameness ] , a small modification of the proof of theorem [ th1 ] shows that there are also no exceptional times where some pair of walks avoids eventually coalescing . our other two main results are modelled after the @xmath37 dynamical percolation results . one of them ( see theorem [ violation ] below ) concerns a kind of violation of the central limit theorem , or more accurately a kind of weak subdiffusivity , by the random walk @xmath40 for exceptional dynamical times @xmath0 ; namely , that @xmath42 for all @xmath43 . the other ( see theorem [ dimension ] ) gives upper and lower bounds on the hausdorff dimension of these exceptional times , that depend nontrivially on the constant @xmath3 so that the dimension tends to zero ( respectively , one ) as @xmath44 ( respectively , @xmath45 ) . this is strikingly in contrast with the dynamical random walks of @xcite where there are no exceptional times for which the law of the iterated logarithm fails . to explain why the walks of @xcite can behave so differently from those of the discrete web , we note that a single switch in the former case affects only a single increment of the walk while some switches in the discrete web change the path of the walker by a `` macroscopic '' amount , as discussed in the next subsection on scaling limits see also figure 1 where switching has changed one of the paths macroscopically . by an obvious symmetry argument , there are also exceptional dynamical times @xmath0 for which @xmath46 . one may ask whether there are exceptional @xmath0 for which @xmath47 . as discussed in remark [ twosided ] below , it can be shown , at least for small @xmath3 , that there are no such exceptional times . the case of large @xmath3 is unresolved . [ fixeds ] be the random walk at dynamical time @xmath0 starting from @xmath48 . this graph , with @xmath13 the horizontal and @xmath49 the vertical coordinate , represents simultaneously the family of functions @xmath50 ( @xmath51 ) . the lowest path , say for @xmath13 greater than about @xmath52 , differs `` macroscopically '' from the others.,title="fig : " ] there is a natural scaling limit of the ( static ) coalescing random walks model , the brownian web ( see @xcite ) . here one does a usual diffusive scaling in which the random walk time @xmath13 is scaled by @xmath53 , and space by @xmath54 so that the random walk path starting from @xmath55 $ ] at time @xmath56 $ ] scales to a brownian motion starting from @xmath57 at time @xmath58 . the collection of all random walk paths from all space - time starting points scales to a collection of coalescing brownian motion paths starting from all points of continuum space - time . now taking the rate of switching to be of order @xmath59 , rescaling time and space respectively by @xmath53 and @xmath54 , and then letting @xmath60 go to @xmath8 leads to a nontrivial limit @xmath61 , the dynamical brownian web . the idea of taking a scaling limit of the dynamical discrete web to obtain a dynamical continuum model is a natural one , which is at the heart of @xcite , although their approach appears to be somewhat different than the one we had already been taking . both approaches are closely related to the brownian net construction of sun and swart @xcite as will be extensively explored in @xcite . as we shall discuss in the next subsection , our approach is based on the construction of a certain poissonian marking of special space - time points of the ( static ) brownian web . these are the so - called @xmath62 points where a single brownian web path enters the point from earlier times and then two paths leave to later times , one to the left and one to the right with exactly one of the those two paths the continuation of the path from earlier time and the other one `` newly - born '' ; see figure 2 . neither the idea of doing a poissonian marking of special points for the brownian web nor the idea of using those marked points to construct a scaling limit of a dynamical discrete model is completely new . in particular , we note that a different type of marking ( of @xmath63 points ) was used in @xcite to study the scaling limits of noisy voter models . also the idea of using marked double points of @xmath64 to construct the scaling limit of two - dimensional dynamical percolation is discussed in @xcite . one motivation for the proposed marking in the @xmath64 context was the analogy with markings of @xmath62 as well as of @xmath63 points of the brownian web . in the dynamical brownian web @xmath65 , one can also consider exceptional dynamical times @xmath0 where the path @xmath66 starting from the origin at continuous time @xmath9 behaves differently than an ordinary brownian motion path . the results of @xcite are very similar to those of this paper for the discrete web . indeed , in some respects , the proofs are simpler since calculations with brownian motions are often easier than those with random walks . there is however one substantial complication , which is the main focus of @xcite and the reason we do not present the dynamical brownian web exceptional time results already in this paper . that complication is the actual construction of the dynamical brownian web a construction that is considerably less trivial than that of the dynamical discrete web , as we explain in the next subsection . [ changedirections ] is the vertical and @xmath49 the horizontal coordinate . if a @xmath67 ( left ) point of the original web ( left side of the figure ) is marked to switch at some @xmath68 $ ] , then the direction of that @xmath62 point in the web @xmath69 is changed at @xmath70 so that it becomes a @xmath71 ( right ) point as on the right side of the figure with the incoming path joined to the rightmost of the two paths starting from that point.,title="fig : " ] at the discrete level the scaling is chosen in such a way that between the dynamical times @xmath8 and @xmath0 , in a macroscopic box ( i.e. , one with size of order @xmath72 in the original lattice ) , the number of arrows that change direction will be of order @xmath53 . the situation can be simplified by focusing on switchings with `` macroscopic '' effects ( i.e. , switchings that will lead to a macroscopic alteration of a walker s trajectory in the initial web @xmath73 ) . a priori , one should also consider combinations of switchings that have macroscopic effects , but it turns out ( this will be proved rigorously in @xcite ) that the probability of macroscopic effects from switching two or more arrows is negligible compared to switching single arrows , and can be neglected . there is a natural way of characterizing those critical switchings . for example , let us consider the forward ( rescaled ) path @xmath74 starting from the origin in @xmath73 and assume that the arrow located at some @xmath75 is orginally oriented to the left . now we ask whether a switching of this single arrow will alter the path in such a way that the altered path will be to the right of @xmath76 , where @xmath77 are both positive macroscopic quantities . this will happen if and only if the backward path @xmath78 starting from @xmath79 hits @xmath74 at time @xmath13 ( more precisely , hits @xmath80 at time @xmath81 ) . more generally , the critical arrows leading to similar alterations are the `` contact '' points between @xmath74 and the backward path @xmath78 at which a switching occurs on @xmath82 $ ] . but it is now fairly easy to see what the statistics of such a set of points are . in fact , let @xmath83 be the random variable counting the number of such switchings up to the macroscopic time @xmath13 . the distribution of @xmath83 is simply given by : @xmath84 where @xmath85 are i.i.d . bernoulli random variables with @xmath86 , which is @xmath87 as @xmath88 . as @xmath88 , @xmath89 converges to the `` local time '' @xmath90 of the forward brownian path @xmath91 starting from the origin along a backward brownian path @xmath92 starting on the right of the path @xmath93 ( the joint distribution of @xmath93 and @xmath92 is analysed in @xcite and this `` local time '' will be defined precisely in @xcite ) . further , it is a standard fact that @xmath94 converges to a poisson process . hence , @xmath83 will converge to a poisson process run by the random clock @xmath95 . in other words , this set of points will consist of a two - dimensional ( @xmath13 and @xmath0 ) poisson point process with intensity measure @xmath96 , where @xmath97 is lebesgue measure and @xmath98 is the local time measure ( note that @xmath99 will be a locally finite measure so that the poisson process is well defined ) . so far , we have only selected the critical switchings inducing a specific type of macroscopic effect . namely , the ones altering the path @xmath93 in such a way that a point originally on one side of @xmath93 will be on the opposite side after switching occurs . but in order to select all the critical arrows leading to any kind of macroscopic changes , we should not only consider a poisson process run by the local time of a single forward path @xmath93 against a single backward path @xmath92 , but rather a poisson process run by the `` local time of the entire forward web along the entire backward web '' multiplied by the intensity @xmath100 . in other words , the set of marked points will be a three - dimensional poisson point process with intensity measure @xmath101 , where @xmath97 is lebesgue measure ( in the variable @xmath0 ) and @xmath102 is the local time measure of the forward web along the backward web . would not be a locally finite measure i.e. , the set of marked points in space - time is actually dense in @xmath103 . however , like what is presented in @xcite ( see p. 11 there ) , one can add an extra coordinate and lift @xmath102 to be a @xmath104-finite measure , or equivalently approximate @xmath102 by a sequence of locally finite measures @xmath105 , do the markings using @xmath105 , and then let @xmath106 . ] since the @xmath62 points of the continuum web are precisely those at which a forward and a backward path meet ( see , e.g. , @xcite ) , the measure @xmath107 will be supported by this set of points . from our previous description of them , it should be clear that each @xmath62 point has a preferred left or right `` direction '' . for example , a @xmath71 ( right ) point is one for which the continuing path ( coming in from earlier time ) is to the right of the `` newly - born '' path . hence , at the continuum level , the analog of an arrow switching will simply be a change of direction of all marked @xmath62 points ( see figure 2 ) . the web @xmath69 at time @xmath108 will be `` simply '' deduced from @xmath109 by switching the direction of all marked @xmath62 points whose @xmath0-coordinate is in @xmath110 $ ] . a last comment concerns the nature of the dependence of the two continuum paths @xmath111 and @xmath112 . these turn out to be a pair of `` sticky '' brownian motions , which are independent except when they touch each other . this is one of the major observations in @xcite ; we give a brief derivation of this fact in section [ pairsofpaths ] by analyzing pairs of paths in the discrete setting to see what must occur in the continuum scaling limit . in section [ tameness ] , we state our main theorem about tameness ; i.e. , that there are no exceptional dynamical times when the random walkers are transient . we also give there some other results about tameness in two extended remarks one about non - coalescence and the other about two - sided bounds of order @xmath113 . then in section [ existence ] , we show that there are exceptional dynamical times when the walkers are ( weakly ) subdiffusive i.e. , have one - sided bounds of order @xmath113 . in section [ hausdorff ] we derive upper and lower bounds on the hausdorff dimension of the set of such exceptional dynamical times . some estimates for random walks that are needed for our arguments are given in appendix [ appendix ] .	the dynamical discrete web ( ddw ) , introduced in recent work of howitt and warren , is a system of coalescing simple symmetric one - dimensional random walks which evolve in an extra continuous dynamical time parameter . the evolution is by independent updating of the underlying bernoulli variables indexed by discrete space - time that define the discrete web at any fixed . in this paper our results are motivated by those about exceptional times for dynamical percolation in high dimension by hggstrom , peres and steif , and in dimension two by schramm and steif . the exceptional behavior of the walks in the ddw is rather different from the situation for the dynamical random walks of benjamini , hggstrom , peres and steif . in particular , we prove that there are exceptional values of for which the walk from the origin has with a nontrivial dependence of the hausdorff dimension on . we also discuss how these and other results extend to the dynamical brownian web , a natural scaling limit of the ddw . the scaling limit is the focus of a paper in preparation ; it was also studied by howitt and warren and is related to the brownian net of sun and swart .	the dynamical discrete web ( ddw ) , introduced in recent work of howitt and warren , is a system of coalescing simple symmetric one - dimensional random walks which evolve in an extra continuous dynamical time parameter . the evolution is by independent updating of the underlying bernoulli variables indexed by discrete space - time that define the discrete web at any fixed . in this paper , we study the existence of exceptional ( random ) values of where the paths of the web do not behave like usual random walks and the hausdorff dimension of the set of exceptional such . our results are motivated by those about exceptional times for dynamical percolation in high dimension by hggstrom , peres and steif , and in dimension two by schramm and steif . the exceptional behavior of the walks in the ddw is rather different from the situation for the dynamical random walks of benjamini , hggstrom , peres and steif . in particular , we prove that there are exceptional values of for which the walk from the origin has with a nontrivial dependence of the hausdorff dimension on . we also discuss how these and other results extend to the dynamical brownian web , a natural scaling limit of the ddw . the scaling limit is the focus of a paper in preparation ; it was also studied by howitt and warren and is related to the brownian net of sun and swart .
0812.2483	i	gamma - ray bursts ( grbs ) are brief , intense flashes of @xmath0-rays originating at cosmological distances , and they are the most luminous objects in the universe . they also have broadband afterglows long - lasting after the @xmath0-ray radiation has ceased . it has been established that the bursts and afterglows are emitted from outflows moving towards us at highly relativistic speeds @xcite , and at least some grbs are associated with the collapse of massive stars ( e.g. , * ? ? ? * ; * ? ? ? observations suggest that the burst is produced by internal dissipation within the relativistic jet that is launched from the center of the explosion , and the afterglow is the synchrotron emission of electrons accelerated in a collisionless shock driven by the interaction of the jet with the surrounding medium ( for recent reviews , * ? ? ? * ; * ? ? ? * ; * ? ? ? in spite of extensive observational and theoretical efforts , several key questions concerning the nature of the central engines of the relativistic jets and the jets themselves remain poorly understood . in fact , some of these questions are very difficult or even impossible to answer with the spectral and lightcurve information currently collected . on the other hand , polarization information , if retrieved , would lead to unambiguous answers to these questions . in particular , polarimetric observations of grbs can address the following : _ magnetic composition of grb jets _ it is highly speculated that strong magnetic fields are generated at the grb central engine , and may play an essential role in the launch of the relativistic jets . however , it is unclear whether the burst emission region is penetrated by a globally structured , dynamically important magnetic field , and whether the burst is due to shock dissipation or magnetic reconnection ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? . _ emission mechanisms of the bursts _ the leading model for the emission mechanism of the prompt burst emission is synchrotron emission from relativistic electrons in a globally ordered magnetic field carried from the central engine , or random magnetic fields generated in - situ in the shock dissipation region @xcite . other suggestions include compton drag of ambient soft photons @xcite , synchrotron self - compton emission @xcite , and the combination of a thermal component from the photosphere and a non - thermal component ( e.g. , synchrotron ) @xcite . _ geometric structure of grb jets _ although it is generally believed that grb outflows are collimated , the distribution of the jet opening angles , the observer s viewing direction , and whether there are small - scale structures within the global jet are not well understood @xcite . to date , robust positive detections of grb polarization have been made only in the optical band in the afterglow phase . varying linear polarizations have been observed in several optical afterglows several hours after the burst trigger , with a level of @xmath6 , which is consistent with the synchrotron emission mechanism of grb afterglow ( for reviews , see * ? ? ? * ; * ? ? ? an upper limit @xmath7 has been obtained for the early @xmath8 optical afterglow of grb 060418 @xcite . also for radio afterglows , we have several upper limits for the polarization degree @xcite ( for some implications , see * ? ? ? as for the prompt burst emission , strong linear polarization of the @xmath0-ray emission at a level of @xmath9 was claimed for grb 021206 based on an analysis of _ rhessi _ data @xcite , although this claim remains controversial because of large systematic uncertainties @xcite . several other reports of high levels of polarization in the prompt burst emission are also statistically inconclusive @xcite . recently , more sensitive observational techniques for x - ray and @xmath0-ray polarimetry have been developed , and there are several polarimeter mission concepts . these include polarimeters for energetic transients ( _ poet _ , * ? ? ? * ; * ? ? ? * ) , polarimeter of gamma - ray observer ( _ pogo _ , * ? ? ? * ) , _ polar _ @xcite , advanced compton telescope ( _ act _ , * ? ? ? * ) , gravity and extreme magnetism ( _ gems _ , * ? ? ? * ) _ xpol _ @xcite , gamma - ray burst investigation via polarimetry and spectroscopy ( _ grips _ , * ? ? ? * ) , and so on . several of these missions , if launched , would provide definitive detections of the burst polarizations and enable us to discuss the statistical properties of the polarization degrees and polarization spectra . although there are several polarimetry mission concepts described in the literature , _ poet _ is the only one to date that incorporates a broadband capability for measuring the prompt emission from grbs , and for this reason it provides a good case study for our simulations . _ poet _ will make measurements with two different polarimeters , both with wide fields of view . the gamma - ray polarimeter experiment ( grape ; 60 - 500 kev ) and the low energy polarimeter ( lep ; 2 - 15 kev ) provide a broad energy range for the observations . suborbital versions of both _ poet _ instruments are currently being prepared for flight within the next few years . grape will fly on a sub - orbital balloon in 2011 , and the gamma - ray burst polarimeter ( grbp , a smaller version of lep ) will fly on a sounding rocket . theoretically , it has been shown that similarly high levels of linear polarization can be obtained in several grb prompt emission models ; the synchrotron model with a globally ordered magnetic field , the synchrotron model with a small - scale random magnetic field @xcite , and the compton drag model @xcite . thus the detections of grb prompt emission polarization would support these three models . in this paper , we show that these models can be distinguished by their statistical properties of observed polarizations . we performed detailed calculations of the distribution of polarization degrees by including realistic spectra of grb prompt emission and assuming realistic distributions of the physical parameters of grb jets , and show that _ poet _ , or other polarimeters with similar capabilities , can constrain the grb emission models . we use the limits of _ poet _ for grb detection and polarization measurements as realistic and fiducial limits . this paper is organized as follows . we first introduce the _ poet _ mission concept in [ sec : poet ] . in [ sec : theory ] , we summarize the properties of the observed linear polarization from uniform jets within the three emission models . based on these models , we perform monte carlo simulations of observed linear polarizations and show how the statistical properties of observed polarization may constrain grb emission mechanisms in [ sec : simulation ] . a summary and discussion are given in [ sec : summary ] .	the emission mechanism and the origin and structure of magnetic fields in gamma - ray burst ( grb ) jets are among the most important open questions concerning the nature of the central engine of grbs . in spite of extensive observational efforts , these questions remain to be answered and are difficult or even impossible to infer with the spectral and lightcurve information currently collected . polarization measurements will lead to unambiguous answers to several of these questions . recent developments in x - ray and-ray polarimetry techniques have demonstrated a significant increase in sensitivity enabling several new mission concepts , e.g. _ poet _ ( polarimeters for energetic transients ) , providing wide field of view and broadband polarimetry measurements .	the emission mechanism and the origin and structure of magnetic fields in gamma - ray burst ( grb ) jets are among the most important open questions concerning the nature of the central engine of grbs . in spite of extensive observational efforts , these questions remain to be answered and are difficult or even impossible to infer with the spectral and lightcurve information currently collected . polarization measurements will lead to unambiguous answers to several of these questions . recent developments in x - ray and-ray polarimetry techniques have demonstrated a significant increase in sensitivity enabling several new mission concepts , e.g. _ poet _ ( polarimeters for energetic transients ) , providing wide field of view and broadband polarimetry measurements . if launched , missions of this kind would finally provide definitive measurements of grb polarizations . we perform monte carlo simulations to derive the distribution of grb polarizations in three emission models ; the synchrotron model with a globally ordered magnetic field ( so model ) , the synchrotron model with a small - scale random magnetic field ( sr model ) , and the compton drag model ( cd model ) . the results show that _ poet _ , or other polarimeters with similar capabilities , can constrain the grb emission models by using the statistical properties of grb polarizations . in particular , the ratio of the number of grbs for which the polarization degrees can be measured to the number of grbs that are detected ( ) and the distributions of the polarization degrees ( ) can be used as the criteria . if and is clustered between 0.2 and 0.7 , the so model will be favored . if instead , then the sr or cd model will be favored . if several events with are observed , then the cd model will be favored .
0812.2483	i	recently there has been an increasing interest in the measurement of x - ray and @xmath0-ray polarization , and the observational techniques can now achieve significant sensitivity in the relevant energy bands . several polarimetry mission concepts , such as _ poet _ , are being planned . the _ poet _ concept has two polarimeters , grape ( 60 - 500 kev ) and lep ( 2 - 15 kev ) both of which have wide fields of view . if launched , missions of this type would provide the first definitive detection of the polarization of grb prompt emission . this would enable the discussion of the statistical properties of the polarization degree and polarization spectra , which will give us diagnostic information on the emission mechanism of grbs and the nature of the grb jets that can not be obtained from current spectra and lightcurve observations . we have performed monte carlo simulations of the linear polarization from grb jets for three major emission models : synchrotron model with globally ordered magnetic field ( so model ) , synchrotron model with small - scale random magnetic field ( sr model ) , and compton drag model ( cd model ) . we assumed that the physical quantities for the emission of the jets are uniform on the emitting surface and that the jets have sharp edges . our jet angle distribution allows the detections of grbs with very small opening angles ( i.e. , smaller than 1 degree ) as suggested by several _ bursts @xcite . we have shown that the _ poet _ mission or other polarimeters with similar capabilities , i.e. , broadband spectral capabilities for the determination of @xmath33 and sensitive broadband polarimetric capabilities to minimize mdp , can constrain the emission models of grbs . furthermore , these simulations indicate that an increase in the lep effective area would be beneficial to compensate for the lower expected polarization at lower energies . as shown in figures [ fig : atorob ] , [ fig : arndb ] , and [ fig : acomp ] , the sr and cd models require off - axis observations of the jets to achieve a high level of polarization , while the so model does not . in this sense the sr and cd models are categorized as _ geometric _ models , and the so model as an _ intrinsic _ model @xcite . the distribution of observed polarizations obtained by our simulations show that the geometric sr / cd models will be ruled out if the number ratio of the @xmath2-measurable bursts to detected bursts is larger than @xmath256 , and in this case the so model will be favored if the measurable polarizations are clustered at @xmath253 . if the number ratio is smaller than @xmath257 , the so model may be ruled out , but we can not distinguish between the sr and cd models with different distributions of @xmath150 , @xmath35 , and @xmath36 , where @xmath0 and @xmath48 are the bulk lorentz factor and the opening angle of the grb jet , respectively , and @xmath35 and @xmath36 are lower and higher indices of the energy spectrum . however , if several bursts with @xmath5 are detected , the cd model which includes an adequate number of small @xmath111 bursts will be favored . if the cumulative distribution of the measurable polarizations favors the so model , the globally ordered magnetic field would be advected from the central engine . if we understand the strength of the magnetic field in the emitting region from the luminosity and the spectrum of the emission , we can constrain the strength of the field at the central engine . if the geometric sr / cd models are favored from the observations , it will be established , independently of the afterglow observations , that grb outflows are not spherical but highly collimated . if the cd model is favored by the observations , we may constrain the distribution of the parameter @xmath258 of grb jets . the cd model needs a dense optical / uv photon field interacting within the relativistic jets @xcite . we have made some simplifications in our simulations , and there are some caveats . we have assumed that the jets are uniform on the emitting surfaces and have sharp edges . to compare the simulations and the observations further , more sophisticated modeling is required ( e.g. , * ? ? ? * ; * ? ? ? we have interpreted bursts as a simple combination of pulses , without taking account of the temporal variation of the lorentz factor @xmath0 of the jet . if this is accounted for , each pulse may have different @xmath150 but the same @xmath149 . we should then average the polarization with respect to fluence of each pulse having different @xmath111 @xcite . however , in the so model , the cumulative distribution of measurable @xmath2 will not be changed significantly as long as @xmath259 , because @xmath2 is clustered into a small range for @xmath129 and @xmath251 . to average the polarization in the case of @xmath219 , the relation between the luminosity and the lorentz factor for each pulse is required to predict the polarization distribution . for the sr model we have assumed that the directions of the magnetic field are confined within the shock plane . they may be more isotropic in reality , in which case the polarization degree in the sr model will be reduced . in the synchrotron model with a combination of the globally ordered magnetic field and the locally random field , @xmath260 , the linear polarization can be calculated by @xmath261 , where @xmath262 and @xmath263 are the stokes parameters from the ordered and random fields , respectively . @xmath264 and @xmath265 are described by equations ( [ eq : atorob ] ) and ( [ eq : arndb ] ) , and @xmath266 . this model will reduce the number ratio of @xmath2-measurable bursts to detected bursts to less than 30% and the clustering of measurable polarizations will be at @xmath267 . this work is supported in part by the grant - 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ronning , n. m. , & mszros , p. 2004 , apj , 601 , l119 zhang , b. 2007 , chin . j. astron . astrophys . ,	if launched , missions of this kind would finally provide definitive measurements of grb polarizations . we perform monte carlo simulations to derive the distribution of grb polarizations in three emission models ; the synchrotron model with a globally ordered magnetic field ( so model ) , the synchrotron model with a small - scale random magnetic field ( sr model ) , and the compton drag model ( cd model ) .	the emission mechanism and the origin and structure of magnetic fields in gamma - ray burst ( grb ) jets are among the most important open questions concerning the nature of the central engine of grbs . in spite of extensive observational efforts , these questions remain to be answered and are difficult or even impossible to infer with the spectral and lightcurve information currently collected . polarization measurements will lead to unambiguous answers to several of these questions . recent developments in x - ray and-ray polarimetry techniques have demonstrated a significant increase in sensitivity enabling several new mission concepts , e.g. _ poet _ ( polarimeters for energetic transients ) , providing wide field of view and broadband polarimetry measurements . if launched , missions of this kind would finally provide definitive measurements of grb polarizations . we perform monte carlo simulations to derive the distribution of grb polarizations in three emission models ; the synchrotron model with a globally ordered magnetic field ( so model ) , the synchrotron model with a small - scale random magnetic field ( sr model ) , and the compton drag model ( cd model ) . the results show that _ poet _ , or other polarimeters with similar capabilities , can constrain the grb emission models by using the statistical properties of grb polarizations . in particular , the ratio of the number of grbs for which the polarization degrees can be measured to the number of grbs that are detected ( ) and the distributions of the polarization degrees ( ) can be used as the criteria . if and is clustered between 0.2 and 0.7 , the so model will be favored . if instead , then the sr or cd model will be favored . if several events with are observed , then the cd model will be favored .
astro-ph0501182	i	clusters of galaxies have received intensive observational study over the last decades . this effort has lead to clear results on the way galaxy properties , such as morphology and star formation rate , vary within clusters and how these properties evolve between clusters at different redshifts ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * see bower & balogh 2004 for a recent review ) . in contrast , comparably detailed studies of galaxy groups and their evolution have only recently begun in earnest . the group environment is likely to have a significant impact on star formation rates in the member galaxies @xcite and recent work has emphasied that even for galaxies now in rich clusters , much of the transformation of the galaxies properties may have taken place in groups embedded in the filamentary structure @xcite . in addition , while few galaxies in the local universe are located in clusters , up to 50 per cent @xcite may be located in galaxy groups . furthermore , this number is strongly redshift dependent , as a larger and larger fraction of galaxies become members of groups as the large - scale structure of the universe develops . thus the properties of galaxies in groups and the impact of the group environment on the evolution of galaxies can have an important bearing on the decline of the cosmic star formation rate from @xmath0 to the present - day @xcite . studies of nearby groups show that their galaxy populations exhibit properties which vary from cluster - like ( mostly early - type ) to field - like ( mostly late type ) @xcite . however we know that groups span a wide range in local density , upon which the morphological composition @xcite and the mean star forming properties @xcite strongly depend ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the wide range of galaxy populations found in nearby groups is likely to be a natural consequence of these correlations . conversely , the powerful dependence of galaxy properties on local densities typical of groups suggests that groups provide the ideal environment for galaxy transformations . this may result in the strong dependence of early type fraction and passive dwarf galaxy abundance on group velocity dispersion and x - ray luminosity , observed in nearby groups @xcite . in particular , galaxy interactions are expected to be common in groups , in which the velocity dispersion is typically not much larger than that of the constituent galaxies @xcite . groups have a much lower density contrast against the background galaxy population , so most work has concentrated on groups which are either unusually compact @xcite or x - ray luminous @xcite . more recently , the advent of large field galaxy redshift surveys has made it possible to study galaxy groups selected purely on the basis of their three dimensional galaxy density . in the local universe , early redshift surveys and more recently the extensive 2df galaxy redshift survey ( 2dfgrs ) and sloan digital sky survey ( sdss ) have generated large group catalogues which can be used as the basis for studies of galaxies in the group environment @xcite however , the properties of higher redshift groups have been relatively little explored . this is largely because of the difficulty in finding suitable systems , and the low success rate of spectroscopic follow - up of group members . @xcite used radio galaxies to preselect groups in order to study the evolution of the blue galaxy fraction with redshift , while @xcite have presented a group catalogue based on the cnoc2 galaxy redshift survey . in this paper , we present new data obtained in the region of 26 cnoc2 groups at @xmath3 with ldss2 on magellan . in sections [ sec : cnoc2groupdata ] and [ sec : whyoiiforsf ] we introduce the data and explain why we have chosen to use the [ oii ] emission line to study statistical trends in star formation . in section [ sec : cnoc2dataprocessing ] we begin by describing the data reduction procedure and our method for determination of redshifts and emission line equivalent widths for each galaxy . section [ sec : grpmem ] then goes on to explain our procedure for group membership allocation . in section [ sec : indivgrps ] we present the properties of the 26 individual groups in order to examine any trends of structural group properties with star formation . finally , in section [ sec : stackedgrp ] groups are stacked to enable detailed statistical analaysis , and we investigate the link between the group environment and star formation by contrasting the stacked group with our sample of field galaxies selected from the same redshift range . in a second paper ( * hereafter known as paper ii ) , we present a comparison of the star forming properties of these intermediate redshift groups with local groups selected from the 2pigg catalogue at @xmath4 @xcite . throughout this paper we assume a @xmath5cdm cosmology of @xmath6 , @xmath7 and @xmath8 .	the evolution of galaxies in groups may have important implications for the evolution of the star formation history of the universe , since many processes which operate in groups may suppress star formation and the fraction of galaxies in bound groups grows rapidly between and the present day . in this paper , we present an investigation of the properties of galaxies in galaxy groups at intermediate redshift ( ) . the groups were selected from the cnoc2 redshift survey as described in , with further spectroscopic follow - up undertaken at the magellan telescope in order to improve the completeness and depth of the sample . we stack the galaxy groups in order to compare the properties of group galaxies with those of field galaxies at the same redshift . the groups contain a larger fraction of passive galaxies than the field , this trend being particularly clear for galaxies brighter than in the higher velocity dispersion groups . these trends are qualitatively consitent with the differences between group and field galaxies seen in the local universe . galaxies : fundamental parameters galaxies : evolution galaxies : stellar content catalogues	the evolution of galaxies in groups may have important implications for the evolution of the star formation history of the universe , since many processes which operate in groups may suppress star formation and the fraction of galaxies in bound groups grows rapidly between and the present day . in this paper , we present an investigation of the properties of galaxies in galaxy groups at intermediate redshift ( ) . the groups were selected from the cnoc2 redshift survey as described in , with further spectroscopic follow - up undertaken at the magellan telescope in order to improve the completeness and depth of the sample . we present the data for the individual groups , and find no clear trend in the fraction of passive galaxies with group velocity dispersion and group concentration . we stack the galaxy groups in order to compare the properties of group galaxies with those of field galaxies at the same redshift . the groups contain a larger fraction of passive galaxies than the field , this trend being particularly clear for galaxies brighter than in the higher velocity dispersion groups . in addition , we see evidence for an excess of bright passive galaxies in the groups relative to the field . in contrast , the luminosity functions of the star forming galaxies in the groups and the field are consistent . these trends are qualitatively consitent with the differences between group and field galaxies seen in the local universe . galaxies : fundamental parameters galaxies : evolution galaxies : stellar content catalogues
cond-mat0406202	i	quantum turbulence , the seemingly chaotic motion of quantized vortex lines in a disordered network , is a prominent characteristic of superfluid @xmath1he - ii , where it has been known to exist for almost half a century.@xcite up to recently , @xmath1he - ii was the only superfluid system in which this phenomenon has been investigated . @xmath1he - ii is believed to display turbulence in the entire superfluid temperature range which so far has been probed with measurements . in superconductors friction in vortex motion is always high and turbulence is not observed : only in the extreme clean limit one might hope to see any signs of other behavior . at present the closest superconducting analogues are dynamically driven vortex avalanches.@xcite superfluid @xmath0he is an intermediate case between these two extremes . the dynamics of vortex motion in the @xmath0he superfluids has primarily been studied in rotating cryostats . in the past the generally accepted view was that the high mutual friction leads to exponentially damped motion and forces vortices to evolve rapidly along well defined trajectories , so that the number of vortex lines remains conserved in dynamic processes . a large number of measurements over the years has proven this to be the case in both @xmath0he - a and @xmath0he - b at @xmath4.@xcite even at low temperatures ( @xmath5 ) a duplication of the classic vinen - vibrating - wire measurement@xcite verified that in @xmath0he - b stable vortex motion persists for hours in the absence of applied flow . in this experiment superfluid circulation was trapped around a thin wire suspended along the symmetry axis of a cylindrical container while the cryostat was rotating . when rotation was stopped , the trapped circulation started to unwind while a vortex filament , stretched between the wire and the cylinder wall , precessed around the wire and spiraled down along the whole length of the 15 mm long cylinder . the precessing spiral motion lasted for more than 35h and the precession frequency remained constant with a precision of 0.5% . the first indications of rapid non - linear vortex proliferation in @xmath0he - b came from measurements of the critical velocity of vortex formation at temperatures @xmath6 ( ref . , see p. 140141 ) . instead of the usual single - vortex formation at a reproducible critical velocity , sudden avalanches of vortices were observed in accelerating rotation . these bursts were interpreted to mean that at lower temperatures mutual - friction damping had decreased sufficiently so that turbulence became possible . the first evidence for tangled vorticity was reported from vibrating wire measurements in a non - rotating cryostat at temperatures below @xmath7.@xcite a vortex network was found to be produced with a vibrating wire resonator when it was driven at high level above a critical velocity of vortex formation . this was inferred by studying the damping of a second wire , vibrating at low level and probing the density of quasiparticle excitations which are andreev retro - reflected by the superflow fields in the vortex tangle . similar later measurements have allowed a determination of the vortex density in the wire - generated network . at zero externally applied pressure and at a temperature of @xmath8 the tangle localized around the vibrating wire turned out to have extremely low density , corresponding to an average inter - vortex distance of 0.2 mm , and to decay away rapidly in about 5s , when the generator wire was switched off.@xcite there exist no immediately obvious techniques by which turbulence can be easily generated and detected in @xmath0he - b . the above two examples suggest two ways which are supplementary , since they work in different temperature regimes . as outlined below in sec . [ experiment ] , nmr on a rotating sample can be used at temperatures down to about @xmath9 . in the zero temperature limit , where the density @xmath10 of the normal component approaches zero , moving objects can be used to generate vortices and , when driven in a high - quality resonance mode , to detect them . in this report we outline the techniques by which turbulence is generated and detected in the intermediate temperature regime 0.4 @xmath11 , where mutual friction damping and @xmath10 are still finite . recently a practical technique was discovered for injecting vortex loops into vortex - free flow.@xcite it then became possible to monitor the nature of vortex dynamics as a function of temperature and flow velocity in a controlled fashion.@xcite the transition , which separates regular vortex motion from turbulence , could now be mapped . the foundation , on which the interpretation of these results is built , was laid down by an earlier set of important hydrodynamic measurements@xcite on mutual friction which provided both the dissipative and reactive mutual friction coefficients @xmath12 and @xmath13 as a function of temperature @xmath14 and pressure @xmath15 . it turns out that in @xmath0he - b the variation of mutual friction with temperature happens to be such that the transition falls in the middle of the experimental temperature range , to 0.5 @xmath11 . these techniques have been employed in three recent studies investigating turbulence in @xmath0he - b.@xcite the first@xcite reports on the flight time of the vorticity when it expands along the rotating column . the second@xcite describes how turbulence starts in rotating vortex - free flow in the presence of neutron radiation . the third@xcite discusses the mutual - friction dependence of the transition from regular to turbulent vortex dynamics , _ i.e. _ the transition line as a function of @xmath16 and @xmath17 at high flow velocities , where the transition is velocity independent . these transition properties will also be illuminated in sec . [ turbtransition ] of this report , but from a different point of view . nmr measurements from the transient period , when the turbulent vorticity decays into the equilibrium rotating state of rectilinear vortex lines , will be analyzed in a forthcoming report.@xcite according to current view no similar kind of turbulence as in @xmath1he - ii or @xmath0he - b exists in the anisotropic superfluid @xmath0he - a . here vortex motion is highly damped at all experimentally accessible temperatures and fast vortex motion is supported by the appearance of a different structure of vorticity , the vortex sheet.@xcite	the experimental investigation of superfluid turbulence inhe - b is generally not possible with the techniques which have been developed forhe - ii . we describe a new method by which a transient burst of turbulent vortex expansion can be generated inhe - b . pacs numbers : 47.37 , 67.40 , 67.57 .	the experimental investigation of superfluid turbulence inhe - b is generally not possible with the techniques which have been developed forhe - ii . we describe a new method by which a transient burst of turbulent vortex expansion can be generated inhe - b . it is based on the injection of a few vortex loops into rotating vortex - free flow . the time - dependent evolution of the quantized vorticity is then monitored with nmr spectroscopy . using these techniques the transition between regular ( _ i.e. _ vortex number conserving ) and turbulent vortex dynamics can be recorded at and a number of other characteristics of turbulence can be followed down to a temperature of . pacs numbers : 47.37 , 67.40 , 67.57 .
nucl-ex0412039	i	an in - flight fragment separation apparatus can be used in two ways : * as a recoil spectrometer , to measure production cross sections or kinematics properties of the fragments ; * as a separation device , aiming at producing high - purity secondary beams of nuclides . the fragment recoil separator ( frs ) @xcite of gsi has been very successfully used for both purposes for more than ten years . by now , several projects across the world are dedicated to the construction of more powerful devices , in terms of larger fragment acceptance ( spectrometer for fission products ) , and/or increased selectivity and high - intensity secondary - beam production . the upper energy range covered by such devices seems to be mostly a technological ( and financial ) question , as increasing the energy requires more powerful magnets and a longer flight path , not even talking about the accelerator itself . but the lower range is determined by physics : it is assumed that only a very low proportion of non - fully stripped fragments can be tolerated in order to obtain a clean separation of fragments and to measure production cross sections . therefore , a whole energy range is somehow forbidden to fragmentation experiments . this low - energy limit has been faced by a recent experiment conducted at the gsi spectrometer frs . the aim of this experiment was to use the inverse - kinematics method to measure production cross sections from residues of the spallation of lead by protons with an incident energy of 500a mev . the results of this experiment will be the subject of a separate , forthcoming publication . this paper is dedicated to the description of the experimental and analysis techniques which were developed for this experiment and to discuss whether or not they proved to be successful . part of these techniques may be used more generally than for the frs setup from gsi . first we will briefly remind the main characteristics of the frs ( section [ chap : frs ] ) . the fragment recoil separator and its set of detectors have been designed using the hypothesis that most , if not all the fragment one wishes to study are fully stripped @xcite . this is of course less and less true with decreasing energy . in section [ chap : qst ] we will discuss the variations of the charge - state probabilities with energy and their consequences on the selectivity of the spectrometer , as well as the possible choices of so - called stripping materials . with a lead beam energy as low as 500a mev , no stripper is efficient enough so that the fraction of non - fully stripped fragments would be negligible . the response of the ionization chambers ( used for the determination of the atomic number of the fragments ) in this situation will be discussed in section [ chap : z ] , as well as a new setup , developed for this experiment , based on an increased gas thickness . in section [ chap : deg ] we will describe a method to use a thick matter of layer as a passive measurement device in order to estimate the atomic number and the charge state of the fragments . we will also discuss , how unexpected problems prevented the measurement of the ionic charge state of ions ( and thus of the mass ) in the above - mentioned experiment . the final sections will be dedicated to new analysis techniques aiming at obtaining production cross sections , even in the case of an incomplete event - by - event mass identification . section [ chap : a ] will present a method to determine the most - likely mass of each fragment and to reduce the number of possible contaminating charge states . then , in section [ chap : cs ] , we will explain how to account for the large fraction of non fully - stripped ions and how to obtain isotopic production rates with low uncertainties despite the ambiguities in the mass determination . we will then conclude and try to answer whether or not the widely admitted low - energy limit has been pushed downwards .	three topics are covered . first , a specific set - up for ionization chambers , based on a very large gas thickness , is presented . the possibility to use a thick layer of matter ( a degrader ) as a passive measurement device to identify the nuclear charge and the ionic charge state of fragments is discussed . the combination of those new experimental and analysis techniques made the 500a mev spallation experiment a success .	the feasibility of low - energy fragmentation experiments using a magnetic spectrometer is discussed . the main challenge is the multiplicity of the ionic charge states , which can hamper the identification in both z and a of the fragments . three topics are covered . first , a specific set - up for ionization chambers , based on a very large gas thickness , is presented . its satisfactory performances are discussed in light of the observations during a 500a mev pb+p experiment performed at the frs ( gsi ) . as a second topic , the possibility to use a thick layer of matter ( a degrader ) as a passive measurement device to identify the nuclear charge and the ionic charge state of fragments is discussed . this method , successfully used for z identification in experiments such as pb+p at 1a gev , fails to measure the charge states at 500a mev for the same system . it is shown that surface defects of the degrader are probably responsible for this failure . the third topic is the description of new analysis techniques developed in order to account for and subtract the contribution of polluting charge states in the spectrometer , thus making possible a clean estimation of the production cross sections of all fragments . the combination of those new experimental and analysis techniques made the 500a mev spallation experiment a success . , , , , , magnetic spectrometer , ionic charge state , production cross section , degrader , ionization chambers 29.30.aj , 29.40.cs , 34.50.bw , 25.40-h , 25.70-z
1509.05427	i	a major outstanding goal in cosmology is to piece together the history of the universe between cosmic dawn , the emergence of the first stars and galaxies , and the end of reionization , when the radiation from these objects had ionized the intergalactic medium ( igm ) . advances in numerical techniques , combined with exquisite measurements of the `` initial '' conditions ( at a redshift @xmath6 ; @xcite , @xcite ) , have led to remarkable simulations ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) of the conditions leading up to the former milestone , occurring at @xmath7 , when the universe was @xmath8 old . however , reconstructing the subsequent several hundred myr of cosmic history has proved far more challenging , due to the difficulties in reliably modeling the numerous forms of feedback from the first astrophysical objects ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in particular , x - rays from the first galaxies can act as a powerful source of feedback ( e.g. * ? ? ? * ; * ? ? ? * ) that exerts influence over a wide range of distance scales . because hard x - rays ( energies @xmath9 ) have mean free paths comparable to the hubble horizon , they can isotropically heat and partially reionize the early igm ( e.g. @xcite ) . in fact , they are expected to be the dominant agent in heating the igm . such heating may suppress star formation @xcite and massive black hole ( bh ) growth @xcite inside low - mass dark matter haloes by raising the jeans and filtering masses of the igm @xcite . on galactic and circum - galactic scales , soft x - rays ( @xmath10 ) can affect the formation of stars and possibly massive black holes ( bhs ) by promoting the formation of molecular hydrogen via electron - catalyzed reactions ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? in addition to their suspected roles in early galaxy evolution , x - rays are important also because they can leave an observable signature that can be exploited to probe the cosmological epoch in question @xcite . their thermal impact on the early universe should be measurable through the redshifted @xmath11 transition line of neutral hydrogen , which is observed in emission or absorption depending on the relative temperature of the igm with respect to that of the cosmic microwave background ( cmb ) . several studies have investigated how forthcoming observations of the sky - average amplitude and power spectrum of the relic @xmath11 line ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) could be used to constrain the astrophysical agent ( or agents ) responsible for heating the early igm . there are sound reasons to expect that the first galaxies produced x - rays in abundance , and rapidly heated the igm . there are two dominant x - ray sources in present - day galaxies both powered by gas accretion onto bhs , and both plausibly prominent shortly after cosmic dawn : gas feeding massive bhs shining as active galactic nuclei ( agn ) , and x - ray binaries , powered by a stellar - mass bh gradually cannibalizing a companion star . estimates of the mass accumulated by nuclear bhs prior to @xmath12 @xcite , the existence of very massive bhs at @xmath13 ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , as well as the observed ( e.g. * ? ? ? * ) and theoretically expected @xcite increase in their duty cycles toward higher redshifts , all hint that x - ray agn may have been much more common during this epoch . likewise , high - mass x - ray binaries ( hmxbs ) dominate the x - ray emission of star - forming galaxies ; the low metallicity and rapid baryonic mass accretion of the earliest galaxies both lend credence to the notion that they were rife with hmxbs . theoretical models suggest that either type of x - ray source could heat the igm to above the cmb temperature as early as @xmath14 , and that this transition should be measurable by the planned @xmath11 experiments . at present , there are too many theoretical uncertainties to determine from the future data which type of x - ray source agn or hmxbs was responsible for driving the thermal evolution of the @xmath15 igm . modeling the early agn x - ray emission is particularly difficult , because the conditions for triggering agn activity are not fully understood even at low redshifts ( e.g. * ? ? ? * ; * ? ? ? because of the uncertainty in the fraction of x - ray photons that is released into the igm as opposed to being trapped inside the accretion flow or reprocessed into the infrared ( e.g. * ? ? ? * ; * ? ? ? * ) ; and because the epoch , initial masses , and birthplaces of the massive bh `` seeds '' are not yet constrained by observations ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? similarly , studies usually estimate the x - ray contribution from early hmxbs by simply inferring empirical relations between x - ray luminosity and star formation rate ( sfr ) in local galaxies ( and modeling the sfr using a semi - analytic cosmological model ) , or combining such relations with one or more free parameters ( e.g. * ? ? ? * ; * ? ? ? the goal of this study is to alleviate the uncertainties in the formation rate and x - ray output of hmxbs in the early universe , by using @xmath1-body simulations of nascent groups of the first ( population iii , henceforth pop iii ) stars . we choose the properties of the star groups in our simulations to reflect those found in hydrodynamical simulations of pop iii star formation at @xmath16 ( @xcite , @xcite ) . we follow the formation and dynamical evolution of compact binaries over thousands to millions of years , including the effects of the background gravitational potential and dynamical friction . this allows us to compute the fraction of pop iii stars that form stable , compact binaries , and eventually undergo an x - ray bright phase . the end result is an estimate of the formation rate of hmxbs in the first protogalaxies , as well as the amount of x - rays they generate per unit star formation . to our knowledge , this is the first published estimate of this type . our simulations predict a binary formation rate which is similar to what is observationally inferred in present - day galaxies . however , we derive a hmxb energy output ( normalized to the star formation rate ) that is a factor @xmath17 higher than in present - day star - forming galaxies , if the hmxb duty cycle is similar to the one in the local universe . we find that the x - ray output does not change significantly within the wide variety of simulation setups considered such as different orientations for collisions between star groups , and ambient gas density and submit that this is a robust estimate . the findings of this study can be used as model inputs in estimating the @xmath11 global signature and power spectrum , but have wider applications . as stated above , the x - ray output of the first galaxies are also of interest for studying feedback on smaller scales , such as subsequent star formation and massive bh formation . our work is also relevant for predicting the rates of long - duration gamma - ray bursts ( lgrbs ) from pop iii stars . lgrbs are important probes that can shed light on the universe out to @xmath18 ( e.g. * ? ? ? according to the collapsar model @xcite , progenitors of lgrbs require rapid rotation of the he core and removal of the h envelope . both criteria are satisfied by pop iii hmxbs , and it is plausible that massive pop iii stars in binary systems are dominant lgrb progenitors in the early universe @xcite . our results on hmxb formation rates can therefore be used to predict and interpret observations of high - redshift lgrbs . the paper is organized as follows . we start in [ sec : dynamics ] by discussing the problem to be solved beginning with the equations of motion , followed by the description of our @xmath1-body code , our choices for the initial conditions , and how the data is interpreted for hmxb formation . we present our results in [ sec : results ] . in [ sec : discussion ] , we discuss the implication of our work for the x - ray output of the first galaxies , as well as for other topics such as lgrbs and smbh formation . we conclude with a summary of our findings in [ sec : summary ] .	the first astrophysical objects shaped the cosmic environment by reionizing and heating the intergalactic medium ( igm ) . in particular , x - rays are very efficient at heating the igm before it became completely ionized , an effect that can be measured through the redshifted 21 cm line of neutral hydrogen . high - mass x - ray binaries ( hmxbs ) , known to be prolific x - ray sources in star - forming galaxies at lower redshifts , are prime candidates for driving the thermal evolution of the igm at redshifts . despite their importance , the formation efficiency of hmxbs from the first stellar populations is not well understood as such , their collective x - ray emission and the subsequent imprint on the 21 cm signature are usually evaluated using free parameters . using-body simulations , we estimate the rate of hmxb formation via mutual gravitational interactions of nascent , small groups of the first stars ( population iii stars ) . we discuss broader implications of our results , such as the rate of long gamma - ray bursts from population iii stars and the direct collapse channel for massive black hole formation . [ firstpage ] cosmology : theory early universe cosmology : dark ages , reionization , first stars stars : population iii intergalactic medium x - rays : binaries stars : kinematics and dynamics	the first astrophysical objects shaped the cosmic environment by reionizing and heating the intergalactic medium ( igm ) . in particular , x - rays are very efficient at heating the igm before it became completely ionized , an effect that can be measured through the redshifted 21 cm line of neutral hydrogen . high - mass x - ray binaries ( hmxbs ) , known to be prolific x - ray sources in star - forming galaxies at lower redshifts , are prime candidates for driving the thermal evolution of the igm at redshifts . despite their importance , the formation efficiency of hmxbs from the first stellar populations is not well understood as such , their collective x - ray emission and the subsequent imprint on the 21 cm signature are usually evaluated using free parameters . using-body simulations , we estimate the rate of hmxb formation via mutual gravitational interactions of nascent , small groups of the first stars ( population iii stars ) . we run two sets of calculations : one in which stars form in small groups of five in nearly keplerian initial orbits , and another in which two such groups collide ( an expected outcome of mergers of host protogalaxies ) . we find that hmxbs form at a rate of one per in newly born stars , and that they emit with a power of in the kev band per solar mass per year of star formation . this value is a factor larger than what is observed in star forming galaxies at lower redshifts ; the x - ray production from early hmxbs would have been even more copious , if they also formed _ in situ _ or via migration in protostellar disks . combining our results with earlier studies suggests that early hmxbs were highly effective at heating the igm and leaving a strong 21 cm signature . we discuss broader implications of our results , such as the rate of long gamma - ray bursts from population iii stars and the direct collapse channel for massive black hole formation . [ firstpage ] cosmology : theory early universe cosmology : dark ages , reionization , first stars stars : population iii intergalactic medium x - rays : binaries stars : kinematics and dynamics
1509.05427	r	here , we summarize the findings of our @xmath1-body simulations , focusing in particular on the properties of the most compact binaries found for each set of runs . [ sec : results ] we ran 20 simulations for @xmath97 and 23 for @xmath99 . for @xmath97 , in 12 out of 20 runs , the two most massive stars ( @xmath113 and @xmath114 , where @xmath115 is the @xmath53-th most massive star ) form the most compact binary we denote such a binary with the notation @xmath116 . similarly , binaries of type @xmath117 ( i.e. made up of the most massive star @xmath113 and the third most massive star @xmath118 ) form the most compact binary in 6 of the runs . the left panel of figure [ fig:1 ] shows a sample set of stellar trajectories for one of the large scale @xmath119 runs . throughout the simulation , the compact binary tends to remain near the center of the halo , as less massive stars repeatedly undergo 3-body interactions with the binary . the fact that they do not stray far from the center of the halo is a combined effect of the background potential and the gravitational potential of the massive binary . it is these 3-body encounters that cause the most compact binary in the simulations to end up as type @xmath116 or @xmath117 . in two of the runs , the most compact binaries after @xmath104 consist of less massive stars . the average value of the semimajor axis after @xmath120 in the large scale , @xmath119 runs is @xmath121 , and the minimum value of @xmath64 across the 20 runs is 60 au . these values for @xmath64 are much larger than that necessary for rlof to take place , @xmath122 au . their characteristic dynamical friction time scales are roughly @xmath123 yrs , which is much longer than their lifetimes ( see equation [ eq7 ] when @xmath124 and equation [ eq11 ] ) . we therefore conclude that in systems of @xmath109 stars and @xmath125 , with the stars initially separated at hundreds of au , hmxbs are unlikely to form . 1c c c large scale & @xmath97 & @xmath99 + number of runs & 20 & 23 + @xmath126 $ ] & 0.60(0.90 ) & 0.56(0.74 ) + @xmath127[au ] & 270 & 340 + for the @xmath99 case , the fraction of runs where the most compact binary after @xmath104 is type @xmath116 or @xmath117 are similar to the @xmath119 simulations : @xmath128 for @xmath116 , and @xmath129 for @xmath116 _ or _ @xmath117 . however , the dynamical evolution is quite different , as can be seen by the right panel of figure [ fig:1 ] . the lower gas densities lead to weaker forces due to dynamical friction and background potential , and stars ( especially less massive ones ) tend to be scattered farther from their initial position , as far as @xmath130 . this also results in less frequent three - body interactions in general , and may explain the larger average value of the semi - major axis after @xmath104 , @xmath131 . the formation of hmxbs appears even more intractable for the @xmath132 case . sample stellar trajectories for the @xmath119 and @xmath132 large scale cases are shown in figure [ fig:1 ] , and a summary of the results is given in table [ tab : tab1 ] . 0.7c c c small scale & @xmath97 & @xmath99 + runs & 86 & 86 + @xmath133 [ au ] & 1.37 & 1.42 + @xmath134[yr ] & @xmath135 & @xmath136 + companion stars & + @xmath137 & 0.070 & 0.070 + @xmath138 [ @xmath139 & 4.6 & 4.6 + for the small scale case , we performed 86 runs of 5-body simulations for each of the number density values @xmath119 and @xmath132 . due to the smaller initial separations of the stars , we run the simulations for a shorter amount of time . we run each simulation for a minimum of @xmath140 , but stop the run if a stable binary forms , and if no further significant dynamical changes are observed . if such a binary does not form , we run the simulations to a maximum duration of @xmath141 . in order to properly compare the results from the @xmath97 calculations with those from the @xmath99 calculations , we use the same initial conditions for each set of runs . in the @xmath97 calculations , the most common scenario is that @xmath113 always forms the most compact binary almost immediately , while stellar scatterings are most common during the first few years to about 40 years . thereafter , a multiple system usually survives and stabilizes , while less massive stars are ejected . a difference between the large - scale and the small - scale scenarios is that , whereas most cases in the large - scale calculations end up with one binary and unbound single stars ( in @xmath142 out of @xmath143 cases ) , in the small - scale runs a multiple system such as triple or quartet ( rather than a simple binary ) forms ( in 59 of 86 cases ) less massive stars take some energy from the multiple system and convert it into their kinetic energies while causing the binary to harden . as an example , figure [ fig:7 ] shows the evolution in the semi - major axis of a compact binary in one of the runs . one can easily notice the quick decrease in the semi - major axis during violent stellar interactions ( before 10 years ) , which clearly indicates the hardening . after a couple of stars are cast away and the multiple system is stabilized and isolated ( after about 10 years ) , dynamical friction plays the main role in the decrease of the semi - major axis ; after this point , we do not expect further dramatic hardening of the binary . in our 86 runs , the last surviving binary is typically of type @xmath144 ( pairing of the most massive and third most massive stars ) . with total mass of @xmath145 and @xmath146 . @xmath147 and the minimum semi - major axis is @xmath148 . the corresponding dynamical friction time scale ( equation [ eq11 ] ) is @xmath149 yr . the ejected stars have speeds of @xmath150 , and @xmath151 . six of the hmxb candidates ( hmxbc hereafter ) have been formed in all runs ( @xmath137 = 0.070 ) . for later use , let us define @xmath138 as the number of hmxbc formed across all simulations , normalized by the total mass of the stars . then @xmath152 ( this term will be used to estimate the x - ray luminosity and is one of the primary results of our study ) . the outcomes of the @xmath132 simulations are quite similar : a triple or higher multiple forms in 65 of 86 runs , and @xmath153 . furthermore , due to the same number of hmxbc , @xmath137 and @xmath154 are the same . one notable difference is that for @xmath132 , the dynamical friction time scale is longer by 2 orders of magnitude compared to @xmath97 , because this quantity is inversely proportional to the number density . interestingly , there are four runs ( for each density value ) in which the most compact binary is eccentric , and inside the requisite separation for rlof at pericenter but outside it at apocenter . we consider only two of them as hmxbc and rule out the other two binaries since the mass of the more massive star is smaller than @xmath155 @xcite . we present the distribution of eccentricity for pericenter distance in figure [ fig:8 ] . in particular , the _ left _ panel shows the distribution for @xmath97 calculations and the _ right _ panel for @xmath99 . the circled point indicates hmxbc with distance at pericenter shorter than the corresponding roche - lobe radius . how accretion proceeds in a highly eccentric binary system under these conditions remains an unsettled issue to date , as studies have claimed that the orbital semimajor axis and eccentricity can either increase or decrease depending on the binary properties at pericenter ( @xcite and @xcite ) . if the rlof does induce circularization , then accretion proceeds normally ( i.e. steadily ) . however , if the rlof instead increases the eccentricity of the system , then , whether accretion can proceed steadily rather than intermittently will depend on the relative timescale between the disk lifetime @xmath156 ( on the order of the viscous timescale ) , and the orbital period of the binary @xmath157 . we computed these timescales for all the eccentric binaries in our simulations ( for which the roche - lobe radius straddles the pericenter and apocenter ) , and found that @xmath158 in all cases but one . this implies that the fraction of binaries whose eccentricities cause intermittent rlof is small , and that as a global average , rlof is steady to a good approximation . the magnitude of the gas density considerably influences the characteristics of the dynamical interactions . while on the one hand @xmath159 of the simulations end up forming the same triples for both density values , on the other hand their trajectories and the center of mass movements differ significantly . figure [ fig:4 ] shows two sample trajectories of 5 stars with low number density ( left panel ) and high number density ( right panel ) after 1000 yr . they were given identical initial conditions for the run , but their trajectories have developed differently . in figure [ fig:3 ] , at 800 yr , even though the same stars form a triple and the same star is ejected for both number densities , their trajectories are clearly different . as can be seen in figure [ fig:2 ] , which shows the change of forces per unit mass exerted on a typical kicked - off star , @xmath160 and @xmath161 are negligible compared to @xmath162 before about 5 years . note that @xmath160 and @xmath161 are synchronized at early times because the motions of the stars are close to the keplerian motion , @xmath163 . the star in figure [ fig:2 ] is ejected at @xmath164 for the high number density ( and at @xmath165 for the low number density ) . this can be understood from the fact that @xmath162 monotonically decreases and @xmath161 increases ( @xmath166 where @xmath88 is the distance from the center of mass ) . at the same time , @xmath167 barely changes since the star moves in the supersonic regime and the speed decreases slowly . there is no noticeable difference in the overall results between the @xmath132 and @xmath119 runs quantities such as @xmath168 , the dynamical friction time scale @xmath169 , the total mass of the most compact binary ( or which star forms the compact binary with @xmath113 ) as summarized in table [ tab : tab2 ] . for both number densities , the companion star of the binary is typically the third most massive star @xmath118 . to sum up , we find that @xmath170 of our simulations form hmxbc , regardless of the gas density value . normalized to the total stellar mass in the simulations , the number of hmxbc formed per stellar mass is @xmath171 . we now explore several different configurations for the star group , and run several sets of simulations with 10 stars ( instead of 5 ) . these are : ( 1 ) 10-body version of the small scale calculation presented above ; ( 2 ) head - on crash of two star groups containing 5 stars each ; ( 3 ) a close encounter and subsequent inspiral and merger of two star groups containing 5 stars each . the latter two scenarios are motivated by the fact that the merger timescales and mass accretion timescales of pop iii host haloes , as well as the lifetimes of the massive pop iii stars themselves , are of the same order , @xmath172 . this suggests that merging haloes will be continuously forming new stars ( perhaps pop ii instead of pop iii ) as they merge with other haloes , and that close interactions and mergers of nascent star groups may be relatively common . we generate stellar masses in the same way as for the 5-body case , but with a larger value for the parameter @xmath173 . we have run each simulation for 500 yr . the results of these simulations are summarized in table [ tab : tab3 ] . we briefly discuss each one , as follows . 0.6c c c c c c scenario & 1 & 2 & 3 & 4a & 4b + runs & 54 & 30 & 30 & 30 & 30 + @xmath174 @xmath175 $ ] & 1.0 & 1.1 & 0.90 & 1.8 & 1.6 + @xmath176 @xmath175 $ ] & 1.6 & 1.5 & 1.8 & 2.4 & 2.0 + @xmath177 @xmath175 $ ] & 0.72 & 0.15 & 0.42 & 1.2 & 0.23 + @xmath178 & 0.33 & 0.33 & 0.27 & 0.13 & 0.27 + @xmath179 [ @xmath139 & 15 & 11 & 9.0 & 4.2 & 8.4 + we set up the simulations as in the 5-body calculations , but with 10 stars . we find that @xmath180 . interestingly , there are 18 out of 54 cases in which @xmath181 . there is a large difference in scale between @xmath182 and @xmath183 , where @xmath182 is the semi - major axis of @xmath116 ( binary made up of the two most massive stars ) and @xmath183 is the semi - major axis of the binary stars other than @xmath113 and @xmath114 . this is a common feature of the 10-body simulations : they often end up with triples whose inner binary is @xmath184 while the outer binary is @xmath185 . our simulations yield @xmath186 and @xmath187 . also note that , in 14 out of 18 hmxbc , the binary is @xmath188 ( i.e. it is not made up of the two most massive stars ) . since the compact binaries in these simulations form quickly and we only follow them for 500 years , it is technically possible that they will be disrupted before one of the stars turns into a bh . however , our simulations for the 5-body scenario showed that compact , quasi - steady binaries are unlikely to be disrupted , and for practical purposes we extrapolate this qualitative result to the 10-body case . we find that a hmxbc forms in a larger fraction of these simulations than in the 5-body case , @xmath189 , for the obvious reason that there are more stars . per unit stellar mass in the simulations , the number of hmxb candidates is @xmath190 , which is a factor @xmath191 higher than we found for the 5-body case . two groups of 5 stars are set up with random initial conditions , in the same manner as for the previous simulations of 5-body groups . the two groups are then arranged to collide head - on , as follows : they are placed at a separation of two to three times their sizes and their disks are aligned so that the mutual inclination is zero . the initial relative speed of the groups is roughly the speed of sound and the center of mass of one group is set to move directly toward the center of mass of the other group . we find that prior to colliding , each group forms a compact binary of type @xmath116 ( the most and second - most massive star ) . when the two groups collide , those two binaries that existed before the collision were broken and the two most massive stars of each group form a new compact binary with high chances . the average @xmath192 is @xmath193 , but @xmath194 and @xmath195 , meaning that the most compact binaries are not formed from the most massive stars . the shorter average separations may be a result of a larger number of early 3-body scatterings , which act to harden the group as a whole . hmxbc form in 10 out of 30 runs , and they are not of type @xmath116 . however , we find a rate of hmxb formation per stellar mass @xmath196 ; this is higher than in the 5-body case and comparable to scenario 1 above . sample trajectories for one of the simulations of scenario 2 are depicted in figure [ fig:10 ] . we have used the same input parameters for the two groups as in scenario 2 , except that we now set the impact parameter to be of order the size of the group , whereas it was set to zero in scenario 2 . the groups are given opposite velocities of @xmath197 along the @xmath198-direction , and are offset by a displacement along the @xmath199-direction that is @xmath200 times the typical size of the star group ( @xmath201 ) so that they merge with a spiral motion . we find that @xmath202 , @xmath203 and @xmath204 . the average separation lies between what we find in scenarios 1 and 2 . this can be interpreted as being due to the fact that these simulations ( in which the two groups merge gradually via inspiral ) have more close 3-body interactions than in scenario 1 ( in which 10 stars in quasi - keplerian orbits evolve in isolation ) but fewer such interactions than in scenario 2 ( in which the two groups merge head - on ) . hmxbs form in 8 out of 30 runs and , as with scenarios 1 and 2 , none of the hmxbs are made up of the two most massive stars . we find a similar hmxb formation rate per stellar mass , @xmath205 . sample trajectories from one of the simulations for scenario 3 are shown in figure [ fig:11 ] . in these two scenarios , we again set two groups of five stars each on a collision course . the difference is that the orbital plane of one star group is tilted , so that the two stellar disks have a mutual inclination @xmath53 . we set the inclination at @xmath206 ( nearly co - rotating ) for scenario 4a , and @xmath207 ( nearly counter - rotating ) for scenario 4b . the groups are initially placed at a separation of two to three times their sizes , and set in motion at the same speeds as for the inspiral case ( scenario 3 ) . we find that @xmath208 , @xmath209 , and @xmath210 for scenario 4a . in scenario 4b , we find @xmath211 , @xmath212 , and @xmath213 . in @xmath214 of the runs for both scenarios , the two most massive stars form the most compact binary . stellar binaries end up with somewhat closer separations in the nearly counter - rotating case , due to the fact that the net angular momentum of the merged star group is smaller . indeed , we find a total of four hmxbc across all the @xmath206 simulations , and eight in a same number of @xmath207 simulations . for the same reason , we find a larger fraction of hmxb candidates per stellar mass simulated in the nearly counter - rotating case ( @xmath215 ) compared to the nearly co - rotating case ( @xmath216 ) . the overall formation rate of hmxb candidates is lower for both cases than the cases in which all the stellar orbits were nearly coplanar ( scenarios 1 , 2 and 3 ) , plausibly due to the additional degree of freedom in the stellar orbits . still , the value of @xmath138 is within a factor of a few for all of our simulations . sample trajectories from runs for scenarios 4a and 4b are depicted in figure [ fig:12 ] and figure [ fig:13 ] , respectively .	we run two sets of calculations : one in which stars form in small groups of five in nearly keplerian initial orbits , and another in which two such groups collide ( an expected outcome of mergers of host protogalaxies ) . we find that hmxbs form at a rate of one per in newly born stars , and that they emit with a power of in the kev band per solar mass per year of star formation .	the first astrophysical objects shaped the cosmic environment by reionizing and heating the intergalactic medium ( igm ) . in particular , x - rays are very efficient at heating the igm before it became completely ionized , an effect that can be measured through the redshifted 21 cm line of neutral hydrogen . high - mass x - ray binaries ( hmxbs ) , known to be prolific x - ray sources in star - forming galaxies at lower redshifts , are prime candidates for driving the thermal evolution of the igm at redshifts . despite their importance , the formation efficiency of hmxbs from the first stellar populations is not well understood as such , their collective x - ray emission and the subsequent imprint on the 21 cm signature are usually evaluated using free parameters . using-body simulations , we estimate the rate of hmxb formation via mutual gravitational interactions of nascent , small groups of the first stars ( population iii stars ) . we run two sets of calculations : one in which stars form in small groups of five in nearly keplerian initial orbits , and another in which two such groups collide ( an expected outcome of mergers of host protogalaxies ) . we find that hmxbs form at a rate of one per in newly born stars , and that they emit with a power of in the kev band per solar mass per year of star formation . this value is a factor larger than what is observed in star forming galaxies at lower redshifts ; the x - ray production from early hmxbs would have been even more copious , if they also formed _ in situ _ or via migration in protostellar disks . combining our results with earlier studies suggests that early hmxbs were highly effective at heating the igm and leaving a strong 21 cm signature . we discuss broader implications of our results , such as the rate of long gamma - ray bursts from population iii stars and the direct collapse channel for massive black hole formation . [ firstpage ] cosmology : theory early universe cosmology : dark ages , reionization , first stars stars : population iii intergalactic medium x - rays : binaries stars : kinematics and dynamics
astro-ph9710182	i	what has been presented in the preceding sections represents the first comprehensive hi study of the _ isolated _ , edge - on , infrared - bright galaxy ngc 3044 . the ir brightness is partly due to proximity , since the massive star formation rate is a factor of 5 lower than that of m 82 ( 5.1 ) . the hi distribution in the galaxy was modelled using all available data points , i.e. hi spectral lines were modelled over the entire galaxy in order to determine the best global density and velocity distributions in the galaxy as well as the best geometrical parameters . the resulting quantities are listed in table [ tab : model ] . a gaussian ring density distribution in the plane was found to be the best fit overall . an important result derived from the model is that the galaxy has a moderately thick hi disk with a gaussian vertical scale height of @xmath138 . this is consistent with previous observations which have also revealed a thick radio continuum disk . ngc 3044 shows a very asymmetric distribution optically , in hi , and in the radio continuum , with excellent agreement between the radio continuum and hi column density distributions ( see [ subsec : asymmetry ] ) . in hi , the asymmetry is particularly apparent from the global profile , which shows a lopsided double - horned structure . otherwise , however , derived global parameters tell the story of a normal sbc galaxy . the column density map confirms the asymmetric distribution of the hi in the galaxy . this is clear from the 27@xmath16 offset of the hi peak to the east of the radio continuum peak . the major - axis rotation curve also shows the asymmetry in that the approaching side of the galaxy appears to be `` truncated '' before reaching terminal velocity while the receding side stays flat for about @xmath139 after reaching terminal velocity . while the galaxy is asymmetric in hi , it also shows an extremely straight disk ( i.e. , no obvious disk warp ) . it is not clear what could have caused the asymmetry in this apparently isolated galaxy . it is likely , though , that the mechanism would have to act on the galaxy after its formation , since it is difficult to explain how the galaxy would form asymmetrically in the first place . it is noted here that asymmetries in isolated galaxies are not uncommon , which indicates that a common mechanism such as past minor mergers may be responsible for it . if this is the case for ngc 3044 , the merger likely took place over 10@xmath105 yrs ago . the velocity channel maps reveal a host of high - latitude hi extensions . we have catalogued a total of 12 such features that appear in at least two consecutive velocity channels . these features are distributed uniformly across the disk of the galaxy and above and below the plane . we derive a lower limit for mass flow to the halo of @xmath109 , = @xmath110 . there is also some correlation between high - latitude hi features and high - latitude radio continuum features ( @xmath140 5.2.3 ) . four of the high latitude features exhibit the signature of an expanding shell and have radii of order a few kpc . based on the assumption that the shells were formed by supernovae energy input , the required input energies are in the range 4 @xmath19 10@xmath115 to 7 @xmath19 10@xmath114 @xmath141 ergs . these values vary somewhat depending on the adopted model , but it is clear , even from the kinetic energies of expansion of the individual supershells , that large numbers ( e.g. up to tens of thousands ) of correlated supernovae are required to form them . this means that ngc 3044 would have to harbour a number of such superclusters ( such as the cluster r136 in the 30 doradus region in the lmc ) , something which is not supported by the current massive star formation rate . the alternative model , that of impacting external clouds , is even less attractive as a formation mechanism for the supershells because of the absence of companions , the fact that the supershells are young ( of order the age of a typical ob association ) and because hi clouds which are massive enough to produce these shells would have been easily detected in our data . we suggest that the supershells are indeed formed internally , but that some additional energy - boost ( e.g. through magnetic fields ) is needed to explain their large energies . the authors wish to thank the staff at the vla for obtaining the hi data and kathy perrett for coordinating the remote observation . thanks also go to denise giguere and jayanne english for many useful discussions on various data reduction techniques . we have also made used of the nasa / ipac extragalactic database ( ned ) . this work is supported by the national research council of canada . bosma , a. 1981 , , 86 , 1825 bottinelli , l. , gouguenheim , l. , paturel , g. , and de vaucouleurs , g. 1984 , , 56 , 381 brinks , e. , and bajaja , e. 1986 , , 169 , 14 burton , w. b. , and gordon , m. a. 1978 , , 63 , 7 chevalier , r. a. 1974 , , 188 , 501 condon , j. j. 1992 , , 30 , 575 frei , b. d. , henriksen , r. n. , irwin , j. a. , and king , d. l. 1997 , , submitted van gorkom , j. h. , and ekers , r. d. 1994 , in synthesis imaging in radio astronomy , ed . perley , r. a. , schwab , f. r. , and bridle , a. h. , ( astronomical society of the pacific conference series , vol . 6 ) , 341 haynes , m. p. , and giovanelli , r. 1984 , , 89 , 758 heiles , c. , 1979 , , 229 , 533 heiles , c. , 1984 , , 55 , 585 heiles , c. , 1990 , , 354 , 483 hernquist , l. , and mihos , j. c. 1995 , , 448 , 41 irwin , j. a. , and seaquist , e. r. 1990 , , 353 , 469 irwin , j. a. , and seaquist , e. r. 1991 , , 371 , 111 irwin , j. a. 1994 , , 429 , 618 kamaya , h. , mineshige , s. , shibata , k. , matsumoto , r. 1996 , , 458 , l25 van der kruit , p. c. 1981 , , 99 , 298 krumm , n. , and salpeter , e. e. 1980 , , 85 , 1312 lequeux , j. 1983 , , 125 , 394 lockman , f. j. 1984 , , 283 , 90 mihos , j. c. , and hernquist , l. 1994 , , 425 , l13 mac low , m .- m . , mccray , r. , & norman . m. l. 1989 , , 337 , 141 norman , c. a. , and ikeuchi , s. 1989 , , 345 , 372 perley , r. a. 1994 , in very large array observational status summary , published by the national radio astronomy observatory quinn , p. j. , hernquist , l. and fullagar , d. p. 1993 , , 403 , 74 rand , r. j. , and van der hulst , j. m. 1993 , , 105 , 2098 rand , r. j. 1994 , , 285 , 833 rand , r. j. , and stone , j. m. 1996 , , 111 , 190 richter , o. -g . , and sancisi , r. 1994 , , 290 , l9 rix , h .- w . , and zaritsky , d. 1995 , , 447 , 82 roberts , m. s. , and haynes , m. p. 1994 , , 32 , 115 snchez - saavedra , m. l. , battaner , e. , and florido , e. 1990 , , 246 , 458 shapiro , p. r. , and field , g. b. 1976 , , 205 , 762 soifer , b. t. , sanders , d. b. , madore , b. f. , neugebauer , g. , and danielson , g. e. 1987 , , 320 , 238 soifer , b. t. , boehmer , l. , neugebauer , and sanders , d. b 1989 , , 98 , 766 solomon , p. m. , and sage , l. j. 1988 , , 334 , 613 sorathia , b. 1994 , m.sc . thesis : a radio continuum survey of edge - on spiral galaxies , queen s university spitzer , l. , jr . 1978 , in physical processes in the interstellar medium , ( new york : john wiley and sons ) staveley - smith , l. , and davies , r. d. 1988 , , 231 , 833 tenorio - tagle , g. , and bodenheimer , p. 1988 , , 26 , 145 tully , r. b. 1988 , nearby galaxies catalog , ( cambridge university press ) vader , j. p. , and chaboyer , b. 1995 , , 445 , 691 de vaucouleurs , g. , de vaucouleurs , a. , corwin , h. g. , jr . , buta , r. j. , paturel , g. , and fouqu@xmath142 , p. 1991 , third reference catalogue of bright galaxies , ( new york : springer - verlag)(rc3 ) visser , h. c. d. 1980 , , 88 , 159 zaritsky d. 1995 , , 448 , l17	the first detailed vla mapping of the neutral hydrogen distribution in the _ isolated _ , edge - on spiral galaxy ngc 3044 is presented . we have modelled the hi spectra in order to derive its global density and velocity distributions . an hi scale height of 420 pc is thus found . the approaching ( northwest ) side of the galaxy is 14% less massive than the receding side and its rotation curve does not reach terminal velocity . the rotation curve of the receding ( southeast ) side however resembles that of a normal galaxy . twelve high - latitude features were catalogued , of which four exhibit the signature of an expanding shell . we have investigated the possibility that the supershells could have been produced by external impacting clouds , but conclude that this scenario is unattractive , given the age of the shells , the isolation of the galaxy , and the lack of any observed features sufficiently massive to form the shells in the vicinity of the galaxy . since the implied input energies from supernovae are extremely high ( e.g. from , corresponding to 400 74,000 supernovae ) , we suggest that some additional energy ( e.g. from magnetic fields ) may be needed to produce the observed supershells .	the first detailed vla mapping of the neutral hydrogen distribution in the _ isolated _ , edge - on spiral galaxy ngc 3044 is presented . physical parameters such as , , etc . determined for this galaxy are typical for galaxies of its morphological class ( sbc ) . we have modelled the hi spectra in order to derive its global density and velocity distributions . an hi scale height of 420 pc is thus found . this can be compared to the impressive radio continuum halo , previously found to extend to above the midplane . the present study reveals an asymmetry in the hi distribution as well as numerous high - latitude hi structures at various galactocentric radii . the approaching ( northwest ) side of the galaxy is 14% less massive than the receding side and its rotation curve does not reach terminal velocity . the rotation curve of the receding ( southeast ) side however resembles that of a normal galaxy . twelve high - latitude features were catalogued , of which four exhibit the signature of an expanding shell . there is some correlation of these features with features observed in the radio continuum from independent data . the most massive shell ( feature 10 ) extends out to 6 kpc above the galactic disk . the radii and masses of these shells range from and , respectively . we have investigated the possibility that the supershells could have been produced by external impacting clouds , but conclude that this scenario is unattractive , given the age of the shells , the isolation of the galaxy , and the lack of any observed features sufficiently massive to form the shells in the vicinity of the galaxy . therefore , an internal origin is suggested . since the implied input energies from supernovae are extremely high ( e.g. from , corresponding to 400 74,000 supernovae ) , we suggest that some additional energy ( e.g. from magnetic fields ) may be needed to produce the observed supershells .
1510.03486	i	in the hierarchical structure formation paradigm , merging is among the dominant mechanisms by which galaxy clusters grow . therefore , detailed studies of merging clusters shed light on the growth of cosmological structures . apart from cosmological interests , merging clusters are also receiving growing attention as astrophysical laboratories , providing rare and invaluable opportunities to investigate the origin of cosmic rays ( e.g. , volk et al . 1996 ; berezinsky et al . 1997 ; feretti et al . 2012 ; brunetti & jones 2014 ) , generation of nonthermal energy in plasma ( e.g. , cassano & brunetti 2005 ) , properties of dark matter ( kahlhoefer et al . 2014 ) , star formation and galaxy evolution driven by merging ( e.g. , stroe et al . 2015 ) , etc .. radio relic " clusters are a subclass of merging clusters that exhibit elongated diffuse radio emissions at the periphery of the systems . these radio relics " often occur in pairs and in most cases stretch nearly perpendicular to observed merger axes . now many observational and theoretical studies support the premise that the relics trace the locations of shock fronts induced by cluster mergers ( e.g. , ensslin et al . detailed analysis of the radio relic data enables us to put independent constraints on the key parameters necessary in our reconstruction of the merging scenario , including the direction of the merger , the projection angle between the merger axis and the plane of the sky , the shock velocity , and the time since the impact ( e.g. , ng et al . 2015 ) . because of the limited observational time window set by both development and deterioration of mature shocks , only a few tens of radio relic clusters are known to date ( e.g. , van weeren et al . 2010 ; 2012 ; 2013 , govoni et al . 2001 , brunetti et al . 2008 ) . the cluster rx j0603.3 + 4214 is a remarkable cluster at @xmath0 whose radio relic stretches over @xmath1 mpc ( figure [ fig_tb ] ) . because of its peculiar morphology composed of the western short ( @xmath7 mpc ) thick band ( brush " ) and a long ( @xmath8 mpc ) thin stripe ( handle " ) , rx j0603.3 + 4214 is nicknamed the toothbrush cluster " ( van weeren et al . together with the much fainter relic found near the southern cluster edge , this asymmetric and remarkably linear feature implies that perhaps the merger might have been complex , involving more than two subclusters ( bruggen et al . this unusual radio morphology is different from that of the ciza j2242.8 + 5301 cluster ( van weeren et al . 2010 ) , possessing a similarly giant but more symmetric sausage "- like radio relic . the toothbrush " relic of rx j0603.3 + 4214 was discovered with the westerbork synthesis radio telescope ( wsrt ) and the giant metrewave radio telescope ( gmrt ) by van weeren et al . for the toothbrush " relic , van weeren et al . ( 2012 ) detected a spectral index gradient from the front ( northern edge ) of the toothbrush " relic toward the back ( southern edge ) . the frontal part of this relic is highly polarized ( @xmath9% at 4.9 ghz ) , which indicates that the merger might be happening nearly in the plane of the sky ( ensslin et al . 1998 ) . van weeren et al . ( 2012 ) also found a north - south elongated x - ray morphology at the location of the cluster based on archival rosat data . bruggen et al . ( 2012 ) carried out a numerical simulation of rx j0603.3 + 4214 by modeling the cluster with two large ( @xmath10 ) and one small ( @xmath11 ) halos and demonstrated that the simulation can generate a giant relic with a similar morphology . ogrean et al . ( 2013 ) studied the cluster with _ xmm - newton _ data , which reveal two distinct x - ray peaks . at both northern and southern edges ( near the relics ) of the cluster , they detected density discontinuities indicating the presence of potential shocks . itahana et al . ( 2015 ) constrained the mach number to be @xmath12 based on this density discontinuity , which is consistent with their independent measurement @xmath13 from the temperature jump obtained from _ suzaku _ data . however , these x - ray - based mach numbers are lower than what the radio data imply ( @xmath14 ; van weeren et al . correlations between the cluster galaxy star formation and the merger environment were studied by stroe et al . ( 2014 ; 2015 ) . despite a number of studies mentioned above on this remarkable system , no reliable mass estimation of the system has been carried out , and little is known about the spatial distribution of its mass and member galaxies . the cluster s underlying mass distribution is one of the critical pieces of information in order to infer the merger scenario responsible for the radio relic morphology ( e.g. , ng et al . 2015 ; dawson 2013 ) . hence , in this paper , as part of our merging cluster collaboration ( mc@xmath15 ) project , we present detailed weak - lensing analysis of rx j0603.3 + 4214 with subaru / suprime cam and _ hubble space telescope ( hst ) _ imaging data . because of the low galactic latitude @xmath2 of the system , some observational challenges , including severe extinction and stellar obscuration , are present . however , in the weak - lensing study of ciza j2242.8 + 5301 ( jee et al . 2015 ) , we already demonstrated that a successful weak - lensing study is still possible when high - resolution imaging observations are carefully planned and analyzed with the state - of - the - art technique . we launched the mc@xmath15 project to study a large sample of merging clusters with a coherent approach . our immediate goals for the current paper are ( 1 ) to map the underlying mass distribution and compare the result with the galaxies and x - ray emission and ( 2 ) to quantify the matter content of the system . these mass properties are among the critical parameters necessary to constrain the merging scenario of the system leading to such an unusual morphology in radio emission . our long - term goals of the mc@xmath15 project include detailed studies of dark matter properties through systematic investigation of the large sample and careful numerical simulations . we present our study as follows . in [ section_observation ] we describe our data and reduction . in [ section_wl ] we review the basic lensing theory of weak lensing and our technique . we present our mass reconstruction results in [ section_mass_reconstruction ] , discussing the source selection , mass distribution , and mass estimation . discussions of our results will follow in [ section_discussion ] before we conclude in [ section_conclusion ] . we assume a flat @xmath16 cold dark matter ( @xmath16cdm ) cosmology with @xmath17 , @xmath18 , and @xmath19 . at the redshift of rx j0603.3 + 4214 , @xmath20 , the plate scale is @xmath21 ( @xmath22 ) . the @xmath23 value that we adopt here as a halo mass is a spherical mass within @xmath24 , inside which the mean density becomes 200 times the critical density of the universe at the redshift of the cluster .	the galaxy cluster rx j0603.3 + 4214 at is one of the rarest clusters boasting an extremely large ( mpc ) radio relic . because of the remarkable morphology of the relic , the cluster is nicknamed the toothbrush cluster " . although the cluster s underlying mass distribution is one of the critical pieces of information needed to reconstruct the merger scenario responsible for the puzzling radio relic morphology , its proximity to the galactic plane has imposed significant observational challenges . we present a high - resolution weak - lensing study of the cluster with subaru / suprime cam and _ hubble space telescope _ imaging data .	the galaxy cluster rx j0603.3 + 4214 at is one of the rarest clusters boasting an extremely large ( mpc ) radio relic . because of the remarkable morphology of the relic , the cluster is nicknamed the toothbrush cluster " . although the cluster s underlying mass distribution is one of the critical pieces of information needed to reconstruct the merger scenario responsible for the puzzling radio relic morphology , its proximity to the galactic plane has imposed significant observational challenges . we present a high - resolution weak - lensing study of the cluster with subaru / suprime cam and _ hubble space telescope _ imaging data . our mass reconstruction reveals that the cluster is composed of complicated dark matter substructures closely tracing the galaxy distribution , in contrast , however , with the relatively simple binary x - ray morphology . nevertheless , we find that the cluster mass is still dominated by the two most massive clumps aligned north - south with a:1 mass ratio ( and for the northern and southern clumps , respectively ) . the southern mass peak is offset toward the south with respect to the corresponding x - ray peak , which has a bullet "- like morphology pointing south . comparison of the current weak - lensing result with the x - ray , galaxy , and radio relic suggests that perhaps the dominant mechanism responsible for the observed relic may be a high - speed collision of the two most massive subclusters , although the peculiarity of the morphology necessitates involvement of additional subclusters . careful numerical simulations should follow in order to obtain more complete understanding of the merger scenario utilizing all existing observations .
1510.03486	c	because we make an approximation that the mass of rx j0603.3 + 4214 is dominated by the two halos associated with the two x - ray peaks , it is useful to examine the validity of the assumption by an independent method . we employ aperture mass densitometry , which allows us to estimate total projected masses within a given aperture without any assumption on the number of halos and their profiles . we will compare this projected mass from aperture mass densitometry with the results from our two halo model by projecting the 3d nfw mass distribution onto the plane of sky . aperture mass densitometry ( fahlman et al . 1994 ; clowe et al . 2000 ) is computed through the following equation : @xmath161 where @xmath162 is the azimuthal average of tangential shears , @xmath163 is the aperture radius , and @xmath164 and @xmath165 are the inner and the outer radii of the annulus , respectively . @xmath166 provides a density contrast of the region inside @xmath167 with respect to the control annulus @xmath168 . we choose @xmath169 and @xmath170 for the control annulus . projecting our nfw fitting results , we estimate the density within this annulus to be @xmath171 . because the control annulus radius is large and the density there is small , the impact of adopting the nfw results on the aperture mass densitometry becomes negligible . the input to the equation of the densitometry is a shear @xmath172 , not a reduced shear @xmath173 . therefore , we need to determine the aperture mass using the relation @xmath174 . we find that the density converges after three or four iterations . the resulting aperture mass is displayed in figure [ fig_aperture_mass ] . also displayed in figure [ fig_aperture_mass ] is the aperture mass estimated by projecting the nfw fitting results above . in order to obtain this estimation , we first projected each nfw profile along the line - of - sight direction and summed the two - halo results . the aperture mass density masses are within the 1@xmath135 upper limits of the nfw masses , which may hint at the possibility that the two - halo representation may not be a perfect choice . however , because the 1@xmath135 error bars from both methods overlap , we argue that the difference should not be considered statistically significant . range of statistical uncertainties . the two results are consistent with each other , and we conclude that no significant mass is excluded by modeling rx j0603.3 + 4214 with two nfw profiles . , width=321 ] a diffuse hot plasma within a cluster is well traced by x - ray emission because the emissivity is in general proportional to the plasma density squared ( given the same plasma temperature ) . since the plasma consists of charged particles subject to ram pressure , the x - ray morphology of merging clusters reveals critical information that can not be probed otherwise . here we compare the x - ray morphology of rx j0603.3 + 4214 with the weak - lensing mass distribution and discuss the implication in the context of the merging scenario responsible for the observed toothbrush " radio relic . rx j0603.3 + 4214 has been observed with both _ xmm - newton _ and _ chandra_. the 82 ks _ xmm - newton _ data were studied by ogrean et al . ( 2013 ) , and van weeren et al . ( 2015 ) analyzed the 237 ks @xmath175 data ( obsid : 15171 , 15172 , and 15323 ) . ogrean et al . ( 2013 ) showed that the intracluster medium of rx j0603.3 + 4214 is dominated by two components , which is confirmed by the chandra study of van weeren et al . in addition , a few new remarkable features are revealed in the high - resolution chandra observation . first , a density jump indicating a shock is detected in the southern edge . this location coincides with the southern edge of the radio halo . across the shock a temperature jump is also found . the two mach numbers derived by both density and temperature jumps are consistent ( @xmath176 and @xmath177 , respectively ) . second , the high - resolution chandra data show that the southern x - ray component has a triangular bullet "- like shape . according to their further temperature analysis , the density jump at the southern edge of the bullet indicates a cold front . the comparison of these x - ray findings with the current weak - lensing results provides a consistent picture regarding the merging scenario of rx j0603.3 + 4214 . we display the comparison in figure [ fig_massoverxray ] , where we illustrate our hypothesized merger axis . despite the somewhat complex galaxy distribution , the x - ray and weak - lensing results suggest that the dominant merger may be approximated by a north - south collision of two components . we find offsets between x - ray and mass peaks . the northern mass peak is offset toward the northwest with respect to the corresponding x - ray peak by @xmath178 whereas the the southern mass peak is offset to the south by @xmath6 . similar to the bullet cluster , the direction of the offsets favors a scenario wherein the two components passed through each other and are still separating . our weak - lensing analysis shows that the northern component is more massive than the southern component by a factor of three . we believe that this mass inequality is consistent with the offset inequality , since the less massive southern component should experience more ram pressure . another supporting evidence for this mass inequality is the location of the toothbrush "- relic . the simulation by van weeren et al . ( 2011 ) predicts that two radio - relics are generated in a two - body encounter and travel along the merger axis with the larger relic associated with the more massive halo . the observation that the @xmath179mpc toothbrush "- relic is located near the northern edge of rx j0603.3 + 4214 is consistent with the northern component being more massive in our weak - lensing analysis . the same trend has been observed in our weak - lensing study of the sausage " cluster ciza j2242.8 + 5301 ( jee et al . 2015 ) and zwcl0008.8 + 5215 ( n. golovich et al . in prep . the study of zwcl0008.8 + 5215 shows that the x - ray emission of the less massive system appears as a clear bullet "- like feature , similar to the bullet " cluster ( clowe et al . 2006 ) , whereas the larger radio relic is found near the edge of the more massive system . the exact physical mechanism is unknown as to the question why does the larger radio relic occur on the higher mass side ? " on the other hand , x - ray observations show that distinct shock features such as density discontinuities , temperature jumps , etc . , are more prominent on the lower - mass side unlike radio relics , which are also believed to trace the location of shock fronts . some may argue that the above mass inequality argument may be challenged by the x - ray luminosity of the southern peak being much higher . needless to say , in general x - ray luminosity is positively correlated with mass . however , in active merging clusters , it is natural to suspect that this correlation between mass and x - ray luminosity can temporarily be altered for many reasons ( e.g. , randall et al . 2002 ; skillman et al . 2013 ) . for example , a cool core ( associated with a lower - mass component ) can survive a head - on collision , whereas a hot core ( associated with a higher - mass component ) can severely be disrupted after a core pass - through . the deep chandra x - ray image of the el gordo " cluster at @xmath180 is a good example . the weak - lensing study shows that the system is composed of two halos with a 2:1 mass ratio , whereas only the cool core associated with the less massive system ( south ) is clearly visible in x - ray ( jee et al . 2014 ; menanteau et al . the hydrodynamical simulation by molnar & broadhurst ( 2015 ) reproduces this asymmetry in brightness between the two x - ray peaks of el gordo " . another example is zwcl0008.8 + 5215 ( n. golovich et al . in prep . ) at @xmath181 mentioned above . by and large the zwcl0008.8 + 5215 cluster is also a binary merging system with one of two x - ray peaks resembling a bullet "- like shape . the bullet " component is brighter than the other component in x - ray , whereas the mass associated with the bullet " is found to be approximately a factor of five smaller . one of the goals of the mc@xmath15 collaboration is to enable quantitative comparisons between observations and simulations for interesting merging clusters . rx j0603.3 + 4214 is a remarkably interesting system and should be followed up by careful numerical analysis . here we discuss some of the puzzling issues of rx j0603.3 + 4214 that future hydrodynamic simulations should address . first , we believe that the extremely high icm temperature of rx j0603.3 + 4214 deserves our attention . van weeren et al . ( 2015 ) constrain the temperatures of the northern and southern x - ray peaks to be @xmath182 kev and @xmath183 kev , respectively . these temperatures are substantially higher than what our weak - lensing masses imply _ if _ we neglect nonthermal energy injection into icm . with the assumption of the isothermal @xmath56 model with @xmath184 kpc and @xmath185 , the weak - lensing masses are converted to @xmath186 kev and @xmath187 kev for the northern and southern halos , respectively . even when we treat rx j0603.3 + 4214 as a single halo with @xmath188 ( i.e. , the sum of the two halos using the values in table 3 ) , the implied temperature ( again with an isothermal @xmath56 model ) becomes only @xmath189 kev , significantly smaller than the global x - ray temperature @xmath190 kev . although this discrepancy may not be considered surprising , given the common understanding that x - ray temperatures of merging clusters are biased indicators of the cluster masses , the level of discrepancy that we witness in rx j0603.3 + 4214 is somewhat extreme when we consider results for other clusters in the literature . for example , even for the bullet "- cluster , clowe et al . ( 2006 ) find that the temperature levels of the system are consistent with their weak - lensing masses . second , although we argue that the two subclusters of rx j0603.3 + 4214 played the dominant roles in creating the current observational features such as the galaxy - mass - relic alignments , the offsets between mass / galaxy and x - ray peaks , etc . , the long asymmetrically linear feature of the toothbrush " relic strongly suggests that a smaller third component might have been involved , as suggested by bruggen et al . ( 2012 ) . however , the mass , path , and timing of this third component are unclear . it is our hope that the weak - lensing substructures revealed in the current study will aid us to reduce the volume of the parameter space that future simulations should explore . third , the implied collision velocity is very high . the high polarization fraction @xmath191% ( van weeren et al . 2012 ) suggests that the merger may be happening in the plane of the sky . according to our redshift analysis ( w. dawson et al . in prep ) , the line - of - sight velocity difference between the northern and southern subclusters is @xmath192 km s@xmath37 . even with the polarization prior @xmath193% , the implied collision velocity is as high as @xmath33500 km s@xmath37 , which exceeds the escape velocity of the rx j0603.3 + 4214 system and thus is hard to accommodate within the current @xmath16cdm paradigm . more detailed discussions will appear in w. dawson et al . ( in prep ) .	our mass reconstruction reveals that the cluster is composed of complicated dark matter substructures closely tracing the galaxy distribution , in contrast , however , with the relatively simple binary x - ray morphology . the southern mass peak is offset toward the south with respect to the corresponding x - ray peak , which has a bullet "- like morphology pointing south .	the galaxy cluster rx j0603.3 + 4214 at is one of the rarest clusters boasting an extremely large ( mpc ) radio relic . because of the remarkable morphology of the relic , the cluster is nicknamed the toothbrush cluster " . although the cluster s underlying mass distribution is one of the critical pieces of information needed to reconstruct the merger scenario responsible for the puzzling radio relic morphology , its proximity to the galactic plane has imposed significant observational challenges . we present a high - resolution weak - lensing study of the cluster with subaru / suprime cam and _ hubble space telescope _ imaging data . our mass reconstruction reveals that the cluster is composed of complicated dark matter substructures closely tracing the galaxy distribution , in contrast , however , with the relatively simple binary x - ray morphology . nevertheless , we find that the cluster mass is still dominated by the two most massive clumps aligned north - south with a:1 mass ratio ( and for the northern and southern clumps , respectively ) . the southern mass peak is offset toward the south with respect to the corresponding x - ray peak , which has a bullet "- like morphology pointing south . comparison of the current weak - lensing result with the x - ray , galaxy , and radio relic suggests that perhaps the dominant mechanism responsible for the observed relic may be a high - speed collision of the two most massive subclusters , although the peculiarity of the morphology necessitates involvement of additional subclusters . careful numerical simulations should follow in order to obtain more complete understanding of the merger scenario utilizing all existing observations .
1510.03486	c	we have presented detailed weak - lensing studies of the toothbrush " relic cluster rx j0603.3 + 4214 with _ hst _ and subaru imaging . together with the sausage " relic cluster ciza j2242.8 + 5301 , rx j0603.3 + 4214 has been known for its giant ( @xmath1mpc ) radio relic , whose peculiar morphology gives the system the nickname toothbrush " . our weak - lensing study provides a high - resolution map of the cluster dark matter , which helps us to constrain the merging scenario responsible for the toothbrush " relic . we find that although the cluster substructure is more complicated than that of ciza j2242.8 + 5301 , the global mass distribution can be approximated by a bimodal distribution with a 3:1 mass ratio . the northern mass clump encloses @xmath194 and coincides with the galaxy luminosity peak . the southern mass component contains @xmath195 and is also in an excellent spatial agreement with the southern luminosity peak . however , the southern mass peak is @xmath6 offset with respect to the southern x - ray peak . the two mass peaks , two x - ray peaks , two luminosity peaks , and the brush " of the toothbrush " relic are collinear , which strongly suggests that the violent merger responsible for the giant radio relic was mainly derived by the collision of the two components . however , the long handle " relic extended northeast from the brush " indicates that a third ( or more ) component might have been involved in this merger . it is interesting that our weak - lensing mass reconstruction reveals a mass clump southwest of the northern mass peak . we find that a galaxy luminosity peak coincides with this mass overdensity . nevertheless , we have yet to carry out detailed simulations in order to quantify the possibility that this observed component might have been involved in the creation of the peculiar radio - relic morphology . the shape of the southern x - ray peak is triangular and is reminiscent of the bullet " in the bullet cluster . a recent chandra study reveals a shock south of this feature traced by both density and temperature jumps . together with the aforementioned offset , these x - ray features show that we may be witnessing a post - collision , where the two cluster components are separating from each other . the high x - ray temperatures of rx j0603.3 + 4214 are discrepant with what the weak - lensing masses imply . we attribute the large differences to substantial departure from the hydrostatic equilibrium . these severe discrepancies support the consensus that using x - ray temperatures is an unreliable way to infer cluster masses in violent merging systems . galaxy clusters are receiving growing attention as cosmic particle accelerators . although every merger case is special and deserves scrutiny , radio - relic clusters are particularly useful thanks to strong constraints on both the geometry and stage of the mergers , which enables us to reduce the parameter search space by substantial factors . of course , careful numerical simulations should follow up the observations in order to come up with quantitatively coherent scenarios , wherein all the observed features fit together within the observational uncertainties . + support for program number hst - 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03 ( baltimore : stsci ) van weeren , r. j. , rttgering , h. j. a. , brggen , m. , & hoeft , m. 2010 , science , 330 , 347 van weeren , r. j. , brggen , m. , rttgering , h. j. a. , & hoeft , m. 2011 , , 418 , 230 van weeren , r. j. , rttgering , h. j. a. , intema , h. t. , et al . 2012 , , 546 , a124 van weeren , r. j. , fogarty , k. , jones , c. , et al . 2013 , , 769 , 101 vlk , h. j. , aharonian , f. a. , & breitschwerdt , d. 1996 , , 75 , 279 von der linden , a. , allen , m. t. , applegate , d. e. , et al . 2014 , , 439 , 2 yagi , m. , kashikawa , n. , sekiguchi , m. , et al . 2002 , , 123 , 66 zwart , j. t. l. , barker , r. w. , biddulph , p. , et al . 2008 , , 391 , 1545	comparison of the current weak - lensing result with the x - ray , galaxy , and radio relic suggests that perhaps the dominant mechanism responsible for the observed relic may be a high - speed collision of the two most massive subclusters , although the peculiarity of the morphology necessitates involvement of additional subclusters . careful numerical simulations should follow in order to obtain more complete understanding of the merger scenario utilizing all existing observations .	the galaxy cluster rx j0603.3 + 4214 at is one of the rarest clusters boasting an extremely large ( mpc ) radio relic . because of the remarkable morphology of the relic , the cluster is nicknamed the toothbrush cluster " . although the cluster s underlying mass distribution is one of the critical pieces of information needed to reconstruct the merger scenario responsible for the puzzling radio relic morphology , its proximity to the galactic plane has imposed significant observational challenges . we present a high - resolution weak - lensing study of the cluster with subaru / suprime cam and _ hubble space telescope _ imaging data . our mass reconstruction reveals that the cluster is composed of complicated dark matter substructures closely tracing the galaxy distribution , in contrast , however , with the relatively simple binary x - ray morphology . nevertheless , we find that the cluster mass is still dominated by the two most massive clumps aligned north - south with a:1 mass ratio ( and for the northern and southern clumps , respectively ) . the southern mass peak is offset toward the south with respect to the corresponding x - ray peak , which has a bullet "- like morphology pointing south . comparison of the current weak - lensing result with the x - ray , galaxy , and radio relic suggests that perhaps the dominant mechanism responsible for the observed relic may be a high - speed collision of the two most massive subclusters , although the peculiarity of the morphology necessitates involvement of additional subclusters . careful numerical simulations should follow in order to obtain more complete understanding of the merger scenario utilizing all existing observations .
astro-ph0408460	i	the study of the emission characteristics from rotation powered pulsars has been a subject of long standing interest . our knowledge of the fundamental properties ( e.g. , mass , spin , and magnetic field ) of the underlying neutron star stems from detailed spectral and timing investigations . to facilitate an understanding of the mechanism by which the loss of rotational energy is converted into high energy radiation , many observational and theoretical studies have sought to determine the relationship between the x - ray luminosity , @xmath0 , and the rate of rotational energy loss or spin down power , @xmath1 . indeed , a correlation of the form @xmath9 was found in einstein data by seward & wang ( 1988 ) . subsequent studies using a larger sample of pulsars led to a relation of the form , @xmath10 based on rosat data ( see becker & trmper 1997 ) and @xmath11 based on asca data ( see saito 1998 ) . recently , a reanalysis of 39 pulsars based on data obtained from several x - ray satellites by possenti et al . ( 2002 ) led to an intermediate relation @xmath12 , similar to that of seward & wang ( 1988 ) . while the deduced existence of a correlation between @xmath0 and @xmath1 suggests that the observed x - rays are produced by a process which taps the rotational energy of the neutron star , a detailed description of the mechanism remains elusive . this is , in part , a result of the fact that the data from different satellites are obtained in different energy ranges . the results can be affected , for example , by interstellar absorption especially for those pulsars studied in the soft x - ray regime of rosat ( 0.1- 2.4 kev ) . in addition , the total x - ray luminosity is composed of contributions from both the pulsed and non - pulsed components , and these components are likely to reflect physical conditions in diverse spatial environments . the x - rays radiated by rotation powered pulsars could include contributions from 5 distinct components with different origins : + 1 . non - thermal non - pulsed diffuse radiation can be emitted from a pulsar wind nebula . the radiation will be discussed in 2 , and we suggest that this emission component is the major contribution to the non - pulsed x - ray radiation in the asca observations of pulsars . non - thermal non - pulsed radiation from the pulsar magnetosphere could be important as suggested by becker et al . ( 2004 ) if the angular resolution of x - ray detector is sufficiently high to separate this contribution from that of the nebula . although such a component may be present in the asca data that we use , due to its low angular resolution , it is not likely to dominate the contribution from the pulsar wind nebula . for example , tennant et al . ( 2001 ) have found a non - thermal non - pulsed component from the crab pulsar by using the high - resolution camera of the chandra x - ray observatory . they estimate that the x - ray luminosity of this component is @xmath13 , whereas , the non - thermal non - pulsed x - ray luminosity from the crab nebula detected by asca ( saito et al . 1997a ) is @xmath14 . the specific origin of the non - thermal non - pulsed component , not associated with the nebula , is not clear . although it contaminates the emission of the nebula , it is small . provided that this contribution is small for all the pulsars we study in this investigation , this component should not affect our analysis . the non - thermal pulsed radiation component is generally believed to be produced from the pulsar magnetosphere . this follows from the fact that the motion of charged particles within the light cylinder is strongly affected by the magnetic field , and the radiation of charged particles in the open field lines should be pulsed . this component could be produced in the vicinity of the polar cap as a result of inverse compton scattering of higher order generation pairs of particles on soft photons emitted by the neutron star ( zhang & harding 2000 ) or in the outer magnetosphere as a result of synchrotron radiation of downward cascades from the outer gap electron / positron particles ( cheng & zhang 1999 ) . the thermal non - pulsed radiation from the pulsar surface can contribute to the soft x - ray bands , typically , characterized by @xmath15 kev ( cheng & zhang 1999 ) . in this paper , we have used the asca data on pulsars so this component will not contribute to the 2 - 10 kev asca energy band . the thermal pulsed radiation from the pulsar surface likely originates in a polar cap on the neutron star surface and can contribute to the hard x - ray band ( @xmath16 kev ) . in analyzing the pulsed emission from pulsars , we follow the model of cheng & zhang ( 1999 ) where the thermal pulsed x - ray emission is included in their model prediction . thus , the x - ray emission observed from pulsars in the asca sample primarily consists of contributions from components 1 , 3 , and 5 . we have assumed that component 2 is not important and component 4 does not significantly contribute to the 2 - 10 kev energy band . on the other hand , becker & trmper(1997 ) have used rosat data and obtained a linear relation between the x - ray luminosity consisting of components 2 and 3 and spin - down power . in the present paper , we concentrate on the x - ray properties in the energy band of asca ( 2 - 10 kev ) . the x - rays , then , consists of a thermal component from the polar cap , a non - thermal pulsed component from the magnetosphere and a non - thermal , non - pulsed emission from the nebula . that is , we have explicitly assumed that the pulsar magnetosphere and the pulsar wind nebula are primarily responsible for the pulsed and non - thermal non - pulsed component respectively . since the pulsed and non - pulsed emission have different origins , the relationship between the total x - ray luminosity and spin down power is not expected , in general , to be represented by a single power law . in fact , the non - thermal pulsed and non - pulsed emission components are distinguished by different spectral signatures and conversion efficiencies . to determine their relative importance and their relationship to the spin down power , we have reexamined the pulsar data obtained in the 2 - 10 kev energy band of the asca satellite , focusing on separating the non - pulsed and pulsed emission data . in the next section , we provide a simplified description of the emission from a pulsar wind nebula , based upon earlier work by chevalier ( 2000 ) , where the relativistic pulsar wind interacts with the interstellar medium . in 3 , the x - ray properties of the pulsed and non - pulsed components are collected and the relation between their luminosities with spin down power and photon spectral index are determined . with these results in hand , the pulsar wind nebula model is used to explain the occurrence of the tail - like emission morphology in geminga and psr b 1757 - 24 in 4 . finally , we summarize and conclude in the last section .	the relation for the pulsed component , on the other hand , is consistent with a magnetospheric emission model . such wind nebulae can contribute to the non - thermal symmetric emission morphology ( point - like ) and elongated emission morphology ( tail - like ) from sources similar to geminga and psr b1757 - 24 .	the general properties of the non - thermal non - pulsed x - ray emission of rotation powered pulsars are investigated in the context of a pulsar wind nebula model . an examination of the observed x - ray emission from a sample of 23 pulsars in the energy range between 2 - 10 kev reveals that the relation of x - ray luminosity , , to the pulsar spin down power , , is steeper for the non - pulsed component than for the pulsed component . specifically , for the non - pulsed component , whereas for the pulsed component . the former relation is consistent with emission from a pulsar wind nebula model in which where is the power law index of the electron energy distribution . the relation for the pulsed component , on the other hand , is consistent with a magnetospheric emission model . in addition , the photon spectral index , , was found to be correlated to the conversion efficiency of spin down power to non - pulsed x - ray emission with greater efficiencies for than for . such a relation is naturally understood within the framework of a pulsar wind nebula model with the former relation corresponding to the emission of x - rays in the fast cooling regime and the latter relation corresponding to emission in the slow cooling regime . the x - ray properties of pulsar wind nebulae are sensitive to the physical conditions ( e.g. , the density and magnetic field ) of the interstellar medium and can lead to important differences between the x - ray emission characteristics ( luminosity , photon spectral index and emission morphology ) of pulsars in various environments . such wind nebulae can contribute to the non - thermal symmetric emission morphology ( point - like ) and elongated emission morphology ( tail - like ) from sources similar to geminga and psr b1757 - 24 . # 1 # 1#2#1 # 2
astro-ph0408460	i	the non - thermal non - pulsed x - ray emission of rotation powered pulsars has been investigated in the context of emission from a pulsar wind nebula . we have confirmed that this emission can significantly contribute to the total x - ray emission , thereby , increasing the x - ray emission above that produced in the pulsar magnetosphere . a reexamination of asca data for pulsars separated into the non - pulsed and pulsed emission components indicates that their non - thermal components , individually , are correlated with spin down power . in particular , the dependence is steeper for the non - pulsed component with @xmath173 as compared to the relation , @xmath174 for the pulsed component . our results are similar to that discovered by becker & trmper(1997 ) , who found that the non - thermal ( pulsed and non - pulsed ) component satisfied the linear relation , @xmath175 , based on rosat data in 0.1 - 2.4 kev range . in this paper , we have used the asca data in the 2 - 10 kev range , which includes the contribution of the additional thermal pulsed component with @xmath176 kev from the polar cap ( cheng & zhang 1999 ) . in this case , the dependence of the x - ray luminosity on spin down power is steeper . because of the poor angular resolution of asca , the possible contribution of non - thermal non - pulsed emission from the magnetosphere is mixed in with that of the nebula . within the framework of a one zone model for the pulsar wind developed by chevalier ( 2000 ) , the power law relation between the non - pulsed luminosity and spin down power provides an important diagnostic for the electron energy distribution in the shock resulting from the interaction of the relativistic wind with the interstellar medium . specifically , @xmath177 where @xmath5 is the power law index of the electron energy distribution , suggesting that the index characterizing these pulsars is relatively high , @xmath178 . the observational results also show that the conversion efficiency of spin down power to x - ray luminosity is a function of spin down power varying from @xmath119 to 0.1 . the efficiencies in the lower ( upper ) end of the range can be understood in terms of emission in the slow ( fast ) cooling regime where the x - ray frequency is less ( greater ) than the electron synchrotron cooling frequency . the spectra from pulsar wind nebulae are distinctly non - thermal , described by a photon power law index , @xmath179 or @xmath180 for the fast or slow cooling regime respectively . this implies a correlation between the photon index and efficiency of conversion of spin down power to non - pulsed x - ray luminosity with steeper photon power law indices associated with higher conversion efficiencies . although the photon power law indices inferred from the pulsars studied have large uncertainties , there are hints from the observed data that such a correlation exists . we note that the low values of @xmath6 and @xmath181 inferred for the extended emission observed from geminga and b 1757 - 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1926 & 0.065 & @xmath192 & 5.0 & 7.0@xmath193 & 1.6@xmath194 & 1.9@xmath195 & 1.4@xmath196 & 2,3 + b0531 + 21 & 0.033 & 4.2@xmath197 & 2.0 & 4.5@xmath198 & 1.1@xmath199 & 6.8@xmath200 & 1.0@xmath201 & 4 + b0833 - 45 & 0.089 & 1.25@xmath197 & 0.3 & 6.9@xmath193 & 1.9@xmath195 & 1.5@xmath202 & 1.8@xmath203 & 4,5,6 + b0633 + 17 & 0.237 & 1.1@xmath204 & 0.16 & 3.2@xmath196 & 8.2@xmath205 & 4.6@xmath205 & 3.6@xmath206 & 7,8 + b1706 - 44 & 0.1025 & 9.3@xmath204 & 1.82 & 3.4@xmath193 & 6.8@xmath202 & 4.1@xmath202 & 2.7@xmath207 & 4 + b1509 - 58 & 0.150 & 1.54@xmath208 & 4.3 & 1.8@xmath199 & 4.0@xmath194 & 1.3@xmath194 & 2.7@xmath194 & 4 + b1951 + 32 & 0.0395 & 5.8@xmath209 & 2.5 & 3.7@xmath193 & 6.2@xmath195 & 6.2@xmath202 & 5.6@xmath203 & 4 + b1046 - 58 & 0.124 & 9.6@xmath204 & 2.98 & 2.0@xmath193 & 9.5@xmath202 & 5.5@xmath202 & 4.5@xmath202 & 4,9 + b1929 + 10 & 0.227 & 1.16@xmath209 & 0.17 & 3.9@xmath203 & 1.54@xmath210 & 5.6@xmath205 & 9.8@xmath205 & 10 + b0656 + 14 & 0.385 & 5.5@xmath204 & 0.76 & 3.8@xmath196 & 1.7@xmath211 & 1.0@xmath211 & 7.0@xmath212 & 4 + b0540 - 69 & 0.05 & 4.8@xmath197 & 49.4 & 1.5@xmath198 & 8.3@xmath213 & 1.3@xmath213 & 7.0@xmath193 & 11 + b0950 + 08 & 0.253 & 2.3@xmath214 & 0.12 & 5.6@xmath207 & 4.6@xmath205 & 1.6@xmath205 & 3.0@xmath206 & 10 + b1610 - 50 & 0.232 & 4.93@xmath197 & 7.26 & 1.6@xmath193 & 9.6@xmath195 & 3.0@xmath195 & 6.6@xmath203 & 9 + b1055 - 52 & 0.197 & 5.83@xmath209 & 1.53 & 3.0@xmath196 & 2.7@xmath210 & 2.0@xmath210 & 7.0@xmath206 & 12 + b1853 + 01 & 0.267 & 5.4@xmath197 & 2.02 & 8.0@xmath215 & 1.4@xmath195 & 1.4@xmath202 & 1.3@xmath203 & 4 + j2229 + 6114 & 0.0516 & 7.8@xmath204 & 3.0 & 2.2@xmath201 & 1.7@xmath195 & 4.0@xmath202 & 1.3@xmath203 & 13 + b0537 - 69 & 0.016 & 5.13@xmath204 & 47 & 4.8@xmath198 & 2@xmath213 & 1.7@xmath200 & 1.8@xmath193 & 14,15 + j1846 - 0258 & 0.32 & @xmath216 & 19 & 1@xmath199 & 1@xmath213 & 4@xmath194 & 1@xmath213 & 16 + b1937 + 21 & 0.00156 & 1.05@xmath217 & 3.6 & 1.1@xmath193 & 5.7@xmath202 & 2.5@xmath202 & 3.2@xmath207 & 17 + j2124 - 3358 & 0.005 & 1.08@xmath217 & 0.25 & 3.5@xmath203 & 4.8@xmath205 & 1.6@xmath205 & 3.2@xmath206 & 18 + b1821 - 24 & 0.003 & 1.6@xmath218 & 5.1 & 2.2@xmath193 & 6.5@xmath195 & 9.4@xmath202 & 5.5@xmath195 & 19 + j0437 - 47 & 0.0058 & 2.0@xmath217 & 0.18 & 4.2@xmath203 & 1.3@xmath210 & 4.0@xmath205 & 9.0@xmath206 & 4 + l c c c c c l psr & @xmath1 & @xmath219 & @xmath220 & @xmath221 & @xmath222 & reference + b1823 - 13 & 2.8@xmath213 & @xmath223 & @xmath224 & @xmath225 & @xmath226 & 1 + j0537 - 6910 & 4.8@xmath227 & @xmath228 & @xmath229 & @xmath230 & @xmath231 & 2 + b0540 - 69 & 1.5@xmath227 & 0.01 & 0.05 & @xmath232 & @xmath233 & 3 + b1509 - 58 & 1.8@xmath199 & @xmath234 & @xmath235 & @xmath236 & @xmath237 & 4 + j0218 + 4232 & 2.5@xmath200 & 4.8@xmath238 & 2@xmath239 & 0.61@xmath240 & @xmath241 & 5 + j0631 + 1036 & 5.4@xmath194 & @xmath242 & @xmath243 & 2.3@xmath244 & @xmath245 & 6 + j1811 - 1926 & @xmath246 & 3@xmath238 & @xmath247 & 1.65@xmath248 & @xmath249 & 7 + b0531 + 21 & 4.5@xmath227 & 1.6@xmath250 & 0.03 & 1.6@xmath251 & 2.1@xmath252 & 8 + b0833 - 45 & @xmath253 & 2@xmath254 & 3@xmath239 & 1.5@xmath255 & 1.67@xmath256 & 9 + b0633 + 17 & 3.2@xmath194 & 1.4@xmath254 & 1.1@xmath257 & 1.0@xmath244 & 1.6@xmath251 & 10,11 + b1055 - 52 & 3@xmath194 & 7@xmath254 & 2@xmath257 & 1.5@xmath255 & 1.9@xmath251 & 12 + b1937 + 21 & 1.1@xmath213 & 2@xmath238 & @xmath258 & 1.71@xmath259 & 0.8@xmath260 & 13 + b1821 - 24 & 2.2@xmath213 & 5@xmath238 & 3@xmath261 & 1.2@xmath244 & @xmath262 & 14 + j2229 + 6114 & 2.2@xmath199 & 2@xmath254 & @xmath80 & 1.51@xmath263 & 1.6@xmath251 & 15 + j1105 - 6107 & 2.5@xmath213 & 6@xmath238 & 1.6@xmath261 & 1.8@xmath264 & 2.2@xmath264 & 16 + b1706 - 44 & 3.4@xmath213 & 1.4@xmath238 & @xmath80 & 1.9@xmath260 & 1.7@xmath244 & 17 + b1757 - 24 & 2.6@xmath213 & @xmath163 & @xmath80 & 1.6@xmath265 & 1.0@xmath260 & 18 + j0205 + 6449 & 2.6@xmath199 & @xmath119 & @xmath266 & 1.1@xmath264 & 1.9@xmath251 & 19 + b1929 + 10 & 3.9@xmath195 & 3@xmath238 & @xmath267 & 1.79@xmath268 & & 20 + b0656 + 14 & 3.8@xmath194 & 3@xmath238 & 2@xmath239 & 1.5@xmath269 & & 21 + j2021 + 3651 & @xmath270 & 3@xmath238 & @xmath243 & 1.5@xmath255 & 1.7@xmath255 & 22 + j1747 - 2958 & 2.5@xmath213 & @xmath163 & 0.02 & 1.8@xmath269 & 2.1@xmath269 & 23 + b1853 + 01 & @xmath271 & @xmath242 & 1.5@xmath261 & @xmath272 & @xmath273 & 24 + l c c c c c c c c l psr & @xmath1 & @xmath274 & @xmath275 & @xmath276 & @xmath277 & @xmath18 & @xmath71 & @xmath278 & reference + & & cm & cm & & & @xmath74 & km s@xmath63 & cm & + b1823 - 13 & 2.8@xmath213 & 6@xmath279 & & 3@xmath195 & 2@xmath195 & 1 & & 7@xmath280 & 1 + j0537 - 6910 & 4.8@xmath227 & 4@xmath279 & & 1.8@xmath213 & 3@xmath213 & & & & 2 + b0540 - 69 & 1.5@xmath227 & 3@xmath279 & & 7@xmath213 & 4@xmath213 & & & & 3 + j1811 - 1926 & @xmath246 & 2@xmath279 & & 1.4@xmath194 & @xmath66 & & & & 4 + b0531 + 21 & 4.5@xmath227 & 4@xmath279 & 3@xmath281 & @xmath282 & 4@xmath213 & 10 & 123 & @xmath283 & 5 + b0833 - 45 & @xmath253 & @xmath284 & 2@xmath281 & 1.8@xmath195 & @xmath285 & 1 & 65 & 8@xmath286 & 6 + b0633 + 17 & 3.2@xmath194 & 5@xmath286 & 4@xmath287 & 4@xmath205 & @xmath288 & 1 & 120 & 4@xmath279 & 7 + j2229 + 6114 & 2.2@xmath199 & 4@xmath279 & & 1.3@xmath195 & 3@xmath195 & & & & 8 + j1105 - 6107 & 2.5@xmath213 & 4@xmath286 & & 4@xmath195 & 3@xmath195 & & & & 9 + b1706 - 44 & 3.4@xmath213 & 3@xmath279 & & 3@xmath202 & 4@xmath202 & & & & 10 + b1757 - 24 & 2.6@xmath213 & 4@xmath286 & @xmath289 & 3@xmath202 & 5@xmath202 & 1 & @xmath290 & @xmath283 & 11 + j0205 + 6449 & 2.6@xmath199 & @xmath284 & & 3@xmath194 & 3@xmath194 & & & & 12 + b1957 + 20 & @xmath291 & 5@xmath286 & 4@xmath286 & 1.6@xmath211 & @xmath292 & 1 & 220 & 4@xmath279 & 13 + j2021 + 3651 & @xmath270 & 8@xmath279 & & 3@xmath203 & 2@xmath195 & & & & 14 + j1747 - 2958 & 2.5@xmath213 & 3@xmath286 & 7@xmath287 & 5@xmath194 & @xmath66 & 0.3 & 600 & 2@xmath280 & 15,16 + j1124 - 5916 & @xmath282 & @xmath284 & 2@xmath279 & 4@xmath196 & @xmath66 & 0.5 & 450 & 6@xmath279 & 17 + b1853 + 01 & @xmath271 & 10@xmath293 & 3@xmath286 & 6@xmath202 & 4@xmath202 & 5 & 375 & @xmath283 & 18 + j1930 + 1852 & 2@xmath213 & @xmath284 & & @xmath285 & 7@xmath202 & 1 & & @xmath283 & 19 + b0453 - 685 & @xmath282 & 6@xmath279 & & 6@xmath194 & 2@xmath194 & 0.4 & & @xmath294 & 20 + j0538 + 2817 & 4@xmath194 & 8@xmath286 & 3@xmath287 & 6@xmath211 & 5@xmath211 & 0.5 & 385 & & 21 +	the general properties of the non - thermal non - pulsed x - ray emission of rotation powered pulsars are investigated in the context of a pulsar wind nebula model . in addition , the photon spectral index , , was found to be correlated to the conversion efficiency of spin down power to non - pulsed x - ray emission with greater efficiencies for than for . such a relation # 1 # 1#2#1 # 2	the general properties of the non - thermal non - pulsed x - ray emission of rotation powered pulsars are investigated in the context of a pulsar wind nebula model . an examination of the observed x - ray emission from a sample of 23 pulsars in the energy range between 2 - 10 kev reveals that the relation of x - ray luminosity , , to the pulsar spin down power , , is steeper for the non - pulsed component than for the pulsed component . specifically , for the non - pulsed component , whereas for the pulsed component . the former relation is consistent with emission from a pulsar wind nebula model in which where is the power law index of the electron energy distribution . the relation for the pulsed component , on the other hand , is consistent with a magnetospheric emission model . in addition , the photon spectral index , , was found to be correlated to the conversion efficiency of spin down power to non - pulsed x - ray emission with greater efficiencies for than for . such a relation is naturally understood within the framework of a pulsar wind nebula model with the former relation corresponding to the emission of x - rays in the fast cooling regime and the latter relation corresponding to emission in the slow cooling regime . the x - ray properties of pulsar wind nebulae are sensitive to the physical conditions ( e.g. , the density and magnetic field ) of the interstellar medium and can lead to important differences between the x - ray emission characteristics ( luminosity , photon spectral index and emission morphology ) of pulsars in various environments . such wind nebulae can contribute to the non - thermal symmetric emission morphology ( point - like ) and elongated emission morphology ( tail - like ) from sources similar to geminga and psr b1757 - 24 . # 1 # 1#2#1 # 2
1512.01473	c	as mentioned in the introduction , the glg model is a very flexible family of distributions which is used to describe asymmetrically distributed data in many real applications . in this paper , we considered estimators which are simultaneously robust and efficient for aft models , when the errors follow a glg distribution and the data may contain censored observations . the estimation procedures have two main components : an initial highly robust but not necessarily efficient estimator and a final efficient estimator which starts with the initial one . we first considered the case , where no covariables are present and , in this case , we proposed an initial estimator that minimizes a @xmath0 scale of the differences between theoretical an empirical quantiles of order smaller than @xmath346 , where @xmath115 is a trimming fraction . the final estimator is a one step weighted likelihood estimator , where the weights penalizing the outliers are derived from the initial estimator . for the case , where covariables are present , the proposed estimators were derived in three steps . in a first step we used a regression mm - estimator as proposed in @xcite to obtain initial slope estimates and to compute the corresponding residuals . in a second step , we computed an initial estimator of the glg parameters by applying the procedure for the no covariables case to these residuals . in the third step we obtained a final estimator of all the parameters using a one step truncated ml starting with the initial estimator . we provided asymptotic results and extensive monte carlo results showing that the final estimators are highly efficient and maintain the same robustness level as the initial ones .	the generalized log - gamma ( glg ) model is a very flexible family of distributions to analyze datasets in many different areas of science and technology . in this paper , we propose estimators which are simultaneously highly robust and highly efficient for the parameters of a glg distribution in the presence of censoring .	the generalized log - gamma ( glg ) model is a very flexible family of distributions to analyze datasets in many different areas of science and technology . in this paper , we propose estimators which are simultaneously highly robust and highly efficient for the parameters of a glg distribution in the presence of censoring . we also introduced estimators with the same properties for accelerated failure time models with censored observations and error distribution belonging to the glg family . we prove that the proposed estimators are asymptotically fully efficient and examine the maximum mean square error using monte carlo simulations . the simulations confirm that the proposed estimators are highly robust and highly efficient for finite sample size . finally , we illustrate the good behavior of the proposed estimators with two real datasets . * keywords * : censored data . quantile distance estimates . estimators . truncated maximum likelihood estimators . weighted likelihood estimators .
astro-ph0509028	r	as mentioned above , our strategy in testing our jet models against the data was to allow the maximum number of model parameters to vary freely during the fit . this allowed us to explore which parameters had the greatest influence on the fits . several parameters settled on fairly similar values for both sources and all observations , which suggests that those parameters could be fixed in future applications of this model . we will discuss this possibility explicitly below . fits with a complicated model can easily lead to false , local minima ; therefore , we began the fitting procedure outside of isis , using unfolded data sets in order to find a set of starting parameters that would yield reduced @xmath34 . for this paper we have chosen to explore only models with rough equipartition between the magnetic and radiating particle pressures ( @xmath35 ) . this assumption is obviously not applicable for poynting flux dominated jets ; however , we consider the very weak acceleration required by observations to be an indication that magnetic domination ( which would generally imply stronger acceleration mechanisms ) is not likely to be very extreme . we use the results of @xcite as a rough guide for consistency , and only consider models with reflection fractions @xmath19 for jet nozzle radii @xmath36 to be ` successful ' fits . for smaller values of the radii , slightly lower values for the reflection fraction would be expected . in all cases the jet models seemed to naturally prefer reflection fractions @xmath37 , so in practice this restriction on reflection fraction was not an issue . [ gx339_comps ] shows a representative model for gx 339@xmath04 in order to illustrate the contribution from the various components which go into the later figures showing actual fits . the radio through ir originates exclusively from self - absorbed synchrotron radiation beginning at @xmath38 and continuing outwards along the jet . optically thin synchrotron emission from the accelerated power - law tail of leptons also contributes to the soft x - ray band . the base of the jet radiates direct synchrotron photons , giving a slight hump in the optical / uv , which are then included as seed photons ( along with disk photons ) for upscattering by the emitting electrons into an ssc / ec `` hump '' in the hard x - rays . the shape of this hump is rounded , due to the quasi - thermal particle distribution assumed in the base , and thus reduces the need for a large fraction of disk - reflected photons to contribute to the spectral break / hardening at @xmath1810 kev . the possibility that there are two correlated continuum components in the x - ray band is supported by our ensemble of simultaneous radio / x - ray observations of cyg x-1 , whose spectra are very well - described by exponentially cut - off , broken power - laws ( @xcite ) . in these models , the soft x - ray spectral slope is very well - correlated with the break of the hard x - ray spectral slope , and the hard x - rays are very well - correlated with the radio @xcite . the multicolor blackbody included in the jet model is also shown in the soft x - ray band . the photons from this component are included in the inverse compton upscattering within the jet . the statistical fits are shown in figs . [ gx339_all ] & [ cyg_all ] , for gx 339@xmath04 and cyg x-1 , respectively . each figure encompasses nine panels , with each row representing a single simultaneous radio and x - ray observation of the source . the first column shows the entire radio through x - ray jet model + soft disk + reflection fit , and the second column focuses just on the x - ray band . the last column shows the thermal compton corona model from eqpair for comparison . values for all fitted parameters are given in tables 24 . the results presented in figs . [ gx339_all ] & [ cyg_all ] and tables [ tab : mffjeti ] , [ tab : mffjetii ] , & [ tab : eqpair ] immediately demonstrate three important results of this work . * * jet models describe the data equally well as pure compton corona models , even when employing the broad - band and high statistics of the rxte data . * there has been question in the literature ( e.g. , @xcite ) as to whether or not jet models can adequately describe the spectral cutoff of the hard tail . while pure synchrotron jet models may not be able to describe the steep cutoff present in some ( but not all ) observations , jets can also successfully account for this hard tail cutoff via comptonization . the primary differences between ` traditional ' coronal models and jet coronal models are that the coronal temperatures are higher in the latter ( @xmath39k vs. @xmath40k ) , and the disk seed photons in jet models are significantly augmented if not dominated by synchrotron seed photons . * * the jet models , similar to the compton corona models , describe a complex continuum with curvature specifically , a hardening above 10kev . * again , the hardening often predominantly ascribed to a ` reflection hump ' is being somewhat subsumed by continuum emission . in the jet model , the steeper slope of the soft x - rays is primarily due to synchrotron emission from the jet , rather than being influenced by the disk photons , while the hardening is due to the ssc / ec component . reflection is present , but represents a smaller fraction of the total hard flux compared to the corona models . note that the fits discussed here are in contrast to earlier incarnations of the jet model which attempted to describe observations solely via the synchrotron component ( e.g. , the studies of xte j1118 + 480 ; @xcite ) . for xte j1118 + 480 , the lack of any discernible break or hardening near 10kev in the continuum spectrum was used to argue for the lack of a reflection component @xcite , which would be consistent with a jet spectrum dominated by the synchrotron component @xcite . in contrast , the fact that all of the xrb spectra shown here harden above 10kev argue for the importance of both the synchrotron and ssc / ec components of the jet spectrum for these fits , as well as the presence of reflection . * * although the jet and compton coronal models describe the x - ray data equally well , only the jet model naturally describes both the amplitude and slope of the radio data without the need for additional free parameters . * it is important to note that the radio spectrum , as well as the bulk of the 3 - 200kev x - ray continuum ( i.e. , the overall amplitude and continuum curvature ) , are almost solely driven by the parameters of the jet : energy input to the jet ( @xmath41 ) , radius of the jet base ( @xmath10 ) , electron temperature at the jet base ( @xmath42 ) , slope of the power - law component of the electron energy distribution ( @xmath43 ) , the equipartition parameter ( @xmath44 ) , and the location of the particle acceleration zone in the jet ( @xmath45 ) . if one begins instead with a corona model and attempts to fit the amplitude and slope of the radio data by assuming a relationship to an extant jet model , this will in essence require the addition of many more parameters to describe just two physical quantities . we argue that nothing can be gained by this approach , which is why we have chosen to study the test case of full coupling . from our set of jet model fits that successfully describe the gx 339@xmath04 and cyg x-1 data , we can now explore the implications of the fitted parameters . cyg x-1 and gx 339@xmath04 are somewhat different sources while in their hard states . the luminosity of gx 339@xmath04 varies much more than that of cyg x-1 . this is apparent in the fitted values for the power normalization @xmath12 and output power @xmath46 shown in the first two columns of table [ tab : mffjeti ] . both sources show best fit @xmath12 in the range of @xmath47 @xmath48 , but gx 339@xmath04 shows significantly more variation in this parameter . differences can also be seen in the other main parameters , for instance on average gx 339@xmath04 favors slightly larger values of the nozzle radius , @xmath10 . this reflects the slightly higher ratio of x - ray to radio flux observed in cyg x-1 . a smaller scale jet base , for a given jet power , increases the jet compactness which in turn gives a slightly higher flux ( with the x - ray flux being more sensitive to this effect ) and pushes all jet emission to slightly higher frequencies . other fit parameters also indicate differences between these two sources ; however , the parameters surprisingly fall roughly in the same range given the _ a priori _ possibility for much greater parameter variations . note that the lowest luminosity gx 339@xmath04 observation , obs i d 40108 - 02 - 03 , has poor enough statistics that the following general statements about the gx 339@xmath04 fits will be based mostly on the brighter two observations . for example , both the electron temperature , @xmath42 , and the location of the start of the acceleration zone , @xmath38 , tend to be larger in gx 339@xmath04 than in cyg x-1 . ( although we were unable to find adequate error bars for the latter parameter , the trend of finding larger values in gx 339@xmath04 was persistent . ) additionally , we note that the electron power law index , @xmath43 , shows more variation in gx 339@xmath04 than in cyg x-1 . although the range in electron temperatures at the base of the jets falls within a range of a factor of @xmath49 for both sources , one of the criticisms of this class of models has been that @xmath50-@xmath51 k is not as `` natural '' a value as the @xmath52kev typically used in thermal comptonization models . the jet model electron temperature , however , is comparable to or slightly greater than the value typically derived for radiatively inefficient accretion flows ( e.g. , * ? ? ? if some fraction of the accreting plasma is fed directly into the jets , and also perhaps heated slightly in the process , we would expect such a temperature . on the other hand , several jet model free parameters seemed to settle quite quickly into similar values for both cyg x-1 and gx 339@xmath04 : the equipartition factor @xmath44 , the fraction of accelerated particles @xmath53 , and the ratio of nozzle length to radius @xmath54 . physically , this suggests that these jets either are close to equipartition , or we have found a local minima of solutions for @xmath55 , and we may find other reasonable minima for @xmath56 , e.g. , magnetically - dominated jets . we plan to explore this particular question in a future work . it seems reasonable , however , to freeze the fraction of accelerated particles at @xmath57 and make the statement that reasonably efficient acceleration is expected to occur in hard state bhc jets . similarly , a compact base / corona region with scale height similar to the radius seems a reasonable assumption . it is likely that this parameter can also be frozen in future applications of the jet model . we listed the two `` acceleration parameters '' , the shock speed relative to the bulk plasma flow , @xmath58 , and the ratio of the scattering mean free path to the gyroradius , @xmath59 , as separate fit parameters . however , as discussed in the appendix , these parameters are perhaps not physically meaningful as currently defined , since we are no longer as convinced that the acceleration process is diffusive fermi acceleration . these parameters enter into the acceleration rate as the factor @xmath60 , which is compared to the sum of the cooling rates from synchrotron and inverse compton radiation , and adiabatic expansion in order to calculate the local maximum accelerated lepton energy . therefore , this parameter can be loosely interpreted as a factor related to the efficiency of the acceleration process and merged for future fits into a single parameter . for the current fits , the individual components were left free to vary , with mixed results . for cyg x-1 , @xmath61 , suggesting a meaningful range of fits . however , for gx 339@xmath04 , @xmath62 ranges over two orders of magnitude , and we suspect that we did not fully explore parameter space meaningfully for this source . in future applications of the model , it is likely that we will combine these two parameters into a single parameter that will absorb our uncertainty about the acceleration process . while we list best fit values for the multicolor blackbody disk model parameters @xmath63 and @xmath64 , as well as the derived inner radius @xmath65 , it is important to keep in mind that because the data only extend down to a few kev , we can not meaningfully constrain this component from spectral fitting . as described in the appendix , the disk photons are not as important to the overall photon field as the locally produced synchrotron photons and thus can mainly be constrained by their direct spectral contribution . this contribution , although weak , is in fact required for a good fit , but it is not unique . @xcite have also fit some of the x - ray data presented here , and for similar reasons fixed the thermal disk parameters . on the other hand , for the disk emission plus comptonization models presented here ( as well as for those presented in @xcite ) , the temperature of the disk was tied to the temperature of the seed photons i.e . , the thermal photons were the _ only _ source of seed photons for comptonization . thus by virtue of these imposed restrictions , much more stringent formal limits for the disk components were attainable . the main result to take away about the accretion flow modeling is that our fits are generally consistent with a sub - eddington accretion disk with temperatures somewhat less than 1 kev . similarly , the total power entering into the jets is roughly consistent with being of the same order as the observed luminosity required in the disk to be consistent with the data . the presence of a weak disk component is necessary for a good fit , and thus disk photons will contribute to the inverse compton component from the jet . we do not , however , feel we can confidently make any statements about the disk geometry and thus the accretion rate at the inner radius assumedly feeding the jets . for both gx 339@xmath04 and cyg x-1 , the amount of reflection required by the jet models is roughly comparable to , although in general slightly lower than , that required by comptonization models . this trend can be understood by the fact that the jet base ssc / ec component dominates above 10kev , and to some extent subsumes the role played by the `` compton hump '' normally attributed to disk reflection . this effect of course brings up an interesting point : there is a clear degeneracy in how the spectral hardening above 10kev can be understood in terms of continuum models . the fact that the jet ssc / ec component has a similar appearance to the compton reflection hump does not preclude the presence of both . clearly , the fluorescent fe line implies that there must be a degree of reflection . what these results ( as well as the comptonization fits ; @xcite ) do suggest is that one can not uniquely determine a reflection fraction independently of the presumed continuum model .	the hard state of x - ray binaries ( xrbs ) is characterized by a power law spectrum in the x - ray band , and a flat / inverted radio / ir spectrum associated with occasionally imaged compact jets . are very similar to the derived plasma conditions at the jet footpoints . here we explore the question of whether the ` corona ' and ` jet base ' are in fact related , starting by testing the strongest premise that they are synonymous . the conditions at the jet base fix the conditions along the rest of the jet , thus creating a direct link between the x - ray and radio emission .	the hard state of x - ray binaries ( xrbs ) is characterized by a power law spectrum in the x - ray band , and a flat / inverted radio / ir spectrum associated with occasionally imaged compact jets . it has generally been thought that the hard x - rays result from compton upscattering of thermal accretion disk photons by a hot , coronal plasma whose properties are inferred via spectral fitting . interestingly , these properties especially those from certain magnetized corona models are very similar to the derived plasma conditions at the jet footpoints . here we explore the question of whether the ` corona ' and ` jet base ' are in fact related , starting by testing the strongest premise that they are synonymous . in such models , the radio through the soft x - rays are dominated by synchrotron emission , while the hard x - rays are dominated by inverse compton at the jet base with both disk and synchrotron photons acting as seed photons . the conditions at the jet base fix the conditions along the rest of the jet , thus creating a direct link between the x - ray and radio emission . we also add to this model a simple iron line and convolve the spectrum with neutral reflection . after forward - folding the predicted spectra through the detector response functions , we compare the results to simultaneous radio / x - ray data obtained from the hard states of the galactic xrbs gx 339 and cygnus x-1 . results from simple compton corona model fits are also presented for comparison . we demonstrate that the jet model fits are statistically as good as the single - component corona model x - ray fits , yet are also able to address the simultaneous radio data .
1108.3764	i	diphoton final states represent a very important testing ground for the standard model ( sm ) , for example they may be one of the main discovery channels for the higgs boson searches at the cern lhc . moreover , similar to the case of dileptons , the inclusive production of two - photon high mass resonance states at the lhc : @xmath2 is considered as a powerful , clean test of new physics ( np ) , would an excess of @xmath3 events be observed with respect to the prediction from the sm cross section . one np scenario of particular importance is the case of the spin-2 kaluza - klein ( kk ) graviton excitations predicted by the randall - sundrum ( rs ) model of gravity in one warped spatial extra dimension @xcite . this model suggests a rich phenomenology that includes the production of diphoton resonances , to be explored at collider energies , see , for example , refs . @xcite . the existence of such graviton excitations can be signalled by the occurrence of peaks in the invariant mass distribution of the photon pairs and , indeed , the lowest lying predicted diphoton peak has recently been searched for in experiments at the @xmath4 fermilab tevatron collider @xcite , and at the 7 tev @xmath5 lhc collider with time - integrated luminosity of the order of 40 @xmath6 @xcite . in these experiments , exclusion mass limits on the lightest rs resonance of the tev order have been set , and graviton mass scales larger than 1 tev will certainly be in the kinematical reach of lhc . assuming that a diphoton peak at an invariant mass value @xmath7 is observed , its association to a specific np scenario would be possible only if we are able to discard other competitor models , potential sources of the peak itself with same @xmath7 and same number of events . basically , for any nonstandard model one can define , on the basis of the foreseeable statistics and uncertainties , a _ discovery reach _ on the relevant heavy resonance @xmath8 as the upper limit of the range in @xmath7 where , in a specific domain of the model parameters called `` signature space '' , the peak is expected to give a signal observable over the sm prediction to a prescribed confidence level . instead , the _ identification reach _ on the model is the upper limit of the range in @xmath7 where it can be identified as the source of the peak , once discovered , or , equivalently , the other competitor models can be excluded for all values of their respective parameters . of course , for many models , identification should be possible only in a subdomain of their signature space . the determination of the spin of an observed resonance clearly represents an important selection among different classes of nonstandard interactions . in the case of the inclusive diphoton production ( [ proc ] ) , the tool to directly test the spin-2 of the rs graviton resonance or , equivalently , exclude the hypothesis of a spin-0 scalar particle exchange , would be provided by the distinctive angular distributions in the angle @xmath9 between the incident quark or gluon and the final photon in the diphoton center - of - mass frame . this is similar to dilepton production , the difference being that in this case the hypotheses of both the spin-0 and the spin-1 exchanges must simultaneously be excluded . the spin-2 test of the lowest - lying rs graviton in lepton - pair collider events , through the direct comparison of the angular distributions for the various spin hypotheses , was earlier discussed in several papers , see , e.g. , refs . @xcite , and experimental angular analysis were attempted at the tevatron in ref . a potential difficulty of the direct - fit angular analysis at the lhc is that generally , due to the symmetry of the proton - proton initial configuration , the determination on an event - by - event basis of the direction of the initial parton , hence of the sign of @xmath10 , is in principle not fully unambiguous , so that cuts in phase space must be applied in this regard . the spin-2 rs graviton analysis of lhc dilepton events proposed in ref . @xcite , makes use of a `` center - edge '' angular asymmetry @xmath0 where the above mentioned ambiguity should not be present @xcite . essentially , in this observable the dilepton events are weighted according to the @xmath10 differential distributions , and the asymmetry is defined between cross sections symmetrically integrated over `` center '' and `` edge '' angular intervals . recently , asymmetries conceptually analogous to @xmath0 , have been applied to heavy quantum states spin identification in refs . @xcite , and a comparison of the performances of different methods for heavy resonances identification has been presented in ref . angular analyses for different spin - mediated drell - yan processes have been applied to a variety of np models in ref . @xcite . here , we propose the application of @xmath11 to the angular analysis of the diphoton production process ( [ proc ] ) at the lhc . as remarked previously , the selection of the spin-2 rs graviton amounts in practice to exclude the hypothesis of a spin-0 particle exchange with same mass @xmath7 and producing the same number of diphoton events . ideally , one advantage of the diphoton channel over dileptons can be represented by the doubled statistics expected in the former case @xcite . also , the automatic exclusion of the spin-1 hypothesis @xcite , should in any case allow a simplification of the analysis from the phenomenological point of view . finally , the consideration of process ( [ proc ] ) , in addition to dilepton production , is needed for an exhaustive test of model @xcite . for our analysis we have used the calculations of the required differential cross sections to next - to - leading order ( nlo ) in qcd , and this is essential at a hadron collider as the theoretical uncertainties get reduced when higher order corrections are included . furthermore , as a result of new interactions in a np model , there will be additional subprocesses that contribute at leading order ( lo ) itself ( e.g. , @xmath12 in the rs model ) and hence the signal can receive enhanced contributions due to the nlo corrections . specifically , in sec . ii we review the definitions of the basic cross sections involved in the asymmetry @xmath0 ; sec . iii will be devoted to the relevant properties and the characteristic angular distributions for the rs graviton and for the competitor scalar particle exchanges in process ( [ proc ] ) , for which we will adopt the model recently proposed in ref.@xcite . in sec . iv we discuss the nlo qcd effects to the diphoton production rates and to the angular distributions , for both kinds of spin exchange . v contains an outline of the @xmath0-based angular analysis and the consequent numerical results for rs identification , in the lhc center - of - mass running configurations @xmath13 tev and @xmath14 tev . finally , sec . vi contains some conclusive remarks .	the high mass neutral quantum states envisaged by theories of physics beyond the standard model can at the hadron colliders reveal themselves through their decay into a pair of photons . once such a peak in the diphoton invariant mass distribution is discovered , the determination of its spin through the distinctive photon angular distributions is needed in order to identify the associated nonstandard dynamics . we here discuss the discrimination of the spin-2 randall - sundrum graviton excitation against the hypothesis of a spin-0 exchange giving the same number of events under the peak , by means of the angular analysis applied to resonant diphoton events expected to be observed at the lhc .	the high mass neutral quantum states envisaged by theories of physics beyond the standard model can at the hadron colliders reveal themselves through their decay into a pair of photons . once such a peak in the diphoton invariant mass distribution is discovered , the determination of its spin through the distinctive photon angular distributions is needed in order to identify the associated nonstandard dynamics . we here discuss the discrimination of the spin-2 randall - sundrum graviton excitation against the hypothesis of a spin-0 exchange giving the same number of events under the peak , by means of the angular analysis applied to resonant diphoton events expected to be observed at the lhc . the spin-0 hypothesis is modelled by an effective interaction of a high mass gauge singlet scalar particle interacting with the standard model fields . the basic observable of our analysis is the symmetrically integrated angular asymmetry , calculated for both graviton and scalar-channel exchanges to next - to - leading order in qcd . desy 11 - 139
astro-ph0301394	i	at visual wavelengths , the dusty bipolar `` homunculus '' ejecta structure around @xmath0 car is primarily a hollow reflection nebula ( see thackeray 1961 ; visvanathan 1967 ; meaburn 1987 ; hillier & allen 1992 ; hamann et al . 1994 ; etc . ) . therefore , by observing localized parts of the homunculus , _ we can indirectly see the star s spectrum from a range of directions in space _ potentially allowing us to reconstruct the shape of @xmath0 car s wind , which is expected to lack spherical symmetry . independent of the large - scale bipolar morphology , hints of non - sphericity have been noted by , e.g. , viotti et al . ( 1989 ) , hillier & allen ( 1992 ) , davidson et al . ( 1995 ) , davidson & humphreys ( 1997 ) , and zethson et al . indeed , hillier & allen ( 1992 ) found a difference between direct and reflected he i emission that originates in the stellar wind , and early space telescope imaging spectrograph ( _ hst_/stis ) observations showed that the reflected h@xmath1 profile depends on location within the homunculus . departures from spherical symmetry are obviously critical for theories of winds and instabilities in the most massive stars ( see lamers & cassinelli 1999 , and papers in wolf , stahl , & fullerton 1998 ) . asphericity in @xmath0 car s wind may also be critical for understanding its 5.5 year cycle ( damineli 1996 ) , its long term variability , and excitation of its ejecta . in addition to its classic status as a very massive unstable star , @xmath0 car is uniquely favorable for this problem because the dusty homunculus has a fairly definite three - dimensional structure ; each projected location on the nebula provides reflected light from a viewing direction whose stellar latitude is approximately known ( davidson et al . 2001 ; smith 2002 ) . we have obtained long - slit stis spectra optimized for studies of the reflected latitude - dependent effects . we find that some features do in fact depend on viewing direction . wind velocities are highest around the pole , as one might expect if stellar rotation reduces the effective gravity and escape velocity at the equator . dominant outflow velocities in the stellar wind are 400 to 600 km s@xmath2 , but some faster material ( @xmath31000 km s@xmath2 ) had been seen ( viotti et al . 1989 ; damineli et al . 1998 ) , and our data now show that these high velocities are polar . we also find a much less anticipated phenomenon : broad p cyg absorption components of h@xmath1 and h@xmath4 , usually weak in our direct view of @xmath0 car , _ are quite deep at higher ( not lower ) latitudes_. traditionally , a slow equatorial wind is supposed to be denser than the associated fast polar wind and the mass - loss rate may increase with decreasing @xmath5 ( friend & abbott 1986 ) ; some examples are b[e ] stars ( zickgraf et al . 1986 ) , wind - compressed disks or zones ( bjorkman & cassinelli 1993 ; ignace , cassinelli , & bjorkman 1996 ; owocki , cranmer , & blondin 1994 ) , and bistable winds ( lamers & pauldrach 1991 ) . our observations of @xmath0 car , however , suggest that its wind is densest near the poles despite higher velocities there . other interpretations are conceivable , but require detailed models of line transfer . if @xmath0 car s wind densities are highest near the poles as one might guess from the deeper hydrogen p cyg absorption , then this tends to support recent comments by owocki and others concerning the importance of non - radial forces and gravity darkening in line - driven winds of massive stars ( owocki , cranmer , & gayley 1996 ; owocki & gayley 1997 ; owocki , gayley , & cranmer 1998 ; maeder & meynet 2000 ; meader & desjacues 2001 ) . specifically , these studies predict that if a luminous star is rotating fast enough for gravity darkening to be important ( i.e. , at @xmath670% of the `` critical '' rotation speed ) , then stronger radiative flux at the hot poles will tend to drive a higher mass flux . glatzel ( 1998 ) and maeder ( 1999 ) have discussed modifications to the `` critical '' rotation rate near the eddington luminosity . we describe new stis observations in 2 below , hydrogen line profiles in 3 , and helium profiles in 4 . in 5 we discuss various likely implications of the observed wind geometry . then in 6 we examine older stis spectra and discuss temporal variability of the wind structure . finally , in 7 we mention consequences that a variable , bipolar wind may have for interpretations of @xmath0 car s 5.5-year spectroscopic cycle .	the homunculus reflection nebula around carinae provides a rare opportunity to observe the spectrum of a star from more than one direction . in the case of car , we present stis spectra of several positions in the homunculus , showing directly that car has an aspherical stellar wind . . the wind geometry and its variability have critical implications for understanding the 5.5 year cycle and long - term variability , but do not provide a clear alternative to the binary hypothesis for generating car s x - rays .	the homunculus reflection nebula around carinae provides a rare opportunity to observe the spectrum of a star from more than one direction . in the case of car , the nebula s geometry is known well enough to infer how line profiles vary with latitude . we present stis spectra of several positions in the homunculus , showing directly that car has an aspherical stellar wind . p cygni absorption in balmer lines depends on latitude , with relatively high velocities and strong absorption near the polar axis . stronger absorption at high latitudes is surprising , and it suggests _ higher mass flux toward the poles _ , perhaps resulting from radiative driving with equatorial gravity darkening on a rotating star . reflected profiles of he i lines are more puzzling , offering clues to the wind geometry and ionization structure . during car s high - excitation state in march 2000 , the wind was fast and dense at the poles , with higher ionization at low latitudes . older stis data obtained since 1998 reveal that this global stellar - wind geometry changes during car s 5.5 year cycle , and may suggest that this star s _ spectroscopic events are shell ejections_. whether or not a companion star triggers these outbursts remains ambiguous . the most dramatic changes in the wind occur at low latitudes , while the dense polar wind remains relatively undisturbed during an event . the apparent stability of the polar wind also supports the inferred bipolar geometry . the wind geometry and its variability have critical implications for understanding the 5.5 year cycle and long - term variability , but do not provide a clear alternative to the binary hypothesis for generating car s x - rays .
math0303218	i	in a series of two papers , the present one and the second one by the second author @xcite , we continue the study of the hurwitz problem @xcite concerning counting ramified coverings of the @xmath1-sphere . roughly speaking , this problem can be formulated as follows : _ given a set of fixed ramification points on the target @xmath1-sphere and a set of ramification types over these points , count the number of non - isomorphic ramified coverings @xmath2 by a @xmath1-surface @xmath3 , having the prescribed ramification types over the prescribed ramification points_. two coverings are considered to be isomorphic if there is a homeomorphism of the covering surfaces taking the first covering to the second one . in fact , we count isomorphism classes with the weight equal to the inverse order of the group of automorphisms of the class ; in this form the problem is more natural , and admits a lot of applications . in a more modern setting this problem can be reformulated as the computation of the gromov witten invariants of the complex projective line . a detailed exposition of the history of the problem and a description of various approaches to its solution can be found in @xcite . hurwitz @xcite himself gave an explicit answer to the problem in the case , where the covering surface is also a sphere , and there is one ramification point with arbitrary ramification , while all others are points of simple ramification . in spite of the importance of the problem , only recently hurwitz s original results were extended to more general cases and treatable answers were obtained : * i. goulden and d. jackson @xcite solved the combinatorial problem that allows one to give the answer to hurwitz s problem for polynomials ( that is , ramified coverings of the sphere by a sphere having a point with a single preimage and arbitrary ramification over other points ) ; later their results were reestablished in @xcite and @xcite by absolutely different methods ; * t. ekedahl , s. lando , m. shapiro , and a. vainshtein @xcite gave an expression for the number of ramified coverings of the sphere by a surface of arbitrary genus with a single point of arbitrary ramification type and all other points of simple ramification , in terms of intersection indices on moduli spaces of curves ( when the covering surface is the sphere , the answer given by the formula coincides with hurwitz s one ) ; another proof of the formula was given in @xcite . here we address the special case of the hurwitz problem , where the covering surface is also a sphere , but in contrast to the hurwitz case , ramification points of arbitrary type are allowed . we are far from solving the problem in this generality , but we suggest a general approach , and show how it works in some special cases , thus producing new enumerative results . to a ramification point (= a critical value ) of multiplicity @xmath4 we assign a partition @xmath5 of @xmath4 , called the _ ramification type_. the elements of @xmath5 are the multiplicities of the critical points that correspond to our critical value . recall the hurwitz theorem . the number @xmath6 of degree @xmath7 coverings of the sphere by the sphere , having the ramification type @xmath8 over one point , @xmath9 , while all other ramification points are fixed and simple , is @xmath10 here @xmath11 is the order of the automorphism group of the partition @xmath5 , @xmath12 is the number of nondegenerate ramification points , and @xmath13 is the number of simple preimages of the multiple ramification point . as a consequence of our approach we obtain , in the second part of this paper @xcite , for example , the following result . the number @xmath14 of degree @xmath7 coverings of the sphere by the sphere , having two double critical points and @xmath15 simple critical points , all the @xmath16 critical values being fixed , is @xmath17 as far as we know , this formula , as well as similar formulas for some other ramification types , is new . first of all we reduce the problem to the calculation of the degree of some map , called the lyashko looijenga map . this step is now standard . the lyashko looijenga map ( below , the @xmath18 map ) takes a meromorphic function to the set of its critical values . its source space can be chosen in a variety of ways ; here we define the @xmath18 map on the hurwitz space @xmath19 constructed in @xcite . it is the space of stable maps from genus zero complex curves to the projective line , having trivial ramification over infinity . all spaces of functions possessing degenerate ramification are considered as subvarieties in this space . these subvarieties form a stratification of the hurwitz space . [ thmml ] the number @xmath20 of ramified coverings of the sphere , having the ramification types @xmath21 over prescribed ramification points with multiplicities @xmath22 , is given by the formula @xmath23 where @xmath24 is the degree of the @xmath18 map restricted to the stratum @xmath25 consisting of functions with these ramification types . this is an instance of a general situation , see e.g. @xcite . indeed , if we fix a ramified covering @xmath26 and choose a complex structure on the target sphere @xmath27 , then there exists a unique complex structure on the covering surface @xmath3 making the function @xmath28 into a meromorphic function . this complex structure is produced by the riemann construction . hence , there is a one - to - one correspondence between ramified coverings with fixed ramification points of given types and meromorphic functions with fixed critical values of the same types . the latter number is exactly the degree of the @xmath18 map on the corresponding moduli space . the coefficient @xmath29 results from the fact that in our construction of the space @xmath19 we choose a numbering of the @xmath7 poles of each rational function . the factor @xmath30 is due to the fact that if we permute the ramification types @xmath31 preserving the multiplicities @xmath22 , we obtain a new set of ramified coverings that lie on the same stratum @xmath25 and have the same image under the @xmath18 map . the space @xmath19 is , in fact , a vector bundle over the deligne mumford moduli space @xmath32 of stable genus zero curves . the latter space is a smooth projective variety . the multiplicative group @xmath33 of nonzero complex numbers acts on this bundle fiberwise . this action consists in just multiplying a meromorphic function by a constant . it preserves the stratification of the space @xmath19 because the multiplication does not change the type of singularities . deleting the zero section of the bundle and taking the quotient modulo this action we reduce the variety to the projectivization @xmath34 of the vector bundle @xmath19 . the projectivization @xmath34 carries the tautological line bundle @xmath35 , and a natural cohomology class @xmath36 , @xmath37 , the class of a hyperplane section . the degree of the lyashko looijenga map restricted to a subvariety in @xmath19 is related to the intersection index of the subvariety with the complementary power of the class @xmath38 . namely , the following statement is true . [ thm1.4 ] the degree @xmath24 of the @xmath18 map restricted to the stratum @xmath25 is equal to @xmath39 here @xmath4 is the dimension of the stratum @xmath40 , @xmath41 is the multiplicity of the @xmath42th ramification point ( or the sum of the elements of @xmath43 ) , and @xmath44 is the coupling between a homology and a cohomology class . this theorem is proved in section [ ssec : strathur ] . theorem [ thm1.4 ] implies that our approach requires the study of the cohomology ring @xmath45 . all cohomology groups we consider are with complex coefficients , and we do not specify the coefficients explicitly . we need * a reasonable description of this ring , say , in terms of generators and relations ; * reasonable expressions for the cohomology classes of the strata and the class @xmath38 in terms of the generators . the solution of the first problem is known since the space @xmath19 is a vector bundle over the moduli space of stable rational curves , whose cohomology is known . the second problem seems to be much more difficult . in fact , we need less than the whole cohomology ring . the symmetric group @xmath46 acts on the space @xmath19 by permuting the indices , whence it acts on the cohomology space @xmath45 . all the cohomology classes we are interested in are symmetric with respect to this action . therefore , we only need to know the @xmath46-symmetric part of the cohomology algebra @xmath45 . this is an additional problem , but its solution can lead to a simplification of the decompositions of the strata . the situation would become even easier if we restrict ourselves to the subalgebra in the cohomology algebra @xmath45 generated by the classes of the strata . consider two closed codimension 1 subvarieties @xmath47 and @xmath48 in @xmath19 ; the first of them is called the _ caustic _ and it is the closure of the space of functions having a critical point of order @xmath1 , the second one is the _ maxwell stratum _ and it is the closure of the space of functions having two distinct critical points with coinciding critical values . [ conj : kazarian ] the subalgebra of the cohomology algebra @xmath45 generated by the cohomology classes of the strata is generated by the two classes @xmath47 and @xmath48 in @xmath49 . up to now , the basis of this conjecture is not too solid . but it does not contradict our sample calculations , and it has a nonformal justification coming from kazarian s theory . kazarian s theory concerns cohomology classes of multisingulatities of a map @xmath50 of two complex manifolds , @xmath51 . its main statement claims that there is a universal way to express these cohomology classes in terms of the characteristic classes of the tangent bundles over the two manifolds @xmath52 and @xmath53 , more precisely in terms of the class @xmath54 , where @xmath55 is the total chern class . it is a development of the theory of the thom polynomial . up to now , only a preliminary version @xcite of the text describing the theory is available , and we are not going to refer directly to statements from it . however , the ideology of the theory seems to be applicable in the situation we are studying , and it leads to a number of conjectures concerning the part of the cohomology ring of the hurwitz spaces we are interested in . in our situation , the variety @xmath52 is the universal curve @xmath56 over the hurwitz space @xmath34 , while the variety @xmath53 is the quotient of @xmath57 by the natural @xmath33 action . the map @xmath28 is the universal map over @xmath34 . it is easy to see that the map @xmath28 almost identifies the tangent spaces @xmath58 and @xmath59 ; more precisely , one has @xmath60 , where @xmath61 and @xmath62 are first chern classes of some linear bundles . however , new complications arise , since we are interested in cohomology classes of @xmath34 and not of @xmath56 . kazarian s ideology leads to conjecture [ conj : kazarian ] . if the conjecture is true , then the computation of intersection numbers of the strata in the hurwitz space with the complementary powers of the class @xmath36 can be split into two independent stages : * express the cohomology class of the required stratum as a ( homogeneous ) polynomial in the classes @xmath48 and @xmath47 ; * find the intersection index of each monomial in @xmath48 and @xmath47 with the complementary degree of the class @xmath38 . another cohomology class in @xmath49 is also distinguished . this is the class @xmath63 dual to the subvariety of functions defined on singular curves . this class also can be expressed in terms of the classes @xmath47 and @xmath48 . this means that the subring in @xmath45 generated by the classes @xmath47 and @xmath48 coincides with that generated by @xmath38 and @xmath63 . the linear relations relating these four classes are as follows : @xmath64 the coefficients in these linear relations are polynomial in @xmath7 , which ( together with the informal support of kazarian s theory ) allows us to sharpen conjecture 1.5 in the following way : each cohomology class dual to a stratum in @xmath34 can be expressed as a homogeneous polynomial in @xmath65 whose coefficients that are polynomials in @xmath7 . therefore the calculations must even be simplified . in section 2 we give precise definitions of notions mentioned in this introduction . section 3 is devoted to the description of the lyashko looijenga map . in section 4 the structure of cohomology of the hurwitz spaces is analyzed . we are greatful to a. zorich who invited us both to rennes , where the main part of this work was accomplished . the work was completed during our participation in the mini - workshop on hurwitz theory and its ramifications , and we thank its organizers j. h. kwak and a. d. mednykh for inviting us . we also thank b. shapiro and m. shapiro for their interest and m. kazarian for explaining the basics of his theory .	the hurwitz space is a compactification of the space of rational functions of a given degree . the lyashko - looijenga map assigns to a rational function the set of its critical values . it is known that the number of ramified coverings of by with prescribed ramification points and ramification types is related to the degree of the lyashko looijenga map on various strata of the hurwitz space . _ [ cols= " > , < " , ]	the hurwitz space is a compactification of the space of rational functions of a given degree . the lyashko - looijenga map assigns to a rational function the set of its critical values . it is known that the number of ramified coverings of by with prescribed ramification points and ramification types is related to the degree of the lyashko looijenga map on various strata of the hurwitz space . here we explain how the degree of the lyashko - looijenga map is related to the intersection theory on this space . we describe the cohomology algebra of the hurwitz space and prove several relations between the homology classes represented by various strata . _ _ [ cols= " > , < " , ]
1312.0832	i	spontaneous breakdown of chiral symmetry ( @xmath4ssb ) @xmath5 characterizes the vacuum and low - energy dynamics of quantum chromodynamics ( qcd ) @xcite . the non - vanishing chiral condensate @xmath6 is considered as one of the order parameters of @xmath7ssb and gives a characteristic scale for hadron physics . @xmath7ssb is considered to be responsible for the origin of constituent quark mass after the current quark mass is given by the higgs condensate slightly . according to the spontaneous breakdown , the pseudoscalar mesons such as @xmath8 appear as the nambu - goldstone ( ng ) bosons . recently , in order to investigate the mechanism of the dynamical mass generation , partial restoration of the chiral symmetry in the nuclear medium has gained considerable attention . this phenomenon is incomplete restoration of chiral symmetry with sufficient reduction of the absolute value of the chiral condensate in the medium and will lead to various changes of hadron properties . once we understand the partial restoration of chiral symmetry , we can predict other in - medium hadronic quantities through low energy theorems and vice versa . from this point of view , vast theoretical and experimental efforts are devoted for this topic . the density dependence of the chiral condensate is evaluated in various approaches , for example , the well - known linear density approximation providing the model - independent low density theorem @xcite , the relativistic bruckner - hartree - fock theory approach@xcite and systematic calculations by in - medium chiral perturbation theory beyond the linear density calculation @xcite . according to the model - independent linear density approximation , the leading density correction to the chiral condensate is determined by the @xmath9n sigma term @xmath10 and with the empirical value of the sigma term it has been found that the leading correction gives enough large contribution at the normal nuclear density : @xmath11 where @xmath12 , @xmath13 is the in - medium and in - vacuum condensate and @xmath14 is the normal nuclear density . recently , an in - medium sum rule satisfied in any density region has been derived model - independently by current algebra method and the low energy theorems , such as the gell mann oakes renner relation , the glashow weinberg relation and the weinberg tomozawa relation , are discussed within the linear density order @xcite . to investigate the pion properties in nuclei , deeply bound pionic atoms have received much attention @xcite . theoretically , the binding energies and decay widths of the 1s and 2p deeply - bound pionic atom states are estimated @xcite and in refs . @xcite hadronic quantities , such as pion optical potential , have been calculated beyond the linear density . experimentally the reduction of the chiral condensate is estimated quantitatively through reduction of the @xmath15-wave isovector parameter @xmath16 in the @xmath17-nucleus optical potential @xcite . the @xmath18 parameter is regarded as an in - medium isovector @xmath17n scattering length . these results show that the reduction of @xmath16 means the repulsive enhancement of the @xmath15-wave @xmath17-nucleon interaction in nucleus . another examples are low energy @xmath17-nucleus scattering and @xmath19 interaction in nuclei in the scalar - isoscalar channel . the low energy @xmath17-nucleus scattering also show that s - wave @xmath17-nucleus interaction are enhanced repulsively @xcite . according to the theoretical discussion given in refs . @xcite , the in - medium @xmath19 interaction in the scalar - isoscalar part will also has attractive enhancement thanks to the partial restoration of chiral symmetry in nuclear medium and the experimental observation of the invariant mass spectrum of the @xmath20 production off nuclear targets performed in refs . @xcite could have a hint of such a enhancement . in particular the pion decay constant is a fundamental quantity of chiral symmetry breaking . the in - medium decay constant also has been investigated in the linear density approximation @xcite and recently the chiral condensate and the decay constant have been evaluated in the next - to - leading order based on chiral order counting @xcite . in this paper , we discuss a general in - medium pion state and evaluate in - medium pionic quantities such as the decay constant , mass and the pseudo scalar coupling beyond linear density approximation . this paper is organized as follows . in sec.[in - medium chpt ] , we explain the general formulation of the in - medium chiral perturbation theory and discuss an expansion by fermi momentum counting . in sec.[decayconst ] , we discuss in - medium pion state and define the in - medium pionic quantities . here we will find that the pion wave function renormalization plays an important role for the in - medium pionic quantities . in sec.[results ] , we evaluate the in - medium pion self energy , wave function renormalization , pion decay constant and pseudo - scalar coupling and show the numerical results of the density dependence of them up to @xmath21 in fermi momentum expansion in symmetric nuclear matter and in isospin limit . we also discuss whether the in - medium low energy theorems , the gell - mann oakes renner relation and the glashow weinberg relation , are satisfied or not . finally we discuss the in - medium @xmath22 process caused by chiral anomaly . in sec.[summary ] , we summarize our paper .	we show that the linear density correction is dominant and the next - to - leading corrections are not so large at the saturation density , while their contributions can be significant in higher densities . we also discuss whether the low energy theorems , the gell - mann oakes renner relation and the glashow	the in - medium pion properties , _ i.e. _ the temporal pion decay constant , the pion mass and the wave function renormalization , in symmetric nuclear matter are calculated in an in - medium chiral perturbation theory up to the next - to - leading order of the density expansion . the chiral lagrangian for the pion - nucleon interaction is determined in vacuum , and the low energy constants are fixed by the experimental observables . we carefully define the in - medium state of pion and find that the pion wave function renormalization plays an essential role for the in - medium pion properties . we show that the linear density correction is dominant and the next - to - leading corrections are not so large at the saturation density , while their contributions can be significant in higher densities . the main contribution of the next - to - leading order comes from the double scattering term . we also discuss whether the low energy theorems , the gell - mann oakes renner relation and the glashow weinberg relation , are satisfied in nuclear medium beyond the linear density approximation . we also find that the wave function renormalization is enhanced as largely as 50% at the saturation density including the next - to - leading contribution and the wave function renormalization could be measured in the in - medium decay .
1312.0832	i	we have discussed the in - medium pion properties , such as the pion decay constant , the pion mass and the wave function renormalization based on the in - medium chiral perturbation theory . first , we have provided a general formalism of the in - medium chiral perturbation theory and have discussed an expansion in terms of fermi momentum . assuming that the renormalization for the in - vacuum quantities is performed in an appropriate way , we use the observed values to determine the low energy constants ( lecs ) in the chiral lagrangian . since we have used the physical values , the higher order corrections for the momentum expansion are implicitly included in the calculation . thus , we focus on the expansion of the fermi momentum of the physical quantities , which are calculated by the qcd current green functions . to calculate the in - medium quantities , we carefully define the in - medium pion state , and we have found that the in - medium wave function renormalization plays an essential role to define the in - medium coupling constants , such as the decay constant and pseudo - scalar coupling constant . we have evaluated the density dependence of the decay constant , the pion mass , the pion wave function renormalization and the pseudo - scalar coupling including the next - to - leading order of the density expansion beyond the well - known linear density approximation based on the in - medium chiral perturbation theory . we have found that the @xmath2 corrections give a few percents changes in the low density region for the decay constant and the pion mass , while in higher density such as three times saturation density , the corrections can be as the order of 10 to 20 percents and can give significant contribution . we have also found that the wave function renormalization is enhanced as largely as 50 percents at the saturation density . the main contribution among the corrections comes from the double scattering term . in addition , we have checked whether the low energy theorems , the gell - mann oakes renner relation and the glashow weinberg relation are satisfied in medium beyond the linear density approximation . we have found that these relations are not satisfied at @xmath2 off the chiral limit . the origin of the breaking is that we use the different energy values to evaluate the pion quantities and the chiral condensate ; we take the soft limit to obtain the chiral condensate , while we take the pion on shell point , that is @xmath296 , to evaluate the pion quantities . finally , we have discussed the density dependence of the @xmath297 decay width . considering the spinor and flavor vertex structure of the chiral interactions , we have found that the density dependence of the @xmath274 width comes from the wave function renormalization alone at linear density order . with this observation , the wave function renormalization @xmath136 would be measured directly in the decay process .	i.e. _ the temporal pion decay constant , the pion mass and the wave function renormalization , in symmetric nuclear matter are calculated in an in - medium chiral perturbation theory up to the next - to - leading order of the density expansion . we carefully define the in - medium state of pion and find that the pion wave function renormalization plays an essential role for the in - medium pion properties . the main contribution of the next - to - leading order comes from the double scattering term . weinberg relation , are satisfied in nuclear medium beyond the linear density approximation .	the in - medium pion properties , _ i.e. _ the temporal pion decay constant , the pion mass and the wave function renormalization , in symmetric nuclear matter are calculated in an in - medium chiral perturbation theory up to the next - to - leading order of the density expansion . the chiral lagrangian for the pion - nucleon interaction is determined in vacuum , and the low energy constants are fixed by the experimental observables . we carefully define the in - medium state of pion and find that the pion wave function renormalization plays an essential role for the in - medium pion properties . we show that the linear density correction is dominant and the next - to - leading corrections are not so large at the saturation density , while their contributions can be significant in higher densities . the main contribution of the next - to - leading order comes from the double scattering term . we also discuss whether the low energy theorems , the gell - mann oakes renner relation and the glashow weinberg relation , are satisfied in nuclear medium beyond the linear density approximation . we also find that the wave function renormalization is enhanced as largely as 50% at the saturation density including the next - to - leading contribution and the wave function renormalization could be measured in the in - medium decay .
0806.0552	c	in the present work a new study has been undertaken of the effects expected from isospin - mixing in nuclear ground - state wave functions on elastic parity - violating electron scattering at momentum transfers extending up to about 1.5 @xmath11 . four n = z 0@xmath7 nuclei have been considered , @xmath1c , @xmath2 mg , @xmath3si , and @xmath4s , each expected to be very close to eigenstates of isospin with @xmath5 in their ground states . however , as first discussed in @xcite ( dds ) , the coulomb interaction occurs asymmetrically between pp and pn / nn nucleon pairs in the nucleus , thereby giving rise to small isospin mixing and thus the nuclear ground states considered here have small admixtures with t@xmath2210 . while such effects are essentially negligible in the parity - conserving cross section , they can play a measurable role in the parity - violating asymmetry , and accordingly , whether the focus is placed on isospin mixing itself or on how these effects may confuse interpretations of the pv asymmetry in terms of standard model tests or with respect to strangeness content in the weak neutral current , it is important to evaluate their influence . in the older work of dds a limited - model - space shell model was employed to estimate the isospin mixing and the mixing via the coulomb interaction was handled perturbatively via a simple two - level approximation . furthermore , in the study of dds the idea of using pv elastic electron scattering to determine ground - state neutron distributions as in the case of @xmath9pb ( which forms the basis of the prex experiment ) was put forward ; here the focus has been limited to a few special n = z nuclei and n@xmath221z cases such as lead have not been re - considered . in the present work a self - consistent axially - symmetric mean - field approximation with density - dependent effective two - body skyrme interactions , including coulomb interactions between pp pairs , has been used in direct determinations of the ground state wave functions . the small differences between the proton and neutron density distributions thereby obtained yield both isoscalar and isovector ground - state coulomb monopole matrix elements and produce modifications in the pv asymmetry from the model - independent result obtained in the absence of isospin - mixing and strangeness contributions . additionally , the effects of pairing in this mean - field approximation have also been investigated , as have effects from strangeness contributions in the single - nucleon form factors and from subtle spin - orbit contributions in the coulomb monopole operators . * in the present work one observes considerably larger effects from isospin mixing than were found in dds , especially since here important matrix elements both diagonal and off - diagonal are naturally included , whereas in the earlier study the restriction of the shell - model space to a single major shell yielded a special constraint on the @xmath12-dependences of the isovector matrix elements . * specific influences of nuclear dynamics ( different forces , different pairing gaps ) and of subtleties in the current operators ( spin - orbit effects ) were investigated and seen not to affect the pv asymmetry at low-@xmath12 significantly . * results using either plane or distorted electron waves were obtained and , for the relatively light nuclei considered in the present work , their differences were seen to be small at low momentum transfers except in the vicinity of a diffraction minimum where the cross section is also small . * kinematic ranges where potential future measurements might be undertaken are discussed by studying both the deviations in the pv asymmetry ( the differences seen with / without isospin mixing ) and the experimental figure - of - merit . we have shown that the isospin mixing effects considered in this work will have a measurable effect on the asymmetries , even for the light nuclei considered . * furthermore , in going from the lightest n = z nuclei to heavier cases one sees that the asymmetry deviations increase making the isospin - mixing effects all the more evident . * in exploring the interplay between the isospin - mixing effects and those effects that may arise from electric strangeness contributions one sees an interesting constructive / destructive interference scenario : with positive electric strangeness the two contributions add at low momentum transfers , whereas when negative they subtract . presently the sign of the electric strangeness form factor is unknown ( the form factor is , in fact , consistent with zero ) and so such interferences may provide information on isospin mixing , namely the main focus of the present work , but also on strangeness . this work was supported by ministerio de ciencia e innovacin ( spain ) under contracts no . fis2005 - 00640 and no . fis2008 - 01301 . thanks ministerio de ciencia e innovacin ( spain ) for financial support . j.m.u . acknowledges support from intas open call grant no 05 - 1000008 - 8272 , and ministerio de ciencia e innovacin ( spain ) under grants fpa-2007 - 62616 and fpa-2006 - 07393 , and ucm and comunidad de madrid under grant grupo de fsica nuclear ( 910059 ) . this work was also supported in part ( twd ) by the u.s . department of energy under contract no . de - fg02 - 94er40818 . twd also wishes to thank ucm - gruposantander for financial support at the universidad complutense de madrid . ccccc isotope & @xmath223 = 0 & @xmath223 = 1 mev & @xmath223 from mass diff . & @xcite @xmath1c & @xmath2240 & @xmath2240 & @xmath2240 & - @xmath2 mg & 56.67 & 54.70 & 38.54 & 58.1 @xmath3si & -45.35 & -43.41 & -28.62 & -57.75 @xmath4s & @xmath2240 & @xmath2240 & @xmath2240 & - cccccccc & & & & @xmath225 & @xmath226 & @xmath227 & @xmath228 & @xmath229 & & @xmath230 = 0.1 @xmath231 & @xmath230 = 0.5 @xmath231 & @xmath230 = 1 @xmath231 & & 0 & 0 & 0.058 & * 0.208 * & 0.229 & 0.145 & & 0 & 1 & 0.168 & 0.005 & 0.136 & * 0.346 * 0 & 1/2 & 0 & 2 & 0.052 & 0.000 & 0.005 & 0.048 & & 1 & 1 & 0.028 & 0.100 & 0.079 & 0.024 & & 1 & 2 & * 0.203 * & 0.011 & * 0.244 * & 0.304 & & 0 & 0 & 0.093 & * 0.335 * & 0.309 & 0.078 & & 0 & 1 & * 0.349 * & 0.013 & * 0.329 * & * 0.555 * 1 & 1/2 & 0 & 2 & 0.048 & 0.000 & 0.006 & 0.048 & & 1 & 1 & 0.093 & 0.330 & 0.217 & 0.047 & & 1 & 2 & 0.018 & 0.001 & 0.023 & 0.018 & & 0 & 0 & 0.184 & * 0.662 * & * 0.610 * & 0.016 & & 0 & 1 & * 0.628 * & 0.024 & 0.592 & * 1.000 * 1 & 3/2 & 0 & 2 & 0.137 & 0.000 & 0.018 & 0.137 & & 1 & 1 & 0.186 & 0.659 & 0.434 & 0.094 & & 1 & 2 & 0.031 & 0.002 & 0.040 & 0.032 & & 0 & 0 & 0.044 & * 0.156 * & * 0.119 * & 0.007 & & 0 & 1 & * 0.061 * & 0.003 & 0.061 & * 0.060 * 2 & 3/2 & 0 & 2 & 0.008 & 0.000 & 0.001 & 0.007 & & 1 & 1 & 0.001 & 0.004 & 0.002 & 0.000 & & 1 & 2 & 0.002 & 0.000 & 0.002 & 0.001 & & 0 & 0 & 0.142 & 0.506 & 0.386 & 0.024 & & 0 & 1 & * 1.000 * & 0.045 & * 1.000 * & * 0.986 * 2 & 5/2 & 0 & 2 & 0.048 & 0.000 & 0.008 & 0.044 & & 1 & 1 & 0.284 & * 1.000 * & 0.541 & 0.075 & & 1 & 2 & 0.379 & 0.003 & 0.049 & 0.021 ccisotope & for @xmath163 @xmath1c & 0.74 @xmath232 q @xmath232 1.42 & 838 @xmath232 @xmath233 @xmath232 1607 & 8.38 @xmath232 @xmath210 @xmath232 16.07 @xmath2 mg & 0.51 @xmath232 q @xmath232 1.10 & 577 @xmath232 @xmath233 @xmath232 1245 & 5.77 @xmath232 @xmath210 @xmath232 12.45 @xmath3si & 0.48 @xmath232 q @xmath232 1.08 & 543 @xmath232 @xmath233 @xmath232 1222 & 5.43 @xmath232 @xmath210 @xmath232 12.22 @xmath4s & 0.45 @xmath232 q @xmath232 1.05 & 509 @xmath232 @xmath233 @xmath232 1188 & 5.09 @xmath232 @xmath210 @xmath232 11.88	their ground - state wave functions have been obtained using a self - consistent axially - symmetric mean - field approximation with density - dependent effective two - body skyrme interactions . some differences from previous shell - model calculations appear for the isovector coulomb form factors which play a role in determining the parity - violating asymmetry . results are obtained not only within the plane - wave born approximation , but also using the distorted - wave born approximation for comparison with potential future experimental studies of parity - violating electron scattering . to this end , for each nucleus the focus is placed on kinematic ranges where the signal ( isospin - mixing effects on the parity - violating asymmetry ) and the experimental figure - of - merit are maximized .	the influence of nuclear isospin mixing on parity - violating elastic electron scattering is studied for the even - even , nucleic , mg ,si , ands . their ground - state wave functions have been obtained using a self - consistent axially - symmetric mean - field approximation with density - dependent effective two - body skyrme interactions . some differences from previous shell - model calculations appear for the isovector coulomb form factors which play a role in determining the parity - violating asymmetry . to gain an understanding of how these differences arise , the results have been expanded in a spherical harmonic oscillator basis . results are obtained not only within the plane - wave born approximation , but also using the distorted - wave born approximation for comparison with potential future experimental studies of parity - violating electron scattering . to this end , for each nucleus the focus is placed on kinematic ranges where the signal ( isospin - mixing effects on the parity - violating asymmetry ) and the experimental figure - of - merit are maximized . strangeness contributions to the asymmetry are also briefly discussed , since they and the isospin mixing contributions may play comparable roles for the nuclei being studied at the low momentum transfers of interest in the present work .
1609.01050	i	finding first integrals is fundamental for characterizing a dynamical system . the motion is confined to submanifolds of lower dimensions on which the orbits evolve , providing an intuitive interpretation of the dynamics and reducing the complexity of the system . in addition , conserved quantities are good candidates when applying the second method of lyapunov for stability analysis . conservative systems related to central forces are typical examples of ( liouville ) integrability , and provide useful analytic results . hamiltonian systems have been widely analyzed in the classical and modern literature to determine adequate integrability conditions . the existence of first integrals under the action of small perturbations occupied ( * ? ? ? * chap . v ) back in the 19th century . later , emmy @xcite established in her celebrated theorem that conservation laws can be understood as the system exhibiting dynamical symmetries . in a more general framework , @xcite analyzed the conditions that yield algebraic first integrals of generic systems . he relied on the kowalevski exponents for characterizing the singularities of the solutions and derived the necessary conditions for existence of first integrals exploiting similarity transformations . conservation laws are sensitive to perturbations and their generalization is not straightforward . for example , the jacobi integral no longer holds when transforming the circular restricted three - body problem to the elliptic case @xcite . nevertheless , @xcite was able to find approximate conservation laws for orbits of small eccentricities . @xcite benefited from the similarities between the elliptic and the circular problems in order to define transformations connecting them . @xcite deepened in the nature of conservation laws and reviewed the concepts of isolating and nonisolating integrals . their study introduced a similarity transformation that embeds one of the constants of motion and transforms the original problem into a simplified one , reducing the degrees of freedom @xcite . @xcite proposed a numerical method for finding the dimension of the manifold in which orbits evolve , i.e. the number of isolating integrals that the system admits . the conditions for existence of integrals of motion under nonconservative perturbations received important attention in the past due to their profound implications . @xcite advanced on noether s theorem and included nonconservative forces in the derivation . relying on hamilton s variational principle , they not only extended noether s theorem , but also its inverse form and the noether - bessel - hagen and killing equations . later studies by @xcite sought integrating factors that yield conservation laws upon integration . examples of application of noether s theorem to constrained nonconservative systems can be found in the work of @xcite . @xcite arrived to a compact formulation using what was later called the neutral action method . remarkable applications exploiting noether s symmetries span from cosmology @xcite to string theory @xcite , field theory @xcite , and fluid models @xcite . in the book by ( * ? ? ? * chaps . 4 and 5 ) , an exhaustive review of the connection between symmetries and conservation laws is provided within the framework of lie algebras . we refer to ( * ? ? ? 3 ) for a formal derivation of noether s theorem , and a discussion on the connection between conservation laws and dynamical symmetries . integrals of motion are often useful for finding analytic or semi - analytic solutions to a given problem . the acclaimed solution to the satellite main problem by @xcite is a clear example of the decisive role of conserved quantities in deriving solutions in closed form . by perturbing the delaunay elements , @xcite solved the dynamics of a satellite subject to atmospheric drag and the oblateness of the primary . they proved the usefulness of canonical transformations even in the context of nonconservative problems . @xcite approached the problem of a central force depending on powers of the radial distance , @xmath0 , and found that there are only fourteen values of @xmath1 for which the problem can be integrated in closed form using elementary functions or elliptic integrals . later , he discussed the solvability conditions for equations involving square roots of polynomials @xcite . @xcite advanced on whittaker s results and found six potentials that are a generalization of the integrable central forces discussed by the latter . these potentials include the referred fourteen values of @xmath1 as particular cases . numerical techniques for shaping the potential given the orbit solution were published by @xcite . classical studies on the integrability of systems governed by central forces are based strongly on newton s theorem of revolving orbits . the problem of the orbital precession caused by central forces was recently recovered by @xcite , who considered potentials involving both powers and logarithms of the radial distance , and the special case of the yukawa potential @xcite . @xcite relied on hamilton s vector to simplify the analytic solutions found by @xcite . more elaborated potentials have been explored for modeling the perihelion precession @xcite . the dynamics of a particle in schwarzschild space - time can also be regarded as orbital motion perturbed by an effective potential depending on inverse powers of the radial distance @xcite . potentials depending linearly on the radial distance appear recursively in the literature because they render constant radial accelerations , relevant for the design of spacecraft trajectories propelled by continuous - thrust systems . the pioneering work by @xcite provided the explicit solution to the problem in terms of elliptic integrals , as predicted by @xcite . by means of a special change of variables , @xcite arrived to an elegant solution in terms of the weierstrass elliptic functions . these functions were also exploited by @xcite when he solved the dynamics of a particle attracted by a central force decreasing with @xmath2 . @xcite solved the tsien problem using the dromo formulation , which models orbital motion with a regular set of elements @xcite . advances on dromo can be found in the works by @xcite and @xcite . the case of a constant radial force was approached by @xcite from an energy - driven perspective . they studied in detail the roots of the polynomial appearing in the denominator of the equation to integrate , and connected their nature with the form of the solution . general considerations on the integrability of the problem can be found in the work of @xcite . another relevant example of an integrable system in celestial mechanics is the stark problem , governed by a constant acceleration fixed in the inertial frame . @xcite provided the complete solution to the motion relying extensively on elliptic integrals and jacobi elliptic functions . a compact form of the solution involving the weierstrass elliptic functions was later presented by @xcite , who also exploited this formalism for building a secular theory for the post - newtonian model @xcite . the stark problem provides a simplified model of radiation pressure . in the more general case , the dynamics subject to this perturbation can not be solved in closed form . an intuitive simplification that makes the problem integrable consists in assuming that the force due to the solar radiation pressure follows the direction of the sun vector . the dynamics are equivalent to those governed by a keplerian potential with a modified gravitational parameter . the present paper introduces a new class of integrable system , governed by a biparametric nonconservative perturbation . this acceleration unifies various force models , including special cases of solar radiation pressure , low - thrust propulsion , and some particular configurations in general relativity . the problem is formulated in sec . [ sec : dynamics ] , where the biparametric acceleration is defined and then reduced to a uniparametric forcing thanks to a similarity transformation . the conservation laws for the energy and angular momentum are generalized to the nonconservative case by exploiting known symmetries of kepler s problem . before solving the dynamics explicitly , we will prove that there are four cases that can be solved in closed form using elementary or elliptic functions . sections [ sec : conic][sec : sinusoidal ] present the properties of each family of orbits and the corresponding trajectories are derived analytically . section [ sec : summary ] is a summary of the solutions , which are unified in sec . [ sec : weierstrass ] introducing the weierstrass elliptic functions . finally , sec . [ sec : connection ] discusses the connection with known solutions to similar problems , and with schwarzschild geodesics .	keplerian orbits appear naturally as particular solutions to the problem . after characterizing the orbits independently , a unified form of the solution these orbits can represent the motion of particles perturbed by solar radiation pressure , of spacecraft with continuous thrust propulsion , and some instances of schwarzschild geodesics . finally , the problem is connected with other known integrable systems in celestial mechanics . [ firstpage ] celestial mechanics methods : analytical radiation : dynamics acceleration of particles	the invariance of the lagrangian under time translations and rotations in kepler s problem yields the conservation laws related to the energy and angular momentum . noether s theorem reveals that these same symmetries furnish generalized forms of the first integrals in a special nonconservative case , which approximates various physical models . the system is perturbed by a biparametric acceleration with components along the tangential and normal directions . a similarity transformation reduces the biparametric disturbance to a simpler uniparametric forcing along the velocity vector . the solvability conditions of this new problem are discussed , and closed - form solutions for the integrable cases are provided . thanks to the conservation of a generalized energy , the orbits are classified as elliptic , parabolic , and hyperbolic . keplerian orbits appear naturally as particular solutions to the problem . after characterizing the orbits independently , a unified form of the solution is built based on the weierstrass elliptic functions . the new trajectories involve fundamental curves such as cardioids and logarithmic , sinusoidal , and cotes spirals . these orbits can represent the motion of particles perturbed by solar radiation pressure , of spacecraft with continuous thrust propulsion , and some instances of schwarzschild geodesics . finally , the problem is connected with other known integrable systems in celestial mechanics . [ firstpage ] celestial mechanics methods : analytical radiation : dynamics acceleration of particles
1309.2669	i	in the past decade ultra - cold quantum gases have emerged as ideal candidates for clean and controllable simulation of condensed matter physics @xcite . ultra - cold quantum gases are now created in a variety of configurations in laboratories worldwide . in particular , both bosonic and fermionic atoms can be trapped and manipulated on optical lattice potentials @xcite . the lack of thermal phonons coupled with the tunability of the interactions by means of feschbach resonances @xcite has allowed for the detailed study of a multitude of phase diagrams , the most celebrated example is perhaps the bose - hubbard model @xcite . + equilibrium properties aside , over the past number of years there has been a surge in interest in the out of equilibrium behavior of closed quantum systems following a quench of a hamiltonian parameter . fundamentally , this is due to a series of spectacular experiments in ultra - cold atoms whereby the high degree of isolation and long coherence times permits the study of dynamics over long timescales @xcite . these experiments have raised a number of important theoretical issues such as the relationship between thermalisation and integrability and the universality of defect generation following evolution across a critical point @xcite . + given the controllability of ultra - cold atomic systems and the current interest in quench dynamics , it is a natural question to ask if there are any out of equilibrium condensed matter physics problems which could be simulated . unfortunately , due to their intrinsic complexity , there are very few examples of exactly solvable problems in the out - of - equilibrium domain . a worthy exception is the phenomenon of orthogonality catastrophe @xcite and the fermi - edge singularity . this problem was first pointed out by p. w. anderson over 40 years ago when he showed that the overlap of two many - body wave - functions , which describe deformed and undeformed fermi seas , vanishes in the thermodynamic limit @xcite . the corresponding ` quench ' problem , was investigated a few years later with the prediction of a universal absorption - edge singularity in the x - ray spectrum of metals , the ` fermi - edge ' singularity @xcite . + the universal physics of the anderson orthogonality catastrophe and the fermi - edge singularity was recently explored by goold _ _ in the context of ultra - cold quantum gases @xcite . in this work it was suggested that the physics maybe simulated in a controlled fashion by the appropriate embedding of a single probe qubit . the approach was further formalized in @xcite where the authors solved the dynamical problem in the inhomogeneous system by means of a linked cluster expansion . this qubit probe approach was further suggested as a mechanism to probe the physics of the orthogonality catastrophe in @xcite . + interestingly enough , a connection was made by heyl and kehrein @xcite between the absorption and emission spectrum in the original x - ray experiments and the so called quantum work distribution and corresponding fluctuation relations in classical and quantum statistical mechanics @xcite . treating a quench problem in manybody physics as a thermodynamic transformation and analyzing the statistics of work done has recently shown to be a useful approach to understand the intrinsic out of equilibrium dynamics in manybody systems @xcite . the approach is based on the study of the moments of a quantity known as the quantum work distribution @xcite which have been found to encode both thermodynamic and universal features of the model in question . + in this work this relationship will be explored in detail in the context of a locally quenched trapped fermi gas . in particular , in section [ sec100 ] the general problem of a system hamiltonian depending on a work - parameter will be introduced , adopting the description based on the grand canonical ensemble @xcite . the formalism provided by the work distribution and its characteristic function will be discussed , and the concept of irreversible work will be explored . in section [ sec200 ] the focus will be moved to a fermi gas in equilibrium with a harmonic trap , being suddenly perturbed by a spatially structure - less perturbation . in section [ lce ] the vacuum persistence amplitude and the linked cluster expansion will be used to reduce the calculation of the characteristic function of work to the sum of connected feynman diagrams . the relation of these diagrams to the characteristic function of work will be covered and an analytic approximation holding at low temperature will be presented . in section [ sec500 ] the first three cumulants of the work distribution will be computed and their link with thermodynamics will be discussed . finally , in section [ sec600 ] the irreversible work will be calculated using a perturbative and a numerical approaches , while section [ concluse ] will provide some further comments and conclusions .	the local quench of a fermi gas , giving rise to the fermi edge singularity and the anderson orthogonality catastrophe , is a rare example of an analytically tractable out of equilibrium problem in condensed matter . it has recently been proposed that the effect could be efficiently simulated in a controlled manner using the tunability of ultra - cold atoms . in this work , the statistics of work are shown to provide an accurate insight into the fundamental physics of the process .	the local quench of a fermi gas , giving rise to the fermi edge singularity and the anderson orthogonality catastrophe , is a rare example of an analytically tractable out of equilibrium problem in condensed matter . it describes the universal physics which occurs when a localized scattering potential is suddenly introduced in a fermi sea leading to a brutal disturbance of the quantum state . it has recently been proposed that the effect could be efficiently simulated in a controlled manner using the tunability of ultra - cold atoms . in this work , we analyze the quench problem in a gas of trapped ultra - cold fermions from a thermodynamic perspective using the full statistics of the so called _ work _ distribution . the statistics of work are shown to provide an accurate insight into the fundamental physics of the process . _ keywords _ : work distribution , non - equilibrium thermodynamics , quantum quench , orthogonality catastrophe .