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in this section we analyze the synthesis of the 512 @xmath66 512 stokes spectra calculated from the dynamo simulation described in [ sec_mhd ] . we only use the numerical solution at one instant since the purpose of the work is to study the kind of spectra characterizing the stationary state of the simulation ( studies of the time dependent behavior is deferred for later ) . we place the simulation at the solar disk center so that the vertical direction follows the line - of - sight . figure [ magneto ] shows the magnetogram that results when applying equation ( [ bruteforce ] ) to the synthetic stokes @xmath0 spectra ( right panel ) . the effect of observing with a 05 seeing representative of the best angular resolution achieved at present ( e.g. , @xcite @xcite ) , is also shown on the left panel . ignoring the underlying substructure , an observer would identify a number of magnetic concentrations in the smeared magnetogram ( e.g. , points @xmath67 , @xmath24 and @xmath59 ) . however , these are difficult to associate with single structures once the underlying substructure is acknowledged . rather , the points with enhanced signal in the 05 magnetogram represent locations where the convective flows are continuously advecting magnetized plasma to balance the plasma that constantly disappears in the downdrafts ( see also 3.2 in @xcite @xcite ) . the fact that the residual polarization signal shows up suggests the presence of a large - scale structure of the advecting velocity . indeed , detailed analysis of the numerical data reveals the existence of a mesogranular flow ( @xcite @xcite ) . except for a few test calculations in [ asym ] , the spectra discussed in this section correspond to a scaling of the dimensionless magnetic field and velocity given by equations ( [ scl3 ] ) and ( [ scl4 ] ) . however , syntheses using @xmath68 km s@xmath35 and @xmath69 g were also tried . we found that the degree of circular polarization increases linearly as @xmath27 , whereas a larger @xmath26 enhances the line asymmetries . on the other hand , the kind of general trends and properties that we analyze here do not depend on the precise value of the scale factors . the amount of magnetic flux and energy in the numerical data is far larger than that detected in the sun as in fields . this difference can be understood as the result of two important factors that hinder the detection of the weak signals emerging from the simulation . first , the magnetic fields are highly disorganized so that the polarization signals tend to cancel as the angular resolution deteriorate ( @xcite @xcite ) . second , most synthetic signals are extremely low , i.e. at and below the sensitivity of the present instrumentation . consequently a large fraction could not be detected at present . in this section we use our synthetic lines to explore these effects . we find that once realistic angular resolution and sensitivity are taken into account , the simulations are in good agreement with the observations . figure [ mean ] shows the mean unsigned signal in the magnetogram of figure [ magneto ] as a function of the seeing ( i.e. , mean @xmath70 over the snapshot versus fwhm of seeing ) . we consider various sensitivities of the magnetograph : moderate ( 20 g ) , good ( 5 g ) and very good ( 0.5 g ) . we account for the limited sensitivity by setting to zero all those points in the smeared magnetogram where the signal is below the hypothetical observational threshold . figures [ mean]b is identical to figure [ mean]a except that it has been normalized to the mean longitudinal field in the simulation ( i.e. , mean @xmath71 g , where the average considers all the points of the simulation that we use ) . according to the standard interpretation ( equation [ [ theory ] ] ) , this is the parameter that one retrieves from a magnetogram . the normalization helps visualizing the fraction of real signal that remains in the magnetogram for a given angular resolution and sensitivity . there are several features in these two figures that deserve comment . even with perfect sensitivity and maximum angular resolution , one detects only 80 % of the existing flux . the cancellation is mostly due to the averaging along the line - of - sight caused by the radiative transfer . at maximum angular resolution , the flux in the magnetogram depends little on the sensitivity since most of the signals exceed 20 g. the decrease in signal strength as the angular resolution deteriorate is severe . for the typical 1angular resolution , the detectable signals are only 10 % of the original ones ( fig . [ mean]b ) . this estimate is optimistic since it holds true if the sensitivity is good ; should the latter be moderate , only traces of the original signals remain ( 1% for 20 g sensitivity ) . figure [ mean]a includes values for solar in magnetic flux densities observed by various authors . the level of detected flux density agrees well with the predictions of the simulations once the angular resolution has been taken into account . note that the observed flux densities are more than a factor of ten smaller than the signals in the original magnetogram . we should not overemphasize the agreement , since the observational points are rather uncertain ( they come from inhomogeneous sources , with different sensitivities and based on disparate techniques : see below ) . however , two conclusions can be drawn . first , intense yet tangled magnetic fields like those in the numerical simulation are compatible with the present solar observations . second , if our spatially fully resolved synthetic spectra were emitted by the sun , they would produce the degree of polarization that we detect on the sun with the present instrumentation . the observations presented in figure [ mean]a required transformation from the numbers quoted in the original works to the quantities plotted in the figure . here we briefly describe these transformations for the sake of completeness . ( the symbols accompanying the citations correspond to those used in fig . [ mean]a . ) @xcite ( @xcite ; bullet sign @xmath72 ) deduce 10 g mean flux density for the quiet sun fields , however , they mention that the apparent flux density decreases by a factor 2.4 if it is estimated from magnetograms . this renders 4.2 g for a 1 angular resolution , a figure derived from the cut off frequency in the fourier domain of the continuum intensity image ( @xcite @xcite ) . the same procedure is used to estimate the angular resolution of the spectra in @xcite ( @xcite ; square @xmath73 ) . the mean flux density , 3.4 g , has been directly provided by the author . @xcite ( @xcite ; asterisk @xmath74 ) point out , explicitly , a 1.65 g flux density for their angular resolution of 2 . @xcite ( @xcite ; times sign @xmath66 ) find some 3.5 g mean flux density ( private communication ) , to which we associate an angular resolution of two pixels or 14 . @xcite ( @xcite ; triangle @xmath75 ) do not directly give a mean flux density for their measurements . however , their figure 3 contains the magnetic fluxes of individual measurements , and the authors provide the scale factor between the magnetic flux and the magnetic flux density ( @xmath76 mx g@xmath35 ) . with this conversion , the mean flux density of these observations is about 4 g. the magnetic features occupy 68 % of the surface , since the rest remains below the sensitivity threshold . consequently , the mean flux density over the whole surface results 0.68 @xmath77 g. @xcite ( @xcite , fig . 1 ; plus sign @xmath78 ) provide the distribution of stokes @xmath0 @xmath15250 signals found in the quiet sun , being the average signal about @xmath79 ( in units of the continuum intensity ) . the authors also point out a calibration constant from stokes @xmath0 signal to flux density . it gives 2 g for the mean observed signal . since these signals fill 40% of the solar surface , the mean flux density is about 0.8 g. we assign to these data an angular resolution twice the sampling interval ( some 23 ) . finally , @xcite ( @xcite ; diamond @xmath80 ) have recently found 17 g mean flux density in a 05 angular resolution magnetogram taken with @xmath16302.5 . figure [ inset ] provides a different illustration of the similarities between the synthetic magnetogram and the real sun . it shows a real magnetogram of the quiet sun obtained in the blue wing of @xmath16302.5 ( @xcite @xcite , fig . 1 ) , i.e. , using the observational setup that we have tried to reproduce ( see [ calibration ] ) . a patch of the real magnetogram with the size of the numerical simulation has been replaced with the synthetic one ( fig . [ inset ] left ) . except for the location of the inset , which we place in an in region , we have not used free parameters to produce the combined magnetogram . the angular resolution has been chosen to match the observation ( 1 ) , whereas the degree of polarization comes directly from the synthesis . despite the absence of fine - tuning , it turns out to be extremely difficult to distinguish the magnetogram with the artificial inset ( fig . [ inset ] left ) from the real one ( fig . [ inset ] right ) . in other words , the synthetic magnetogram contains structure with a spatial distribution similar to the observed one , and with a degree of polarization which fits within the observed range . in the absence of gradients of magnetic and velocity fields within the resolution element , the stokes profiles have to obey well defined symmetries ( see [ sec_introduction ] ) . this kind of symmetries are never found in the quiet sun , instead profiles frequently show extreme asymmetries ( @xcite @xcite ; @xcite @xcite ; @xcite @xcite ) . because the magnetic field in the numerical simulation has a highly intermittent structure ( @xcite @xcite ; @xcite @xcite ) , we expected the resulting synthetic stokes profiles to be asymmetric . in the following , we compare our synthetic profiles with observed ones and study in a statistical sense their differences and similarities . we proceed by first classifying the types of stokes @xmath0 profiles produced by the simulation . the @xmath81 stokes @xmath0 profiles in the snapshot were assorted using a cluster analysis algorithm identical to that employed with real data by @xcite ( @xcite ; 3.2 ) . the procedure identifies and groups profiles with similar shape , irrespective of their degree of polarization and polarity , since it employs stokes @xmath0 profiles normalized to the largest blue peak ( see @xcite @xcite for details ) . the classification is summarized in figure [ vasym0 ] . for each different class , the averaged stokes @xmath0 profile over the ensemble is plotted . the mean is taken after each individual profile has been multiplied by the sign of its largest blue peak . this avoids cancellation of different polarities . the mean profiles are numbered ( upper left corner in each panel ) according to the percentage of profiles in the simulation that are elements of their class , with # 0 being the most probable and # 17 the least probable . the probability to find a profile of a given class is indicated in the upper right corner of each panel . note the various possibilities . from virtually anti - symmetric stokes @xmath0 ( implying no asymmetry ) , to profiles with one ( e.g. , # 11 and # 13 ) or three lobes ( e.g. , # 12 and # 14 ) . all these asymmetries are produced by gradients of magnetic and velocity fields along the line - of - sight . the peak polarization is considerable , some 1% in units of the continuum intensity . this has to be the case to yield the large flux density shown in figure [ mean]a for perfect angular resolution . another detail worthwhile noting is the balance between the number of profiles having a large blue lobe and those whose principal lobe is the red one . the line shapes in figure [ vasym0 ] are difficult to compare with observed profiles since observations of the quiet sun have much lower angular resolution . figure [ vasym1 ] shows another classification having all the features explained above , except that the simulation data have been smeared with a 1 seeing , typical of the real observations . first , the polarization signals are reduced by one order of magnitude with respect to the original profiles ; compare them with those in figure [ vasym0 ] . second , new more complicated line shapes have arisen as the result of the large spatial smearing ( radiative transfer smoothes over only 100 km , whereas the spatial smearing does it over 725 @xmath66 725 km@xmath82 ) . stokes profiles having all these very asymmetric shapes are indeed observed in the real quiet sun ( see @xcite @xcite , fig . 12 ; @xcite @xcite , fig . 7 ; @xcite @xcite , fig . 4 , 5 and 6 ; @xcite @xcite , fig . this qualitative agreement is again a notable feature of the simulation , since there was no obvious a priori reason to expect it . however , despite such general qualitative agreement , one can find quantitative differences between the synthetic and the observed profiles . as it happens with the fully resolved profiles ( fig . [ vasym0 ] ) , the number of synthetic profiles having a principal blue lobe and those with a principal red lobe is similar ( e.g. , the pairs # 12 and # 18 ; # 31 and # 34 ; # 33 and # 35 ) . such balance is not present among the observed profiles , where the blue lobe usually dominates ( e.g. , @xcite @xcite , fig . 4 ; @xcite @xcite , fig . another qualitative difference with observations concerns the profiles that are most frequently obtained in the simulation . they show almost no asymmetry ( see classes # 0 to # 7 ) . contrariwise , the observational counterpart have a well defined asymmetry characterized by a large blue lobe ( similar to those observed in plage and enhanced network regions ) . this lack of significant asymmetry can be traced back to the original syntheses ( fig . [ vasym0 ] , classes # 0 to # 4 ) , and therefore to the variations along the line - of - sight of the magnetic field and velocity . the probable cause is discussed in the next paragraph . figure [ brms ] summarizes the kind of variations along the line - of - sight existing in the numerical simulation . several definitions are required before it can be interpreted . the variations are described using standard statistical parameters , namely , the line - of - sight mean value @xmath83 , the line - of - sight standard deviation @xmath84 , and the line - of - sight correlation coefficient @xmath85 , @xmath86 @xmath87^{1/2 } , \label{stat2}\ ] ] @xmath88 \big/ \bigl[\overline{\delta f}_{ij}~\overline{\delta g}_{ij}\bigr].\ ] ] the arrays @xmath89 and @xmath90 may represent any component of the fields , and their indexes vary according to the position in the horizontal plane ( @xmath91 and @xmath92 ) and in the vertical direction ( @xmath93 ) . the symbol @xmath94 stands for the number of grid points in the vertical direction . we should bear in mind that the line - of - sight averages defined in equations ( [ stat2 ] ) depend on the horizontal coordinates . we need to characterize the typical properties of these line - of - sight mean values for each range of mean longitudinal magnetic field strength . for this purpose we define the average @xmath95 and the dispersion @xmath96 of the quantity @xmath97 among all those points in the simulation with a given line - of - sight mean longitudinal magnetic field @xmath98 , i.e. , @xmath99 @xmath100^{1/2},\ ] ] with @xmath101 and @xmath102 note that the symbol @xmath97 may represent any of the statistical parameters in equation ( [ stat2 ] ) ( @xmath103 , @xmath104 or @xmath105 ) , and @xmath106 and @xmath107 correspond to the grid points in the two horizontal directions . the bin size @xmath108 has to be chosen to guarantee having enough points per bin . following these definitions , we can now interpret figure [ brms ] . the different quantities represented are plotted as function of the line - of - sight mean magnetic field . the first panel in figure [ brms ] shows the variation of @xmath109 and @xmath110 . the limited dispersion of the vertical velocities provides an explanation for the predominance of profiles with small asymmetries . the dispersion must be of the order of the line width to produce a substantial modification of the line shape . the typical standard deviation of the vertical velocities along the line - of - sightturns out to be between 0.2 and 0.3 km s@xmath35 ( @xmath110 , fig . [ brms]a , the solid line ) , whereas the line widths are of the order of 2 km s@xmath35 ( see [ sec_spectra ] ) . the magnetic field itself is probably not responsible for the moderate asymmetries since its variations along the line - of - sight are large . for example , figure [ brms]b shows the standard deviation of the mean longitudinal magnetic field @xmath111 , which is frequently larger than the absolute value of @xmath112 . in fact , the variations of the longitudinal magnetic fields are so important that @xmath65 very often changes sign along the line - of - sight(fig . [ brms]c ) . note that none of these statements on large magnetic field gradients apply to the intrinsically strong fields , a case discussed separately in the next paragraph . above , say , 200 g , the variations of field strength are mild and the longitudinal field maintains a constant sign along the line - of - sight ( figs . [ brms]b and [ brms]c ) . concerning the balance between the number of asymmetries towards the blue and towards the red in figures [ vasym0 ] and [ vasym1 ] , it is probably due to the lack of a definite sign for the correlation between magnetic field and velocity . works on the asymmetries in plage and network regions repeatedly indicate the need for a negative correlation to account for the observed preponderance of the stokes @xmath0 blue lobe , explicitly , @xmath113 ( see , e.g. , @xcite @xcite ; @xcite @xcite ; @xcite @xcite ; @xcite @xcite ; @xcite @xcite ; @xcite @xcite ) . such condition is satisfied when downflows and magnetic fields are spatially separated , i.e. , when the strongest downflows tend to occur in weakly magnetized plasma . ( note that @xmath114 corresponds to downflows . ) one can see in figure [ brms]d that the correlation between @xmath115 and @xmath116 has a well defined negative value only for the largest field strengths . since theses points represent a small fraction of the synthetic profiles , they contribute very little to the classification in figure [ vasym0 ] which , consequently , shows no obvious preference for a blue asymmetry . those patches in the simulation with the largest field strength show a clear negative correlation fulfilling the criterion in equation ( [ correlation2 ] ) ( see fig . [ brms]d ) . do they produce the observed stokes @xmath0 profiles with a main blue lobe ? they do not , since the asymmetry of the profiles emerging from concentrations of intense field strength are minimal . this fact can be understood using figures [ brms]a and [ brms]b , which reveal gradients of both magnetic field and velocity too small for the requirements described in the previous paragraph . despite this apparent disagreement , the key ingredients to yield the right shapes are already present in the simulation . if one artificially increases the gradients of magnetic field and velocity already existing in the simulation , large asymmetries similar to the observed ones automatically show up . figure [ net_like ] contains synthetic profiles emerging from the three more intense magnetic concentrations in the snapshot ( labeled as @xmath67 , @xmath24 and @xmath59 in fig . [ magneto ] , left ) . note that they already have the stokes @xmath0 asymmetries that characterizes network and in regions . ( figure [ net_like]d includes one of these observed stokes @xmath0 profiles for reference , namely , one network profile in @xcite @xcite ) . in order to produce theses new synthetic profiles with enhanced asymmetries , we increased the intensity of the flow with respect to the scaling in [ sec_spectra ] by using @xmath117 . in addition , we increased the variations of magnetic field strength by averaging all the absorption and emission over 05 of the simulation ( i.e. , over all the points in a box of this size ) . the qualitative agreement between synthetic and real profiles is remarkable . the above considerations lead to an interesting question . how should the numerical simulations be modified in order to produce asymmetries closer to the observed ones ? first , the dispersion of velocities at the smallest scales must be increased , which implies a decrease in the kinematic viscosity . second , magnetic and non - magnetic regions should be even more intermittent to strengthen the correlation ( [ correlation2 ] ) . this can be achieved by decreasing the magnetic diffusivity , which would both increase the tangling of magnetic field lines and the dispersion of field strengths existing in the intense concentrations . one of the observational constraints on the existence of a complex and tangled magnetic field in the solar photosphere comes from the work by @xcite ( @xcite ) ( see also @xcite @xcite ; @xcite @xcite ) . if a tangled magnetic field exist , it has to broaden the spectral lines of the solar spectrum according to their magnetic sensitivities ( i.e. , according to their effective land factors ) . all other things being the same , those with larger sensitivity should be slightly broader . @xcite ( @xcite ) looked for such effect in the solar unpolarized spectrum with no success . from the error budget of the measurement the authors set an upper limit to the field strength of the existing fields ( @xcite @xcite , equation [ 12 ] ) , @xmath118 in this section we analyze if the magnetic fields in the simulations produce line broadenings compatible with such observational upper limit . this exercise allows to address the question of whether magnetic fields as intense as those in the simulation may exist on the sun , and still remain below the present observational detection limit . we already know that the degree of circular polarization of the simulation stays well within the observational bounds ( [ flux_density ] ) . here we address the question from a different perspective , using a totally different observational constrain that depends on the magnetic fields in a intrinsically different way . our synthetic stokes @xmath61 spectra have an excess of broadening caused by the presence of magnetic fields . figure [ dif ] shows the difference between the mean stokes @xmath61 profile produced by the region , and the mean profile produced when the syntheses are repeated with no magnetic field , but keeping everything else identical . the magnetic profile is broader and shallower at the line center , producing a residual with three lobes . is this extra broadening compatible with the observational limit ( [ limit ] ) ? a detailed modeling of the procedure employed by @xcite ( @xcite ) is clearly beyond our possibilities , since it requires the synthesis of hundreds of spectral lines with different temperature and magnetic field sensitivities . fortunately , the essence of the procedure is simple . if two lines are identical except for their magnetic sensitivity , the small excess of width @xmath119 can be directly related to an _ apparent _ magnetic field strength @xmath120 according to the rule , @xmath121 the scale factor @xmath122 depends of the wavelength , the difference of land factor , and the mean line width @xmath123 . for two lines with the wavelength and strength of @xmath16302.5 , one magnetic and another one non - magnetic , the scaling factor turns out to be @xmath124 which follows from the equations ( 7 ) and ( 8) in @xcite ( @xcite ) . the estimate of the apparent magnetic field strength using equations ( [ broa3 ] ) and ( [ broa4 ] ) is a matter of determining the excess of broadening @xmath125 associated with the residuals in figure [ dif ] . following @xcite ( @xcite ) , the two mean intensity profiles where fitted using gaussian functions , i.e. , @xmath126,\ ] ] where @xmath1 stands for the wavelength relative to the line center and @xmath127 represents the continuum intensity . then the difference between the widths @xmath123 for the syntheses with and without magnetic field directly yields @xmath128 or , using equations ( [ broa3 ] ) and ( [ broa4 ] ) , @xmath129 note that the gaussian fits reproduce fairly well the difference between the two synthetic profiles ( see the dashed line in fig . [ dif ] ) . the field strength of our synthetic profiles ( equation [ [ limit2 ] ] ) apparently come into conflict with the observational limit in equation ( [ limit ] ) . should the inconsistency be real , it points out an excess of magnetic fields in the numerical simulations as compared to the solar case ( an excess of magnetic field strength , area coverage of the fields , etc . ) . however , the marginal discrepancy is probably not significant in view of the uncertainties affecting both the syntheses and the observational limit . actually , the similarity between the observational limit and the predicted width should be understood as real chance to test whether complex tangled fields like those in the numerical simulations are present in the solar photosphere . a slight refinement of the currently available diagnostic tools ( e.g. , stenflo & lindegren s technique ) should be able unambiguously to confirm them or discard them . we return to this point in [ conclusions ] .

the synthetic stokes profiles have properties in common with those observed in the quiet sun . the intensity profiles are broadened by the magnetic fields in fair agreement with observational limits . differences between synthetic and observed polarized spectra can also be found . there is a shortage of stokes asymmetries , that we attribute to a deficit of structuring in the magnetic and velocity fields from the simulations as compared to the sun . we consider the possibility that intense and tangled magnetic fields , like those in the simulations , exist in the sun . the existing flux would exceed by far that carried by active regions during the maximum of the solar cycle . detecting these magnetic fields

we employ the magnetic and velocity fields from turbulent dynamo simulations to synthesize the polarization of a typical photospheric line . the synthetic stokes profiles have properties in common with those observed in the quiet sun . the simulated magnetograms present a level of signal similar to that of the inter - network regions . asymmetric stokes profiles with two , three and more lobes appear in a natural way . the intensity profiles are broadened by the magnetic fields in fair agreement with observational limits . furthermore , the hanle depolarization signals of the line turn out to be within the solar values . differences between synthetic and observed polarized spectra can also be found . there is a shortage of stokes asymmetries , that we attribute to a deficit of structuring in the magnetic and velocity fields from the simulations as compared to the sun . this deficit may reflect the fact that the reynolds numbers of the numerical data are still far from solar values . we consider the possibility that intense and tangled magnetic fields , like those in the simulations , exist in the sun . this scenario has several important consequences . for example , less than 10% of the existing unsigned magnetic flux would be detected in present magnetograms . the existing flux would exceed by far that carried by active regions during the maximum of the solar cycle . detecting these magnetic fields would involve improving the angular resolution , the techniques to interpret the polarization signals , and to a less extent , the polarimetric sensitivity .

1205.4429

i

we study the well - posedness of two - dimensional steady supersonic euler flows past a curved lipschitz wall containing strong vortex sheets / entropy waves in the @xmath2norm . the inviscid compressible flows are governed by the two - dimensional steady euler system : @xmath3 with @xmath4 , @xmath5 , @xmath6 , and @xmath7 representing the fluid velocity , scalar pressure , density , and total energy , respectively . furthermore , the total energy @xmath7 is explicitly given by @xmath8 where the internal energy @xmath9 can be written as a function of @xmath10 defined through the thermodynamical relations . the temperature @xmath11 and entropy @xmath12 are the other two thermodynamic variables . in the case of an ideal gas , the pressure _ p _ and internal energy _ e _ can be expressed as @xmath13 with the adiabatic index @xmath14 given by @xmath15 in particular , in terms of the density @xmath6 and entropy _ s _ , we have @xmath16 the constants @xmath17 , and @xmath18 in the above relations are all greater than zero . when the entropy @xmath12 = constant , the flow is called _ isentropic_. in this case , the pressure @xmath5 can be written as a function of the density @xmath6 , @xmath19 , and the flow is governed by the isentropic euler equations : @xmath20 then , by scaling , the pressure - density relation is @xmath21 the adiabatic exponent @xmath22 corresponds to the isentropic polytropic gas . the limiting case @xmath23 corresponds to the isothermal flow . define @xmath24 as the sonic speed . for polytropic gases , the sonic speed is @xmath25 . the flow type is classified by the _ mach number _ @xmath26 . when @xmath27 , system or governs a _ supersonic _ flow ( i.e. , @xmath28 ) , which has all real eigenvalues and is hyperbolic . for @xmath29 , system or governs a _ subsonic _ flow ( i.e. , @xmath30 ) , which has complex eigenvalues and is elliptic - hyperbolic mixed and composite . when @xmath31 , the flow is called sonic_. we are interested in whether compressible vortex sheets / entropy waves in supersonic flow over the lipschitz wall are always stable under the @xmath0 perturbation of the incoming flow . multidimensional steady supersonic euler flows are important in many physical applications ( cf . courant - friedrichs courant - friedrichs-1948 ) . in particular , when the upstream flow is a uniform steady flow above the plane wall in @xmath32 all the time , the flow downstream above a lipschitz wall in @xmath33 is governed by a steady euler flow after a sufficiently long time . moreover , compressible vortex sheets and entropy waves occur ubiquitously in nature and are fundamental waves . furthermore , since steady euler flows are asymptotic states and may be global attractors of the corresponding unsteady euler flows , it is important to establish the existence of steady euler flows and understand their qualitative behavior to shed light on the long - time asymptotic behavior of the unsteady compressible euler flows , one of the most fundamental problems in mathematical fluid dynamics which is still wide open . we observe that the stability of contact discontinuities for the cauchy problem for strictly hyperbolic systems in one space dimension under a @xmath0 perturbation has been studied by sabl@xmath34-tougeron sable-1993 and corli sabl@xmath34-tougeron corli - sable-1997 . in particular , the reflection coefficients , such as @xmath35 here , are required to be less than one , which is the stability condition for the mixed problem in the strip @xmath36 in the earlier works ; see , e.g. , sabl@xmath34-tougeron sable-1993 . working with the non - isentropic euler system and a uniform upstream flow , chen - zhang - zhu chen - zhang - zhu-2007 first proved the global existence in @xmath0 of supersonic euler flows containing a strong vortex sheet / entropy wave under the @xmath0 perturbation of the lipschitz wall by using the glimm scheme . the essential difference between system as analyzed in chen - zhang - zhu-2007 ( and in sections 27 here ) and strictly hyperbolic systems as considered in corli - sable-1997 , sable-1993 is that two of the four characteristic eigenvalues coincide and have two linearly independent eigenvectors which determine precisely the compressible vortex sheets and entropy waves so that two independent parameters are required to describe them , respectively . in this paper , for completeness , we first show , via the wave - front tracking method , the existence of solutions to the problem when a small @xmath0 perturbation is added to the uniform incoming flow . then the @xmath2stability of entropy solutions containing strong vortex sheets / entropy waves is established . as corollaries of these results , the estimates on the uniformly lipschitz semigroup @xmath37 of entropy solutions generated by the wave - front tracking approximations are obtained , and the uniqueness of weak solutions containing strong vortex sheets / entropy waves is established in a larger set of solutions , namely the class of viscosity solutions . in the following , we focus mainly on the problem in the region @xmath38 over the lipschitz wall for the supersonic euler flows @xmath39 governed by system , given that the corresponding problem for the isentropic system is simpler to analyze . the subsequent figure provides the schematic diagram for the problem we study : the boundary and initial data in the problem are as follows : * there is a lipschitz function @xmath40 such that @xmath41 and @xmath42 denote @xmath43 , @xmath44 , and @xmath45 = @xmath46 as the outer normal vectors to @xmath47 at the respective points @xmath48 ( cf . [ figure1 ] ) . * the incoming flow @xmath49 at @xmath50 is composed of two parts : 1 . the upstream flow @xmath51 consists of one straight vortex sheet / entropy wave @xmath52 and two constant vectors @xmath53 , when @xmath54 , and @xmath55 , when @xmath56 , satisfying @xmath57 where @xmath58 is the sonic speed of state @xmath59 . 2 . the @xmath0 perturbation @xmath60 at @xmath61 so that @xmath62 . then we consider the following initial - boundary value problem for system : @xmath63 * definition 1.1 * ( _ admissible entropy solutions _ ) . a @xmath0 function @xmath64 is said to be an entropy solution of the initial - boundary value problem and if and only if the following conditions hold : * @xmath65 is a weak solution of ( 2.1 ) and satisfies @xmath66 * @xmath65 satisfies the _ steady entropy clausius inequality _ : @xmath67 in the distributional sense in @xmath38 including the lipschitz wall boundary . one of the essential developments within this paper is to develop suitable methods to deal with the challenges caused by the nonstrictly hyperbolicity of the system and the lipschitz wall boundary , in comparison with the previous progress with the strictly hyperbolic systems of conservation laws , particularly to the analysis of the cauchy problem . for supersonic euler flow with a strong shock - front emanating from the wedge vertex , chen - li chen - li-2008 worked out the issue for a lipschitz wedge boundary . we now discuss some main differences in our work here from the cauchy problem and the resulting key difficulties . we remark that , in the case of the cauchy problem concerning only @xmath68 waves , the decrease of the lyapunov functional and the @xmath2stability of the solutions were obtained through the cancellation of distances on both sides of waves . in the presence of a strong shock , for the @xmath2stability of solutions of the cauchy problem for strictly hyperbolic systems of conservation laws , the lyapunov functional was found to decrease by employing the strength of the strong shock to control the strengths of weak waves of the other families ( e.g. , see lewicka - trivisa lewicka - trivisa-2002 ) . in contrast with our lipschitz wall problem , which is a problem of initial - boundary value type , there is no such cancellation by the boundary as only one - side is possible near it . furthermore , no strong vortex sheets / entropy waves ( characteristic discontinuities ) nor strong shocks are present to handle the strength of the weak waves of the other families , and the terms in the estimates for the first and fourth family carry different signs . as such , it is difficult to say whether the functional can be made to decrease for our case of strong vortex sheets and entropy waves with multiplicity of eigenvalues . one of the key steps to resolve this is to use the physical feature of the boundary condition that the flow of two solutions near the boundary must run in parallel ( also see chen - li-2008 ) . this observation helps us to obtain additional quantitative relations near the boundary . then , applying suitable weights and adjustments in the coefficients of the lyapunov functional and using the cancellation between the different families , the functional is found to decrease in the flow direction . the rest of the paper is organized as follows . in section 2 , we recall some fundamental properties of the two - dimensional steady euler system and discuss related nonlinear waves and wave interaction estimates . in section 3 , the wave - front tracking algorithm is discussed , working in the presence of strong vortex sheets / entropy waves , the suitable interaction potential @xmath69 is constructed , including the effect of the lipschitz wall , and the existence of entropy solutions in @xmath0 is established for the initial - boundary value problem . in section 4 , we construct the lyapunov functional @xmath70 ( equivalent to the @xmath2distance between two entropy solutions @xmath65 and @xmath71 ) to include the nonlinear waves produced by the wall boundary vertices . then , in section 5 , the monotone decrease of the functional @xmath70 is established in the flow direction , leading to the @xmath2stability of the solutions containing strong vortex sheets / entropy waves . using the estimates established in sections 35 , in section 6 , we obtain the existence of a lipschitz semigroup of solutions generated by a wave - front tracking approximation , as well as some estimates on the uniformly lipschitz semigroup @xmath37 produced by the limit of wave - front tracking approximations . moreover , the uniqueness of solutions with strong vortex sheets / entropy waves is obtained in the larger class of viscosity solutions .

we establish the well - posedness of compressible vortex sheets and entropy waves in two - dimensional steady supersonic euler flows over lipschitz walls under a boundary perturbation . in particular , when the total variation of the incoming flow perturbation around the background strong vortex sheet / entropy wave is small , we prove that the two - dimensional steady supersonic euler flows containing a strong vortex sheet / entropy wave past a lipschitz wall arestable . both the lipschitz wall ( whose boundary slope function has small total variation ) and incoming flow perturb the background strong vortex sheet / entropy wave . the weak waves are reflected after nonlinear waves interact with the strong vortex sheet / entropy wave and the wall boundary . using the wave - front tracking method , the existence of solutions in over lipschitz walls is first shown , when the incoming flow perturbation of the background strong vortex sheet / entropy wave has small total variation . then we establish thecontraction of the solutions with respect to the incoming flows . to achieve this , a lyapunov functional , equivalent to thedistance between two solutions containing strong vortex sheets / entropy waves , is carefully constructed to include the nonlinear waves generated both by the wall boundary and from the incoming flow . this functional is then shown to decrease in the flow direction , leading to thestability , as well as the uniqueness , of the solutions . furthermore , the uniqueness of solutions extends to a larger class of viscosity solutions .

we establish the well - posedness of compressible vortex sheets and entropy waves in two - dimensional steady supersonic euler flows over lipschitz walls under a boundary perturbation . in particular , when the total variation of the incoming flow perturbation around the background strong vortex sheet / entropy wave is small , we prove that the two - dimensional steady supersonic euler flows containing a strong vortex sheet / entropy wave past a lipschitz wall arestable . both the lipschitz wall ( whose boundary slope function has small total variation ) and incoming flow perturb the background strong vortex sheet / entropy wave . the weak waves are reflected after nonlinear waves interact with the strong vortex sheet / entropy wave and the wall boundary . using the wave - front tracking method , the existence of solutions in over lipschitz walls is first shown , when the incoming flow perturbation of the background strong vortex sheet / entropy wave has small total variation . then we establish thecontraction of the solutions with respect to the incoming flows . to achieve this , a lyapunov functional , equivalent to thedistance between two solutions containing strong vortex sheets / entropy waves , is carefully constructed to include the nonlinear waves generated both by the wall boundary and from the incoming flow . this functional is then shown to decrease in the flow direction , leading to thestability , as well as the uniqueness , of the solutions . furthermore , the uniqueness of solutions extends to a larger class of viscosity solutions .

1001.4991

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our first conclusion , in agreement with other work , is that pm simulations are inefficient for calculating cmb lensing due to strongly nonlinear structures ( see fig . [ fig2 ] and comments in section [ comparison ] ) . while it is not impossible to simulate these effects with a pm code the required resolution is so large that the additional short - scale resolution provided by ap3 m ( or other high resolution n - body technique ) is far more efficient at capturing the lensing effect . hence our development of a combined parallel ap3m - ray - tracing code is a necessary step to estimate the lensing signal at high @xmath4 . only the @xmath220 effect ( see section [ nbody ] ) produced by scales smaller than @xmath257 between redshifts @xmath258 and @xmath259 has been estimated with ap3 m simulations . this choice is appropriate for the following reasons : ( 1 ) all the strongly nonlinear scales are taken into account ; ( 2 ) omitting scales greater than @xmath257 makes our ray - tracing procedure efficient ( see section [ nbody ] ) ; ( 3 ) the effect produced by scales greater than @xmath260 ( @xmath221 in section [ nbody ] ) can be studied by using the linear version of cmbfast ; and , ( 4 ) the lensing due to scales smaller than @xmath257 , at redshift @xmath261 ( @xmath222 in section [ nbody ] ) , can be computed using standard semi - analytical methods implemented in cmbfast . given that our study has strongly focused on the @xmath220 signal , we exhaustively investigated the numerical issues involved when estimating this signal . our main conclusions can be summarized as follows : * the lensing contribution between @xmath132 and @xmath77 is negligible * for each rls , a few realizations suffice to get a good average @xmath49 spectrum and , moreover , each single simulation gives a very good spectrum rather similar to the average one * rlss , which are essentially identical except for the preferred directions , give similar spectra ( the ray - tracing procedure has little variance ) * simulation boxes of @xmath262 are not fully necessary for @xmath263 ; however , for @xmath211 , these large sizes lead to the most reliable spectra and , moreover , such sizes should lead to very good spectra in the @xmath4-interval ( @xmath264@xmath265 ) * simulations in boxes of @xmath159 lead to good @xmath49 spectra for @xmath266 * for @xmath267 , all the rlss lie in a region of width @xmath2680.5 @xmath237k , indicating that the rlss give consistent estimates of the signal in this range * the signal in the range @xmath269 is @xmath270k , which is @xmath271 @xmath237k higher than that found elsewhere ( @xcite ) despite some simulation uncertainties , our code and technique have lead to a robust estimate of the lensing effect in the @xmath4-interval @xmath272 , where it clearly dominates the primary anisotropy . moreover , the estimated power is larger than that obtained with semi - analytical methods and the cmbfast code . we thus suggest that the resulting value of a few micro - kelvin may explain the excess power at high @xmath4 in the bima and cbi observations . this conclusion is supported by recent studies based on the millennium simulation @xcite , where the authors have reported a small contribution from nonlinearity at @xmath273 . however , the methods of @xcite have been designed to build all - sky lensed maps , and do not have the resolution necessary to perform an accurate estimate of the weak lensing by strongly nonlinear structures in the @xmath4-interval where we have found our main effect . our direct estimation of the potential gradients at photon positions using pp corrections from the local dark matter particles appears to be the main origin of the difference between our results and other research relying either on planes or grid interpolations . however , we emphasize that differences only occur at the large @xmath274 values we have been investigating . our method employs extremely fine time resolution , namely that used by ap3 m simulations and also a very good angular resolution ( see above ) . due to current limitations in our method it is not possible for us to determine the precise role of temporal resolution in an accurate lensing calculation . it is well known that on small scales baryons do not follow the dark matter distribution . thus , while we have attempted to be as accurate as possible in this dark matter simulation , we are now probing scales where contributions from baryons are beginning to become significant . an investigation of the impact of baryons by @xcite considered two types of simulations , the first with non - radiative baryons while the second included dissipation and star formation . they found that for @xmath275 an effect of between 1% to 10% on the weak - lensing shear angular power spectrum , as calculated from dark matter alone , was possible . the largest difference was produced in the run with dissipation and star formation , where a 10% increase in the ( shear ) @xmath234s at @xmath169 was observed . future work is definitely necessary to determine the impact of this physics on lensing statistics . we plan to conduct simulations with baryons and feedback processes both to identify its impact on the signal we find , and also to systematically evaluate the combined impact of the sz effect and weak lensing . for calculations that are accurate to high @xmath4 it seems to be necessary to move cmb photons through the simulation box while structures are evolving , which ensures the spatial gradients are accurately calculated on the photon positions ( test particles ) . once the n - body code has been modified to compute spatial gradients at particle test positions , there are no theoretical or technical reasons to take a temporal resolution different from that defined by the simulation time step . from the theoretical point of view , the time step resolution is obviously most compatible with the n - body technique ( and thus takes into account the entire evolution of the simulation ) . from the technical point of view , the use of the time step resolution requires the minimum memory cost as the number of test particles between two successive times , although large , is minimized . because of these considerations , temporal resolution is not a parameter to be varied in our calculations . our ap3 m code adapted to cmb lensing calculations can be run for different values of the parameters defining the lss ; hence , this code allows us to see how the resulting angular power spectra depend on the parameters defining both the n - body simulation and the ray - tracing procedure . we thank the anonymous referee for suggestions that improved the clarity and content of the paper . fullana , j.v . arnau and d. sez acknowledge the financial support of the spanish ministerio de educacin y ciencia , mec - feder project fis2006 - 06062 . rjt and hmpc acknowledge funding by individual discovery grants from nserc . rjt is also supported by grants from the canada foundation for innovation and the canada research chairs program . hmpc acknowledges the support of the canadian institute for advanced research . simulations were performed at the _ computational astrophysics laboratory _ at saint mary s university . antn l. , cerd - durn , p. , quilis , v. , and sez , d. 2005 , , 628 , 1 arnau j.v . , aliaga , a. , and sez , d. 2002 , , 382 , 1138 bond , j.r . , 2005 , , 626 , 12 burigana , c. , and sez , d. 2003 , , 409 , 423 carbone , c. , springel , v. , baccigalupi , c. , bartelmann , m. , & matarrese , s. , 2008 , mnras , 388 , 1618 carbone , c. , baccigalupi , c. , bartelmann , m. , matarrese , s. , and springel , v. , 2009 , mnras , 396 , 668 cerd - durn , p. , quilis , v. , and sez , d. 2004 , , 69 , 043002 cooray , a. , and melchiorri , a. 2002 , , 66 , 083001 couchman , h. m. p. , 1991 , , 368 , 23 das , s. , & bode , p. , 2008 , apj , 682 , 1 dawson , k.s . , holzapfel , w.l . , carlstrom , j.e . , joy , m. , and laroque , s.j . , 2006 , , 647 , 13 efstathiou , g. , davis , m. , white , s. d. m. & frenk , c. , 1985 , apjs , 57 , 241 fosalba , p. , , 2008 , mnras , 391 , 435 grski , k.m . , hivon , e. , and wandelt , b.d . 1999 , in proc . mpa / eso cosmology conf . , banday , r.k . sheth and l. n. da costa ( garching : european southern observatory ) ( astro - ph/9812350 ) hamana , t. , , 2001 , a&a , 367 , 18 harrison , e. r. , 1970 , phys . d. , 1 , 2726 hernquist , l. & katz , n. , 1989 , apjs , 70 , 419 hilbert , s. , , 2009 , a&a , 499 , 31 hinshaw , g. , et al . , arxiv:0803.0732 hockney r.w . , and eastwood j.w . 1988 , computer simulations using particles ( bristol : iop ) jain , b. , seljak , u. , and white , s. 2000 , , 530 , 547 jing , y. p. , zhang , p. , lin , w. p. , gao , l. , and springel , v. , 2006 , , 640 , l119 knox , l. 1995 , , 52 , 4307 kim , j. , , 2008 , arxiv:0812.1392 komatsu , e. , & seljak , u. , 336 , 1256 komatsu , e. , et al . , arxiv:0803.0547 lewis , a. , and challinor , a. 2006 , , 429 , 1 moore , b. , governato , f. , quinn , t. , stadel , j. , & lake , g. , 1998 , , 499 , l5 moutarde , f. , alimi , j .- m . , bouchet , f.r . , pellat , r. , and ramani , a. 1991 , , 382 , 377 perlmutter , s. , 1999 , apj , 517 , 565 puchades , n. , fullana , m.j . arnau , j.v . and sez , d. 2006 , , 370 , 1849 quilis , v. , ibez , j.m . , and sez , d. 1998 , , 502 , 518 riess 1998 , aj , 116 , 1009 sez , d. , holtmann , e. , and smoot , g.f . 1996 , , 473 , 1 sez , d. , puchades , n. , arnau , j.v . and fullana , m.j . 2006 , proceedings of science , 058 sandarin , s.f . , and zeldovich , ya . b. 1989 , rev . phys . , 61,185 sato , m. , , 2009 , arxiv:0906.2237 scott , d. , srednicki , m. and white , m. 1994 , , 421 , l5 seljak , u. , and zaldarriaga , m. 1996 , , 469 , 437 seljak , u. 1996 , , 463 , 1 shapiro , c. , & cooray , a. , 2006 , jcap , 603 , 7 sievers , j.l . , , 2009 , arxiv:0901.4540 smith , r.e , 2003 , mnras , 341 , 1311 spergel , d. 2007 , apjs , 170 , 377 springel , v. , , 2005 , nature , 435 , 629 teyssier , r. , , 2009 , a&a , 497 , 335 thacker , r. j. , & couchman , h. m. p. , 2006 comm . , 174 , 540 van waerbeke , l. , , 2001 , mnras , 322 , 918 vianna , p. t. p. & liddle , a. 1996 , mnras , 281 , 323 white , m. , and hu , w. 2000 , , 537 , 1 zeldovich , ya . b. 1970 , , 5 , 84

we estimate the impact of weak lensing by strongly nonlinear cosmological structures on the cosmic microwave background . the lensing deviations are evaluated while structure evolves during the simulation so that all evolution steps rather than just a few outputs are used in the lensing computations . the new code also includes a ray - tracing procedure that avoids periodicity effects in a universe that is modeled as a 3-d torus in the standard way . we find that a box size of mpc is sufficient to provide a robust estimate of the weak lensing angular power spectrum in the-interval ( 2,0007,000 ) . for a reaslistic cosmological model the power^{1/2}$ ] takes on values of a few in this interval , which suggests that a future detection is feasible and may explain the excess power at high in the bima and cbi observations .

we estimate the impact of weak lensing by strongly nonlinear cosmological structures on the cosmic microwave background . accurate calculation of large multipoles requires n - body simulations and ray - tracing schemes with both high spatial and temporal resolution . to this end we have developed a new code that combines a gravitational adaptive particle - particle , particle - mesh ( ap3 m ) solver with a weak lensing evaluation routine . the lensing deviations are evaluated while structure evolves during the simulation so that all evolution steps rather than just a few outputs are used in the lensing computations . the new code also includes a ray - tracing procedure that avoids periodicity effects in a universe that is modeled as a 3-d torus in the standard way . results from our new simulations are compared with previous ones based on particle - mesh simulations . we also systematically investigate the impact of box volume , resolution , and ray - tracing directions on the variance of the computed power spectra . we find that a box size of mpc is sufficient to provide a robust estimate of the weak lensing angular power spectrum in the-interval ( 2,0007,000 ) . for a reaslistic cosmological model the power^{1/2}$ ] takes on values of a few in this interval , which suggests that a future detection is feasible and may explain the excess power at high in the bima and cbi observations .

1310.0560

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radiative efficiencies of the disk accretion processes in individual qsos are related to the spins of the central mbhs , which may be profoundly connected to the mbh assembly history as suggested by a number of recent studies ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? it is therefore of great importance to estimate the radiative efficiency of individual qsos and investigate its statistical distribution among qsos . in this study , we estimate the radiative efficiency individually for a large number of sdss qsos . we first estimate the accretion rate for each qso by matching the detected optical band luminosity(/-ies ) with that predicted by the disk model , by adopting the thin disk accretion model and assuming that the true mass of the central mbh is the same as that given by the virial mass estimator(s ) . we also estimate the bolometric luminosity of each qso by adopting the empirical spectral energy distribution suggested by various multi - wavelength observations of small qso samples . with the estimated accretion rate and the bolometric luminosity , we obtain the radiative efficiency for each sdss qso . we find an apparent strong correlation between the radiative efficiency and the mbh virial mass in low redshift bins and it becomes weak in high redshift bins . in the lowest redshift bin ( @xmath260 ) , this apparent correlation ( @xmath261 , and @xmath262 ) is roughly consistent with that found by @xcite for the dl qsos in a similar redshift range . we also find that the mean radiative efficiencies of the sdss qsos are consistent with being a constant @xmath154 ( though with large scatters ) over the redshift range from @xmath113 to @xmath161 , which does not suggest any significant evolution with redshift . this estimate of the mean radiative efficiency of qsos is totally independent of but roughly consistent with those estimations based on the sotan argument ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . with the enormous large sample of the sdss qsos , it is possible to statistically model the various biases in the estimations of the radiative efficiency and the selection effects of the sdss qsos . to do so , we generate mock sdss qso samples according to the true mbh mass function and the eddington ratio distribution obtained in @xcite , by involving the selection criteria of the sdss qsos and the uncertainties in the mbh virial mass estimations and the inclination angles . we estimate the radiative efficiency for qsos in each mock sample by adopting the same method as that for the sdss qso and obtain the probability density distribution of those mock qsos in the radiative efficiency versus the mbh virial mass plane . we find that the @xmath0@xmath102 correlations for the sdss qsos in different redshift bins can be well explained by the selection effects and the biases induced by the usage of @xmath102 as the true mbh mass , and the selection effects play the dominant roles in leading to the @xmath0@xmath102 correlation , as suggested by @xcite . we conclude that the current sdss qso data is consistent with no intrinsic correlation between the qso radiative efficiency and the true mbh mass . in principle , the accretion rate of a qso may be better determined by fitting the qso spectrum covering a wide range of wavelengths ( e.g. , from the infrared band to the hard x - ray band ) , through an elaborate accretion disk model , and the constraints on the mbh spin and consequently the radiative efficiency may be also simultaneously obtained . in the future , if observations can obtain the spectra for a large sample of qsos , with good wavelength , luminosity and redshift coverage , it may be possible to estimate their radiative efficiencies in a more self - consistent way and then further investigate the relationship , if any , between the radiative efficiency and the mbh mass , which would shed light on not only the assembly history of mbhs ( e.g. , * ? ? ? * ) but also the physical reasons for the small spread in the sed shapes of qsos pointed by @xcite . we thank qingjuan yu for constructive suggestions and discussions , andreas schulze and changshuo yan for helpful discussions . this work was supported in part by the national natural science foundation of china under nos . 10973017 and 11033001 , the national basic research program ( 973 programme ) of china ( grant 2009cb824800 ) , and the bairen program from the national astronomical observatory of china , chinese academy of sciences .

we estimate the radiative efficiency of individual type 1 sdss qsos by using their bolometric luminosities ( ) and accretion rates ( ) , which may be related to the assembly histories and spins of the central massive black holes ( mbhs ) . we estimate by using the empirical spectral energy distributions of qsos and by fitting the observed optical luminosity(/-ies ) with the thin accretion disk model , assuming the mbh masses given by the virial mass estimator(s ) ( ) . we find an apparent correlation between and , which is strong at redshift , weak at , and consistent with that found by for pg qsos at . to investigate whether this correlation is intrinsic or not , we construct a mock sample of qsos according to the true mbh mass and eddington ratio distributions given in . by comparing the results obtained from the mock sample with that from the sdss sample , we conclude that the current sdss qso data is consistent with no strong intrinsic correlation between radiative efficiency and true mbh mass and no significant redshift evolution of radiative efficiencies .

we estimate the radiative efficiency of individual type 1 sdss qsos by using their bolometric luminosities ( ) and accretion rates ( ) , which may be related to the assembly histories and spins of the central massive black holes ( mbhs ) . we estimate by using the empirical spectral energy distributions of qsos and by fitting the observed optical luminosity(/-ies ) with the thin accretion disk model , assuming the mbh masses given by the virial mass estimator(s ) ( ) . we find an apparent correlation between and , which is strong at redshift , weak at , and consistent with that found by for pg qsos at . to investigate whether this correlation is intrinsic or not , we construct a mock sample of qsos according to the true mbh mass and eddington ratio distributions given in . by comparing the results obtained from the mock sample with that from the sdss sample , we demonstrate that the apparent correlation can be produced by and mainly due to the selection effects of the sdss sample and the bias induced by the usage of as the true mbh mass . the mean values of of those sdss qsos are consistent with being a constant over the redshift range of . we conclude that the current sdss qso data is consistent with no strong intrinsic correlation between radiative efficiency and true mbh mass and no significant redshift evolution of radiative efficiencies . accretion , accretion discs black hole physics galaxies : nuclei galaxies : active quasars : general

1502.06508

i

apart from hierarchical structure of massive neutrinos a fundamental qualitative nature of these elusive particles whether they are dirac or majorana type is yet unknown . neutrinoless double beta decay ( @xmath7 ) mode is able to discriminate between the two different types . positive evidence of the above experimental search will be able to determine the majorana nature of neutrinos assuming the above decay is mediated due to light neutrino . several @xmath7 experiments are ongoing and planned . in ref . @xcite a brief discussion about some of the important experiments is presented . among them , exo-200@xcite experiment puts an upper limit on the relevant neutrino mass matrix element @xmath6 within a range as @xmath8 ( 0.14 - 0.35 ev ) . further , next-100 @xcite experiment will be able to bring down the above value of the order of 0.1 ev . thus in an optimistic point of view such property of neutrino could be testified by the next generation experiments . however , even if it is possible to pin down the value of @xmath6 , it is still difficult to predict the values of the majorana phases until we can fix the absolute neutrino mass scale . it is shown in ref.@xcite that in addition to the @xmath7 decay experiments , lepton number violating processes in which the majorana phases show up are also corroborative to determine the individual majorana phases . another interesting physical aspect such as contribution of the majorana phases to the generation of @xmath9 within the present @xmath10 range of neutrino oscillation global fit data is also studied in the literature@xcite . @xcite discusses how to constrain the majorana phases using the results from cosmology and double beta decay . thus it is worthwhile to study the calculability of the majorana phases in terms of a general neutrino mass matrix ( @xmath11 ) parameters . in the present work we evaluate individual majorana phases in terms of the parameters of a general @xmath11 using three rephasing invariants @xmath1 , @xmath2 and @xmath3 presented in ref.@xcite on the basis of mohapatra - rodejohann s phase convention@xcite . although there are several papers which discusses the general procedure for calculating the majorana phases , motivation behind taking the rephasing invariants is that the methodology we present here is capable of calculating the majorana phase in a model independent way even if one of the eigenvalue is zero which is still allowed as far as the present neutrino oscillation global fit data is concerned . moreover as one of the rephasing invariant ( @xmath3 ) is directly proportional to @xmath12 , therefore it vanishes if @xmath13 and hence shows a strong dependency of the majorana phases with the light neutrino masses . in the present work we evaluate the majorana phases for a general complex symmetric neutrino mass matrix ( @xmath11 ) taking into account the global fit oscillation data and the upper bound on the sum of the three light neutrino masses ( @xmath4 ) along with the @xmath5 decay parameter for both the hierarchical cases . we then conclude except the case of quasi degeneracy ] , the methodology presented in this work is able to calculate the majorana phases , given any model of neutrino masses and for convenience , we further numerically estimate the ranges of each majorana phase for both types of hierarchies , in the context of a cyclic symmetric model as well as a model with scaling ansatz property . it is also shown that all the sub cases we present in inverted hierarchy section of the general discussion can be realized through the choice of a model with scaling ansatz with texture zeros within the framework of inverse seesaw while one of the phenomenologically viable sub case of the normal hierarchy section is yet to be identified . the plan of the paper is as follows . [ [ section ] ] in section [ s2 ] we briefly discuss the basic formalism to set the convention of the majorana phase representation within the framework of neutrino oscillation phenomena . cp violating rephasing invariants are presented in section [ s3 ] . section [ s4 ] contains explicit calculation of the majorana phases for both types of neutrino mass hierarchies along with phenomenologically viable different sub cases . numerical estimation of the majorana phases , their connection to the physical observables and discussions about their testability for the general case taking into account the constraints from the extant data for both types of neutrino mass hierarchies are presented in section [ s5 ] . in section [ s6 ] application of the above methodology in the context of cyclic symmetric and scaling ansatz invariant models is presented . section [ s7 ] contains summary of the present work .

we find them interesting as they allow us to evaluate each majorana phase in a model independent way even if one eigenvalue is zero . utilizing the solution of a general complex symmetric mass matrix for eigenvalues and mixing angles we determine the majorana phases for both the hierarchies , normal and inverted , taking into account the constraints from neutrino oscillation global fit data as well as bound on the sum of the three light neutrino masses ( ) and the neutrinoless double beta decay ( ) parameter . this methodology of finding the majorana phases is applied thereafter in some predictive models for both the hierarchical cases ( normal and inverted ) to evaluate the corresponding majorana phases and it is shown that all the sub cases presented in inverted hierarchy section can be realized in a model with texture zeros and scaling ansatz within the framework of inverse seesaw although one of the sub case following the normal hierarchy is yet to be established . except the case of quasi degenerate neutrinos , the methodology obtained in this work is able to evaluate the corresponding majorana phases , given any model of neutrino masses . = 1

we evaluate the majorana phases for a general complex symmetric neutrino mass matrix on the basis of mohapatra - rodejohann s phase convention using the three rephasing invariant quantities , and proposed by sarkar and singh . we find them interesting as they allow us to evaluate each majorana phase in a model independent way even if one eigenvalue is zero . utilizing the solution of a general complex symmetric mass matrix for eigenvalues and mixing angles we determine the majorana phases for both the hierarchies , normal and inverted , taking into account the constraints from neutrino oscillation global fit data as well as bound on the sum of the three light neutrino masses ( ) and the neutrinoless double beta decay ( ) parameter . this methodology of finding the majorana phases is applied thereafter in some predictive models for both the hierarchical cases ( normal and inverted ) to evaluate the corresponding majorana phases and it is shown that all the sub cases presented in inverted hierarchy section can be realized in a model with texture zeros and scaling ansatz within the framework of inverse seesaw although one of the sub case following the normal hierarchy is yet to be established . except the case of quasi degenerate neutrinos , the methodology obtained in this work is able to evaluate the corresponding majorana phases , given any model of neutrino masses . = 1

hep-ph9304234

c

in this paper we examined in some detail the computation of false vacuum decay rates at finite temperatures in the regime in which quantum fluctuations are negligibly small compared to thermal fluctuations . we have shown that temperature corrections to the nucleation barrier can be obtained from a saddle - point evaluation of the partition function in a dilute gas approximation . in fact , the temperature corrections are simply due to the positive eigenvalues from stable fluctuations around the critical bubble . that is , they are the entropic contributions due to thermally induced deformations on the bubble . even though this result has been known in classical statistical mechanics for more than two decades @xcite , we believe that a consistent treatment within field theory is still lacking . although we left many questions unanswered , we hope to have clarified some of the issues involved in the calculation of finite - temperature decay rates . of particular importance is the fact that the bounce is _ not _ obtained from the full 1-loop corrected effective potential , but from the potential excluding the scalar loops . thus , for a self - interacting scalar , the bounce is obtained from the tree - level potential . the full finite temperature potential appears in the exponent only after properly accounting for the positive eigenvalues of the determinantal prefactor . that is , the scalar contributions account for entropic corrections to the nucleation barrier . we obtained a temperature corrected nucleation barrier which can differ from the usual result . we showed this to be particularly true for sufficiently large scalar self - couplings in the vicinity of the critical temperature for the transition . also , we found that the interaction with other fields gives rise to a potential which is better behaved in the infrared . ( see also ref . this result is the finite - temperature equivalent to what e. weinberg found for the zero - temperature case , once the integration over the other fields is performed @xcite . the reader may be wondering if our results will have any consequences to current work on the electroweak phase transition . the answer depends on the higgs mass . for a sufficiently light higgs it is consistent to neglect the contribution from scalar loops to the effective potential . in this case , the usual estimate for the nucleation barrier is a valid approximation . however , the situation may change for a heavier higgs . given that the experimental lower bound on the higgs mass is now above 60 gev , we believe it worthwhile to study this question in more detail , keeping in mind that the transition becomes weaker as the higgs mass increases . we would like to thank a. linde for many important discussions on these and related issues . we would like to thank the institute for theoretical physics in santa barbara where , during the program on cosmological phase transitions , this work begun . at itp this work was supported in part by a national science foundation grant no . phy89 - 04035 at itp . ( mg ) was supported in part by a national science foundation grant no . ( gcm ) aknowledges financial support from fapesp ( so paulo , brazil ) and ( ror ) from conselho nacional de desenvolvimento cientfico e tecnolgico - cnpq ( brazil ) . * figure 1 : * a typical asymmetric double - well potential . + * figure 2 : * a comparison of the nucleation barrier as a function of temperature , in units of mass parameter @xmath193 , obtained by including ( stars ) and excluding ( dots ) scalar loops in the computation of the bounce . the parameters in the tree - level potential are @xmath194 . + * figure 3 : * a comparison of the terms @xmath195 and @xmath196 appearing in appendix b. the parameters in the tree - level potential are @xmath197 . + where the prime in @xmath199 means that the negative eigenvalue , @xmath200 , and the three zero eigenvalues , @xmath201 , are now excluded from the product . the term for @xmath202 in @xmath203 , can be handled as in ref . @xcite , resulting in the factor @xmath204^{\frac{3}{2}}$ ] in eq . ( [ eigenratio ] ) . separating the @xmath202 modes both in the numerator and the denominator of ( [ aratio ] ) , and using the identity ( [ idenpi ] ) , we get , @xmath205^{\frac{3}{2 } } \exp\left\{\left(-4 + \sum_{i } - \sum_{j}\ ; ' \right ) { \rm ln } \prod_{n=1}^{+\infty } \omega_{n}^{2 } - { \rm ln } \left ( e_{-}^{2 } \right)^{1/2 } - { \rm ln } \left [ \frac{\sin(\frac{\beta}{2 } |e_{-}|)}{\frac{\beta}{2 } |e_{-}| } \right ] + \right . & + & \left . \left(\sum_{j}\ ; ' - \sum_{i}\right ) { \rm ln } \beta + \sum_{i } \left [ \frac{\beta}{2 } e_{f}(i ) + { \rm ln } \left ( 1 - e^{- \beta e_{f}(i ) } \right ) \right ] + \right . \nonumber \\ & - & \left . \sum_{j } \ ; ' \left [ \frac{\beta}{2 } e_{b}(j ) + { \rm ln } \left ( 1 - e^{- \beta e_{b}(j ) } \right ) \right ] \right\ } \ : . \label{aexplicity}\end{aligned}\ ] ] & + & \left . \sum_{i } \left [ \frac{\beta}{2 } e_{f}(i ) + { \rm ln } \left ( 1 - e^{- \beta e_{f}(i ) } \right ) \right ] - \sum_{j } \ ; ' \left [ \frac{\beta}{2 } e_{b}(j ) + { \rm ln } \left ( 1 - e^{- \beta e_{b}(j ) } \right ) \right ] \right\ } \label{aendexplicitly}\end{aligned}\ ] ] @xmath213^{2 } & = & \det ( - \not{\ ! \partial } -i g \varphi).\det ( - \not{\ ! \partial } + i g \varphi ) = \nonumber \\ & = & \det \left [ ( -\box_{e } + g^{2 } \varphi^{2 } ) 1_{4 \times 4 } - i g \gamma_{e}^{\mu } \partial_{\mu } \varphi \right ] \ : , \label{bident}\end{aligned}\ ] ] @xmath227_{\beta } + { \rm tr } \ln \left [ - \box_{e } + g^{2 } \varphi_{b}^{2 } - g \frac { \partial \varphi_{b}}{\partial r } \right]_{\beta } - \right . \nonumber \\ & - & \left . 2 { \rm tr } \ln \left [ - \box_{e } + g^{2 } \varphi_{f}^{2 } \right]_{\beta } \right\ } \ : . \label{bdetbf}\end{aligned}\ ] ] @xmath228 \right ] + \right . \nonumber \\ & + & \left . { \rm tr } \ln \left [ 1 + s_{\beta}(\varphi_{f } ) \left [ g^{2 } ( \varphi_{b}^{2 } - \varphi_{f}^{2 } ) - g \frac { \partial \varphi_{b}}{\partial r } \right ] \right ] \right\ } \ : , \label{bexpratio}\end{aligned}\ ] ] @xmath230 \right ] & = & \sum_{m= 1}^{+ \infty } \frac{(-1)^{m+1}}{m } \int d^{3}x \left [ g^{2 } ( \varphi_{b}^{2 } - \varphi_{f}^{2 } ) \pm g \frac { \partial \varphi_{b}}{\partial r } \right]^{m } \times \nonumber \\ & \times & \sum_{n= -\infty}^{+ \infty } \int \frac{d^{3 } k } { ( 2 \pi)^{3 } } \frac{1 } { \left [ \bar{\omega}_{n}^{2 } + \vec{k}^{2 } + g^{2 } \varphi_{f}^{2 } \right]^{m } } \ : , \label{btraceln}\end{aligned}\ ] ] where @xmath231 . as before , ( [ btraceln ] ) can be expressed as a graphic expansion similar to ( [ graphic ] ) , with the propagators @xmath112 replaced now by @xmath232 and the external lines given by @xmath233 or @xmath234 . the determinant factor in ( [ gammaw ] ) , coming from the functional integration of the scalar field , can be evaluated by the same methods of sec . 3 . in ( [ gammaw ] ) , the determinant term @xmath235_{\beta}$ ] , with @xmath236 , has a negative eigenvalue , @xmath200 , associated with the instability of the critical bubble , and the three zero eigenvalues , associated with the translational invariance of the bubble . these eigenvalues can be handled as usual , giving the preexponential term in ( [ endgammaw ] ) . the part of the determinant involving the positive eigenvalues can be written as an expansion exactly as in ( [ traceln ] ) , @xmath237^{- \frac{1}{2 } } = \exp \left\ { - \frac{1}{2 } { \rm tr } \ ; \ln \bigl [ 1 + \hat{g}_{\beta}(\varphi_{f } ) \left [ \hat{v}_{\psi}''(\varphi_{b } ) - \hat{v}_{\psi}''(\varphi_{f } ) \right ] \bigr ] \right\ } \ : , \label{bdetbos}\ ] ] @xmath239 \right\ } & = & \sum_{m=1}^{+ \infty } \frac { ( -1)^{m+1 } } { m } \int d^{3 } x \left[\hat{v}_{\psi}''(\varphi_{b } ) - \hat{v}_{\psi}''(\varphi_{f } ) \right]^{m } \times \nonumber \\ & \times & \sum_{n= -\infty}^{+ \infty } \int \frac { d^{3 } k } { ( 2 \pi)^{3 } } \frac{1 } { \left [ \omega_{n}^{2 } + \vec{k}^{2 } + m_{\beta}^{2 } ( \varphi_{f } ) \right]^{m } } \ : . \label{btrlnw}\end{aligned}\ ] ] the sum in @xmath42 in both ( [ btraceln ] ) and ( [ btrlnw ] ) can be performed as in eq . ( [ traceln ] ) ) . therefore , from eqs . ( [ bexpw ] ) , ( [ btraceln ] ) and ( [ btrlnw ] ) , we can write the relevant part of eq . ( [ gammaw ] ) as @xmath240^{- \frac{1}{2 } } e^{- \delta w_0 } = \left [ \frac { \det ( -\box_{e } + \hat{v}_{\psi}''(\varphi_{b}))_{\beta } } { \det ( -\box_{e } + \hat{v}_{\psi}''(\varphi_{f}))_{\beta } } \right]^{- \frac{1}{2 } } \ : \ : \frac { \det ( - \not{\ ! \partial } - i g \varphi_{b } ) _ { \beta } } { \det ( - \not{\ ! \partial } - i g \varphi_{f } ) _ { \beta } } \ : \ : e^{-\delta s } = } \nonumber \\ & & = { \cal v}\frac{t^{4}}{i |e_{-}| } \frac{\beta \frac{|e_{-}|}{2 } } { \sin \left ( \beta \frac{|e_{-}|}{2 } \right ) } \left [ \frac{\delta w_0 } { 2 \pi } \right]^{\frac{3}{2 } } \exp \left\ { - \delta s + \int d^{3 } x \sum_{n= -\infty}^{+ \infty } \int \frac{d^3 k}{(2 \pi)^3 } \left [ \ln \left ( 1 + \frac{g^2 ( \vp_{b}^{2 } - \vp_{f}^{2 } ) + g \frac{\partial \vp_{b}}{\partial r}}{\bar{\omega}_{n}^{2 } + \vec{k}^2 + g^2 \vp_{f}^{2 } } \right ) + \right . \nonumber \\ & & + \left . \left . \ln \left ( 1 + \frac{g^2 ( \vp_{b}^{2 } - \vp_{f}^{2 } ) - g \frac{\partial \vp_{b}}{\partial r}}{\bar{\omega}_{n}^{2 } + \vec{k}^2 + g^2 \vp_{f}^{2 } } \right ) - \frac{1}{2 } \ln \left ( 1 + \frac{m_{\beta}^2 ( \vp_{b } ) - m_{\beta}^{2 } ( \vp_{f}^{2 } ) } { \omega_{n}^{2 } + \vec{k}^2 + m_{\beta}^{2 } ( \vp_{f}^{2 } ) } \right ) \right ] \right\ } \ : , \label{bdeterminantal}\end{aligned}\ ] ] apart from the derivative terms @xmath243 , the momentum integral reproduces the finite temperature corrections to the the tree - level potential appearing in @xmath67 . when we wrote the expression for @xmath244 in eq . ( [ dft ] ) , these terms were not included in the effective potential @xmath245 . there are two reasons for negleting this term . first , due to the graphic expansion we used for the determinants , it is easy to see that at least at the tadpole level , their contribution cancels . since the tadpole gives the dominant temperature contribution to the potential , terms that depend on @xmath243 will be sub - dominant . second , it is possible to explicitly compare the terms @xmath246 and @xmath247 , by obtaining @xmath6 numerically . we have performed this comparison for the same set of parameters used in figs . 2 and 3 , and convinced ourselves that the derivative term will indeed be sub - dominant . a typical example is shown in fig . neglecting the term @xmath243 , we can use eqs . ( [ bdeterminantal ] ) and ( [ finaldeltaw ] ) to obtain the expression for @xmath94 in ( [ dft ] ) . m. gleiser and e. w. kolb , _ phys . lett . _ * 69 * , 1304 ( 1992 ) ; fermilab preprint no . pub-92/222-a ; _ int . phys . _ * c3 * , 773 ( 1992 ) ; m. gleiser , e. w. kolb , and r. watkins , _ nucl . phys . _ * b364 * , 411 ( 1991 ) . c. a. carvalho , g. c. marques , a. j. silva and i. ventura , _ nucl . * b265 * , 45 ( 1986 ) ; c. a. carvalho , d. bazeia , o. j. p. eboli , g. c. marques , a. j. silva and i. ventura _ phys . rev . _ * d31 * , 1411 ( 1985 ) ;

we examine the computation of the nucleation barrier used in the expression for false vacuum decay rates in finite temperature field theory . by a detailed analysis of the determinantal prefactor we compute the nucleation barrier for a model of scalar fields coupled to fermions , and compare our results to the expression commonly used in the literature . we find that , for large enough self - couplings , the inclusion of scalar loops in the expression of the nucleation barrier leads to an underestimate of the decay rate in the neighborhood of the critical temperature .

we examine the computation of the nucleation barrier used in the expression for false vacuum decay rates in finite temperature field theory . by a detailed analysis of the determinantal prefactor , we show that the correct bounce solution used in the computation of the nucleation barrier should not include loop corrections coming from the scalar field undergoing decay . temperature corrections to the bounce appear from loop contributions from other fields coupled to the scalar field . we compute the nucleation barrier for a model of scalar fields coupled to fermions , and compare our results to the expression commonly used in the literature . we find that , for large enough self - couplings , the inclusion of scalar loops in the expression of the nucleation barrier leads to an underestimate of the decay rate in the neighborhood of the critical temperature . pacs number(s ) : 98.80.cq , 64.60.qb . + e - mail : [email protected] ; [email protected] ; [email protected] .

astro-ph0312216

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according to the popular cosmological models dominated by cold dark matter ( cdm ) , the formation of large galaxies occurs in a hierarchical fashion , through the coalescence of smaller systems ( blumenthal et al . 1984 ; navarro , frenk , & white 1997 ; klypin , nolthenius , & primack 1997 ) . during mergers , the dissipationless dark matter components combine to form the extended dark halos of larger galaxies . the gas of the dwarf systems , however , dissipates its kinetic energy during mergers , decouples from the dark matter , and falls either into the center or onto the equatorial plane , forming the bulge and disk . dwarf galaxies observed today , such as the dwarf spheroidal ( dsph ) satellites of the milky way , represent surviving members of the original population of building blocks from which the milky way was formed . along with the success of this picture , however , has come the realization of new problems , both in the theory and in comparisons with observations . three problems are of particular interest here . one difficulty is the so - called `` over - cooling problem . '' in the cdm scenario , the magnitude of linear density fluctuations , @xmath3 is a decreasing function of the mass scale , @xmath4 . such a fluctuation spectrum causes low mass systems to become nonlinear and virialize at earlier epochs , and within a more dense background , than larger systems . cooling is very efficient at early epochs , due both to the generally higher densities at high red redshift as well as the rapid increase in the rate of inverse compton cooling with redshift . the early growth of smaller systems , coupled with the more efficient cooling at early epochs , leads to the expectation of rapid condensation of small , dense gas clouds within the dark - matter halos of dwarf galaxies . but , unless star formation can be suppressed , most of the gaseous ordinary matter would be converted into stars well before these galactic building blocks can be assembled into present - day large galaxies such as the milky way ( white & rees 1978 ) . a second problem is the deficit of observed satellite dwarf galaxies relative to theoretical expectations . observationally , the cdm scenario naturally leads to a `` bottom - up '' hierarchical galaxy formation picture that is qualitatively consistent with dwarf galaxies having halos with higher phase - space densities than those around larger normal galaxies . high - resolution numerical simulations show , however , that dwarf galaxies with higher internal densities retain the integrity of their cores while their loosely bound halos merge with each other during the formation of larger galaxies ( moore et al . 1999 ; klypin et al . consequently , the number density of surviving satellite dwarf galaxies expected from the cdm scenario is much larger than that observed in the local group . early bursts of star formation could lead to the preservation of ordinary matter in a gaseous form , followed by its removal from the dark matter potential . such a process may account for the deficit of detectable satellite galaxies . the third problem involves the building up of large galaxies from the dwarf systems . under the action of dynamical friction from the surrounding sea of dark matter , the dwarf galaxy building blocks lose energy and orbital angular momentum before they eventually merge into larger disk galaxies . if the gas within the dwarf systems cools and contracts within their dark matter potentials , the mergers are delayed , leading to the formation of disk systems which are much smaller and denser than observed ( e.g. , navarro & benz 1991 ; navarro & white 1994 ) . the separation of gas from the dark matter potential of dwarf galaxies is one possible mechanism for the ordinary matter to retain sufficient angular momentum to form normal - size disk galaxies ( weil , eke & efstathiou 1998 ; navarro & steinmetz 1997 ; sommer - larsen , gelato & vedel 1999 ) . resolution of the above problems may require that the conversion of gas into stars within the dwarf systems be inefficient . recent theoretical investigations suggest that the conversion of gas into stars in dwarf galaxies may be suppressed by the background uv radiation at large redshifts ( weinberg , hernquist & katz 1997 ; kepner , babul & spergel 1997 ) . integrating the full equations of radiative transfer , heating , cooling and non - equilibrium chemistry for nine species : @xmath5 , @xmath5 , @xmath6 , @xmath7 , @xmath8 , @xmath9 , @xmath10 , @xmath11 , @xmath12 , @xmath13 , kepner et al . ( 1997 ) computed the quasi - hydrostatic equilibrium states of gas in spherically symmetric dark matter potentials roughly corresponding to those of dwarf galaxies , and found that a typical background uv radiation field can easily delay cooling and collapse of gas in halos corresponding to @xmath14 cdm perturbations with circular velocities less than @xmath15 . those results , however , introduce an inconsistency with other observed properties of low - mass dwarf galaxies . the color - magnitude diagrams of most dsphs indicate that star formation began within them at an early epoch . indeed , ursa minor and draco , whose stellar velocity dispersions are only a few @xmath16 , and whose total masses are less than @xmath17 , are composed primarily of very old stars . in some dsphs , such as carina and fornax , the coexistence of multiple generations of young and intermediate - age stars ( grebel 1997 ; grebel & stetson 1998 ) provides evidence of protracted and recent star formation episodes . this is again difficult to account for , because little atomic or molecular gas is found in them today ( knapp , kerr & bowers 1978 ; mould et al . 1990 ; bowen et al 1997 ; carignan et al . 1998 ) , though some gas has been detected around some more distant dsphs , such as sculptor . while it is natural to expect that either internal star formation or external ram - pressure stripping might easily remove any residual gas from the shallow potentials of dsphs ( noriega - crespo et al . 1989 ; mori & burkert 2000 ) , it is difficult to reconcile the lack of either cool or warm gas with the presence of young stars . a more complete picture of the early evolution of dwarf galaxies , and of their role in the formation of massive systems , therefore requires a more thorough understanding of the various physical processes , both external and internal , that act to trigger and regulate star formation within them . in this paper , we present an investigation of the hydrodynamic evolution and star formation history of dwarf galaxies . we construct a code which integrates a realistic star formation recipe , feedback , and radiative transfer in a 1d spherically symmetric lagrangian scheme . the code allows us to follow the evolution of both the state of the gas and the star formation of dwarf galaxies subjected to different background uv fluxes and different external perturbations . in examining the parameter space , we seek answers to the following questions : 1 ) . is star - formation in dwarf galaxies triggered by a decrease in the background uv radiation , or by external perturbations ? 2 ) . what is the star formation efficiency , _ i.e. _ the fraction of the initial mass of gas that is converted into stars ? 3 ) . what is the mechanism for triggering multiple bursts of star - formation , such as are observed in some dsphs ? in 2 of this paper , we describe the dwarf galaxy model , the star formation recipe , feedback , and the strmgren shell model for radiative transfer and photoionization . we combine all of these into a 1d spherically symmetric lagrangian hydrodynamical scheme . in 3 we discuss the results of our simulations , and in 4 we discuss the implications of our results .

previous work has indicated that the background uv flux can easily ionize the gas within typical dwarf galaxies , delaying or even preventing cooling and star formation within them . , we consider the dynamical evolution of gas in dwarf galaxies using a one - dimensional , spherically symmetric , lagrangian numerical scheme to compute the effects of radiative transfer and photoionization . this scheme allows us to follow the history of the gas and of star formation within dwarf galaxies , as influenced by both external and internal uv radiation . the results of our theoretical models reproduce the observed correlation .

we examine the star formation history and stellar feedback effects of dwarf galaxies under the influence of extragalactic ultraviolet radiation . previous work has indicated that the background uv flux can easily ionize the gas within typical dwarf galaxies , delaying or even preventing cooling and star formation within them . many dwarf galaxies within the local group are , however , observed to contain multiple generations of stars , the oldest of which formed in the early epochs of cosmic evolution , when the background uv flux was intense . in order to address this paradox , we consider the dynamical evolution of gas in dwarf galaxies using a one - dimensional , spherically symmetric , lagrangian numerical scheme to compute the effects of radiative transfer and photoionization . we include a physically - motivated star formation recipe and consider the effects of feedback . this scheme allows us to follow the history of the gas and of star formation within dwarf galaxies , as influenced by both external and internal uv radiation . our results indicate that star formation in the severe environment of dwarf galaxies is a difficult and inefficient process . in potentials with total mass less than a few , and velocity dispersion less than a few km s , residual gas is efficiently photoionized by cosmic background uv radiation . since the density scale height of the gas within these galaxies is comparable to their size , gas may be tidally removed from them , leaving behind starless residual dark matter clumps . for intermediate mass systems , such as the dsphs around the galaxy , star formation can proceed with in early cosmic epochs despite the intense background uv flux . triggering processes such as merger events , collisions , and tidal disturbance can lead to density enhancements , reducing the recombination timescale , allowing gas to cool and star formation to proceed . however , the star formation and gas retention efficiency may vary widely in galaxies with similar dark matter potentials , because they depend on many factors , such as the baryonic fraction , external perturbation , imf , and background uv intensity . we suggest that the presence of very old stars in these dwarf galaxies indicates that their initial baryonic to dark matter content was comparable to the cosmic value . this constraint suggests that the initial density fluctuation of baryonic matter may be correlated with that of the dark matter . for the more massive dwarf elliptical galaxies , the star formation efficiency and gas retention rate is much higher . their mass to light ratio is regulated by star formation feedback , and is expected to be nearly independent of their absolute luminosity . the results of our theoretical models reproduce the observed correlation .

astro-ph0312216

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in this paper , we consider a series of one - dimensional numerical models to examine the efficiency of star formation in dwarf galaxies under the influence of local cooling , heating by uv photons from both the background radiation and hot stars , and the winds and supernovae associated with massive stars . radiative transfer is handled using a simple `` strmgren shell '' approximation . completely ionized gas is assumed to have temperature of 15,000 k , while heating and cooling are followed dynamically in gas that is not completely ionized . the effects of supernovae and winds from massive stars are included in the momentum equation of the gas . stars can form in gas that has cooled sufficiently for the jeans mass to be within the range of stellar masses , which is not tidally limited , and for which the free - fall timescale is short compared to the pre - main sequence evolution time of massive stars , @xmath52 . the rate of conversion of gas into stars is a fraction of the gas free - fall timescale . feedback from the massive stars which form is delayed by the free - fall time , plus @xmath52 . the most important parameters explored in the models are : 1 ) the depth of the galactic potential , 2 ) the baryonic fraction , 3 ) the background uv flux , 4 ) @xmath52 , 5 ) the imf , and 6 ) compressional perturbation ( see tables 1 and 2 ) . we initially confirm the results of kepner et al ( 1997 ) , that for a low mass system ( @xmath239 ) with baryonic fraction @xmath240 , even today s background uv flux is adequate to totally ionize the gas such that no stars can form . with increasing baryonic fraction , however , these systems eventually become self - shielded from the background uv , and the gas is able to cool and collapse , leading to star formation . for @xmath217 ( comparable to the ratio of @xmath171 today ) , a low mass system with @xmath241 kpc is able to convert @xmath242 gas ( @xmath243 ) into stars in about 2 billion years . feedback from star formation leads to rapid expansion of the gas within the shallow galactic potential . the lower recombination efficiency of the expanded gas allows it to be completely ionized by the external uv radiation , and star formation is terminated after the initial , weak burst . modest retention of gas is possible , if the imf of the stars formed in these system is biased towards the low - mass stars . in the presence of much stronger background uv radiation , appropriate to early epochs , star formation may still occur in small galaxies having @xmath244 . in such systems , self - shielding is sufficient to prevent ionization initially within the cores , even with the higher uv background . star formation then proceeds , governed solely by internal time scales and feedback , while the external radiation acts only at late times , to prevent further star formation . the requirement for a relatively large concentration of ordinary matter in these shallow potential is in contrast to the low-@xmath134 estimate made by kepner _ et al _ ( 1997 ) based on the assumption of bondi accretion into dark matter potentials . although the accretion process may be more effective when the pristine gas is cold before the epoch of reionization , all present - day dwarf galaxies must have acquired their ordinary matter content prior to the formation of massive stars in other nearby dwarf galaxies . the relatively short dynamical time scales within the dwarf galaxies suggests that such a precise timing may be difficult to achieve . alternatively , prior to the epoch of dwarf galaxy formation , density fluctuation of the baryonic matter may be well correlated and coupled to that of the dark matter . star formation is much more efficient in higher mass systems , due both to increased self - shielding and to the enhanced ability of the galactic potential to retain ionized gas . a ten - fold increase in the dark matter mass , from @xmath245 typical of dsphs , to @xmath246 typical of dwarf ellipticals ( des ) or dwarf irregulars ( dirrs ) , may lead to an order of magnitude increase in the gas - to - star conversion efficiency . in the most massive systems , the star formation rate is self - regulated by internal feedback , independent of the external uv flux . for marginal systems , with low external flux , star formation occurs in a rapid initial burst , followed by expansion and ionization by the external flux , similar to the low - mass systems . the presence of a higher external uv flux , however , lessens the initial star formation rate , reducing the subsequent feedback , and allowing star formation to proceed at a slow pace for an extended period . observational data suggest that in the satellite dsphs around the galaxy , the baryonic matter content varies widely , while the dark matter not only dominates but also has widely varying masses . but , in dwarf galaxies with mass more than @xmath247 , the total mass - to - light ratio has a nearly constant value @xmath248 2.0 ( see mateo _ the results of our calculation are consistent with this apparent dichotomy . in order to make a direct comparison with fig . 7 in mateo _ ( 1998 ) , we plot the total mass to light ratio @xmath249 within @xmath24 as a function of the absolute visual magnitude @xmath250 of the different dwarf galaxies in models d1 - 5 , a1 - 3 , and g0 - 5 . for very low - mass ( @xmath251 ) dark matter halo , star formation may be completely suppressed even if @xmath134 is 0.5 . in these low - mass systems , the pressure scale height of the photoionized gas is comparable to the galaxy s radius and in the vicinity of the galactic disks , and the tidal perturbation of nearby host galaxy would induce efficient mass loss ( murray _ et al . it is entirely possible that that the halo of the milky way may be populated by many dark matter halos of the ` missing dwarf galaxies ' . for the intermediate - mass ( @xmath252 ) dwarf galaxies , the gas retention efficiency depends on many factors such as the background uv flux , the imf , the baryonic to dark matter ratio etc . in figure [ fig : mlmv ] , the @xmath253-@xmath250 correlation for this mass range merely indicate that a transition mass for the gas retention efficiency . for the high - mass dwarf galaxies , the baryonic matter represents a significant fraction of the total mass and the constant @xmath249 is a reflection of the self - regulated star formation process . by contrast , in low mass systems , @xmath254 exceeds the dynamical time on which the gas evolves within the galactic potential . if sufficient gas is present to shield the core from external uv , then gas in the core may accumulate significantly before the onset of feedback , leading to strong bursts of star formation . the same is observed in larger systems , for which we have considered larger values of @xmath52 . if the initial burst of star formation causes the gas to expand , and its density to decrease to the point at which the external uv is able to ionize the galaxy completely , then star formation is terminated after a single burst . in somewhat more massive systems , gas in the core is still self - shielded after the massive stars formed in the initial burst fade away . the gas can then cool , contract , and trigger additional bursts of star formation , as is observed in some of our models . in all systems which undergo either one or multiple episodes of star formation , the feedback is eventually sufficiently strong as to drive the gas out of the system . episodic star formation may also result from reducing the efficiency of feedback , either by reducing the conversion efficiency of gas into stars , or the fraction of massive stars which form . in high mass models with such variations , we observe episodic star formation . within the environment of a galaxy cluster , or near to a massive galaxy , a dwarf system shall experience tidal forces , that shall vary over time , resulting in occasional , or even periodic compressions . if dwarf systems form in large numbers around more massive overdense regions , they shall also experience collisions . the merger process which builds larger galactic entities can also lead to collisions and disturbances . both mechanisms lead to enhancements in the density , and therefore the recombination efficiency of the gas within dwarf galaxies . in small systems at early epochs , this may allow the galaxy to form some stars , when it might otherwise be completely ionized by the external uv radiation . in more massive systems , the star formation rates are enhanced by as much as an order of magnitude relative to unperturbed systems for realistic compression speeds . perturbations such as considered here would be expected to be stronger in dense cluster environments , or near to massive galaxies . in the former , collisions would be more frequent , while in the latter , tidal variations due to elliptical orbits around the parent system are strongest . these are also environments where tidal stripping , ram pressure , and external uv radiation are all enhanced , which would be expected to act to reduce star formation efficiencies , and so it is unclear whether the effect of perturbations alone would lead to environmental dependences for stellar populations within dwarf galaxies . as indicated in earlier work , star formation in the lowest mass dwarf galaxies is difficult at early epochs , and the observed population of dsphs appear to be at the very edge of the ability of small galaxies to form stars . the difficulty is due to the strong uv background , which easily ionizes the galaxies throughout , preventing the gas from cooling and contracting within the weak gravitational potential of the dwarf system . star formation may still occur , even in the smallest systems , however , if the gas within them can become self - shielded from the external uv . such might be the case if they form with a relatively large baryonic fraction , if they accrete additional gas , or if they undergo compressions due to either tidal forces or collisions . such processes may help to explain the existence of old stellar populations in even the smallest dsphs . feedback from star formation also forms a natural means for avoiding the `` over - cooling '' problem among the dwarf progenitors of massive galaxies . in small systems , star formation tends to occur in bursts , the feedback from which either expels the gas completely from the galaxy , or drives it to large radii , making it vulnerable to either tidal or ram - pressure stripping . subsequent generations of star formation would , therefore , appear to be unlikely . the gas lost to a dwarf system , however , leaves at small speeds ( @xmath255 km s@xmath1 ) . it shall not , therefore , move to large distances from the dwarf as it orbits within the potential of either a massive galaxy or within a cluster , and may be re - accreted by the dwarf at apogalacticon , possibly leading to subsequent bursts of star formation . some small dwarf systems , therefore , might be expected to show periodic bursts of star formation , with a burst period determined by the orbital period of the dwarf . by contrast , in larger systems , where the feedback time is short compared to the dynamical time of the system , and where the potential is capable of retaining ionized gas , feedback tends to lead to steady , self - regulated star formation . the gas within the system does , however , expand under the influence of stellar feedback , and so may also be subject to stripping within galactic cluster environments ( murray , dong , & lin 2003 ) . the possibility of severe mass loss from dwarf galaxies following star formation indicates that the currently observed baryonic - to - dark matter ratios can provide only lower limits , possibly very weak limits , to the values present when the galaxies formed . our models indicate that the star formation efficiencies , and the ability of galaxies to retain gas following star formation depend very sensitively dependences upon the evolutionary histories of the galaxies , and upon the galactic potentials , which may account for the large dispersion in the stellar to dark - matter fraction observed today among the dwarf galaxies . we thank drs . a. burkert , and k - s . oh for useful conversations . we also thank the anonymous referee for valuable comments . this work was performed under the auspices of the u.s . department of energy by university of california , lawrence livermore national laboratory under contract w-7405-eng-48 . this work is partially supported by nasa through an astrophysical theory grant nag5 - 12151 . cclrcrcr a1 & 0.6 & 0.001 & 1 & 1.0 & 1 & 0.5 & 0.0 + a2 & 0.6 & 0.1 & 1 & 1.0 & 1 & 0.5 & 2.6 + a3 & 0.6 & 0.2 & 1 & 1.0 & 1 & 0.5 & 3.7 + b1 & 0.3 & 0.1 & 1 & 1.0 & 1 & 0.5 & 1.3 + b2 & 0.3 & 0.2 & 1 & 1.0 & 1 & 0.5 & 1.9 + b3 & 0.3 & 0.5 & 1 & 1.0 & 1 & 0.5 & 2.5 + c1 & 0.3 & 0.1 & 100 & 1.0 & 1 & 0.5 & 0.0 + c2 & 0.3 & 0.2 & 100 & 1.0 & 1 & 0.5 & 0.7 + c3 & 0.3 & 0.5 & 100 & 1.0 & 1 & 0.5 & 1.5 + d1 & 0.3 & 0.1 & 1 & 1.0 & 1 & 0.5 & 1.3 + d2 & 0.6 & 0.1 & 1 & 1.0 & 1 & 0.5 & 2.6 + d3 & 2.0 & 0.1 & 1 & 1.0 & 1 & 0.5 & 14.2 + d4 & 4.0 & 0.1 & 1 & 1.0 & 1 & 0.5 & 68.4 + d5 & 6.0 & 0.1 & 1 & 1.0 & 1 & 0.5 & 83.2 + e1 & 0.3 & 0.1 & 100 & 1.0 & 1 & 0.5 & 0.0 + e2 & 0.6 & 0.1 & 100 & 1.0 & 1 & 0.5 & 0.0 + e3 & 2.0 & 0.1 & 100 & 1.0 & 1 & 0.5 & 19.7 + e4 & 4.0 & 0.1 & 100 & 1.0 & 1 & 0.5 & 66.3 + e5 & 6.0 & 0.1 & 100 & 1.0 & 1 & 0.5 & 67.6 + f1 & 4.0 & 0.01 & 0 & 1.0 & 1 & 0.5 & 24.5 + f2 & 4.0 & 0.01 & 1 & 1.0 & 1 & 0.5 & 24.1 + f3 & 6.0 & 0.01 & 0 & 1.0 & 1 & 0.5 & 47.7 + f4 & 6.0 & 0.01 & 1 & 1.0 & 1 & 0.5 & 45.4 + g0 & 0.6 & 0.2 & 1 & 1.0 & 1 & 0.5 & 3.7 + g1 & 0.6 & 0.2 & 1 & 0.1 & 1 & 0.5 & 3.5 + g2 & 0.6 & 0.2 & 1 & 1.0 & 10 & 0.5 & 11.7 + g3 & 0.6 & 0.2 & 1 & 1.0 & 1 & 5.0 & 6.3 + g4 & 0.6 & 0.2 & 1 & 0.1 & 10 & 5.0 & 22.4 + h0 & 4.0 & 0.1 & 1 & 1.0 & 1 & 0.5 & 68.4 + h1 & 4.0 & 0.1 & 1 & 1.0 & 1 & 5.0 & 71.7 + h2 & 4.0 & 0.1 & 1 & 1.0 & 1 & 50 . & 35.0 + h3 & 4.0 & 0.1 & 1 & 0.1 & 1 & 5.0 & 69.7 + h4 & 4.0 & 0.1 & 1 & 0.01 & 1 & 5.0 & 49.4 + h5 & 4.0 & 0.1 & 1 & 0.1 & 10 & 5.0 & 85.7 + cclrcrcr i0 & 0.6 & 0.1 & 1 & 0 & 1 & 0.5 & 3.7 + i1 & 0.6 & 0.1 & 1 & 3 & 1 & 0.5 & 4.2 + i2 & 0.6 & 0.1 & 1 & 15 & 1 & 0.5 & 6.3 + i3 & 0.6 & 0.1 & 1 & 30 & 1 & 0.5 & 27.3 + i4 & 0.6 & 0.1 & 1 & 150 & 1 & 0.5 & 89.3 + k0 & 2.0 & 0.1 & 1 & 0 & 1 & 0.5 & 14.2 + k1 & 2.0 & 0.1 & 1 & 3 & 1 & 0.5 & 32.1 + k2 & 2.0 & 0.1 & 100 & 0 & 1 & 0.5 & 19.7 + k3 & 2.0 & 0.1 & 100 & 3 & 1 & 0.5 & 23.7 +

we examine the star formation history and stellar feedback effects of dwarf galaxies under the influence of extragalactic ultraviolet radiation . since the density scale height of the gas within these galaxies is comparable to their size , gas may be tidally removed from them , leaving behind starless residual dark matter clumps . for intermediate mass systems , such as the dsphs around the galaxy , however , the star formation and gas retention efficiency may vary widely in galaxies with similar dark matter potentials , because they depend on many factors , such as the baryonic fraction , external perturbation , imf , and background uv intensity . we suggest that the presence of very old stars in these dwarf galaxies indicates that their initial baryonic to dark matter content was comparable to the cosmic value . this constraint suggests that the initial density fluctuation of baryonic matter may be correlated with that of the dark matter . for the more massive dwarf elliptical galaxies ,

we examine the star formation history and stellar feedback effects of dwarf galaxies under the influence of extragalactic ultraviolet radiation . previous work has indicated that the background uv flux can easily ionize the gas within typical dwarf galaxies , delaying or even preventing cooling and star formation within them . many dwarf galaxies within the local group are , however , observed to contain multiple generations of stars , the oldest of which formed in the early epochs of cosmic evolution , when the background uv flux was intense . in order to address this paradox , we consider the dynamical evolution of gas in dwarf galaxies using a one - dimensional , spherically symmetric , lagrangian numerical scheme to compute the effects of radiative transfer and photoionization . we include a physically - motivated star formation recipe and consider the effects of feedback . this scheme allows us to follow the history of the gas and of star formation within dwarf galaxies , as influenced by both external and internal uv radiation . our results indicate that star formation in the severe environment of dwarf galaxies is a difficult and inefficient process . in potentials with total mass less than a few , and velocity dispersion less than a few km s , residual gas is efficiently photoionized by cosmic background uv radiation . since the density scale height of the gas within these galaxies is comparable to their size , gas may be tidally removed from them , leaving behind starless residual dark matter clumps . for intermediate mass systems , such as the dsphs around the galaxy , star formation can proceed with in early cosmic epochs despite the intense background uv flux . triggering processes such as merger events , collisions , and tidal disturbance can lead to density enhancements , reducing the recombination timescale , allowing gas to cool and star formation to proceed . however , the star formation and gas retention efficiency may vary widely in galaxies with similar dark matter potentials , because they depend on many factors , such as the baryonic fraction , external perturbation , imf , and background uv intensity . we suggest that the presence of very old stars in these dwarf galaxies indicates that their initial baryonic to dark matter content was comparable to the cosmic value . this constraint suggests that the initial density fluctuation of baryonic matter may be correlated with that of the dark matter . for the more massive dwarf elliptical galaxies , the star formation efficiency and gas retention rate is much higher . their mass to light ratio is regulated by star formation feedback , and is expected to be nearly independent of their absolute luminosity . the results of our theoretical models reproduce the observed correlation .

0904.2137

i

one of the most important unresolved questions in particle physics is how exactly the electroweak symmetry is broken . the standard model higgs mechanism provides ample motivation to come up with alternatives . an interesting new possibility is provided by higgsless models @xcite with a warped extra dimension @xcite . a higgs field localized on the ir brane of an rs background is decoupled by taking its vev to be very large , while the masses of the @xmath2 and @xmath3 bosons remain finite and are set by the size of the extra dimension . unitarity of the gauge boson scattering amplitudes can then be ensured via heavy kk gauge boson exchange . such models would solve the little hierarchy problem of randall - sundrum setups and have very distinctive phenomenological consequences . however , it is not clear whether these higgsless rs models can be made completely viable : a large correction to the s parameter makes it difficult to match electroweak precision data , the cutoff scale has to be adequately raised to ensure unitarization happens at weak coupling , and generically fcnc s are not adequately suppressed . many of these initial difficulties have been at least partially addressed . one can tune the effective s - parameter away by making the fermion left - handed fermion wave functions close to flat @xcite , and choosing the right fermion representations can prevent the large top mass from introducing coupling deviations in the @xmath4-vertex @xcite . the cutoff scale can also be raised by lowering the curvature of the extra dimension @xcite . however , once the fermion wave functions are required to be close to flat , the traditional anarchic rs approach to flavor @xcite ( where fermion wave function overlaps generate fermion mass hierarchies and also give a protection called rs - gim against fcnc s @xcite ) can no longer be applied . a possible resolution to this problem is to introduce a genuine five - dimensional gim mechanism , which uses bulk symmetries to suppress flavor violation @xcite . the trick is to impose global flavor symmetries on the bulk , with a large subgroup left unbroken on the ir brane and flavor mixing forbidden anywhere except the uv brane . one can then construct a model where tree - level fcnc s are genuinely vanishing , with the downside that we are no longer trying to explain the quark mass and mixing hierarchies , merely accommodating them . the aim of this paper is to examine the flavor bounds ( similar to @xcite on higgsless models and to present a viable flavor construction for these theories ( see @xcite for other examples in an rs context ) . we have to circumvent the problems usually associated with higgsless models by ensuring that all fcncs are sufficiently suppressed , all tree - level electroweak precision constraints are satisfied , the cutoff scale is sufficiently high . we show that the simplest versions of such a model can not be realistic : imposing an exact gim mechanism for all three generations either drives up the cutoff scale or prevents the s - parameter from being cancelled . instead , the realistic flavor model we propose will have next - to minimal flavor violation ( nmfv ) @xcite , featuring a custodially protected quark representation for the third generation , and an exact gim mechanism implemented for the first two generations only . this choice of representations allows us to isolate the lighter quarks from the dangerous top mass and prevent a large s - parameter without having to increase the bulk coupling and decrease the cutoff scale . flavor - changing neutral currents are controlled by two main mechanisms : the surviving flavor symmetry between the first two generations forces all the mixing to go through the third generation ( hence nmfv ) , which is vital to reduce @xmath5 and @xmath6 mixing . kinetic mixing terms on the uv confine the right - handed fermions to the uv brane and reduce bulk contributions to the couplings , which are the source of off - diagonal neutral couplings . this results in an rs - gim - like flavor suppression mechanism for the right - handed fermions . we also have some freedom to distribute the required charged - current mixing amongst the up- and down - sectors , which reduces neutral - current mixing in each sector . all of this is necessary to sufficiently suppress flavor violation . we find that experimental fcnc bounds systematically constrain the down - sector mixing angles , forcing them to lie within a volume of angle space that is enclosed by a well - defined surface . _ assuming _ the uv kinetic mixing terms obey a cabibbo - type mixing hierarchy , this volume occupies @xmath7 of available angle space . this paper is structured as follows : in section [ s.background ] we review the 5d gim mechanism and introduce the quark representations we will be using . in section [ s.nmfv ] we outline our nmfv quark model and show compliance with electroweak precision data ( ewpd ) . we also examine in detail the errors introduced by the zero mode approximation , and find that one can have zero s - parameter without flatness , provided there is a lot of kk mixing on the ir brane . the flavor suppression mechanisms of the nmfv model are derived in section [ s.flavor ] and demonstrated with the gluon kk contribution to fcnc s in section [ s.fcncbounds ] . numerical results for the mixing constraints are presented in section [ s.numerical ] , and we conclude with section [ s.conclusion ] .

1.5 cm * a flavor protection for warped higgsless models * 0.2 cm * csaba cski and david curtin * _ institute for high energy phenomenology + newman laboratory of elementary particle physics + cornell university , ithaca , ny 14853 , usa _

we examine various possibilities for realistic 5d higgsless models and construct a full quark sector featuring next - to - minimal flavor violation ( with an exact bulk protecting the first two generations ) satisfying electroweak and flavor constraints . the `` new custodially protected representation '' is used for the third generation to protect the light quarks from flavor violations induced due to the heavy top . a combination of flavor symmetries , and rs - gim for the right - handed quarks suppresses flavor - changing neutral currents below experimental bounds , assuming ckm - type mixing on the uv brane . in addition to the usual higgsless rs signals , this model predicts an exotic charge- quark with mass of about 0.5 tev which should show up at the lhc very quickly , as well as nonzero flavor - changing neutral currents which could be detected in the next generation of flavor experiments . in the course of our analysis , we also find quantitative estimates for the errors of the fermion zero mode approximation , which are significant for higgsless - type models . 1.5 cm * a flavor protection for warped higgsless models * 0.2 cm * csaba cski and david curtin * _ institute for high energy phenomenology + newman laboratory of elementary particle physics + cornell university , ithaca , ny 14853 , usa _ + [email protected] , [email protected] 0.3truecm

0904.2137

c

[ s.conclusion ] we examined various possibilities for higgsless rs model - building , and constructed a model with next - to - minimal flavor violation satisfying tree - level electroweak precision and meson - mixing constraints , as well as cdf bounds . the theory has a sufficiently high cutoff of @xmath304 to unitarize @xmath39-scattering at lhc energies , the third generation is in the custodial quark representation to protect the bottom couplings , and a combination of flavor symmetries and uv confinement of the right - handed quarks suppress fcncs . using numerical scans , we were able to demonstrate that our model can satisfy flavor bounds as long as the down - sector mixing angles are cabibbo - type and satisfy systematic constraints . we also found quantitative error estimates for the zero mode approximation , which are important for rs model - building with a low kk scale . this model has distinctive experimental signatures , allowing it to be excluded early on at the lhc . apart from the absence of the higgs , the usual higgsless rs signals include @xcite a relatively light @xmath164 with a mass below 1 tev , as well as @xmath43 and @xmath305 which are harder to detect ( see section [ ss.cdf ] ) . more specific to our setup is an exotic @xmath95-quark with charge @xmath1 and a mass of @xmath306 , which could be detected with less than @xmath147 pb@xmath148 of data @xcite . the nmfv model also predicts non - zero correlated flavor - changing neutral currents , which lie relatively close to current experimental bounds and would be detected in the next generation of flavor experiments .

we examine various possibilities for realistic 5d higgsless models and construct a full quark sector featuring next - to - minimal flavor violation ( with an exact bulk protecting the first two generations ) satisfying electroweak and flavor constraints . a combination of flavor symmetries , and rs - gim for the right - handed quarks suppresses flavor - changing neutral currents below experimental bounds , assuming ckm - type mixing on the uv brane . in addition to the usual higgsless rs signals , this model predicts an exotic charge- quark with mass of about 0.5 tev which should show up at the lhc very quickly , as well as nonzero flavor - changing neutral currents which could be detected in the next generation of flavor experiments . in the course of our analysis , we also find quantitative estimates for the errors of the fermion zero mode approximation , which are significant for higgsless - type models .

we examine various possibilities for realistic 5d higgsless models and construct a full quark sector featuring next - to - minimal flavor violation ( with an exact bulk protecting the first two generations ) satisfying electroweak and flavor constraints . the `` new custodially protected representation '' is used for the third generation to protect the light quarks from flavor violations induced due to the heavy top . a combination of flavor symmetries , and rs - gim for the right - handed quarks suppresses flavor - changing neutral currents below experimental bounds , assuming ckm - type mixing on the uv brane . in addition to the usual higgsless rs signals , this model predicts an exotic charge- quark with mass of about 0.5 tev which should show up at the lhc very quickly , as well as nonzero flavor - changing neutral currents which could be detected in the next generation of flavor experiments . in the course of our analysis , we also find quantitative estimates for the errors of the fermion zero mode approximation , which are significant for higgsless - type models . 1.5 cm * a flavor protection for warped higgsless models * 0.2 cm * csaba cski and david curtin * _ institute for high energy phenomenology + newman laboratory of elementary particle physics + cornell university , ithaca , ny 14853 , usa _ + [email protected] , [email protected] 0.3truecm

cond-mat9910079

i

excitons in semiconductor crystals @xcite and nanostructures @xcite,@xcite are a very interesting and challenging object to search for the process of bose - einstein condensation ( bec ) . nowadays there is a lot of experimental evidence that the optically inactive para - excitons in cu@xmath0o can form a highly correlated state , or the excitonic bose einstein condensate @xcite,@xcite,@xcite . a moving condensate of para - excitons in a 3d cu@xmath0o crystal turns out to be spatially inhomogeneous in the direction of motion , and the registered velocities of coherent exciton packets turn out to be always less , but approximately equal to the longitudinal sound speed of the crystal @xcite . analyzing recent experimental @xcite,@xcite,@xcite and theoretical @xcite-@xcite studies of bec of excitons in cu@xmath1o , we can conclude that there are essentially two different stages of this process . the first stage is the kinetic one , with the characteristic time scale of @xmath2ns . at this stage , a condensate of long - living para - excitons begins to be formed from a quasi - equilibrium degenerate state of excitons ( @xmath3 , @xmath4 ) when the concentration and the effective temperature of excitons in a cloud meet the conditions of bose - einstein condensation @xcite . note that we do not discuss here the behavior of ortho - excitons ( with the lifetime @xmath5ns ) and their influence on the para - exciton condensation process . for more details about the ortho - excitons in cu@xmath1o , ortho - para - exciton conversion , etc . see @xcite,@xcite , @xcite , @xcite . the most intriguing feature of the kinetic stage is that formation of the para - exciton condensate and the process of momentum transfer to the para - exciton cloud are happening simultaneously . if the diameter of an excitation spot on the crystal surface is large enough , @xmath6 , and the energy of a laser beam satisfies @xmath7 , nonequilibrium acoustic phonons may play the key role in the process of momentum transfer . as a result , the mode with macroscopical occupancy of the excitons appears to be with @xmath8 where @xmath9 and @xmath10 is the packet velocity . indeed , the theoretical results obtained in the framework of the `` phonon wind '' model @xcite,@xcite and the experimental observations @xcite,@xcite,@xcite are the strong arguments in favor of this idea . to the authors knowledge , there are no realistic theoretical models of the kinetic stage of para - exciton condensate formation where quantum degeneracy of the appearing exciton state and possible coherence of nonequilibrium phonons pushing the excitons would be taken into account . indeed , the condensate formation and many other processes involving it are essentially nonliner ones . therefore , the condensate , or , better , the _ macroscopically occupied mode _ , can be different from @xmath11 , and the language of the states in @xmath12-space and their occupation numbers @xmath13 may be not relevant to the problem , see @xcite . in this study , we will not explore the stage of condensate formation . instead , we investigate the second , quasi - equilibrium stage , in which the condensate has already been formed and it moves through a crystal with some constant velocity and characteristic shape of the density profile . in theory , the time scale of this `` transport '' stage , @xmath14 , could be determined by the para - exciton lifetime ( @xmath15s @xcite ) . in practice , it is determined by the characteristic size @xmath16 of a high - quality single crystal available for experiments : @xmath17 where @xmath18 is the longitudinal sound velocity . we assume that at the `` transport '' stage , the temperature of the moving packet ( condensed@xmath19noncondensed particles ) is approximately equal to the lattice temperature , @xmath20 then we can consider the simplest case of @xmath21 and disregard the influence of all sorts of _ nonequilibrium _ phonons ( which appear at the stages of exciton formation , thermalization @xcite ) on the formed moving condensate . any theory of the exciton bec in cu@xmath0o has to point out some physical mechanism(s ) by means of which the key experimental facts can be explained . ( for example , the condensate moves without friction within a narrow interval of velocities localized near @xmath18 , and the shape of the stable macroscopic wave function of excitons resembles soliton profiles @xcite . ) here we explore a simple model of the ballistic exciton - phonon condensate . in this case , the general structure of the hamiltonian of the moving exciton packet and the lattice phonons is the following : @xmath22 here @xmath23 is the bose - field operator describing the excitons , @xmath24 is the field operator of lattice displacements , @xmath25 is the momentum density operator canonically conjugate to @xmath24 , and @xmath26 is the momentum operator . note that the hamiltonian ( [ ham1 ] ) is written in the reference frame moving with the exciton packet , i.e. @xmath27 and @xmath28 is the ballistic velocity of the packet .

we explore a nonlinear field model to describe the interplay between the ability of excitons to be bose - condensed and their interaction with other modes of a crystal . we calculate the condensate wave function and energy , and a collective excitation spectrum in the semiclassical approximation ; the inside - excitations were found to follow the asymptotic behavior of the macroscopic wave function exactly . the stability conditions of the moving condensate are analyzed by use of landau arguments , and landau critical parameters appear in the theory . finally , we apply our model to describe the recently observed interference and strong nonlinear interaction between two coherent exciton - phonon packets in cuo . -10 mm -0.5 cm * bosons in a lattice : * * exciton - phonon condensate in cuo * d. roubtsov and y. lpine _ groupe de recherche en physique et technologie des couches minces , _ _ dpartement de physique , universit de montral , _ c.p . 6128 , succ .

we explore a nonlinear field model to describe the interplay between the ability of excitons to be bose - condensed and their interaction with other modes of a crystal . we apply our consideration to the long - living para - excitons in cuo . taking into account the exciton - phonon interaction and introducing a coherent phonon part of the moving condensate , we derive the dynamic equations for the exciton - phonon condensate . these equations can support localized solutions , and we discuss the conditions for the moving inhomogeneous condensate to appear in the crystal . we calculate the condensate wave function and energy , and a collective excitation spectrum in the semiclassical approximation ; the inside - excitations were found to follow the asymptotic behavior of the macroscopic wave function exactly . the stability conditions of the moving condensate are analyzed by use of landau arguments , and landau critical parameters appear in the theory . finally , we apply our model to describe the recently observed interference and strong nonlinear interaction between two coherent exciton - phonon packets in cuo . -10 mm -0.5 cm * bosons in a lattice : * * exciton - phonon condensate in cuo * d. roubtsov and y. lpine _ groupe de recherche en physique et technologie des couches minces , _ _ dpartement de physique , universit de montral , _ c.p . 6128 , succ . centre - ville , montreal , pq , h3c3j7 , canada e - mail : [email protected] pacs numbers : 71.35.+z , 71.35.lk

1111.0883

i

the possible existence of a neutral weakly coupled light spin-@xmath6 gauge @xmath0-boson @xcite , which is originated from supersymmetric extensions of the standard model with an extra @xmath7 symmetry , has recently attracted much attention due to its multifaceted influences in particle physics , nuclear physics , astrophysics and cosmology . for instance , the @xmath0-boson can provide annihilation of light dark matter which can be responsible for the excess flux of @xmath8 kev photons coming from the central region of our galaxy observed by the spi / integral satellite jean03,boe04a , boe04b , boe04c . it is also proposed that the @xmath0-boson can be mediator of the putative fifth force " providing a possible mechanism for non - newtonian gravity , i.e. , the violation of the inverse - square - law ( isl ) of newtonian gravitational force at short distance fuj71,ark98,fis99,pea01,hoy03,lon03,ade03,uza03,dec05,rey05,pok06,kap07,nes08,kam08,aza08,new09,ger10,luc10 . thus far various upper limits on the deviation from the isl have been put forward down to femtometer range @xcite . furthermore , the @xmath0-boson can involve a rich phenomenology in particle physics and nuclear physics and may have observable effects in particle decays @xcite and nucleon scattering processes @xcite , which can also put limits on the @xmath0-boson properties . studying properties of the @xmath0-boson is thus important for understanding the relevant new physics beyond the standard model . very recently , the effects of the @xmath0-boson on the nuclear matter equation of state ( eos ) and neutron star structure have been investigated kri09,wen09,zha11,wen11 and it is shown that the vector @xmath0-boson can significantly stiffen the nuclear matter eos and thus enhance drastically the maximum mass of neutron stars . in particular , by considering the @xmath0-boson , the stability and observed global properties of neutron stars can be reasonably explained by using the neutron - rich matter eos with a supersoft nuclear symmetry energy at supersaturation densities consistent with the available terrestrial laboratory data on the @xmath9 radio in relativistic heavy - ion collisions from fopi / gsi @xcite , while the supersoft nuclear symmetry energy at supersaturation densities generally can not support a canonical mass ( @xmath10 ) neutron star if the @xmath0-boson is not introduced @xcite . the @xmath0-boson has also been introduced to describe the recently discovered new holder of neutron star maximum mass of @xmath11 @xmath12 from psr j1614 - 2230 @xcite using soft eos s consistent with existing terrestrial nuclear laboratory experiments for hybrid neutron stars containing a quark core described by mit bag model using reasonable parameters @xcite , and it is found that the constraints on the @xmath0-boson properties are consistent with existing constraints from neutron - proton and neutron - lead scatterings nes08,kam08 as well as the spectroscopy of antiproton atoms @xcite . in the studies about the @xmath0-boson influences on neutron star structure @xcite , the exchange term contribution of the @xmath0-boson to the nuclear matter eos has been neglected and only the direct term contribution has been considered , leading to that the nuclear matter eos depends only on the ratio the coupling strength to mass squared of the @xmath0-boson , namely , @xmath3 . physically , the exchange term contribution of the @xmath0-boson to the nuclear matter eos will depend on both the coupling constant @xmath13 and the @xmath0-boson mass @xmath4 due to the finite - range interaction mediated by the @xmath0-boson . it is thus interesting to see how the exchange term contribution of the @xmath0-boson will influence the nuclear matter eos . furthermore , neutron stars are expected to have a solid inner crust surrounding a liquid core . knowledge on properties of the crust plays an important role in understanding many astrophysical observations bps71,bbp71,pet95a , pet95b , lat00,lat07,ste05,lin99,hor04,bur06,owe05 . the inner crust spans the region from the neutron drip - out point to the inner edge separating the solid crust from the homogeneous liquid core . while the neutron drip - out density @xmath14 is relatively well determined to be about @xmath15 g/@xmath16 @xcite , the transition density @xmath1 at the inner edge is still largely uncertain mainly because of our very limited knowledge on the eos of neutron - rich nucleonic matter , especially the density dependence of the symmetry energy @xcite . the transition density @xmath1 and the corresponding pressure @xmath2 at the inner edge might be measurable indirectly from observations of pulsar glitches @xcite . since the @xmath0-boson can have significant influence on the nuclear matter eos , it is therefore very interesting to see how the @xmath0-boson will affect the inner edge of neutron star crusts . in the present work , we investigate effects of the light vector @xmath0-boson on the transition density @xmath1 and pressure @xmath2 at the inner edge of neutron stars crust . the density matrix expansion ( dme ) approach neg72,xuj10b is used to describe the exchange term contribution of the finite - range interaction due to the @xmath0-boson exchange . based on the skyrme effective nucleon - nucleon interactions , we use three methods , i.e. , the thermodynamical approach , the curvature matrix approach and the vlasov equation approach to determine the transition density @xmath1 . as expected , our results indicate that the @xmath1 and @xmath2 depend on not only the ratio of coupling strength to mass squared of the @xmath0-boson @xmath3 but also its mass @xmath4 due to the finite range interaction from the @xmath0-boson exchange . furthermore , we find that the @xmath1 and @xmath2 are sensitive to both @xmath3 and @xmath4 if the @xmath0-boson mass @xmath4 is larger than about @xmath5 mev and both @xmath3 and @xmath4 can have significant influence on the mass - radius relation and the crustal fraction of total moment of inertia of neutron stars . we also demonstrate that the exchange term has minor influence on the nuclear matter eos as well as the @xmath17 and @xmath2 for the parameter values of @xmath3 and @xmath4 considered in this work .

three methods , i.e. , the thermodynamical approach , the curvature matrix approach and the vlasov equation approach are used to determine the transition density with the skyrme effective nucleon - nucleon interactions . we find that the and depend on not only the ratio of coupling strength to mass squared of the-boson but also its mass due to the finite range interaction from the-boson exchange . in particular , our results indicate that the and are sensitive to both and if the-boson mass is larger than about mev . furthermore , we show that both and can have significant influence on the mass - radius relation and the crustal fraction of total moment of inertia of neutron stars . in addition , we study the exchange term contribution of the-boson based on the density matrix expansion method , and demonstrate that the exchange term effects on the nuclear matter equation of state as well as the and are generally negligible .

we explore effects of the light vector-boson , which is weakly coupled to nucleons , on the transition density and pressure at the inner edge separating the liquid core from the solid crust of neutron stars . three methods , i.e. , the thermodynamical approach , the curvature matrix approach and the vlasov equation approach are used to determine the transition density with the skyrme effective nucleon - nucleon interactions . we find that the and depend on not only the ratio of coupling strength to mass squared of the-boson but also its mass due to the finite range interaction from the-boson exchange . in particular , our results indicate that the and are sensitive to both and if the-boson mass is larger than about mev . furthermore , we show that both and can have significant influence on the mass - radius relation and the crustal fraction of total moment of inertia of neutron stars . in addition , we study the exchange term contribution of the-boson based on the density matrix expansion method , and demonstrate that the exchange term effects on the nuclear matter equation of state as well as the and are generally negligible .

0810.5126

i

a wide variety of cosmological observations seem to point to a two - component dark sector , in which approximately 73% of the energy density of the universe is in dark energy and 23% is in non - baryonic dark matter ( dm ) . ordinary matter constitutes the remaining 4% @xcite . the physics of the dark matter sector is plausibly quite minimal : an excellent fit to the data is obtained by assuming that dark matter is a cold , collisionless relic , with only the relic abundance as a free parameter . the well - known `` wimp miracle '' @xcite is the fact that a stable , neutral particle with weak - scale mass and coupling naturally provides a reasonable energy density in dm . particles of this type arise in models of low - scale supersymmetry @xcite or large extra dimensions @xcite , and provide compelling dm candidates . in the contemporary universe , they would be collisionless as far as any conceivable dynamical effects are concerned . nevertheless , it is also possible to imagine a rich phenomenology within the dark sector . the dark matter could be coupled to a relatively strong short - range force that could have interesting consequences for structure on small scales @xcite . alternatively , dm could also be weakly coupled to long - range forces , which might be related to dark energy @xcite . one difficulty with the latter is that such forces are typically mediated by scalar fields , and it is very hard to construct natural models in which the scalar field remains massless ( to provide a long - range force ) while interacting with the dm at an interesting strength . in this paper , we explore the possibility of a long - range _ gauge _ force coupled to dm , in the form of a new unbroken abelian field , dubbed the @xmath3 `` dark photon . '' we imagine that this new gauge boson @xmath4 couples to a dm fermion @xmath5 , but not directly to any standard model ( sm ) fields . our model is effectively parameterized by only two numbers : @xmath6 , the mass of the dm , and @xmath1 , the dark fine - structure constant . if @xmath6 is sufficiently large and @xmath1 is sufficiently small , annihilations of dm particles through the new force freeze out in the early universe and are negligible today , despite there being equal numbers of positively- and negatively - charged particles . the dark matter in our model is therefore a plasma , which could conceivably lead to interesting collective effects in the dm dynamics . remarkably , the allowed values of @xmath6 and @xmath1 seem quite reasonable . we find that the most relevant constraint comes from demanding that accumulated soft scatterings do not appreciably perturb the motion of dm particles in a galaxy over the lifetime of the universe , which can be satisfied by @xmath7 and @xmath8 tev . for values near these bounds , the alterations in dm halo shapes may in fact lead to closer agreement with observation @xcite . however , for such regions of parameter space , if @xmath3 were the only interaction felt by the @xmath5 particles , the resulting relic abundances would be slightly too large , so we need to invoke an additional annihilation channel . we show that @xmath5 can in fact be a wimp , possessing @xmath9 quantum numbers in addition to @xmath3 charge . such a model provides the correct relic abundance , and is consistent with particle - physics constraints so long as the mixing between ordinary photons and dark photons is sufficiently small . we consider a number of other possible observational limits on dark electromagnetism , and show that they do not appreciably constrain the parameter space . since the dm halo is overall neutral under @xmath3 , there is no net long - range force that violates the equivalence principle . although there are new light degrees of freedom , their temperature is naturally lower than that of the sm plasma , thereby avoiding constraints from big - bang nucleosynthesis ( bbn ) . energy loss through dark bremsstrahlung radiation is less important than the soft - scattering effects already mentioned . the coupling of dm to the dark radiation background can in principle suppress the growth of structure on small scales , but we show that the dm decouples from the dark radiation at an extremely high redshift . on the other hand , we find that there are plasma instabilities ( _ e.g. _ the weibel instability ) that can potentially play an important role in the assembly of galactic halos ; however , a detailed analysis of these effects is beyond the scope of this work . the idea of an unbroken @xmath0 coupled to dark matter is not new . forces have , of course , also been considered , see _ e.g. _ ref . @xcite ] de rujula et al . @xcite explored the possibility that dark matter was charged under conventional electromagnetism ( see also @xcite ) . gubser and peebles @xcite considered structure formation in the presence of both scalar and gauge long - range forces , but concentrated on a region of parameter space in which the gauge fields were subdominant . refs . @xcite considered several models for a hidden dark sector , including one manifestation in which the dark matter consists of heavy hidden - sector staus interacting via a copy of electromagnetism . the effect of dimension-6 operators containing a new @xmath0 gauge boson and sm fields was considered in ref . @xcite , for models where the only fields in a hidden sector are charged under the new force . additional models which contain unbroken abelian gauge groups may be found , for example in refs . @xcite . in this paper , we construct minimal models of dark matter coupled to a new unbroken @xmath3 , leaving the dark fine - structure constant and dark - matter mass as free parameters , and explore what regions of parameter space are consistent with astrophysical observations and what new phenomena might arise via the long - range gauge interaction . in section [ sec : earlyuniverse ] , we introduce our notation for a minimal dark - matter sector including a new abelian symmetry @xmath3 . we then consider the bounds on the new dark parameters from successful thermal production of sufficient quantities of dark matter as well as requiring that bbn and cosmic microwave background ( cmb ) predictions remain unchanged . the restrictions of parameter space are closely related to those resulting from standard short - range wimp dark matter . in section [ sec : galacticdynamics ] , we consider the effect of long range interactions on dm particle interactions in the halos of galaxies . by requiring that our model not deviate too greatly from the predictions of collisionless dm , we find that the allowed regions of @xmath10 parameter space from section [ sec : earlyuniverse ] are essentially excluded . in order to evade these constraints , section [ sec : su2 ] describes an extended model , where the dark - matter candidate is charged under both @xmath9 and the new @xmath3 . additional effects of dark radiation are presented in section [ sec : newlimits ] , and we conclude in section [ sec : conclusion ] . we note that our model does not address the hierarchy problem , nor provide a high - energy completion to the sm . however , new gauge groups and hidden sectors may be generic results of many such high - energy theories ( _ e.g. _ string and grand unified theories ) , and a wimp coupled to an unbroken @xmath0 is certainly a plausible low - energy manifestation of such theories . the most important lesson of our model is that interesting physics might be lurking in the dark sector , and it is worthwhile to consider a variety of possible models and explore their consequences for astrophysics and particle physics .

we explore the feasibility and astrophysical consequences of a new long - range gauge field ( `` dark electromagnetism '' ) that couples only to dark matter , not to the standard model . the dark matter consists of an equal number of positive and negative charges under the new force , but annihilations are suppressed if the dark matter mass is sufficiently high and the dark fine - structure constant is sufficiently small . the correct relic abundance can be obtained if the dark matter also couples to the conventional weak interactions , and we verify that this is consistent with particle - physics constraints . these values are easily compatible with constraints from structure formation and primordial nucleosynthesis . we raise the prospect of interesting new plasma effects in dark matter dynamics , which remain to be explored .

we explore the feasibility and astrophysical consequences of a new long - range gauge field ( `` dark electromagnetism '' ) that couples only to dark matter , not to the standard model . the dark matter consists of an equal number of positive and negative charges under the new force , but annihilations are suppressed if the dark matter mass is sufficiently high and the dark fine - structure constant is sufficiently small . the correct relic abundance can be obtained if the dark matter also couples to the conventional weak interactions , and we verify that this is consistent with particle - physics constraints . the primary limit on comes from the demand that the dark matter be effectively collisionless in galactic dynamics , which implies for tev - scale dark matter . these values are easily compatible with constraints from structure formation and primordial nucleosynthesis . we raise the prospect of interesting new plasma effects in dark matter dynamics , which remain to be explored .

1507.00882

i

observations show recurrent formation and reshuffling of cool and dense material in coronal loops . the small scale ( @xmath2 km ) coronal rain is observed as cold , dense elongated blob - like features condensing in a much hotter loop and descending along one of its legs . the rain is guided by the loop magnetic field @xcite , dropping from heights of tens of mm into the chromosphere @xcite . similar phenomena have been observed by analysing absorption profiles in euv spectral lines @xcite . seen to propagate from the top of the loop towards its footpoints @xcite , systematic intensity variations in euv spectral lines are confirmed as downflows of cool plasma , rather than representing slow magneto - acoustic waves @xcite . besides downflows towards footpoints , @xcite also found upflows towards the loop apex . @xcite observed and tracked coronal rain in 30 active region loops and found more than one hundred descending condensations within 71 minutes . tracing the cool material towards loop footpoints , @xcite observed propagating patterns suggesting a hot upflow following the downflows , supplying hot plasma into the loops . @xcite suggested that coronal rain consists of plenty of small blobs , with sizes around 300 km in width and 700 km in length on average and they also estimated the occurrence rate of coronal rain in active region loops to be once every two days . since the solar corona is swamped with magnetic loops , this suggests a scenario where coronal rain is rather common . considering the very small sizes involved , one of the most attractive features of coronal rain is that it can be used to probe the local magnetic field structure , or that it can expose valuable properties of the local thermodynamic conditions inside coronal loops @xcite . indeed , the magnetic field structure has a much longer lifetime than the timescale for condensations to form and fall @xcite . additionally , due to the low temperature ( of order @xmath3 k ) of these condensations , coronal rain is normally observed in cold chromospheric lines @xcite . coronal rain results from thermal instability , with its non - linear counterpart and evolution also known as thermal non - equilibrium or catastrophic cooling . the linear thermal instability takes places whenever radiative losses locally overcome the heating input and is governed by well - known stability criteria for uniform radiative plasma conditions @xcite . these can be met in the coronal temperature range , as one encounters locally negative slopes in the radiative loss function @xmath4(t ) as function of temperature . when thermal conduction is insufficient in transporting enough energy to cooling ( and condensing ) material , the temperature reduces over time . as a consequence of thermal instability , temperature and gas pressure drop dramatically in the perturbed region , resulting in matter sucked in from the surroundings to the perturbed region , forming an increasingly larger and cooler condensation . this runaway effect will continually increase the density and decrease the temperature of condensations until heating and cooling achieve a balance again at lower temperatures and higher densities.numerical simulations have contributed to our understanding of thermal instability over the last 40 years @xcite . early numerical work shows that in the million degrees solar corona , small temperature contrasts could be enhanced by line and recombination - driven radiative losses within several minutes @xcite . catastrophic cooling drives recombination of elements in the cool condensations , making them partially ionized and visible in cool chromospheric lines . @xcite concluded that the rate of condensation is determined by hydrodynamical processes mainly . an important progress in modeling was obtained in @xcite , by using a spatially dependent heating increase that is localized nearer to the chromospheric footpoints than to the loop midpoint . with this localized heating at the footpoints , @xcite pointed out that another key requirement to generate a stable , prominence - like condensation is a dipped geometry in the loop . with an adaptive grid code , @xcite showed , in a 1d model , that the complete growth of a condensation reached a quasi - steady state after @xmath5 5000 s. in a similar 1d setup , @xcite calculated the linear instability criterion from numerical results and proved that the onset of coronal condensation indeed satisfies the linear isochoric instability criterion @xcite . in the solar corona , the fairly high densities required for the instability onset are thought to be obtained by evaporating material with heating located near the footpoints of coronal loops in the chromosphere or by direct mass injection into the corona @xcite , resulting e.g. from nano - heating events . influenced by magnetohydrodynamic forces ( gravity , lorentz force and gas pressure gradients ) , condensations , once formed , either fall from the corona down to the chromosphere as coronal rain or they collect into larger structures and remain suspended in the corona over long time periods as prominences , supported by the magnetic field . many numerical works addressed formation and dynamics of coronal rain , but adopted simplifying one - dimensional ( 1d ) approximations reducing the problem to gas dynamic , thermodynamic evolutions along individual field lines @xcite . since coronal rain occurs in many active region loops , the heating input is generally thought to be concentrated at the loop footpoints @xcite , which evaporates chromospheric plasma into the loops and increases the density . with a persistent heating , the anisotropic thermal conduction and optically thin radiation lead these coronal hot loops to reach thermally unstable regimes with a higher density in a timescale of hours @xcite . then catastrophic cooling sets in locally , resulting in the fast formation of cool condensations , as demonstrated in 1d models @xcite . numerical simulations by @xcite emphasized that a loss of equilibrium at the loop apex and the process of catastrophic cooling is caused by constant heating concentrated at the footpoints of the loop rather than a drastic decrease of the total loop heating which was used in earlier models . @xcite compared observations from an eit shutterless campaign with simulations of coronal loops and confirmed that observed localized brightenings and fast flows are consistent with this model . an important conclusion from @xcite was that the structure and dynamics of the coronal rain blobs are more sensitive to the pressure variations arising from catastrophic cooling than to gravity itself . this is in agreement with @xcite , who suggested that the internal pressure evolution of the loops , rather than gravity , determines the condensation speeds . furthermore , @xcite indicated that if a loop is predominantly heated by alfvn waves , coronal rain is inhibited since they tend to heat the loop uniformly . hence , coronal rain may not only point to the spatial distribution of the heating in coronal loops but also to the agent of the heating itself . they thus propose coronal rain as a marker for coronal heating mechanisms . @xcite pointed out that steady heating is not necessary to sustain the condensation . once the condensation is formed , it keeps growing even after localized heating ceases . @xcite simulated a three - dimensional sheared double arcade with a large ensemble of 1d independent flux tubes and observed the formation of both prominence threads and coronal rain . recently , @xcite presented the first multidimensional , magnetohydrodynamic simulations which captured the initial formation and the long - term sustainment of the coronal rain phenomenon . there we found that coronal rain in arcades is always accompanied by fast counter - streaming siphon flows in neighbouring flux bundles and we statistically analysed 80 minutes of virtual coronal rain in terms of sizes , mass , and velocity patterns . our 2.5d simulations showed how blobs deform into v - shaped patterns , and had blobs that levitate , evaporate in - situ , or fall into the transition region at speeds below free - fall . iris data recently revealed also many coronal rain impact events , with up to supersonic speeds above sunspots @xcite . we therefore revisited our mhd setup from @xcite , at even further increased numerical resolution and for much longer time , going up to 6 hours in total . we now analyse blob formation and blob impact into the transition region in more detail , focusing on multi - dimensional aspects not probed by 1d setups . furthermore , the high - resolution coronal imager ( hi - c ) in july 2013 provided a much more detailed look at the fine structure and dynamics in the solar corona . with data from hi - c , @xcite reported that anti - parallel flows have been directly imaged along fundamental filament threads within the million degree corona . they measured relative flow velocities of similar magnitude as in our previous simulations , namely 70 - 80 km s@xmath1 . both observations and our simulations hence suggest that such counter - streaming flows are likely commonplace . we observed that siphon flows establish naturally in a raining arcade , with velocity differences on adjacent field lines up to 80 km s@xmath1 . we thus also extended our simulations to further argue how our setup in a low field ( order 12 g ) magnetic arcade relates to the observed clumps of falling coronal rain @xcite and to unresolved fine - scale structure in solar coronal loop - tops @xcite . the paper is then organized as follows : in 2 we describe the numerical setup , in 3.1 we describe the multidimensional aspects of the condensations , focusing on rebound shocks and their prominence - corona - transion region ( pctr ) structure , 3.2 discusses the condensation rates and the long term coronal rain limit cycle obtained , 3.3 quantifies blob impact on the transition region and concurrent upflows , in 3.4 we investigate the counter - streaming flows , and in 3.5 we describe the shear flow effects . conclusions are drawn in 4 .

we quantify how in - situ forming blob - like condensations grow along and across field lines and show that rain showers can occur in limit cycles , here demonstrated for the first time in 2.5d setups . we discuss dynamical , multi - dimensional aspects of the rebound shocks generated by the siphon inflows and quantify the thermodynamics of a prominence - corona - transition - region like structure surrounding the blobs .

we extend our earlier multidimensional , magnetohydrodynamic simulations of coronal rain occurring in magnetic arcades with higher resolution , grid - adaptive computations covering a much longer ( hour ) timespan . we quantify how in - situ forming blob - like condensations grow along and across field lines and show that rain showers can occur in limit cycles , here demonstrated for the first time in 2.5d setups . we discuss dynamical , multi - dimensional aspects of the rebound shocks generated by the siphon inflows and quantify the thermodynamics of a prominence - corona - transition - region like structure surrounding the blobs . we point out the correlation between condensation rates and the cross - sectional size of loop systems where catastrophic cooling takes place . we also study the variations of the typical number density , kinetic energy and temperature while blobs descend , impact and sink into the transition region . in addition , we explain the mechanisms leading to concurrent upflows while the blobs descend . as a result , there are plenty of shear flows generated with relative velocity difference around 80 km s in our simulations . these shear flows are siphon flows set up by multiple blob dynamics and they in turn affect the deformation of the falling blobs . in particular , we show how shear flows can break apart blobs into smaller fragments , within minutes .

1507.00882

r

in our previous work @xcite , we already described the formation process for the first condensation and emphasized how it perturbed the overall force balance in a 2d fashion . in this work , we discuss more of the multi - dimensional details for the forming condensations , and compare the results of our 2.5d simulations with previous 1d simulation works @xcite and insights from observations @xcite , in particular paying attention to the cross - field effects . the forming process of the first condensation in our 2.5d simulation is shown by fig . [ first ] which presents the temporal evolution of number density ( left columns ) , temperature ( middle columns ) and gas pressure ( right columns ) at @xmath91 101.2 , 101.5 and 102.2 minutes . when we compare these results with the corresponding fig . 5 and fig . 7 of 1d hydrodynamic simulations in @xcite , we conclude that all three parameters behave similarly in the forming process , as the number density increases rapidly from @xmath92 @xmath54 to @xmath93 @xmath54 , while the temperature decreases down to 0.01 mk . along each arched field line , this is analogous to the sudden thermal instability onset in 1d runs . this similarity confirms the applicability of restricted 1d model efforts which assume a rigid 1d loop under the prevailing plasma @xmath94 conditions , which takes on a local value of around 0.06 . the middle panel in the right column of fig . [ first ] also shows a significantly increased gas pressure inside the condensation and a layer of low gas pressure surrounding it after its formation . in the bottom panels of fig . [ first ] , we notice that density , temperature and gas pressure all reveal a front propagating as expanding wings on both sides of the condensation . this phenomenon is because fast siphon inflows are driven into the forming condensation by a strong pressure gradient between the lower gas pressure around the condensation and relatively higher gas pressure away from the condensation , as seen in the middle panel in the right column of fig . [ first ] . these two siphon flows meet up with the blobs , and dynamically impact on the blob to generate two rebound shocks . hence , while thermal instability and runaway cooling triggers a growing condensation , one also forms two rebound shock fronts that propagate away from the blob . the slightly different formation time at different parts of the condensation on adjacent magnetic field lines @xcite , which are due to gradual variations in length and chromospheric footpoint conditions , is the reason that these two expansion shock fronts display a fan - shaped structure , forming earliest in the blob center and spreading away from the blob . this fan - shaped structure of the rebound shocks is also clearly observed in @xcite . however , not every condensation realizes this nearly left - right symmetric situation as seen near the loop apex for this first condensation from fig . [ first ] . due to slightly asymmetric conditions already prevailing after the numerical relaxation process and due to perturbations from existing condensations , most of the following condensations initiate in loop limbs ( also shown in the online movies of @xcite ) . the field - projected gravity force on the limbs leads to asymmetric plasma distributions , as seen e.g. in the number density map in panel a of fig . [ rs ] at @xmath95 minutes , the moment when local catastrophic cooling begins there ( about 10 minutes after the first condensation ) . the higher central gas pressure indicates the initial forming location of this condensation in panel b of fig . [ rs ] . due to its limb - loop location , the number density map points out that the right of the condensation holds a relatively denser ( @xmath96 @xmath54 ) and wider plasma distribution than the left part ( @xmath97 @xmath54 ) . still , strong pressure gradients drive siphon flows from both sides towards this condensation . after a short time at @xmath98 , the denser and heavier plasma at the right of this condensation realizes a ( left - directed ) siphon flow with a slower speed of 23 km / s , compared to the left siphon flow ( which is right - directed ) at a speed of 42 km / s , shown by the velocity magnitude map in panel c of fig . [ rs ] . as discussed above , the impact of siphon flows on the condensation naturally generates rebound shocks , whose speeds are determined by the original speeds of the siphon flows and the mass contrast between the condensation and the siphon flows . the slower and heavier siphon flow on the right of the blob here leads to a much slower rebound ( right - directed ) shock seen to separate at 7 km / s , while the left one ( left - directed ) travels at 21 km / s . these two rebound shocks are identifiable in the gas pressure map in panel e of fig . [ rs ] at @xmath99 minutes . the condensation itself has a velocity of 5 km / s , meaning that basically the right rebound shock barely can sweep up and heat little siphon flow plasma . because the central condensation keeps sucking in plasma from nearby and the rebound shock at the right of the blob is too slow to sweep and heat up plasma , the gas pressure there does not rise to a higher value and keeps a strong pressure gradient at the right of the blob , as shown in panel e of fig . about 3 minutes later at @xmath100 minutes , this persistent pressure gradient at the right of the blob accelerates the left - directed siphon flow to a higher speed of 52 km / s ( shown in panel i of fig . [ rs ] ) , therefore the corresponding right - directed rebound shock finally speeds up to 28 km / s and begins to sweep and shock - heat the plasma on its way . in short , initial asymmetric situations on the condensation can lead to a complicated thermal and dynamical evolution and result in a delay of rebound shocks spreading at one side of the condensation . additionally , we also find another special case , namely blob a in fig . [ os ] , which has only one rebound shock on its left side . [ os ] shows the gas pressure map ( a ) and ( b ) at @xmath91 134.8 and 137.6 minutes , with a dotted isocontour of the number density at @xmath101 @xmath54 overplotted . this density contour at @xmath101 @xmath54 is one of the criteria which identifies whether a cell contains cool plasma belonging to coronal rain , as used further on . panel a in fig . [ os ] indicates a similar situation for blob a as in the second row of fig . [ rs ] in which only the left rebound shock spreads out . in contrast to what happens in the third row of fig . [ rs ] , for blob a we do not find a right rebound shock in fig . [ os ] until the collision and merging of blob a with blob b. the reason is that when the thermal instability triggers the condensation labeled there as blob a , another existing condensation labeled as blob b in the same coronal loop already depleted the plasma between these two blobs . therefore the small pressure gradient in the emptied loop between the two blobs can not drive a fast siphon flow to create a strong rebound shock for blob a , even though the gas pressure on the right of blob a is low enough ( panel a in fig . [ os ] ) , afterwards , when blob a catches up and merges with blob b because of the strong pressure gradient outside these two blobs , the rebound shock at the right side of blob a is still not fast enough to show clear separation and propagation . we also observe the details of a gas pressure substructure within these shock - bounded regions around the condensation in the simulations . these reveal the establishment of a prominence - corona - transition - region ( pctr ) like structure around all blobs . the gas pressure substructure around the first condensation consists of three components shown in panel a of fig . [ pctr ] and panel i of fig . [ first ] , namely a high gas pressure outside of the condensation , a low gas pressure at the boundary of the condensation , and a higher gas pressure in the center of the condensation . actually not only this first condensation in fig . [ first ] has this kind of gas pressure substructure , but also all the blobs which establish a dynamic equilibrium around themselves have it , e.g. all the blobs in fig . [ rs ] and fig . [ os ] . to better quantify this , we identify a field line crossing the center of the blob shown in panel a of fig . [ pctr ] and plot gas pressure , temperature and radiative loss along this field line in panel c of fig . the temperature declines from a coronal temperature of 0.35 mk to a cool plasma temperature of 0.01 mk in 200 km and density increases from @xmath102 @xmath54 to @xmath103 @xmath54 , therefore basically this 200 km area could be considered as a pctr . within this area , we find that two highly radiative loss peaks exist , introduced by a temperature around 0.02 mk . this corresponds to the two dips of gas pressure at the boundary of the blob . these two strong radiation areas also indicate the location in which catastrophic cooling takes place that ensure that the condensation keeps growing . indeed , the two dips in gas pressure always relocate with the boundary of the blobs , coincident with the strong emissive loss . although the temperature of 0.01 mk inside the blob is lower than in the surrounding coronal plasma , a much higher density at the center of the condensation ( @xmath104 @xmath54 ) leads to a little higher gas pressure there . the high gas pressure outside of the condensation reflects the post shock conditions prevailing there after the rebound shocks run against the condensation inflows . note that our resolution is such that we have about 7 grid points along the field line through the pctr at each side of the blob in fig . [ pctr ] , clearly resolving the pctr around the blob in our simulation . the gas pressure difference between inside and outside the condensation is found to persist throughout the lifetime of the blobs and plays a role in the movement of the blobs . especially when the blobs fall along the field lines toward footpoints , the gas pressure and temperature ahead of the descending blob increase as shown in panel b of fig . [ pctr ] , due to the blob compressing the plasma ahead of it in the loop and the strong evaporation at the loop footpoints . we also identify a field line crossing the center of the blob shown in panel b of fig . [ pctr ] and plot gas pressure , temperature and radiation loss along this field line in panel d of fig . [ pctr ] , which shows also an obvious pctr . due to the gravity variation and the strong gas pressure gradient between the two sides of the blob , the lower part of this blob has a higher density distribution , which naturally leads to a higher radiative loss . this strong gas pressure gradient slows down the acceleration of the blob in its descent . this was also pointed out in @xcite , where we stated that sometimes , it can even lift lighter blobs to cross the loop apex . panel a of fig . [ tm ] shows the temporal evolution of total mass of cool ( solid ) and hot ( dashed ) plasma in the corona , and panel b of fig . [ tm ] represents the number of blobs for the entire time interval of our 2.5d simulation . the criteria to identify whether a cell contains cool plasma belonging to coronal rain are that ( i ) the number density is higher than @xmath105 @xmath54 , ( ii ) the temperature is lower than @xmath106 k , and ( iii ) the location is above the chromosphere - corona - transition - region . we dynamically locate the height of the transition region at each @xmath107-position as @xmath108 by searching the vertical position of the ( first ) maximum gradient value of temperature from the bottom boundary . each blob is defined as a collection of neighbouring cells which hold cool plasma . however , if the number of grid cells in one blob is smaller than 10 at our highest resolution , we remove this blob from the blob list to avoid counting spurious transient features that do not collect into a clearly resolvable blob , and also to mimic the observational resolution . as stated before , we adopt a 4 times higher resolution than in @xcite , but also extend the simulation to a two times longer time of around 370 minutes ( previously 190 mins ) . by running our 2.5d simulation for these much longer times , we find that the whole coronal rain process shows limit cycles , which has been discussed in earlier 1d simulations @xcite , as well as in observational work @xcite . this is the first time that we can report limit cycles of coronal rain in a multidimensional simulation , which confirms that constant heating conditions which provide enough energy , can form secondary ( or even more ) coronal rain cycles in a single arcade . from panel a and b of fig . [ tm ] , we find the time interval between the first and secondary cycle to be around 175 minutes , when measured between successive maxima in cool mass matter . panel a of fig . [ tm ] shows the temporal evolution of total mass of hot coronal plasma which is the mass in the corona , excluding the cool plasma identified by the above criteria . we find that at @xmath109 minutes , the total mass of cool plasma reaches its peak in the first cycle in panel a of fig . [ tm ] , while at @xmath110 minutes the catastrophic cooling process has cooled down most of the hot plasma in the corona shown in panel a of fig . from about @xmath111 minutes , blobs begin to fall into the transition region , then the evaporation of plasma in the chromosphere driven by the extra heating @xmath62 fills the evacuated loops left by blobs which already sank into the chromosphere . from this moment , until the onset of the secondary cycle of our coronal rain shower at @xmath112 minutes , it takes about 120 minutes , which is of similar duration as the time for the first cycle to reach its onset ( about 100 minutes ) . so although we infer from the total mass evolution of cool plasma in panel a that there is only about 50 minutes between the ending of the first and the beginning of the second cycle , actually the continued heating at the chromosphere spontaneously begins to fill the empty corona already 70 minutes before . we also see that the total mass of hot plasma before the onset of the secondary cycle is higher than in the first cycle ( panel a ) , which leads to a longer lasting secondary cycle with more mass in condensations . panel a of fig . [ tm ] indicates that at @xmath113 minutes ( before the first blob falls into the chromosphere ) , there is at least @xmath114 g cm@xmath1 cool plasma in the corona , which originally was hot plasma . meanwhile panel a of fig . [ tm ] also suggests that compared with the corona before the onset of catastrophic cooling at @xmath115 minutes , the decrement in the same time of total mass of hot plasma at @xmath109 minutes is only @xmath116 g cm@xmath1 . the difference between the increase in cool plasma and the decrease in hot , indicates that during these 30 minutes since onset at @xmath115 minutes , the evaporation in the chromosphere evaporates @xmath117 g cm@xmath1 into the corona , i.e. at an evaporation rate of 2.2 g cm@xmath1 s@xmath1 . we can similarly estimate an evaporation rate of 2.3 g cm@xmath1 s@xmath1 between the onset of the secondary cycle and the moment its first blob falls into the transition region . till the onset of the first cycle at @xmath115 minutes , the increment of total hot plasma from turning on the extra heating @xmath62 is about @xmath118 g cm@xmath1 in total , further confirming this evaporation rate of 2.2 g cm@xmath1 s@xmath1 . based on these estimates , we infer that anywhere in both simulated cycles , the constant extra heating @xmath62 leads to a nearly constant evaporation rate . we can thus extrapolate to even more cycles expected further on , and interpret these limit cycles as a chronological sequence of mass recycling between chromosphere and corona : heating in the chromosphere brings plasma to the corona by evaporation , where it ultimately triggers catastrophic cooling , the cooling process manages itself into a coronal rain where plasma drains back to the chromosphere , and persistent heating causes the chromospheric material to evaporate again towards the corona . although the duration and peak value of the total mass in both computed cycles are similar , their initial condensation rates ( in contrast to the previously discussed evaporation rate ) computed from the temporal variation of their total mass curve work out to be 6.7 and 4.5 g cm@xmath1 s@xmath1 , respectively and thus are different . it is known from linear thermal instability theory @xcite and 1d simulation results in @xcite , that this initial condensation rate in catastrophic cooling depends on parameters controlling the energy input from heating . one notices that the condensation rate ( the local derivative of the solid curve in panel a of fig . [ tm ] ) varies dramatically even within one cycle , despite a constant heating energy input in our multidimensional simulation . we now will interpret the reason for the changes seen in the condensation rate , by surveying especially the process of growth for the first condensation which forms under a relatively simple and almost symmetric condition . the solid line in panel a of fig . [ first_t ] shows the temporal evolution of the mass accumulation for this first condensation ( the one from fig . [ first ] ) from @xmath115 to 110 minutes . its near linear behavior quantifies that the condensation rate remains almost constant in this time interval at a value of about 2.3 g cm@xmath1 s@xmath1 . we deliberately do not discuss what happens to the first condensation after @xmath119 minutes , since afterwards it breaks into two smaller blobs . in the same figure panel a , the dashed line displays the growth of the total mass of cool plasma as seen on a single field line through the center of the first condensation , i.e. in a 1d fashion . to show this , we identify the group of grid points which are passed by the field line . the total mass of cool plasma determined on the single field line keeps growing in time , but its growth rate is much smaller than that for the whole 2d condensation . panel b of fig . [ first_t ] quantifies the temporal evolution of typical lengths for the first condensation , where we quantify both the length parallel to the magnetic field lines and the length perpendicular to the magnetic field lines . this indicates that blob growth in the perpendicular direction is much faster than in the parallel one , which can be seen visually as well in all columns in fig . [ first ] and fig . as discussed in @xcite , the low pressure region surrounding the first condensation onset leads to magnetic restoring forces on adjacent loops . these inturn influence in which location the catastrophic cooling will take place on the adjacent loops , which are all close to the thermal instability onset . the different growth rates found for blob sizes in these two directions then relate to the fairly fast ` growth ' along the perpendicular direction due to sympathetic runaway cooling onset , versus the slower growth seen in the parallel one , which is the only one found in 1d setups . the average density of each cell of the condensation is quantified in panel c of fig . [ first_t ] , and this density stays basically the same in the forming process , meaning that the total mass of the condensation is just proportional to the increasing number of neighbouring grid cells that contain cool plasma . while the number of cells in the condensation increases in both directions , the larger condensation rate of the whole blob in panel a of fig . [ first_t ] again directly reflects the faster growth in size in the perpendicular direction . we conclude that the growth of total mass of individual blobs in our simulation is mainly determined by the onset of catastrophic cooling in neighbouring loops rather than the growth along the loops in which catastrophic cooling gets triggered . we can indeed verify this 2d growth aspect by further showing a correlation between the total mass of cool plasma and two other measures , which holds up even for a longer time than the first 10 minutes , i.e. when several blobs have started to form . this is shown in panel d in fig . [ first_t ] where we plot the temporal evolution of total mass of cool plasma , the size of the onset transition region , and the total blob region width . the total blob region width indicates the total width of all magnetic loops where catastrophic cooling takes place on . the size of onset transition region means the corresponding width as found at the transition region height , of all the loops undergoing catastrophic cooling . because the magnetic arcade configuration adopted , these size measures for the affected loops give higher values for higher locations , i.e. the total blob region width always exceeds the ( field aligned remapped ) onset transition region size . the latter size of the onset transition region shows a nice correlation with the total mass of cool plasma evolution . in the simulation , we observe plenty of blobs hitting the transition region and disappearing into the lower chromosphere , as also known to occur in observations @xcite . @xcite observed high - speed downflows and concurrent upflows in coronal loops close to the footpoints and argue in favor of upflows in coronal loops at higher temperatures . @xcite confirmed that the high - speed downflows represent the cool plasma , which is corresponding to the falling blobs in our simulation ( see once more also the online movie of @xcite ) . meanwhile , our 2.5d simulation also shows the possibility of triggering concurrent upflows as observed by @xcite and @xcite . panel a in fig . [ hit1 ] shows the number density map at @xmath120 at a moment when falling blobs sink into the transition region and compress the plasma on its way ( at about @xmath121 mm ) . panel b in fig . [ hit1 ] shows the vertical velocity map at the same location and instant , which clearly displays the concurrent upflows rising at the tails of the declining blobs in the same field line bundles . hence , this answers the question in @xcite whether the upflows can flow along the same field lines as the downflows . these upflows in our simulation are actually rebound shocks from the impact of the blobs on the transition region ( tr ) . they arise immediately when the blobs impact on the tr , and spread from one footpoint to another footpoint in around 5 minutes with a velocity of around 50 km s@xmath1 . from panel a we can see the enhanced density left after passage of these rebound shocks . however , panel c in fig . [ hit1 ] which quantifies temperature indicates that the temperature in the loop already increases before the rebound shocks have reached far into the loop , since the parametrized background heating @xmath122 heats the low density loops left by falling blobs very efficiently . panel d shows also the temperature , but now on a larger domain and at a later time . it shows that afterwards the rebound shocks heat the low density loops to an even higher temperature of 2.0 mk . after the rebound shocks reach the other footpoint , the loops are at high temperature of about 2 mk but with a low number density of @xmath102 @xmath54 . we distinguish this from further upflows coming from evaporation due to the extra strong heating @xmath62 located in the chromosphere . this enhances the density to @xmath123 @xmath54 again and the temperature to 2.3 mk . however , these upflows from evaporation rise with a much slower velocity of around 15 km s@xmath1 . to quantify even further the detailed fate of a blob when it hits and descends into the tr , fig . [ hit ] shows the temporal evolution of the mass , density , velocity , kinetic energy , momentum , and temperature of the first coronal rain blob to hit the transition region from the corona and to sink down into the chromosphere . the vertical dashed line in each panel of fig . [ hit ] points at @xmath124 minutes when this blob hits the transition region . because the density and temperature of plasma in the transition region is comparable with those of the blobs , we can not use only the density and temperature as a criterium to distinguish blobs when they are near or partially below the transition region anymore . in order to identify plasma belonging to the blob as it hits and descends in the transition region after @xmath124 minutes , we change our criteria to require the local velocity to be larger than 3 km s@xmath1 and the location are below the transition region line @xmath108 after @xmath124 minutes . since the velocity of plasma in the transition region is almost zero , this velocity - based criterion captures the location of sinking blobs . in panel a of fig . [ hit ] , we find that the mass identified as blob material by the above criteria begins to increase at t@xmath5 132.7 minutes . this is because the mass detected not only includes the blob itself , but also counts mass compressed and accelerated by the blob impact . at @xmath125 minutes , the total mass affected reaches its peak at six times the original blob mass . after @xmath125 minutes , due to the combined influence of reflection - transmission processes at the transition region , and the higher gas pressure from the impact , the velocities in much of the blob impacted area decrease to values smaller than the criterion 3 km s@xmath1 . this is then seen as a mass decrease in our panel a. in panel b of fig . [ hit ] , the density versus time profile keeps rising while the blob hits the transition region . as we know , this blob impact compresses the transition region plasma swept up by the blob and transfers momentum from the sinking blob to the impacted plasma , and therefore in panel c of fig . [ hit ] we find that the average velocity of the region identified keeps decreasing during the whole process , as well as the kinetic energy shown in panel d. panel e of fig . [ hit ] shows the total momentum of the mass identified . due to the gravitational acceleration , the blob momentum keeps increasing until it reaches its maximum value at @xmath91 136 minutes , then it reduces quickly . this is a combination of the mass evolution in panel a and the velocity info from panel c. the momentum and velocity decreasing after the impact relate to momentum transfer to the surrounding transition region and upper chromosphere plasma , until the regions selected by the velocity - based criteria vanishes : the local conditions settle to static chromosphere conditions . panel f of fig . [ hit ] shows the average temperature evolution during the blob impact . the temperature increases before hitting the tr due to the compressional heating when the blob descends through the higher gas pressure region just above the transition region . after the impact , since also more cooler material gets identified as impacted matter , one settles back to upper chromospheric temperature values . the impact speed of blobs in fig . [ hit ] is around 30 km s@xmath1 , and the highest impact speed of all blobs in our simulation is around 60 km s@xmath1 and number densities range from 4 to 6@xmath126 @xmath54 . our maximum impact speed is much lower than the falling speeds reported in @xcite which went up to 200 km s@xmath1 . they report that these coronal rain events with high impact speeds are correlated with local brightenings which probably indicate an increase of density and temperature in the transition region . panel b of fig . [ hit ] and panel a of fig . [ hit1 ] confirm the expected increase of the number density of impacts in our simulation . we also find another interesting phenomenon in our numerical simulation , namely the self - consistent establishment of counter - streaming flows . such anti - parallel flows are very commonly found in solar observations , especially also in prominences @xcite . panels a , b and c in fig . [ sf ] respectively show the signed velocity magnitude map ( with the sign taken from the horizontal velocity component ) , the gas pressure map and the number density map at @xmath127 minutes . panel d shows the signed velocity magnitude map as in panel a , but at a later time , namely at @xmath128 minutes . these four panels in fig . [ sf ] display many cases of counter - streaming flows established on neighbouring field line bundles in our simulation and allow to explain the origins of counter - streaming flows . after thermal instability inducing a runaway catastrophic cooling and initial growth in an almost static state , the condensations lose their delicate force balance and begin to slide towards one footpoint along magnetic field lines . whether a particular condensation segment slides to the left or right is influenced by its initial location and local total force balance ( gravity , gas pressure gradient and magnetic field force ) . once in motion , they are accelerated by the field - projected gravitational force , meanwhile catastrophic cooling keeps taking place around the condensations . as discussed in section [ s - rebound ] , the initial catastrophic cooling process depletes the local plasma and sucks in fast inflows , then the spontaneous rebound shocks heat the plasma and increase the gas pressure . afterwards , no stronger inflows are driven again due to the increased gas pressure . however , there can be several blob pairs lying in the same or neighbouring field line bundles , as shown in panel c of fig . [ lp ] shows gas pressure maps with magnetic field lines at @xmath129 and 113.0 minutes . the black contour relates to the temperature distribution and is an isocontour at 0.1 mk . both the gas pressure and temperature in panel a in fig . [ lp ] indicate the clear pctr around the blob as previously discussed in fig . [ pctr ] . after 3 minutes , the panel b of fig . [ lp ] shows two white ( low ) pressure sections after the blob breaks into three segments . these low pressure sections slant through the field lines and they are the elongated pctr cross sections from the original parts of the whole blob in panel a of fig . [ lp ] . because the strong radiation in the pctr , the temperatures inside these elongated regions stay low during their deformation . as a result , we could consider these cross sections to undergo an isothermal expansion . because the condensed mass in these narrow regions grows much slower than their areal growth due to elongation , the densities inside these elongated cross sections decrease faster as well as the gas pressure . this leads to blob sequences with low pressure sections in between them . this is also seen in panel b of fig . [ sf ] where a sequence of blobs show up with white ( low ) pressure sections in between them . the depleted areas trigger siphon inflows to refill these regions . then this pair of siphoned fast inflows establish the counter - streaming flows between the pair of neighbouring blobs . panels a and b in fig . [ sf ] also show that falling condensations with larger velocities induce larger density depletions and lower gas pressure areas on their way down , which leads to faster inflows than those found for more static condensations . panel d in fig . [ sf ] indicates another different origin of counter - streaming flows at @xmath128 minutes . as we discuss in section [ s - impact ] , we observe that after blobs decline into the transition region , concurrent upflows rise up towards the loop apex . upflows labeled as a in panel d in fig . [ sf ] are the concurrent upflows shown in panel b of fig . [ hit1 ] , but about 3 minutes later ( concurrent with the later temperature panel d of fig . [ hit1 ] ) . upflows arising from blob impacts also have the chance to establish a counter - streaming flow if there is an opposite flow pattern in the neighbouring loops . the difference between these two different origins for counter - streaming flows is that the one based on depleted sections between a pair of blobs lying on neighbouring field line bundles can last through the whole falling process of blobs , or on time scales of about 10 minutes , while the other ones will vanish after the upflows refill the loops , typically in a shorter time scale of about 5 minutes . the sheared flows that are established by the detailed blob dynamics could also in return influence the further evolution of the condensations . an example is shown in panel a of fig . [ se ] , where we show a signed velocity map , with overlaid contours of the density distribution of condensations at levels of 7 , 25 and 50 @xmath130 @xmath54 at @xmath131 minutes . concentrating on the density feature labeled with a , after its initial formation , sheared flows already begin to take shape . about 10 minutes later , this segment a is seen as segment a1 and a2 in panel b of fig . [ se ] and the condensation has broken into two distinct segments with increasing separation between them . segment a2 is also going to break into two segments a little later . at the @xmath91 123.7 minutes in panel a of fig . [ se ] , this segment a feature is more like one whole elongated condensation . however , by @xmath132 in panel b in fig . [ se ] , several condensations behave totally separate to each other . another example is the one of segment b in panel a and panel b. this breaks up into segment b1 and segment b2 in panel c at @xmath91 136.2 minutes . then segment b1 further breaks into segment b1 and b3 in panel d at @xmath91 139.8 minutes . this gradual change from one elongated dense blob or strand breaking into several segments , surrounded by fast sheared flows , hints at the influence of kelvin - helmholtz instabilities ( khi ) . however , there is no clear vorticity pattern emerging in our simulation that would clearly identify khi development , which may not have enough time to develop . we speculate that other khi related substructure may well arise under different parameter settings ( field strength , heating scale height ) , but already establish that sheared flows contribute to the breaking up of elongated condensations into smaller fragments .

we point out the correlation between condensation rates and the cross - sectional size of loop systems where catastrophic cooling takes place . we also study the variations of the typical number density , kinetic energy and temperature while blobs descend , impact and sink into the transition region . in addition , we explain the mechanisms leading to concurrent upflows while the blobs descend . as a result , there are plenty of shear flows generated with relative velocity difference around 80 km s in our simulations . these shear flows are siphon flows set up by multiple blob dynamics and they in turn affect the deformation of the falling blobs . in particular , we show how shear flows can break apart blobs into smaller fragments , within minutes .

we extend our earlier multidimensional , magnetohydrodynamic simulations of coronal rain occurring in magnetic arcades with higher resolution , grid - adaptive computations covering a much longer ( hour ) timespan . we quantify how in - situ forming blob - like condensations grow along and across field lines and show that rain showers can occur in limit cycles , here demonstrated for the first time in 2.5d setups . we discuss dynamical , multi - dimensional aspects of the rebound shocks generated by the siphon inflows and quantify the thermodynamics of a prominence - corona - transition - region like structure surrounding the blobs . we point out the correlation between condensation rates and the cross - sectional size of loop systems where catastrophic cooling takes place . we also study the variations of the typical number density , kinetic energy and temperature while blobs descend , impact and sink into the transition region . in addition , we explain the mechanisms leading to concurrent upflows while the blobs descend . as a result , there are plenty of shear flows generated with relative velocity difference around 80 km s in our simulations . these shear flows are siphon flows set up by multiple blob dynamics and they in turn affect the deformation of the falling blobs . in particular , we show how shear flows can break apart blobs into smaller fragments , within minutes .

1207.0109

i

a beautiful consequence of mike freedman s disk embedding theorem is the existence of non - smoothable @xmath0-manifolds . in the easiest setting , his result can be stated as follows . [ thm : classification ] any odd unimodular symmetric form @xmath1 is realized as the intersection form of exactly _ two _ closed simply - connected oriented 4manifolds ( up to homeomorphism ) . these 4manifolds are homotopy equivalent and are distinguished by the following ( equivalent ) criteria : exactly one of the manifolds 1 . is smoothable after crossing with @xmath2 . is smoothable after connected sum with finitely many copies of @xmath3 . 3 . has a linear reduction of its micro normal bundle . has vanishing kirby - siebenmann invariant in @xmath4 . exhibits the following formula for a quadratic refinement @xmath5 of @xmath6 : @xmath7 by donaldson s theorem a @xcite , _ exactly _ the diagonalizable odd forms @xmath6 are realized by closed _ smooth _ diagonal forms are realized by connected sums of complex projective planes ( with varying orientations ) ; in fact , most such forms are now known to admit infinitely many smooth representatives ( all being homeomorphic by the above theorem ) , see e.g. @xcite . criterion ( v ) is the most elementary and will be explained in detail in section [ sec : ks ] . the key is the following geometric interpretation for the quadratic refinement @xmath8 . in a simply - connected closed 4manifold @xmath9 , any class in @xmath10 can be represented by a ( topologically generic ) immersed sphere @xmath11 . this means that @xmath12 looks locally like @xmath13 , except for finitely many double points around which @xmath12 looks like @xmath14 . one can add more local self - intersection points to @xmath12 until their algebraic sum is zero . this implies that one can choose _ whitney disks _ @xmath15 , pairing all these self - intersection points . these are ( topologically generic ) immersed disks @xmath16 whose boundary consists of two arcs , each going between the two intersection points but on different sheets , see figure [ fig : whitney - move ] . we will explain in lemma [ lem : c ] why @xmath8 equals an intersection invariant @xmath17 , computed by summing the ( topologically generic ) intersections between an immersed sphere @xmath12 , representing the characteristic @xmath18 , and ( the interiors of ) framed whitney disks @xmath15 for @xmath12 : @xmath19 in @xcite , this invariant was called the _ kervaire - milnor invariant _ because these authors first proved rohlin s formula below @xcite for the case where @xmath9 is smooth and @xmath20 is represented by an embedded sphere , implying the properties @xmath21 . [ rem : framing ] the figure above shows a _ framed _ whitney disk @xmath15 in the sense that there are two _ disjoint _ parallel copies of @xmath15 , as needed for the whitney move on the right hand side . in general , a whitney disk comes with a framing of its boundary and hence admits a well defined euler number in @xmath22 , its _ twist_. the operation of _ boundary twisting _ @xcite allows to assume that all whitney disks are framed , i.e. have twist zero . moreover , one can also assume that the @xmath15 are ( disjointly ) embedded disks , by pushing all ( self)-intersections off the boundary . a generalization of rohlin s theorem @xcite says that this geometric invariant determines the kirby - siebenmann invariant of a closed oriented 4manifold @xmath9 by the formula @xmath23 explaining the equivalence of criteria ( iv ) and ( v ) above . in section [ sec : ks ] we ll recall a definition of @xmath24 which makes the above formula hold for all closed oriented 4manifolds @xmath9 ( without assuming that @xmath20 is spherical ) . the 2-complex @xmath25 in @xmath9 is referred to as a _ whitney tower _ of order 1 , built on @xmath12 , with order 1 whitney disks @xmath15 . the invariant @xmath26 used above is the first _ intersection invariant _ of such whitney towers . it has again _ order 1 _ , the order zero intersection invariants being given by the intersection form @xmath27 . in a sequence of papers , the authors generalized this invariant to higher orders , see for example our survey @xcite . the idea is that if @xmath28 vanishes then all intersections between @xmath12 and @xmath15 can be paired by _ order 2 _ whitney disks @xmath29 and there should be a second - order intersection invariant @xmath30 measuring the obstruction for finding order 3 whitney disks , and so on . in @xcite we worked out this higher - order intersection theory in detail for whitney towers built on immersed disks in the @xmath0ball bounded by framed links in the @xmath31sphere . in this simply connected setting the invariant @xmath32 of an order @xmath33 ( framed ) whitney tower @xmath34 takes values in an abelian group @xmath35 ( where @xmath36 is number of link components ) , and the vanishing of @xmath32 implies that the link bounds and order @xmath37 whitney tower . for links bounding _ twisted _ whitney towers there is an analogous obstruction theory and intersection invariant @xmath38{infty2.pdf}\end{minipage } } { \begin{minipage}{.12in}\includegraphics[width=.12in]{infty2.pdf}\end{minipage } } { \begin{minipage}{.10in}\includegraphics[width=.10in]{infty2.pdf}\end{minipage } } { \begin{minipage}{.08in}\includegraphics[width=.08in]{infty2.pdf}\end{minipage } } } } _ k({\mathcal{w}})\in{\mathcal{t}}^{{\mathchoice { \begin{minipage}{.15in}\includegraphics[width=.15in]{infty2.pdf}\end{minipage } } { \begin{minipage}{.12in}\includegraphics[width=.12in]{infty2.pdf}\end{minipage } } { \begin{minipage}{.10in}\includegraphics[width=.10in]{infty2.pdf}\end{minipage } } { \begin{minipage}{.08in}\includegraphics[width=.08in]{infty2.pdf}\end{minipage } } } } _ k(m)$ ] , and in the second part of this paper we develop an algebraic theory of quadratic forms , leading to a beautiful relation between these framed and twisted obstruction groups , spelled out in theorem [ thm : exact ] . this result is used in the computation of the whitney tower filtration on classical links described in @xcite . * acknowledgments : * the main part of this paper was written while the first two authors were visiting the third author at the max - planck - institut fr mathematik in bonn . they all thank mpim for its stimulating research environment and generous support . the third author was also supported by nsf grants dms-0806052 and dms-0757312 .

we first remind the reader of a simple geometric description of the kirby - siebenmann invariant of a 4manifold in terms of a quadratic refinement of its intersection form . this is the first in a sequence of higher - order intersection invariants of whitney towers , studied by the authors , particularly for the 4ball . in the second part of this paper , a general theory of quadratic forms

we first remind the reader of a simple geometric description of the kirby - siebenmann invariant of a 4manifold in terms of a quadratic refinement of its intersection form . this is the first in a sequence of higher - order intersection invariants of whitney towers , studied by the authors , particularly for the 4ball . in the second part of this paper , a general theory of quadratic forms is developed and then specialized from the non - commutative to the commutative to finally , the symmetric settings . the intersection invariant for twisted whitney towers is shown to be the universal symmetric refinement of the framed intersection invariant . as a corollary we obtain a short exact sequence that has been essential in the understanding of whitney towers in the 4ball .

1305.0729

i

let @xmath2 and consider the @xmath1 hypergeometric differential equation @xmath3 where @xmath4 and @xmath5 . assuming , as we do , that @xmath6 , @xmath7 , and the @xmath8 s and @xmath9 s are distinct , the @xmath10-functions @xmath11 where @xmath12 denotes omit @xmath13 , are linearly independent solutions to ( [ deq ] ) . here @xmath1 is the hypergeometric function @xmath14 and @xmath15 . equation ( [ deq ] ) is regular away from @xmath16 and its monodromy group @xmath17 is generated by the local monodromies @xmath18 ( @xmath19 ) gotten by analytic continuation of a basis of solutions along loops about @xmath20 , and @xmath21 respectively , see @xcite for a detailed description . the local monodromies of equations that come from geometry are quasi - unipotent which is one reason for our restricting @xmath8 and @xmath9 to be rational . we restrict further to such @xmath17 s which after a suitable conjugation are contained in @xmath22 . according to @xcite , this happens if the characteristic polynomials of @xmath23 and @xmath24 , whose roots are @xmath25 and @xmath26 respectively , are products of cyclotomic polynomials . in particular for each @xmath27 there are only finitely many such choices for the pair @xmath28 in @xmath29 . @xcite also determine the zariski closure @xmath30 of @xmath17 explicitly in terms of @xmath31 . furthermore the integrality conditions that we are imposing imply that @xmath17 is self dual so that @xmath32 is either finite , @xmath33 ( @xmath10 even ) or @xmath34 . the signature of the quadratic form in the orthogonal case is determined by the relative locations of the roots @xmath28 ( see section [ beuksum ] ) . our interest is whether @xmath17 is of finite or infinite index in @xmath35 $ ] . in the first case we say that @xmath17 is _ arithmetic _ and in the second case that it is _ thin_. this distinction is important in various associated number theoretic problems ( see @xcite ) and this paper is concerned with understanding which case happens and which is typical . in a given example , if @xmath17 is arithmetic one can usually verify that it is so by producing generators of a finite index subgroup of @xmath36 , on the other hand if @xmath17 is thin then there is no general procedure to show that it is so . our main result is a robust certificate for showing that certain @xmath17 s are thin . until recently , other than the cases where @xmath17 ( or equivalently @xmath32 ) is finite , there were few cases for which @xmath17 itself was known . for @xmath37 it is well known that all the @xmath17 s are arithmetic and we show that the same is true for @xmath38 . for @xmath39 brav and thomas @xcite showed very recently that the dwork family @xcite @xmath40 as well as six other hypergeometrics with @xmath41 which correspond to families of calabi - yau three - folds , are thin . in fact they show that the generators @xmath23 and @xmath42 of the above @xmath17 s play generalized ping - pong on certain subsets of @xmath43 , from which they deduce that @xmath17 is a free product and hence by standard cohomological arguments that @xmath17 is thin . on the other hand , venkataramana shows in @xcite that for @xmath10 even and @xmath44 @xmath17 is arithmetic ( in @xmath45 ) . in particular , there are infinitely many arithmetic @xmath17 s . in @xcite many more examples with @xmath46 and for which @xmath17 is arithmetic are given . another example for which @xmath47 can be shown to be thin is @xmath48 , @xmath49 , see @xcite . in this case @xmath50 is orthogonal and has signature @xmath51 and @xmath36 splits as a product of @xmath52 s . all of our results are concerned with the case that @xmath32 is orthogonal and is of signature @xmath0 over @xmath53 . we call these hyperbolic hypergeometric monodromy groups . there is a unique ( up to a scalar multiple ) integral quadratic form @xmath54 for which @xmath55 , or what is the same thing an integral quadratic lattice @xmath56 with @xmath57 . in section [ quadform ] we determine a commensurable quadratic sublattice explicitly which facilitates many further calculations . in this hyperbolic setting @xmath58 acts naturally as isometries of hyperbolic @xmath59-space @xmath60 and we will use this geometry as a critical ingredient to provide a certificate for @xmath17 being thin . our first result is the determination of the @xmath28 s for which @xmath32 is hyperbolic , see theorem [ theo ] . firstly , these only occur if @xmath10 is odd and for @xmath61 they are completely described by seven infinite parametric families . for @xmath62 there are sporadic examples which are listed in tables 2 and 3 of section [ numeric ] . our determination of the seven families is based on a reduction to @xcite s list of families of @xmath32 s which are finite ( i.e. those @xmath32 s for which @xmath63 and have signature ( @xmath64 ) ) . for @xmath38 , if @xmath17 is not finite then it is hyperbolic and as we noted all @xmath65 of these hyperbolic groups are arithmetic . this is verified separately for each case , there being no difficulty in deciding whether a finitely generated subgroup of @xmath66 is thin or not ( the latter is a double cover of @xmath67 , see the appendix . for @xmath68 the hyperbolic monodromies behave differently . our certificate of thinness applies in these cases and it is quite robust as exemplified by [ theorem1 ] the two families of hyperbolic monodromies @xmath17 with @xmath68 and odd * @xmath69 * @xmath70 are thin . in particular infinitely many of the @xmath17 s are thin and as far as we know these give the first examples in the general monodromy group setting of thin monodromy groups for which @xmath71 is high dimensional and simple . the normalized @xmath1 s corresponding to ( i ) and ( ii ) above ( see @xcite for the normalization ) are @xmath72 respectively . the second has integral coefficients while the first does not , hence this arithmetic feature of @xmath73 is not reflected in the arithmeticity of the corresponding @xmath47 ( see the end of section [ familyclassification ] for more about the integrality of the coefficients ) . our certificate for thinness applies to a number of the families and many of the sporadic examples . the full lists that we can handle thus far are recorded in theorems [ thinfamilythm ] and [ secondthin ] of section [ mindistgraph ] as well as table [ table3 ] of section [ numeric ] . there remain some families for which the method does not apply ( at least not directly ) . in any case we are led to [ allthinconj ] all but finitely many hyperbolic hypergeometric @xmath17 s are thin . we turn to a brief description of our methods . in general if there is an epimorphism @xmath74 with @xmath75 of infinite index in @xmath76 , then clearly @xmath17 must be of infinite index in @xmath36 . in principle , @xmath77 could be infinite which would imply that @xmath17 is thin since the latter is essentially generated by involutions , however we know very little about these cohomology groups for the full @xmath78 . instead we use variations of the quotient @xmath79 where @xmath80 is the vinberg reflective subgroup of @xmath78 . namely , @xmath80 is the group generated by the elements of @xmath78 which induce reflections of hyperbolic space @xmath60 ( that is the induced action on one of the two sheeted hyperboloids in @xmath10-space , see section [ cartaninvol ] ) . vinberg @xcite and nikulin @xcite have shown that except for rare cases @xmath76 is infinite , see section [ cartaninvol ] for a review of their results which we use . to apply this we need to understand the image of @xmath17 in @xmath76 . the key observation is that the element @xmath42 in @xmath17 , which is a linear reflection of @xmath10-space , induces a cartan involution of @xmath60 , that is it is an isometry of @xmath60 which is an inversion in a point @xmath81 . the reflection subgroup @xmath82 of @xmath17 is the group generated by the cartan involutions @xmath83 , @xmath84 and @xmath85 is cyclic . thus essentially up to commensurability the question of whether @xmath17 is thin is a special case of deciding whether a subgroup @xmath86 of @xmath78 generated by cartan involutions is thin or not . we approach this by examining the image of such a @xmath86 in @xmath87 ( when the latter is infinite ) . at this point the study is about @xmath78 , @xmath87 , and a general such @xmath86 ( and @xmath10 need nt be odd ) . we define a graph @xmath88 , the `` distance graph , '' associated with root vectors of @xmath54 which is central to the analysis . we assume that @xmath54 is even ( that is @xmath89 for @xmath90 ) and for @xmath91 or @xmath92 let @xmath93 be the corresponding root vectors ( in the case that @xmath94 for all @xmath95 which comes up in some cases we also allow @xmath96 to be @xmath97 ) . the root vectors define linear reflections lying in @xmath78 given by @xmath98 . by our choice of the signature of @xmath54 , for @xmath99 the map @xmath100 induces a cartan involution on @xmath60 while for @xmath101 it induces a hyperbolic reflection on @xmath60 . assume that the cartan involutions generating @xmath86 come from root vectors in @xmath102 . @xmath88 has for its vertices the set @xmath102 and we join @xmath103 to @xmath104 if @xmath105 , this corresponds to @xmath103 and @xmath104 having the smallest distance allowed by discreteness , as points in @xmath60 . the graph @xmath88 is a disjoint union of its connected components @xmath106 and these satisfy ( see section [ graphprop ] for a detailed statement ) * the components @xmath107 consist of finitely many isomorphism types . * [ [ ( ii ) ] each type is either a singleton or an infinite homogeneous graph corresponding to a transitive isometric action of a coxeter group with finite stabilizer . * if @xmath107 is a connected component of @xmath88 , then the group generated by the corresponding cartan roots , @xmath108 is up to index @xmath109 contained in the reflection group @xmath110 . with this the certificate for showing that @xmath86 is thin is clear : according to vinberg and nikulin , @xmath111 is infinite except in rare cases ( and nikulin has a classification of thee ) , hence if ( iii ) is satisfied for the generators of @xmath86 then @xmath86 must be thin . the calculations connected with the minimal distance graph can be carried out effectively in general and even explicitly for some of our families . the process in the general case invokes an algorithm for computing the fundamental polyhedral cell for a discrete group of motions of hyperbolic space which is generated by a finite number of reflections . such an algorithm is provided in section [ thinguys ] . the above leads to the cases discussed in sections [ mindistgraph ] and [ numeric ] for which @xmath17 is shown to be thin . to end we note that it is possible that a much stronger version of vinberg s theorem in the following form is valid : for all but finituely many rational quadratic forms @xmath54 ( at least if @xmath10 is large enough ) the full `` weyl subgroup '' @xmath112 generated by _ all _ reflections in @xmath113 ( that is , both those inducing hyperbolic reflections and cartan involutions on @xmath60 ) is infinite index in @xmath114 ( see nikulin @xcite ) . if this is true then conjecture [ allthinconj ] would follow easily from our discussion . in section [ cartaninvol ] we give an example in dimension @xmath115 with @xmath116 being thin and @xmath117 arithmetic , so there is no general commensurability between these groups . finally , we note that when our analysis of the thinness of @xmath47 succeeds , it comes with a description of @xmath47 as a subgroup ( up to commensurability ) of a geometrically finite subgroup of @xmath116 and this opens the door to determine the group structure of @xmath47 itself . we leave this for the future .

we give a criterion which ensures that a group generated by cartan involutions in the automorph group of a rational quadratic form of signature is `` thin '' , namely it is of infinite index in the latter . the criterion is shown to be robust for showing that many hyperbolic hypergeometric groups for are thin .

we give a criterion which ensures that a group generated by cartan involutions in the automorph group of a rational quadratic form of signature is `` thin '' , namely it is of infinite index in the latter . it is based on a graph defined on the integral cartan root vectors , as well as vinberg s theory of hyperbolic reflection groups . the criterion is shown to be robust for showing that many hyperbolic hypergeometric groups for are thin .

0811.1085

i

the purpose of the present paper is two - fold . first of all , we would like to give an introduction to the beautiful combinatorics related with box - ball systems , and secondly , to relate the latter with the `` classical combinatorics '' revolving around transportation matrices , tabloids , the lascoux schtzenberger statistics charge , macdonald polynomials , @xcite,@xcite , haglund haiman loehr s formula @xcite , and so on . as a result of our investigations , we will prove that two statistics naturally appearing in the context of box - ball systems , namely _ energy function _ and _ tau - function _ , have nice combinatorial properties . more precisely , the statistics energy @xmath4 is an example of a generalized machonian statistics @xcite , section 2 , whereas the statistics @xmath5 related with kostka macdonald polynomials , see section 5.2 of the present paper . box - ball systems ( bbs for short ) were invented by takahashi satsuma @xcite as a wide class of discrete integrable soliton systems . in the simplest case , bbs are described by simple combinatorial procedures using box and balls . despite its simple outlook , it is known that the bbs have various remarkably deep properties ; * time evolution of the bbs coincides with isomorphism of the crystal bases @xcite . thus the bbs possesses quantum integrability . * bbs are ultradiscrete ( or tropical ) limit of the usual soliton systems @xcite . thus the bbs possesses classical integrability at the same time . * inverse scattering formalism of the bbs coincides with the rigged configuration bijection originating in completeness problem of the bethe states @xcite . let us say a few words about the main results of our paper . * in the case of statistics _ , our main result can be formulated as a computation of the corresponding partition function for the bbs in terms of the values of the kostka macdonald polynomials at @xmath6 * in the case of the statistics _ energy _ , our result can be formulated as an interpretation of the corresponding partition function for the bbs as the @xmath0-weight multiplicity in the tensor product of the fundamental representations of the lie algebra @xmath7 we _ expect _ that the same statement is valid for the bbs corresponding to the tensor product of rectangular representations . + we are reminded that a _ @xmath0-analogue of the multiplicity _ of a highest weight @xmath8 in the tensor product @xmath9 of the highest weight @xmath10 @xmath11 irreducible representations @xmath12 of the lie algebra @xmath13 is defined as @xmath14 = \sum_{\eta}~k_{\eta , r}~k_{\eta , \lambda}(q),\ ] ] where @xmath15 stands for the parabolic kostka number corresponding to the sequence of rectangles @xmath16 see e.g. @xcite , @xcite . * we give several equivalent descriptions of _ paths _ which appear in the description of partition functions for bbs : in terms of transportation matrices , tabloids , plane partitions . we expect that such interpretations may be helpful for better understanding connections of the bbs and other integrable models such as melting crystals @xcite , @xmath0-difference toda lattices @xcite , ... . our result about connections of the energy partition functions for bbs and @xmath0-weight multiplicities suggests a deep hidden connections between partition functions for the bbs and characters of the demazure modules , solutions to the @xmath0-difference toda equations , cf.@xcite . as an interesting open problem we want to give raise a question about an interpretation of the sums @xmath17 where @xmath18 denotes the kostka macdonald polynomials @xcite , as _ refined partition functions _ for the bbs corresponding to the tensor product of rectangular representations @xmath19 . see conjecture [ conj : tau ] . in other words , one can ask : what is a meaning of the second statistics ( see @xcite ) in the kashiwara theory @xcite of crystal bases ( of type a ) ? organization of the present paper is as follows . in section 2 , we review necessary facts from the kirillov reshetikhin crystals . especially we explain an explicit algorithm to compute the combinatorial @xmath20 and the energy function . in section 3 , we introduce several combinatorial descriptions of paths . then we define several statistics on paths such as haglund s statistics , energy statistics @xmath21 and tau statistics @xmath22 . in section 4 , we collect necessary facts from the bbs which will be used in the next section . in section 5 , we present our main result ( theorem [ th : main ] ) as well as several relating conjectures . we conjecture that @xmath22 gives independent statistics depending on one parameter @xmath23 although they all give rise to the unique generating function up to constant shift of power . in section 6 , we show that the energy statistics @xmath21 belong to the class of statistics @xmath22 ( theorem [ th : e = tau ] ) . therefore @xmath22 gives a natural extension of the energy statistics @xmath21 .

we give several equivalent combinatorial descriptions of the space of states for the box - ball systems , and connect certain partition functions for these models with the-weight multiplicities of the tensor product of the fundamental representations of the lie algebra . as an application , we give an elementary proof of the special case of the haglund haiman + mathematics subject classification ( 2000 ) 05e10 , 20c35 .

we give several equivalent combinatorial descriptions of the space of states for the box - ball systems , and connect certain partition functions for these models with the-weight multiplicities of the tensor product of the fundamental representations of the lie algebra . as an application , we give an elementary proof of the special case of the haglund haiman loehr formula . also , we propose a new class of combinatorial statistics that naturally generalize the so - called energy statistics . + mathematics subject classification ( 2000 ) 05e10 , 20c35 . + key words and phrases : crystals , paths , energy and tau functions , box ball systems , kostka macdonald polynomials . + + + + + + + + +

0904.1448

i

over the course of the past few decades , li abundances have been measured for many metal - poor main - sequence turn - off stars , in hopes of placing constraints on the nature of big bang nucleosynthesis ( bbn ) . the first such investigation , by @xcite , revealed that warm metal - poor main - sequence stars exhibited a constant li abundance . this so - called spite plateau was interpreted as a result of the synthesis of light nuclei in the first several minutes of the evolution of the universe ( it is conventionally assumed that li is not destroyed at the surface of such stars because of their shallow surface convection zones ) . since then , measurements of li abundances have been obtained over wide ranges of effective temperature and metallicity , confirming that the scatter of the li abundances in most stars with @xmath7@xmath8 k and [ fe / h]@xmath9 is small , if present at all ( * ? ? ? * and references therein ) . = @xmath10 , and @xmath11 for elements a and b. lithium abundances are conventionally presented as @xmath3(li ) instead of @xmath12 . ] however , it has been recognized that the spite plateau value of a(li ) ( @xmath13 ) is 0.30.4 dex lower than the li abundance predicted by standard bbn models @xcite , adopting the baryon density determined by recent measurements of the cosmic microwave background ( cmb ) radiation with the wmap satellite @xcite . this discrepancy indicates the existence of poorly understood processes that deplete li in metal - poor turn - off stars ( e.g. * ? ? ? * ; * ? ? ? * ) , astration of li in the gas that formed these stars ( perhaps by massive zero - metallicity progenitors ; piau et al . 2006 ) , problems in the measured abundances of li in metal - poor stars , systematic uncertainties in the standard bbn model predictions , or exotic processes in the early universe arising from nonstandard particle physics ( cyburt et al . 2008 and references therein ) . recent measurements of very metal - poor turn - off stars also suggest a decreasing trend of li abundances with decreasing metallicity @xcite . in particular , @xcite investigated the li abundances for a sample that includes eight stars with [ fe / h ] @xmath6 . they showed that the li abundances of these stars are lower than those of stars with higher metallicity , investigating very carefully the scatter and trend of li abundances with metallicity and effective temperature . another unsolved problem is the low li abundance found in he 13272326 , a hyper metal - poor turn - off star having [ fe / h]@xmath14 @xcite . only an upper - limit on the li abundance has been determined , @xmath3(li)@xmath15 @xcite . although the star has probably evolved to the subgiant branch @xcite , the effective temperature of this object ( 6180 k ; frebel et al . 2005 ) is still sufficiently high that depletion of li by surface convection is not expected . another possible explanation for the apparent depletion of li is mass accretion from an evolved companion star @xcite , in particular because this star is highly carbon - enhanced ( [ c / fe ] @xmath16 ; aoki et al . 2006 ) . however , no signature of binarity has been found yet for this object @xcite . thus , concerning the @xmath17li abundances in very metal - poor stars , we are confronted with three problems : ( 1 ) the discrepancy between the observed spite plateau value and the prediction of standard bbn models adopting the baryon density determined by cmb measurements ; ( 2 ) a possible trend of the li abundance as a function of metallicity in extremely metal - poor stars ; and ( 3 ) the low li abundance in he 13272326 ( see also the summary by piau et al . although possible connections between the above three problems are still unknown , we have obtained measurements of li abundances for several extremely metal - poor turn - off stars in a search for hints to solving these li puzzles . in this paper we report measurements of li abundances for very and extremely metal - poor stars . our sample includes eight stars with [ fe / h ] @xmath6 , among which four stars are studied for the first time . the sample selection and high - resolution spectroscopy are described in [ sec : obs ] . section [ sec : ana ] reports the determination of stellar parameters and details of the measurement of li abundances . uncertainties and comparisons with previous work are also discussed in this section . we discuss the implications of our measurements in [ sec : disc ] , and consider possible correlations with the derived stellar atmospheric parameters , other elemental abundances , and the kinematics of the sample .

effective temperatures are determined by a profile analysis of h and h . while seven stars have li abundances as high as the spite plateau value , the remaining four objects with [ fe / h ] have(li )(li / h) , confirming the existence of extremely metal - poor turn - off stars having low li abundances , as reported by previous work . correlations of the li abundance with effective temperatures , with abundances of na , mg and sr , and with the kinematical properties are investigated , but no clear correlation is seen in the extremely metal - poor star sample .

we have determined li abundances for eleven metal - poor turn - off stars , among which eight have [ fe / h ] , based on lte analyses of high - resolution spectra obtained with the hds on the subaru telescope . the li abundances for four of these eight stars are determined for the first time by this study . effective temperatures are determined by a profile analysis of h and h . while seven stars have li abundances as high as the spite plateau value , the remaining four objects with [ fe / h ] have(li )(li / h) , confirming the existence of extremely metal - poor turn - off stars having low li abundances , as reported by previous work . the average of the li abundances for stars with [ fe / h] is lower by 0.2 dex than that of the stars with higher metallicity . no clear constraint on the metallicity dependence or scatter of the li abundances is derived from our measurements for the stars with [ fe / h] . correlations of the li abundance with effective temperatures , with abundances of na , mg and sr , and with the kinematical properties are investigated , but no clear correlation is seen in the extremely metal - poor star sample .

0904.1448

c

figure [ fig : life ] shows the li abundances as a function of [ fe / h ] for our sample and others . values of @xcite and @xcite are adopted without any correction . the solar fe abundance adopted by @xcite is 7.51 , while that of @xcite is determined by their own analysis of the solar spectrum . @xcite also reported fe abundances from lines , which are systematically higher by 0.08 dex than those from lines according to the authors . hence , a possible shift of [ fe / h ] values by at most 0.1 dex should be taken into consideration in the comparisons of the three works . ] we confirm that the li abundance of the `` reference '' star bd+26@xmath193578 ( [ fe / h]@xmath76 ) determined by our analysis agrees well with the measurement by @xcite . by contrast , stars with [ fe / h ] @xmath6 ( the extremely metal - poor , or emp , stars ) appear to have lower li abundances on average , and also exhibit some scatter . we discuss this point further below . the average of @xmath3(li ) ( i.e. , @xmath77(li)@xmath78 ) of the eight stars with [ fe / h]@xmath6 is 2.03 , with a sample standard deviation ( @xmath65 ) of 0.09 dex . the standard deviation is comparable with , or slightly smaller than , the measurement errors of our analysis ( 0.070.23 dex ) . hence , we do not detect any significant scatter of the li abundances in our sample of emp stars . the @xmath77(li)@xmath78 is lower by 0.24 dex and 0.20 dex than the the average of our two reference stars ( 2.27 ) and the average of the results of the lte analysis by asplund et al . ( 2006 ) for six stars in @xmath79[fe / h]@xmath80 ( 2.23 ) , respectively . the difference of 0.2 dex is significant , compared to the @xmath65 @xmath81=0.09/@xmath82=0.03 dex , where @xmath29 is the number of objects in the extremely metal - poor sample . we note that the li abundances for stars in @xmath83 [ fe / h]@xmath84 are well determined by asplund et al . ( 2006 ) , and the scatter is small ( @xmath850.04 dex and @xmath65 @xmath81=0.02 dex ) . we conclude that the li abundances for stars with [ fe / h]@xmath6 are 0.2 dex lower than those of stars with higher metallicity on average , while no significant scatter or trend with metallicity is detected in our emp sample . a similar conclusion was reached by @xcite ; our new measurements for stars in the lowest metallicity range supports their results . such a difference can obviously be produced by a decreasing trend ( slope ) of @xmath3(li ) as a function of metallicity . the possible slope of @xmath3(li ) was discussed by @xcite in detail . however , no clear physical reason for the slope , which appears only at the lowest metallicity range , has yet been identified . another possibility is that scatter of @xmath3(li ) increases in the range [ fe / h ] @xmath18 , and , as a result , the average decreases . this case would be relatively easily explained by depletion of li , although some reason for the metallicity dependence of the depletion is also required . if the effective temperatures estimated from the @xmath36 colors using the scales of @xcite and @xcite are employed , the li abundances of our stars would be systematically higher . the effective temperatures derived using the scale of @xcite are systematically higher by 220 k and 150 k than the values from the balmer line analysis for emp stars and for stars with [ fe / h]@xmath76 , respectively , resulting in 0.15 dex and 0.10 dex higher li abundances . although the difference of li abundances between the emp stars and less metal - poor stars becomes slightly smaller than the result derived adopting the effective temperature from the balmer line analysis , the difference is still significant . by contrast , if the effective temperatures estimated using the scales of @xcite are adopted , the values are 290 k and 150 k higher than those from the balmer lines , resulting in 0.20 dex and 0.10 dex higher li abundances . in this case , the difference of li abundances between the stars with [ fe / h]@xmath0 and @xmath86 is only 0.1 dex , which is no longer significant compared to our measurement errors . [ [ correlations - with - stellar - parameters - elemental - abundances - and - kinematics ] ] correlations with stellar parameters , elemental abundances , and kinematics ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ although no statistically significant scatter of @xmath3(li ) is found for our full emp sample , within our measurement errors , the existence of _ some _ star - to - star differences in @xmath3(li ) is suggested . for instance , even if the stars with the largest measurement errors are excluded from the evaluation , a similar scatter of @xmath3(li ) remains . a difference of 0.14 dex is found in @xmath3(li ) for the two bright stars g 6412 and g 6437 , as found by @xcite and @xcite . in this subsection , we investigate correlations between @xmath3(li ) and the adopted stellar parameters , in order to search for a hint for understanding the lower li abundances among the emp stars . figure [ fig : liteff ] shows @xmath3(li ) as a function of @xmath7 . no clear correlation can be seen in this figure . it should be noted that the random error of the effective temperature propagates into the derived li abundance , which is represented by the arrows shown in the diagram . an increasing trend of li abundance with decreasing @xmath7 is potentially influenced by this error . our sample includes stars that have already evolved to the subgiant branch . their effective temperatures during the main - sequence stage should be higher than the current values , and might be as high as the hottest stars among the main - sequence sample . the stars having @xmath87 are over - plotted by large circles representing candidate subgiants in the figure . if these stars are excluded , we find that stars cooler than 6150 k exhibit higher and almost constant li abundances , while the warmer stars show some scatter . however , this probably reflects a metallicity effect , as the cooler stars ( excluding subgiants ) are objects having [ fe / h ] @xmath88 studied by @xcite , while the warmer stars have [ fe / h ] @xmath89 . that is , the sample of very metal - poor stars ( [ fe / h ] @xmath90 ) have @xmath7@xmath91 k , or are subgiants . this could be due to a bias in the sample selection caused by the fact that distant stars must be observed to cover lower metallicity ranges , and intrinsically faint stars are not sampled . other than this point , no clear correlation appears between the li abundances and effective temperature , even if subgiants are removed from the plot , or if the highest temperature among the sample ( @xmath92 k ) is assigned for them as their @xmath7 during their main - sequence phase . figure [ fig : limgsr ] shows li abundances as functions of [ na / fe ] , [ mg / fe ] , and [ sr / fe ] . an anti - correlation between the li abundance and the [ na / fe ] ratio was reported for the globular cluster ngc 6752 by @xcite . such a trend is , however , not seen in our sample ( fig . [ fig : limgsr ] ) : the two low li stars he 11480037 and sdss 0040 + 16 have comparatively high [ na / fe ] ratios , while that of the other low li star , cs 22948093 , is low . if the nlte effects on the na abundances are taken into consideration , the abundances of less metal - poor stars become lower by about 0.3 dex . however , this correction does not result in any correlation between the li and na abundances . no significant scatter is found for [ mg / fe ] in our sample . also , no correlation is found between the abundances of li and the mg abundances . in contrast , a large scatter of measured sr abundances exists , which could reflect the contribution of a neutron - capture process that is efficient in the very early galaxy @xcite , as well as the contribution of the main r - process to higher metallicity objects . no correlation is found between the li and sr abundances , indicating that the li production or depletion is not likely to be related to neutron - capture nucleosynthesis processes . we are also interested in exploring whether the kinematics of the stars with lower @xmath3(li ) exhibit any peculiarities that distinguish them from the rest of the stars . for this exercise , we combined our present sample with that of bonifacio et al . proper motions of sdss stars are listed in the public dr6 database , while those of other stars are taken from the nomad database ( zacharias et al . distances were estimated from the luminosity classifications given by either the present paper or in bonifacio et al . ( 2007 ) , applying the methods described by beers et al . stars with @xmath93 were considered dwarfs , those with @xmath94 were considered main - sequence turnoff stars , and those with @xmath95 were considered subgiants . the adopted surface gravities , metallicities , photometry , distances , radial velocities , and proper motions are listed in table [ tab : kine1 ] . these data were used to derive the full space motions and other orbital information , following the procedures described by carollo et al . ( 2007 ) ; results are listed in table [ tab : kine2 ] . figure [ fig : kine ] shows the derived rotational velocity with respect to the galactic center , @xmath96 , as a function of [ fe / h ] . the stars with low values of @xmath3(li ) are labeled by filled circles . we note that three stars with `` normal '' @xmath3(li ) are on highly prograde orbits ( an additional star , cs 310610032 , with @xmath96 = 205 km s@xmath30 , may be a member of the metal - weak thick disk ) . this is somewhat unexpected , given the essentially zero net rotation of the inner halo , and net retrograde rotation of the outer halo . we plan to study these stars in more detail in the near future . based on the derived space velocities and orbital parameters , an attempt was made to assign approximate population memberships for these stars , listed in the second column of table [ tab : kine2 ] . the assignments take into account the values of the velocity ellipsoids derived for the inner and outer halo , and the thick disk ( including the metal - weak thick disk ; d. carollo et al . , in preparation ) , as well as the derived @xmath97 ( the maximum distance from the galactic plane in the vertical direction ) for each star . we did not attempt to assign a membership to the four highly prograde stars , because , as was mentioned above , they require further investigation ( fi in the second column of table [ tab : kine2 ] ) . note that in some cases it was not possible to uniquely distinguish a single population assignment , so multiple assignments are given . inspection of these assignments indicates no tendency for the stars with low @xmath3(li ) to be associated preferentially with either the inner- or outer - halo populations . this is similar to the conclusions drawn by bonifacio et al . ( 2007 ) based on inspection of radial velocities alone . however , the sample size ( especially of low @xmath3(li ) stars ) and the existing errors on the li abundance determinations preclude a final determination . our measurements of the li doublet for extremely metal - poor stars based on the effective temperatures from the balmer lines showed that the li abundances in the metallicity range [ fe / h ] @xmath6 are lower , on average , than for stars with higher metallicity . the same conclusion is also reached by adopting the effective temperatures from @xmath36 using the scales of @xcite and @xcite , although the li abundances are systematically higher if the latter is adopted . if the temperature scale of @xcite for @xmath36 is adopted , the dependence of the li abundances on metallicity becomes marginal . although no scatter or trend of li abundances is detected within the sample of extremely metal - poor stars , the metallicity dependence of the li abundance could be a key to understanding the li problems found for metal - poor stars . observations to obtain better quality spectra for such extremely metal - poor stars , to improve measurements of the li feature itself , as well as for improved determination of @xmath7 from the h@xmath1 and h@xmath2 profiles , will provide a useful constraint on the possible scenarios proposed to explain the li problems . moreover , measurements of li abundances for even lower metallicity stars ( [ fe / h ] @xmath98 ) are also vital . measurements of li abundances in this metallicity range have been reported so far only for one system , a double - lined spectroscopic binary ( cs 22876032 : * ? ? ? * ; * ? ? ? we plan additional investigations of this metallicity range by high - resolution spectroscopic studies of extremely metal - poor star candidates discovered by the hamburg / eso survey and sdss / segue in the near future . the authors would like to thank the anonymous referee for useful comments for improving this paper . w. a. is supported by a grant - in - aid for science research from jsps ( grant 18104003 ) . b is a royal swedish academy of sciences research fellow supported by a grant from the knut and alice wallenberg foundation . s. b also acknowledges support from the swedish research council . t. c. b. acknowledges support from the us national science foundation under grants ast 04 - 06784 and ast 07 - 07776 , as well as from grants phy 02 - 16783 and phy 08 - 22648 ; physics frontier center / joint institute for nuclear astrophysics ( jina ) . n.c . acknowledges support from the knut and alice wallenberg foundation . colors with those from the balmer line analysis . the differences of the effective temperature from those from the balmer line analysis are shown for the scales of @xcite ( circles ) , @xcite ( squares ) , and @xcite ( triangles ) . , width=453 ] . the results of the present work are plotted by filled circles with error bars . the open triangles and squares indicate the results by @xcite and @xcite , respectively . large open circles are overplotted for subgiant stars ( @xmath47 @xmath99).,width=453 ] , [ mg / fe ] , and [ sr / fe ] for our sample . filled circles indicate stars having [ fe / h ] @xmath102 . the upper limit of the sr abundance of cd @xmath20 ( [ sr / fe ] @xmath103 ) is not plotted in this figure.,width=453 ] as a function of [ fe / h ] for our sample and that of @xcite . the filled circles indicate stars with @xmath3(li ) @xmath104 , while the open ones indicate stars with @xmath3(li ) @xmath105 . a typical error of fe abundance determination is 0.15 dex . note the presence of several stars with rather high @xmath96 . , width=453 ] llcrcr & 28 feb . 2005 & 225 & 16,500 & 2453429.86 & @xmath106 + cs 22948093 & 19 june 2005 & 174 & 5,900 & 2453541.06 & @xmath107 + cs 22965054 & 20 june 2005 & 100 & 5,000 & 2453541.97 & @xmath108 + he 11480037 & 27 feb . 2005 & 160 & 15,000 & 2453428.94 & @xmath109 + cd @xmath20 & 20 june 2005 & 20 & 14,000 & 2453542.12 & @xmath110 + sdss 0040 + 16 & 14 sep . 2006 & 80 & 4,800 & 2453992.90 & @xmath111 + sdss 1033 + 40 & 10 feb . 2007 & 160 & 4,100 & 2454141.98 & @xmath112 + g 6412 & 22 feb . 2003 & 300 & 103,000 & 2453507.76 & @xmath113 + g 6437 & 18 may 2005 & 420 & 211,000 & 2453508.83 & @xmath114 + hd 84937 & 22 feb . 2003 & 180 & 626,000 & 2452692.83 & @xmath115 + bd+26@xmath193578 & 17 may 2005 & 132 & 342,000 & 2453508.00 & @xmath116 + lcccccccc & 6380 & 6290 & 6320 & 150 & 3.9 & 1.5 & 3.96 & 3.88 + cs 22948093 & 6320 & 6410 & 6380 & 150 & 4.4 & 1.5 & 4.02 & 4.02 + cs 22965054 & 6390 & 6270 & 6310 & 200 & 3.9 & 1.5 & 4.61 & 4.56 + he 11480037 & 6100 & 5940 & 5990 & 200 & 3.7 & 1.5 & 3.99 & 3.90 + cd @xmath20 & 6150 & 6190 & 6180 & 150 & 4.4 & 1.5 & 4.05 & 4.17 + sdss 0040 + 16 & 6350 & 6360 & 6360 & 200 & 4.4 & 1.5 & 4.16 & 4.25 + sdss 1033 + 40 & 6380 & 6370 & 6370 & 200 & 4.4 & 1.5 & 4.22 & 4.29 + g 6412 & 6260 & 6280 & 6270 & 100 & 4.4 & 1.5 & 4.08 & 4.20 + g 6437 & 6310 & 6280 & 6290 & 100 & 4.4 & 1.5 & 4.23 & 4.33 + hd 84937 & 6330 & 6270 & 6290 & 100 & 3.9 & 1.2 & 5.30 & 5.35 + bd+26@xmath193578 & 6370 & 6330 & 6340 & 100 & 3.9 & 1.5 & 5.17 & 5.20 + lccccccccc & 14.450 & 0.318 & 1.248 & 0.026 & 0.020 & 0.023 & 6408 & 6659 & 6508 + cs 22948093 & 15.180 & 0.360 & 1.175 & 0.018 & 0.008 & 0.013 & 6497 & 6777 & 6618 + cs 22965054 & 15.069 & 0.497 & 1.620 & 0.089 & 0.131 & 0.110 & 6180 & 6269 & 6263 + he 11480037 & 13.614 & 0.404 & 1.342 & 0.022 & & 0.022 & 6215 & 6381 & 6282 + cd @xmath20 & 12.18 & 0.33 & 1.373 & 0.025 & 0.027 & 0.027 & 6184 & 6328 & 6250 + sdss 0040 + 16 & 15.231 & 0.310 & 1.202 & 0.047 & 0.058 & 0.052 & 6685 & 7044 & 6847 + sdss 1033 + 40 & 15.990 & 0.360 & 1.289 & 0.013 & 0.018 & 0.015 & 6278 & 6449 & 6363 + g 6412 & 11.453 & 0.385 & 1.245 & 0.028 & 0.003 & 0.003 & 6295 & 6484 & 6379 + g 6437 & 11.140 & 0.370 & 1.217 & 0.027 & 0.014 & 0.014 & 6417 & 6632 & 6527 + hd 84937 & 8.28 & 0.41 & 1.218 & 0.037 & 0.007 & 0.007 & 6310 & 6456 & 6469 + bd+26@xmath193578 & 9.37 & 0.35 & 1.226 & 1.106 & 0.010 & 0.010 & 6318 & 6469 & 6474 + bs 16545089 & @xmath1173.49 & 15.3 & 2.02 & 0.12 & 0.17 & @xmath1170.12 & 0.25 & @xmath1170.34 + cs 22948093 & @xmath1173.43 & 12.4 & 1.96 & 0.12 & 0.17 & @xmath1170.22 & 0.13 & 0.13 + cs 22965054 & @xmath1172.84 & 20.3 & 2.16 & 0.12 & 0.19 & 0.05 & 0.26 & 0.45 + he 11480037 & @xmath1173.46 & 19.3 & 1.90 & 0.08 & 0.17 & 0.14 & 0.25 & @xmath1170.64 + cd @xmath20 & @xmath1173.40 & 21.2 & 2.08 & 0.06 & 0.13 & @xmath1170.13 & 0.31 & @xmath1180.9 + sdss 0040 + 16 & @xmath1173.29 & 13.6 & 1.99 & 0.14 & 0.20 & 0.19 & 0.32 & @xmath1170.39 + sdss 1033 + 40 & @xmath1173.24 & 16.5 & 2.09 & 0.18 & 0.23 & @xmath1170.24 & 0.03 & @xmath1170.32 + g 6412 & @xmath1173.37 & 22.4 & 2.18 & 0.02 & 0.07 & @xmath1170.06 & 0.37 & 0.08 + g 6437 & @xmath1173.23 & 16.2 & 2.04 & 0.02 & 0.07 & @xmath1170.14 & 0.24 & 0.01 + hd 84937 & @xmath1172.15 & 24.7 & 2.26 & 0.02 & 0.07 & 0.28 & 0.28 & 0.22 + bd+26@xmath193578 & @xmath1172.28 & 23.7 & 2.28 & 0.02 & 0.07 & 0.22 & 0.35 & 0.04 + lcccccccccc & 6380 & 1.96 & & 6356 & 1.94 & @xcite & & & & + cs 22965054 & 6310 & 2.16 & & 6089 & 2.03 & @xcite & & & & + bd+26@xmath193578 & 6340 & 2.28 & & 6335 & 2.25 & @xcite & & 6150 & 2.15 & @xcite + g 6412 & 6270 & 2.18 & & 6074 & 2.15 & @xcite & & 6222 & 2.14 & @xcite + g 6437 & 6290 & 2.04 & & 6122 & 1.97 & @xcite & & 6240 & 2.09 & @xcite + cd @xmath20 & 6180 & 2.08 & & & & & & 6070 & 1.97 & @xcite + hd 84937 & 6290 & 2.26 & & & & & & 6160 & 2.17 & @xcite + lccrcccrrrrr bs 160230046 & 4.50 & @xmath1172.97 & 14.170 & 0.378 & 0.017 & 0.935 & @xmath1177.5 & @xmath11740.0 & 2.0 & @xmath11740.0 & 1.0 + bs 169680061 & 3.75 & @xmath1173.05 & 13.260 & 0.430 & 0.048 & 0.712 & @xmath11780.7 & @xmath11738.0 & 11.0 & @xmath11736.0 & 8.0 + bs 175700063 & 4.75 & @xmath1172.92 & 14.510 & 0.330 & 0.039 & 1.275 & @xmath117184.4 & 38.0 & 4.0 & @xmath11730.0 & 1.0 + cs 221770009 & 4.50 & @xmath1173.10 & 14.270 & 0.401 & 0.044 & 0.869 & @xmath117208.4 & 11.8 & 5.9 & @xmath11762.5 & 5.8 + cs 228880031 & 5.00 & @xmath1173.30 & 14.900 & 0.413 & 0.014 & 0.968 & @xmath117125.1 & 47.1 & 5.2 & @xmath11720.6 & 5.2 + cs 229480093 & 4.25 & @xmath1173.30 & 15.180 & 0.360 & 0.015 & 1.346 & 364.3 & @xmath11715.6 & 5.1 & @xmath11722.8 & 4.8 + cs 229530037 & 4.25 & @xmath1172.89 & 13.640 & 0.367 & 0.027 & 0.753 & @xmath117163.3 & 31.3 & 6.1 & 37.0 & 6.1 + cs 229650054 & 3.75 & @xmath1173.04 & 15.069 & 0.497 & 0.131 & 1.532 & @xmath117281.5 & 26.0 & 1.0 & 0.0 & 3.0 + cs 229660011 & 4.75 & @xmath1173.07 & 14.555 & 0.422 & 0.013 & 0.830 & @xmath11713.5 & 15.1 & 6.0 & @xmath11742.2 & 6.0 + cs 294990060 & 4.00 & @xmath1172.70 & 13.030 & 0.370 & 0.019 & 0.726 & @xmath11758.7 & 15.4 & 4.9 & 22.4 & 4.9 + cs 295060007 & 4.00 & @xmath1172.91 & 14.180 & 0.382 & 0.045 & 1.189 & 56.4 & @xmath1173.6 & 7.9 & @xmath11730.3 & 7.9 + cs 295060090 & 4.25 & @xmath1172.83 & 14.330 & 0.399 & 0.046 & 1.035 & @xmath11721.3 & @xmath11712.5 & 7.9 & @xmath11739.1 & 7.9 + cs 295180020 & 4.50 & @xmath1172.77 & 14.003 & 0.415 & 0.023 & 0.741 & @xmath11722.2 & 26.1 & 4.8 & @xmath11710.4 & 4.8 + cs 295180043 & 4.25 & @xmath1173.20 & 14.566 & 0.371 & 0.019 & 1.064 & 144.8 & 26.0 & 5.0 & @xmath1176.0 & 1.0 + cs 295270015 & 4.00 & @xmath1173.55 & 14.260 & 0.400 & 0.021 & 1.114 & 50.9 & 48.6 & 12.8 & @xmath11722.5 & 12.8 + cs 303010024 & 4.00 & @xmath1172.75 & 12.950 & 0.420 & 0.064 & 0.646 & @xmath11767.7 & @xmath11933.8 & 1.8 & @xmath11723.1 & 1.7 + cs 303390069 & 4.00 & @xmath1173.08 & 14.750 & 0.360 & 0.009 & 1.572 & 34.9 & 22.0 & 5.0 & @xmath11716.0 & 12.0 + cs 310610032 & 4.25 & @xmath1172.58 & 13.874 & 0.409 & 0.036 & 0.818 & 21.0 & @xmath1171.3 & 5.6 & @xmath11711.6 & 5.7 + bs 165450089 & 3.90 & @xmath1173.49 & 14.450 & 0.318 & 0.023 & 1.356 & @xmath117161.5 & 14.0 & 2.0 & @xmath11722.0 & 3.0 + cs 229480093 & 4.40 & @xmath1173.43 & 15.180 & 0.360 & 0.013 & 1.346 & 369.2 & @xmath11715.6 & 5.1 & @xmath11722.8 & 4.8 + cs 229650054 & 3.90 & @xmath1172.84 & 15.069 & 0.497 & 0.110 & 1.532 & @xmath117281.7 & 26.0 & 1.0 & 0.0 & 3.0 + he 11480037 & 3.70 & @xmath1173.46 & 13.614 & 0.404 & 0.022 & 0.844 & @xmath11710.9 & @xmath11746.0 & 8.0 & @xmath11742.0 & 1.0 + cd @xmath20 & 4.40 & @xmath1173.40 & 12.180 & 0.330 & 0.027 & 0.386 & 136.6 & 202.0 & 2.3 & @xmath117185.8 & 1.6 + sdss 0040 + 16 & 4.40 & @xmath1173.29 & 15.231 & 0.310 & 0.052 & 1.714 & @xmath11749.4 & 24.0 & 4.0 & @xmath11720.0 & 2.0 + sdss 1033 + 40 & 4.40 & @xmath1173.24 & 15.990 & 0.360 & 0.015 & 2.150 & @xmath117132.9 & 7.7 & 6.2 & 14.7 & 6.5 + g 6412 & 4.40 & @xmath1173.37 & 11.453 & 0.385 & 0.003 & 0.217 & 434.7 & @xmath117230.4 & 2.4 & @xmath11780.3 & 1.8 + g 6437 & 4.40 & @xmath1173.23 & 11.140 & 0.370 & 0.014 & 0.210 & 76.7 & @xmath11754.3 & 3.6 & @xmath117399.5 & 1.8 + hd 84937 & 3.90 & @xmath1172.15 & 8.280 & 0.410 & 0.007 & 0.073 & @xmath11714.6 & 373.8 & 1.2 & @xmath117774.7 & 0.4 + bd+26@xmath193578 & 3.90 & @xmath1172.28 & 9.370 & 0.350 & 0.010 & 0.137 & -91.2 & 0.9 & 0.6 & @xmath117172.4 & 1.4 + llcrrrrcrrr bs 160230046 & ih & 2.18 & 9 & @xmath117237 & 30 & @xmath11717 & 0.901 & 8.3 & 0.4 & 1.1 + bs 169680061 & ih & 2.17 & 51 & @xmath117165 & @xmath11744 & 54 & 0.722 & 8.3 & 1.3 & 1.1 + bs 175700063 & ih / oh & 2.05 & 60 & @xmath117322 & @xmath11745 & @xmath117108 & 0.499 & 9.3 & 3.1 & 1.3 + cs 221770009 & ih / oh & 2.20 & @xmath117298 & @xmath11780 & 147 & 126 & 0.840 & 32.8 & 2.8 & 13.9 + cs 228880031 & ih / oh & 2.03 & 196 & @xmath117153 & 50 & 65 & 0.788 & 12.5 & 1.4 & 2.8 + cs 229480093 & ih / oh & 1.92 & @xmath117329 & @xmath117120 & @xmath117201 & 99 & 0.854 & 38.3 & 3.0 & 30.9 + cs 229530037 & fi & 2.16 & 191 & 109 & 89 & 338 & 0.677 & 37.2 & 7.1 & 8.0 + cs 229650054 & ih & 2.06 & 250 & @xmath117189 & 90 & 0 & 0.999 & 16.3 & 0.0 & 7.5 + cs 229660011 & ih & 1.91 & @xmath11719 & @xmath117164 & 7 & 55 & 0.716 & 8.3 & 1.3 & 0.8 + cs 294990060 & fi & 2.16 & 82 & 51 & 53 & 270 & 0.346 & 15.7 & 7.6 & 2.3 + cs 295060007 & ih & 2.15 & @xmath117106 & @xmath117126 & @xmath11756 & 98 & 0.557 & 8.8 & 2.5 & 1.8 + cs 295060090 & ih & 2.10 & @xmath11790 & @xmath117172 & 24 & 51 & 0.758 & 8.6 & 1.1 & 0.8 + cs 295180020 & td / ih & 2.13 & 43 & @xmath11768 & 38 & 152 & 0.304 & 8.8 & 4.7 & 1.2 + cs 295180043 & ih & 2.14 & 85 & @xmath117105 & @xmath117121 & 116 & 0.453 & 10.3 & 3.8 & 4.6 + cs 295270015 & ih & 2.08 & 150 & @xmath117209 & @xmath11781 & 7 & 0.970 & 11.3 & 0.1 & 2.9 + cs 303010024 & td / ih & 2.10 & 60 & @xmath117108 & @xmath11723 & 111 & 0.493 & 8.4 & 2.8 & 0.6 + cs 303390069 & ih & 2.13 & 68 & @xmath117176 & @xmath11722 & 44 & 0.774 & 8.8 & 1.1 & 1.6 + cs 310610032 & td & 2.22 & @xmath11719 & @xmath11715 & @xmath11733 & 205 & 0.073 & 9.1 & 7.9 & 0.9 + bs 165450089 & ih & 2.02 & @xmath117192 & @xmath11787 & @xmath11795 & 132 & 0.655 & 16.3 & 3.4 & 4.4 + cs 229480093 & oh & 1.96 & @xmath117332 & @xmath117120 & @xmath117205 & 99 & 0.857 & 39.8 & 3.0 & 32.4 + cs 229650054 & ih / oh & 2.16 & 250 & @xmath117190 & 90 & 0 & 1.000 & 16.3 & 0.0 & 7.5 + he 11480037 & ih & 1.90 & 71 & @xmath117185 & @xmath117124 & 39 & 0.727 & 9.29 & 1.47 & 5.8 + cd @xmath20 & oh & 2.08 & 135 & @xmath117388 & @xmath117294 & @xmath117169 & 0.607 & 28.9 & 7.0 & 23.7 + sdss 0040 + 16 & ih / oh & 1.99 & 91 & @xmath117269 & @xmath117110 & @xmath11759 & 0.688 & 10.6 & 1.9 & 5.0 + sdss 1033 + 40 & fi & 2.09 & @xmath11786 & 127 & @xmath117101 & 347 & 0.602 & 37.1 & 9.2 & 9.8 + g 6412 & oh & 2.18 & @xmath11748 & @xmath117308 & 391 & @xmath11789 & 0.657 & 40.2 & 8.3 & 39.0 + g 6437 & ih / oh & 2.04 & @xmath117183 & @xmath117332 & @xmath117131 & @xmath117113 & 0.642 & 14.3 & 3.1 & 6.1 + hd 84937 & ih & 2.26 & @xmath117214 & @xmath117203 & 0 & 15 & 0.955 & 13.5 & 0.3 & 0.0 + bd+26@xmath193578 & td / ih & 2.28 & @xmath11751 & @xmath117112 & @xmath11752 & 108 & 0.497 & 8.7 & 2.9 & 0.9 +

the average of the li abundances for stars with [ fe / h] is lower by 0.2 dex than that of the stars with higher metallicity . no clear constraint on the metallicity dependence or scatter of the li abundances is derived from our measurements for the stars with [ fe / h] .

we have determined li abundances for eleven metal - poor turn - off stars , among which eight have [ fe / h ] , based on lte analyses of high - resolution spectra obtained with the hds on the subaru telescope . the li abundances for four of these eight stars are determined for the first time by this study . effective temperatures are determined by a profile analysis of h and h . while seven stars have li abundances as high as the spite plateau value , the remaining four objects with [ fe / h ] have(li )(li / h) , confirming the existence of extremely metal - poor turn - off stars having low li abundances , as reported by previous work . the average of the li abundances for stars with [ fe / h] is lower by 0.2 dex than that of the stars with higher metallicity . no clear constraint on the metallicity dependence or scatter of the li abundances is derived from our measurements for the stars with [ fe / h] . correlations of the li abundance with effective temperatures , with abundances of na , mg and sr , and with the kinematical properties are investigated , but no clear correlation is seen in the extremely metal - poor star sample .

1211.3440

r

figures 1 - 3 present our narrow - band nir images . our h@xmath0 2.12-@xmath4 , h@xmath0 2.25-@xmath4 , [ ] , and continuum - subtracted line images are shown in figure 1 . figure 2 displays the continuum - subtracted h@xmath0 2.12-@xmath4 image with the regions used to identify molecular hydrogen emission - line objects ( mhos ) , compact emission - line sources thought to be associated with outflows . two other emission features that are not mhos are also identified : fluorescent gas in a photo - dissociation region ( pdr ) and a region where the h@xmath0 2.12 @xmath4/2.25 @xmath4 flux ratio is less than one ( marked as ` anomaly ' ) . the anomalous h@xmath0 emission is discussed further in 4.1 . for the mhos , we follow the numbering scheme of the on - line catalog of these objects , hosted by the joint astronomy centre in hawaii ( davis et al . 2010 ) . in all , we identify 12 new mhos in addition to five that have been catalogued previously ( see figure 1 : bottom left panel , figure 2 , & table 1 ) . the feature originally identified as mho 867 by varricatt et al . ( 2010 ) actually encompasses both the pdr and the bow - shaped feature we associate with the mho . although the _ iras _ source appears to be offset at the eastern edge of the pdr in the h@xmath0 2.12-@xmath4 and [ ] images , it is centrally located in the h@xmath0 2.25-@xmath4 images ( figures 1 : top and bottom middle panels ) and the 3-color wide - field infrared survey explorer ( wise : wright et al . 2010 ) image presented in figure 4 . the presence of shocked gas to the west of the _ iras _ source may explain the enhancement of h@xmath0 2.12-@xmath4 and [ ] emission in this direction . table 1 lists the mho designations ( column 1 ) , areas used in the aperture photometry ( column 2 ) , positions of the peak emission ( columns 3 & 4 ) , h@xmath0 2.12-@xmath4 line fluxes ( column 5 ) , h@xmath0 2.25-@xmath4 line fluxes ( column 6 ) , and h@xmath0 2.12-@xmath4/h@xmath0 2.25-@xmath4 flux ratios ( column 7 ) . columns 8@xmath1910 present results for fluxes integrated over 2-pixel circular apertures centered on 2.25-@xmath4 peaks . where the h@xmath0 2.25-@xmath4 line flux is below 3 times the noise ( 3@xmath20 ) within an aperture , the h@xmath0 2.25-@xmath4 line is regarded as undetected and no value is given in columns 6 or 9 . in these cases , lower limits to the h@xmath0 2.12-@xmath4/h@xmath0 2.25-@xmath4 flux ratios are calculated using the 3@xmath20 value for that aperture as an upper limit for the h@xmath0 2.25-@xmath4 line flux . the difference in extinction at 2.12 @xmath4 and 2.25 @xmath4 is very small , only a tenth of a magnitude ( assuming a@xmath21 ) , yielding a corresponding brightness ratio of @xmath71.1 , which has a negligible effect on the flux ratios . the expected h@xmath0 2.12-@xmath4/2.25-@xmath4 line ratio for uv excitation ( as in pdrs ) is @xmath7 1.9 . it is significantly higher for h@xmath0 excited by shocks , with a ratio of @xmath7 3 - 20 for different types of shocks ( e.g. , black & van dishoeck 1987 ; smith 1994 ; gredel & dalgarno 1995 ; smith 1995 ; smith et al . 2003 ) . two types of shocks are observed in outflows from star - forming regions . continuous ( or c - type ) shocks occur when the shock is magnetically cushioned by a relatively high transverse magnetic field , such that the shock thickness is broad and deceleration of gas is relatively gradual , resulting in lower excitation and temperatures than in jump ( or j - type ) shocks . in the latter , the gas undergoes a sharp increase in temperature within a narrow zone , where molecules are dissociated ( e.g. , barsony et al . 2010 ; smith 2012 ) . the observed line ratios for objects listed as mhos are consistent with shock excitation , but not for the pdr and anomaly . since the high flux ratios for many of the mhos may reflect the fact that 2.25-@xmath4 emission is not detected over the full extent of the apertures used for the 2.12-@xmath4 emission ( see table 1 , columns 5 - 7 ) , we also computed flux ratios using a circular aperture of radius 2 pixels centered on the 2.25-@xmath4 emission peaks ( see table 1 , columns 8 - 10 ) . a comparison of columns 10 and 7 indicates that although h@xmath0 2.12-@xmath4/2.25-@xmath4 flux ratios are typically lower in the 2-pixel radius apertures , the ratios are still consistent with shock excitation . the [ ] 1.64-@xmath4 line probes fast , dissociative shocks with velocities @xmath5 50 km s@xmath16 . when it is observed in jets from low- and intermediate - luminosity ysos , it is typically localized in compact spots , representing only a small fraction of the region emitting in h@xmath0 , and its presence does not appear to correlate strictly with the evolutionary stage of the driving source ( caratti o garatti et al . fewer [ ] observations have been reported for high - luminosity objects , in part due to the greater extinction at 1.64 @xmath4 . curiously , caratti o garatti et al . ( 2008 ) found that the only [ ] emission toward the h@xmath0 jet associated with the massive young stellar object ( myso ) _ iras _ 20126@xmath174104 is close to the source . table 2 lists the three [ ] emission - line features we detected . the first two features are associated with mho 864 , and the third feature is associated with , and largely overlaps , mho 867 , the bright bow- or ` bean'-shaped feature that opens toward the _ iras _ source . in mho 864 , the two [ ] emission - line features lie along the inferred jet axis of the outflow . one is located at the apex of the mho and the other is close to core d , which presumably harbors the driving source of the outflow ( see figure 2 and 4.2.4 ) . in mho 867 , the morphology of the [ ] emission is similar to the mho , but over a smaller region . to investigate excitation conditions in these mhos , we computed line ratios in 2-pixel radius apertures along the major and minor axes of mho 864 , and along and transverse to the bow - shaped structure of mho 867 . placement of these apertures is indicated in figure 3 and emission line flux ratios are presented in table 3 . for the apertures with h@xmath0 2.25-@xmath4 detections , 2.12 @xmath4/2.25 @xmath4 flux ratios range from 6.8 - 14.5 . 1.64-@xmath4/2.12-@xmath4 flux ratios range from 0.03 - 0.9 for mho 864 apertures and 0.5 - 1.9 for mho 867 apertures . we interpret these results in 4.1 . the terms `` green fuzzies '' and `` extended green objects '' ( egos ) have been applied to regions of extended 4.5-@xmath4 emission that are often associated with shocked h@xmath0 emission from outflows ( e.g. , cyganowski et al . the nomenclature reflects the use of green as the representative color for the infrared array camera ( irac : fazio et al . 2004 ) 4.5-@xmath4 band in spitzer space telescope 3-color images produced from galactic legacy infrared mid - plane survey extraordinaire observations ( glimpse : benjamin et al . 2003 ; churchwell et al . figure 4 uses a similar 3-color scheme to represent the wise 3.4 , 4.6 , & 12-@xmath4 bands . here , objects that are bright in the 4.6-@xmath4 band appear to be green . mhos 864 , 865 , & 866 are the only mhos that are clearly prominent in the 4.6-@xmath4 band . mhos 864 & 865 have the highest h@xmath0 2.12-@xmath4 fluxes in mol 121 . on the other hand , there are several patches of faint 4.6-@xmath4 emission that do not correspond to mhos . we note that this result is similar to that of lee et al . ( 2012 ) , who imaged 34 spitzer glimpse egos with the united kingdom infrared telescope ( ukirt ) and noted that shocked molecular hydrogen emission is typically more extended than egos and that egos occasionally trace scattered continuum light ( see also barsony et al . this suggests that although the 4.5-@xmath4 & 4.6-@xmath4 bands may be useful in identifying features associated with bright outflows , they are not always dominated by shocked outflow emission . our carma 3-mm continuum data reveal five cores in the mol 121 region . figure 5 shows contours for the 3-mm continuum emission overlaid on the relevant portion of our continuum - subtracted h@xmath0 2.12-@xmath4 image . table 4 lists physical properties of the cores . assuming a distance of 1.7 kpc , deconvolved core diameters , @xmath22 , range from 790 au - 3500 au . the cores are discussed individually in 4.2 . assuming the dust emission is optically thin at 3 mm , the mass of a core is calculated in the following manner : @xmath23 here , @xmath24 is the distance to the source , @xmath25 is the total flux density , @xmath26 is the gas - to - dust ratio , @xmath27 is the planck function at dust temperature @xmath28 , and @xmath29 is the dust opacity per gram of gas ( e.g. , enoch et al . we use @xmath29 = 0.178 @xmath30 g@xmath16 , the value obtained by extrapolating from table 1 in ossenkopf & henning ( 1994 ) using a power law ( @xmath31 ) with @xmath32 = 1.8 , and assuming dust grains with thin ice mantles coagulated for 10@xmath33 yr at a gas density of 10@xmath34 @xmath35 . typically , dust temperatures in protostellar cores are assumed to be @xmath7 20 k ( e.g. , rosolowsky et al . 2010 ; lee et al . 2011 ; chen et al . 2012 ) , but dust temperatures in pdrs and some massive protostellar cores are closer to 30 k ( e.g. , molinari et al . 2008 ; anderson et al . 2012 ) , and enoch et al . ( 2007 ) note that plausible values might vary from 5@xmath1930 k. the sed of _ iras _ 20188@xmath173928 has been fit with a cold dust component of 39 k and warm dust component of 100 k ( mccutcheon et al . 1995 ) . most of the cores detected by carma are probably colder than this , so we have opted to calculated masses for t@xmath36 = 20 k & 40 k ( table 3 , columns 7 & 8) . for t@xmath36 = 40 k , derived masses are @xmath7 2.1 times lower than for t@xmath36 = 20 k. we calculate the column density from the peak flux density @xmath37 in a similar manner to enoch et al . ( 2007 ) : @xmath38 here , @xmath26 , @xmath29 , and @xmath27 , are the same as in equation ( 1 ) , @xmath39 is the size of carma s main beam at 3 mm , and @xmath40 is the mass of molecular hydrogen . columns 9 & 10 in table 3 show the results of this calculation for both dust temperatures used in the mass calculation . theoretical work predicts a mass column density threshold @xmath41 1 g @xmath42 for massive star formation ( krumholz & mckee 2008 ; krumholz et al . the mass column density is the column density @xmath43 multiplied by @xmath40 and a factor of 1.36 to account for elements heavier than hydrogen ( simon et al . regions where intermediate mass stars are thought to be forming typically have mass column densities @xmath7 0.1 - 0.5 g @xmath42 ( e.g. , arvidsson et al . 2010 ; wolf - chase et al . 2003 ; wolf - chase , walker , & lada 1995 ) . all of the carma cores have mass column densities significantly @xmath5 1 g @xmath42 , the smallest value being @xmath7 6 g @xmath42 for core e at t@xmath36 = 40 k. we have discovered three 95-ghz ch@xmath3oh masers in the mol 121 region , coincident with mhos 864 , 865 , and 892 . they are all unresolved by carma s 2@xmath8 resolution , and each appear in two contiguous velocity channels . there are very slight ( @xmath21@xmath8 ) shifts in position of the masers between channels , and that , combined with our relatively coarse 1.538 km s@xmath16 channel width , means that our masers may each be multiple , tightly clustered masers , but without better spatial and spectral resolution we will set aside this possibility . for each maser , we measured the total flux and estimated the central velocity , and these results are presented in table 5 . one 44-ghz class i ch@xmath3oh maser was previously discovered in the mol 121 region ( s. kurtz , private communication ) , at the same location as the brightest 95-ghz maser and with a velocity of 2.3 km s@xmath16 . the channel width of the 44-ghz data was 0.166 km s@xmath16 , accounting for the discrepancy with our estimated velocity . the 44-ghz entries in table 5 were identified from vla data provided by kurtz and are discussed in 4.4 .

2.12-m / h 2.25- m flux ratios indicate another region dominated by fluorescence from a photo - dissociation region ( pdr ) , and one region that displays an anomalously low h 2.12-m / h 2.25- m flux ratio ( ) and coincides with a previously reported deeply embedded source ( des ) . continuum observations at 3 mm reveal five dense cores ; the brightest core is coincident with the des . one of these is coincident with the _ iras _ source ; the other lies at the centroid of a compact outflow defined by bipolar mhos .

we have discovered 12 new molecular hydrogen emission - line objects ( mhos ) in the vicinity of the candidate massive young stellar object , in addition to five that were previously known . 2.12-m / h 2.25- m flux ratios indicate another region dominated by fluorescence from a photo - dissociation region ( pdr ) , and one region that displays an anomalously low h 2.12-m / h 2.25- m flux ratio ( ) and coincides with a previously reported deeply embedded source ( des ) . continuum observations at 3 mm reveal five dense cores ; the brightest core is coincident with the des . the next brightest cores are both associated with cm continuum emission . one of these is coincident with the _ iras _ source ; the other lies at the centroid of a compact outflow defined by bipolar mhos . the brighter of these bipolar mhos exhibits [ ] emission and both mhos are associated with choh maser emission observed at 95 ghz and 44 ghz . masses and column densities of all five cores are consistent with theoretical predictions for massive star formation . although it is impossible to associate all mhos with driving sources in this region , it is evident that there are several outflows along different position angles , and some unambiguous associations can be made . we discuss implications of observed h 2.12-/h 2.25- and [ ] 1.64-/h 2.12- flux ratios and compare the estimated total h luminosity with the bolometric luminosity of the region . we conclude that the outflows are driven by massive young stellar objects embedded in cores that are likely to be in different evolutionary stages . = 1

1211.3440

c

lorenzetti et al . ( 2002 ) found that [ ] 1.64-@xmath4/h@xmath0 2.12-@xmath4 flux ratios for knots associated with a jet from irs 8 in the vela molecular ridge ranged from @xmath7 0.1 - 1.1 ( uncorrected for extinction ) . since the [ ] and h@xmath0 emitting regions are unsurprisingly physically distinct , they computed flux ratios based on two sets of zones , defined by the [ ] peak emission and the h@xmath0 peak emission . they argue that these high ratios require the presence of a fast j - shock component , which produces [ ] 1.64-@xmath4/h@xmath0 2.12-@xmath4 flux ratios in the range 0.5 - 2 for a wide range of parameters ( hollenbach & mckee 1989 ) . given that the effects of extinction make our observed [ ] 1.64-@xmath4/h@xmath0 2.12-@xmath4 flux ratios lower limits , this suggests the presence of j - shocks in both mhos 867 & 864 ; however , the high observed h@xmath0 2.12-@xmath4/2.25-@xmath4 ratios across all of the apertures with 2.25-@xmath4 detections ( 6.8 - 14.5 ) in table 3 suggest the presence of c - shocks as well . for the high excitation temperatures associated with j - shocks , one expects h@xmath0 2.12-@xmath4/2.25-@xmath4 @xmath7 3 @xmath19 4 , and for the lower - excitation c - shocks , @xmath7 6 @xmath19 20 . above 20 , the excitation temperature is @xmath2 1000 k , and observable emission is not expected ( smith 1994 , 1995 ; smith et al . in fact , both types of shocks may be found in jets from ysos . typically , the molecular emission arises from the flanks of a bow shock , and the atomic or ionized component originates close to the apex ( smith 2012 ) . neither fluorescence nor shocks can explain a h@xmath0 2.12-@xmath4/2.25-@xmath4 flux ratio @xmath2 1 , which is the case for the `` anomaly '' listed in table 1 and indicated on figure 2 . we hand - checked each image for possible saturation effects near the bright _ iras _ source . our combination of narrow - band filters and short exposure times ( 30 s ) kept even the brightest sources below 30k adu , well within the linear range of the detector ( 3% linear to 54.4k adu ) and far below its full - well capacity of more than 100k adu . therefore , we conclude that this effect is real . to the best of our knowledge , this is the first time an observed h@xmath0 2.12-@xmath4/2.25-@xmath4 flux ratio @xmath2 1 has been reported . although high - resolution nir spectroscopy is essential to determining the nature of this emission , we note that dove et al . ( 1987 ) found that certain circumstances could produce population inversions in para - hydrogen transitions . they suggested future work to include the ortho - hydrogen transitions and more completely model the processes occurring in shock - heated clouds . another intriguing possibility is that the anomalous emission comes from the immediate front of a fast dissociative shock ( t@xmath4110,000 k ) , where statistical equilibrium is not reached ( m. smith , private communication ) . if statistical equilibrium is not achieved , the 2.12-@xmath4/2.25-@xmath4 ratio should be the ratio of the transition probabilities . the transition probabilities for the h@xmath0 2.12-@xmath4 1 - 0 s(1 ) and h@xmath0 2.25-@xmath4 2 - 1 s(1 ) transitions are 3.47@xmath44 s@xmath16 and 4.98@xmath44 s@xmath16 , respectively ( turner et al . 1977 ) . in this case , the expected ratio would be about 0.7 . although this is still somewhat larger than we calculate in table 1 , the ratio is affected by choice of aperture size . the anomaly is bright in both line and continuum nir images ( see fig . 1 ) , and it is coincident with a deeply embedded infrared source ( des ) identified from polarimetric patterns in the scattered nir emission ( yao et al . the des is also coincident with core c , the brightest 3-mm core in the mol 121 region ( see 4.2.3 ) . in this section , we discuss each of the five cores we detected with carma , previous related observations , and the possible association of cores with outflows , individually . there is direct evidence of massive star formation occurring in three of the five cores ( a , c , & d ) . the remaining two cores ( b & e ) may be starless . in the absence of significant external heating , these cores are likely to have temperatures @xmath45 20 k , in which case the derived masses and mass column densities suggest that they may be sites of future massive star formation . core a is associated with the _ iras _ source and several signposts of massive star formation , including a compact region observed at 3.6 cm and 6 cm ( jenness et al . 1995 ; molinari et al . 1998 ) , a pdr detected in our h@xmath0 2.12-@xmath4 , 2.25-@xmath4 , and [ ] 1.64-@xmath4 observations ( figs . 1 & 2 ) and evident in the wise image ( fig . 4 ) , and h@xmath0o maser emission ( palla et al . 1991 ; brand et al . 1994 ; anglada et al . 1997 ) . furthermore , core a lies at or near the continuum peak identified through previous sub - millimeter and millimeter observations ( fir 2 - jenness et al . 1995 ; mccutcheon et al . 1995 ; curran & chrysostomou 2007 ; motte et al . core a may be associated with a @xmath7e - w outflow defined by several mhos . in particular , the bow - shaped mho 867 opens toward this source , as does mho 938 further to the west ( see figures 2 & 5 ) . mho 867 also exhibits strong [ ] emission . there are several mho groupings toward the east , which do not align in any obvious way ( mhos 939@xmath19942 ) . core b has not been detected previously with millimeter or sub - millimeter observations , nor is it associated with any obvious signposts of star formation such as masers , radio continuum , or obvious outflow activity . it is located at the northern end of the bright pdr , coincident with an apparent dip in the nir emission , which suggests high extinction towards this core . it may be prestellar in nature . if this is true , its temperature may be lower than we assumed , and thus its mass may be larger . core c has not been detected previously with millimeter or sub - millimeter continuum observations , even though it has the largest integrated flux of the cores we detected with carma . it does , however , coincide with the location of the des reported by yao et al . ( 2000 ) , as well the peak of the anomalous h@xmath0 emission . although motte et al . ( 2007 ) mapped the entire cygnus x molecular cloud complex in 1.2-mm continuum at iram , they detected only one dense core with their 11@xmath8 beam within the region we identify as a pdr associated with _ iras _ 20188@xmath173928 . our cores a , b , & c all lie within this region . little et al . ( 1988 ) first detected a bipolar molecular outflow in the vicinity of _ iras _ 20188@xmath173928 from co and hco@xmath46 observations . the molecular outflow is aligned roughly n - s , with the redshifted gas to the north . using a distance of 4 kpc , they noted the outflow properties were similar to other massive outflows such as cep a and ngc 2071 . zhang et al . ( 2005 ) identified an outflow with the same orientation from co 2@xmath151 observations at a similar resolution to the observations of little et al . they derived significantly smaller outflow mass and energetic parameters ; however , they used a distance of only 0.3 kpc , which is much smaller than the most recent estimate of the distance ( mottram et al . zhang et al . ( 2005 ) noted that the outflow appears to be centered @xmath76@xmath8 to the north of the _ iras _ source , coincident with the des identified by yao et al . ( 2000 ) ; however , given their @xmath730@xmath8 beam and spatial sampling , it is impossible to identify the driving source(s ) . the k@xmath47 image of yao et al . ( 2000 ) shows nir reflection nebulosity oriented generally n - s in the vicinity of the _ iras _ source ; however , the polarization vectors exhibit a different pattern in a nw - se direction about the des ( coincident with the bar - shaped extension of the anomaly evident in figs . 2 & 5 ) . yao et al . ( 2000 ) suggest this may indicate the direction of a newly - burst outflow from the des . the association of core c with the des identified by yao et al . ( 2000 ) , strong millimeter flux , and corresponding lack of cm - continuum emission , make this object an excellent candidate myso in a pre - uc phase of evolution . if this is the case , anomalous h@xmath0 emission might be a signpost for the early outflow phase of a myso , but clearly high - resolution nir spectroscopy is necessary to search for any such evolutionary trends . core d is associated with a h@xmath0o maser and faint continuum emission at 3.6 cm and 6 cm , indicative of the presence of a uc region ( jenness et al . 1995 ; molinari et al . 1998 ) . using the ukt14 receiver at the jcmt , jenness et al . ( 1995 ) detected a submillimeter source ( fir 1 ) at a position between our cores d & e from 450 @xmath4 & 800 @xmath4 @xmath7 18@xmath8-resolution observations . mhos 864 & 865 , the brightest mhos in the region ( with the exception of mho 867 , which may be contaminated with fluorescent emission from the pdr ) , exhibit bipolar morphology in a ne - sw direction about core d. both mhos are associated with ch@xmath3oh maser emission at 95 ghz & 44 ghz . we have also detected [ ] emission at two positions within mho 864 . several mhos lie near or along a slightly different position angle from the direction defined by mhos 864 & 865 : to the ne , mhos 863 , 891 & 892 , and to the sw , mho 937 . mho 892 is also coincident with ch@xmath3oh maser emission at 95 ghz & 44 ghz . given the presence of both radio continuum emission and one or more well - collimated h@xmath0 outflow , this object may be close to transitioning to a stage where an expanding uc region destroys the myso(s) accretion disk . the bright mho 866 lies directly to the nw of core d , but its association is unclear . the position of core e coincides with the position of a dense core detected by motte et al . ( 2007 ) in 11@xmath8-resolution 1.2-mm continuum observations using the iram 30-m telescope . for an assumed distance of 1.7 kpc and temperature of 20 k , motte et al . ( 2007 ) derive a core mass of 40 m@xmath6 and density , n(h@xmath0 ) , of 3.5@xmath48 @xmath35 . for the same temperature , we derive a core mass of 12.8 m@xmath6 . the difference can be explained if the carma observations resolve out some of the large - scale structure revealed in sub - millimeter jcmt maps ( mccutcheon et al . 1995 ; jenness et al . 1995 ; curran & chrysostomou 2007 ) . mhos 893@xmath19897 lie in the vicinity of core e , but it is not possible to associate any of these with a driving source presently . wss12 noted that the myso , mol 160 , exhibits a very high l@xmath49/l@xmath50 ratio , falling approximately a factor of two above the relationship that was determined for low - mass ysos ( caratti o garatti et al . 2006 ) and extended to mysos based on results for iras 20126@xmath174104 ( caratti o garatti et al . 2008 ) . although it is not generally possible to link individual outflows with driving sources in massive star - forming regions , and caution must be exercised in attempting to draw conclusions about the nature of myso outflows from the l@xmath49/l@xmath50 relationship alone ( wss12 ) , it is instructive to compare the total h@xmath0 luminosity from all detected outflows to the total bolometric luminosity of the mol 121 region . if the h@xmath0 flows are produced by low- or intermediate - mass ysos , one would expect the h@xmath0 emission to be under - luminous with respect to the bolometric luminosity , which comes primarily from the _ iras _ source . there are many uncertainties in estimating the total h@xmath0 luminosity , including the distance to mol 121/_iras _ 20188@xmath173928 , the extinction toward individual h@xmath0 knots , and the ratio of total h@xmath0 to h@xmath51 luminosity . nevertheless it is possible to place reasonable limits on the assumptions . without spectra of the mhos , we can only estimate the effects of extinction . although the extinction is very large in the dense cores , most of the mhos are located in the more extended cloud . it seems reasonable to assume the column density derived for the parsec - scale nh@xmath3 clump in this region by anglada et al . ( 1997 ) , n(h@xmath0 ) = 5.5@xmath52 @xmath42 . using the relation a@xmath53/n(h@xmath0 ) @xmath54 5.3 @xmath55 @xmath30 mag yields an estimate of the visual extinction a@xmath53 @xmath54 29 mag . further assuming an optical parameter for dense clouds of r@xmath53 = 5 , yields a@xmath51 @xmath54 3.6 mag ( allen 2000 ) . the luminosity of the h@xmath0 2.12 @xmath4 emission is given by : @xmath56 f@xmath51 = 4.59 @xmath57 10@xmath58 w m@xmath59 , summed over all the mhos listed in table 1 ( including the pdr and anomaly increases f@xmath51 by a factor of @xmath7 2.5 . ) depending upon the temperature of the shocked h@xmath0 , the 2.12-@xmath4 luminosity is typically @xmath7 5 - 10% of the total ro - vibrational h@xmath0 emission , l@xmath49 ( e.g. , caratti o garatti 2006 , 2008 ) . this yields l@xmath49 @xmath7 11.7 - 23.3 l@xmath6 for the combined mho luminosity . the bolometric luminosity of _ iras _ 20188@xmath173928 , calculated from the far - infrared sed and assuming d = 1.7 kpc , is 8.2@xmath5710@xmath60 l@xmath6 ( mottram et al . these results place mol 121 a factor of 1.5 to three above the l@xmath49/l@xmath50 relationship determined by caratti o garatti et al . ( 2006 , 2008 ) . this is very similar to the result obtained by wss12 for mol 160 , and strongly suggests that the h@xmath0 flows are driven by massive ysos . class i ch@xmath3oh masers are well - correlated with molecular outflows in massive star - forming regions ( cyganowski et al . 2009 and references therein ; fontani et al . 2010 ) and with the presence of compact 3-mm continuum emission ( schnee & carpenter 2009 ) , suggesting that these masers are signposts of an early stage in the evolution of a myso before an expanding uc region has destroyed the accretion disk . the strongest ch@xmath3oh maser detection ( m1 ) in mol 121 is associated with mho 864 ( figure 5 ) . it is by far the brightest at 95 ghz and was the only previously detected maser at 44 ghz ( s. kurtz , private communication ) . mho 865 and the associated maser ( m3 ) are positioned exactly opposite core d , while mho 892 and its associated maser ( m2 ) lie along a slightly different position angle , though they also appear to be associated with core d. the masers all have low velocities , close to the v@xmath61 of the ambient cloud , which is reported to be 1.5 km s@xmath16 by zhang et al . ( 2005 ) and listed as 2.1 km s@xmath16 in the rms catalog ( mottram et al . this is consistent with the suggestion that ch@xmath3oh masers arise in systemic gas in outflow cavity walls ( debuizer et al . 2009 ) . wss12 suggested that the 95-ghz/44-ghz ratio might prove to be a useful diagnostic for the shortest - lived ( e.g. , very early ) phases of massive star formation . in order to estimate the flux ratios of our masers , we binned the 44-ghz data ( provided by s. kurtz ) to approximate our wider velocity channels . this summed data lowered the noise and revealed 44-ghz maser emission at the location of all three of our masers , not just the one known previously . we were then able to measure and compare the fluxes at 44 ghz and 95 ghz . these fluxes are all presented in table 5 . all three masers are brighter at 95 ghz than at 44 ghz , in contrast to the statistical result reported by fontani et al . ( 2010 ) , who concluded that the 95-ghz line is intrinsically fainter based on their detection rates . m1 and m3 , which are associated with the same outflow angle , have remarkably similar flux ratios ( 3.73 and 3.69 , respectively ) . m2 , which is associated with mho 892 , has a 95-ghz to 44-ghz flux ratio of 6.63 , dramatically higher than the other two . mho 892 is much more compact than mhos 864 & 865 , though we do not know if this is related in any way . we can tentatively order the dense cores in mol 121 by evolutionary stage , based on their continuum and spectral - line properties . ( 1 ) core a is associated with the _ iras _ source , a compact pdr , and bright cm - continuum emission , suggesting it is the oldest site of massive star formation in mol 121 . ( 2 ) core d , with its associated faint cm - continuum emission , luminous h@xmath0 outflow , ch@xmath3oh masers , and emission may harbor one or more massive objects that has not yet destroyed its accretion disk . ( 3 ) core c , with its des , likely contains a myso in a pre - uc region phase of evolution . ( 4 ) b & e appear to be massive starless or prestellar cores . we note that cores b & c also lie near the periphery of the pdr , which suggests that mol 121 would be an excellent candidate for follow - up studies to explore the possibility of star formation triggered by the expanding region associated with _ iras _ 20188@xmath173928 .

the next brightest cores are both associated with cm continuum emission . the brighter of these bipolar mhos exhibits [ ] emission and both mhos are associated with choh maser emission observed at 95 ghz and 44 ghz . masses and column densities of all five cores are consistent with theoretical predictions for massive star formation . although it is impossible to associate all mhos with driving sources in this region , it is evident that there are several outflows along different position angles , and some unambiguous associations can be made . we discuss implications of observed h 2.12-/h 2.25- and [ ] 1.64-/h 2.12- flux ratios and compare the estimated total h luminosity with the bolometric luminosity of the region .

we have discovered 12 new molecular hydrogen emission - line objects ( mhos ) in the vicinity of the candidate massive young stellar object , in addition to five that were previously known . 2.12-m / h 2.25- m flux ratios indicate another region dominated by fluorescence from a photo - dissociation region ( pdr ) , and one region that displays an anomalously low h 2.12-m / h 2.25- m flux ratio ( ) and coincides with a previously reported deeply embedded source ( des ) . continuum observations at 3 mm reveal five dense cores ; the brightest core is coincident with the des . the next brightest cores are both associated with cm continuum emission . one of these is coincident with the _ iras _ source ; the other lies at the centroid of a compact outflow defined by bipolar mhos . the brighter of these bipolar mhos exhibits [ ] emission and both mhos are associated with choh maser emission observed at 95 ghz and 44 ghz . masses and column densities of all five cores are consistent with theoretical predictions for massive star formation . although it is impossible to associate all mhos with driving sources in this region , it is evident that there are several outflows along different position angles , and some unambiguous associations can be made . we discuss implications of observed h 2.12-/h 2.25- and [ ] 1.64-/h 2.12- flux ratios and compare the estimated total h luminosity with the bolometric luminosity of the region . we conclude that the outflows are driven by massive young stellar objects embedded in cores that are likely to be in different evolutionary stages . = 1

astro-ph9512169

i

ionized gas is known to extend ( up to @xmath81 kpc ) out of the plane in normal spiral galaxies ( e.g. dettmar 1992 ) . the origin and maintenance of this component of the interstellar medium in normal galaxies is not completely understood , but most theories support the notion that it is energized by outflows from the galaxy disk ( cf . rand 1995 ) . in powerful infrared ( ir ) galaxies , extraplanar ionized gas is much more luminous and is detectable much further ( up to tens of kpc , heckman , armus & miley 1990 ) out into the halo . the origin of these more extended structures is also explained by outflows from the galaxy . nuclear starbursts in these galaxies produce stellar winds and supernovae which rapidly heat the gas in the nuclear region . this high - pressure gas then expands rapidly and blows a wind out of the nuclear region , along the rotation axis of the disk , where the pressure gradient is lowest . this ` superwind ' interacts with clouds of dense gas in the galaxy and its halo , producing optical emission - line filaments ( see , e.g. , heckman , armus & miley 1990 ) . material swept up by the wind accumulates behind the shock front , forming a large shell ( or ` bubble ' ) along the minor axis . line emission which is observed from the shell should then have two velocity components , one from the front surface of the shell and one from the rear surface . such double - peaked emission - line profiles are indeed commonly found in minor axis spectra of superwind galaxies ( cf . heckman , lehnert & armus 1993 ) , corroborating that wind - blown bubbles are present . superwinds also manifest themselves at radio and x - ray wavelengths . the radio halos in edge - on starburst galaxies produce synchrotron emission from relativistic electrons in the wind . thermal x - rays are emitted by hot , expanding gas in the bubble and by low - density halo clouds which have been shocked by the wind . a well studied example of an extended halo is that in the edge - on starburst galaxy m82 ( radio : e.g. , seaquist & odegard 1991 ; x - ray : bregman 1994 ) . more examples are discussed in a recent review of observational and theoretical aspects of superwinds in starburst galaxies by heckman , lehnert & armus ( 1993 ) . approximately 1% of spiral galaxies have an active ( seyfert ) nucleus , which is commonly believed to be an accretion - powered supermassive black hole , i.e. , a scaled - down version of a quasar ( see , e.g. , terlevich 1992 for an alternate view ) . the emission from the active galactic nucleus ( agn ) dominates the luminosity at most wavelengths , so most studies of seyferts have focused on observing the properties of the agn itself and the environment it creates in and immediately around the nuclear region ( see , e.g. , antonucci 1993 ) . there is good evidence that nuclear outflows exist on pc scales in some seyferts ( cf . wilson 1993 ) , but it is not clear that these small - scale ( @xmath91 kpc ) outflows are connected with large - scale galactic outflows . observations of the large - scale ( @xmath01 kpc ) emission in seyferts do show that , in some cases , galactic - scale minor - axis outflows are present ( e.g. , hummel , van gorkom & kotanyi 1983 , hamilton & keel 1987 , corbin 1988 , wehrle & morris 1988 ) . in a sample of seyfert galaxies selected for extended optical or radio emission , baum ( 1993 ) found kpc - scale radio emission extending preferentially along the minor axes in seven out of ten cases and suggested that the emission comes from galactic winds blowing out of the galaxy disks . a particularly good example of a galactic outflow can be found in the edge - on seyfert galaxy ngc 5506 . diffuse radio emission is found out to @xmath3300 pc from the nucleus in the direction of the minor axis ( wehrle & morris 1987 ) and double - peaked emission - line profiles are found in minor axis spectra from regions @xmath3500 pc above and below the disk ( wilson , baldwin & ulvestad 1985 ) . the question of what powers galactic outflows in seyferts remains open , but viable sources of kinetic energy are nuclear starbursts and the active nucleus . why study galactic outflows in seyferts ? so far , only anecdotal evidence has been presented for them and they have not been systematically studied . one would like to know how galactic outflows in seyferts are different from those in more powerful agns ( e.g. radio galaxies , balqsos ) and also from those in starburst galaxies . from a broader standpoint , one would like to know what influence the outflows have on the agn and its host galaxy . galactic outflows drive large amounts of gas ( and metals ) out of the nuclear region , whereas the agn needs a constant supply of gas flowing inward . thus , galactic outflows in seyferts may regulate the power output and lifetime of the active nucleus . if the outflows are driven by starbursts , then what role , if any , do these nuclear starbursts play in the formation and evolution of the active nucleus ? many workers have proposed scenarios in which seyferts and starbursts are connected in an evolutionary sense ( e.g. scoville 1992 ) , but the issue remains open . the outflows may also have a strong influence on the physical state of the intergalactic medium . plasma which is blown out of the galaxy will increase the density of the intergalactic medium , heat it , and enhance its metallicity . in order to address these questions , we have begun a research program to systematically study a complete sample of edge - on seyfert galaxies . we shall search for observational evidence of galactic outflows , determine their physical properties and investigate possible energy sources for driving the outflows . in paper i , we present optical emission - line images and/or minor - axis spectra of the ionized gas in 22 edge - on seyfert galaxies . our future work will consist of analyzing the large - scale radio and x - ray emission from these outflows , using the same sample of edge - on seyferts . in section 2 , we introduce a statistical sample of seyfert galaxies which we shall use for continuing studies . observations and data reduction techniques are described in section 3 and images and spectra are presented for individual objects in section 4 . in section 5 , we discuss the frequency of occurrence of large - scale outflows in seyferts and discuss possible interpretations of energy sources driving the outflows . a hubble constant of 75 km s@xmath7 mpc@xmath7 is assumed throughout this paper .

we have launched a search for large - scale ( kpc ) minor - axis outflows in edge - on seyfert galaxies in order to assess their frequency of occurrence and study their properties . here we present optical continuum and 2 line images and/or minor - axis long - slit spectra of 22 edge - on seyfert galaxies .

we have launched a search for large - scale ( kpc ) minor - axis outflows in edge - on seyfert galaxies in order to assess their frequency of occurrence and study their properties . here we present optical continuum and 2 line images and/or minor - axis long - slit spectra of 22 edge - on seyfert galaxies . six of these galaxies show at least one of the following : ( i ) bi - symmetric h halos extending along the minor axis , ( ii ) bright emission - line complexes at distances kpc ( in projection ) out of the disk , and ( iii ) double - peaked emission - line profiles from the gas along the minor - axis , suggesting that a wind - blown bubble is present . our results indicate that of seyferts have good evidence for minor - axis galactic outflows . kinetic luminosities of the galactic outflows in our sample seyferts are erg s , assuming all of the observed minor - axis emission is produced by the outflow . these values are , in general ,.1 as large as those for well - studied cases of superwinds in starburst galaxies ( heckman , armus & miley 1990 ) . however , far - infrared luminosities of our sample seyferts are also.1 as large . both starburst - driven superwinds and wide - angled outflows from the active galactic nucleus are possible explanations for the observed large - scale outflows . 2h+[nii ]

astro-ph9512169

r

descriptions of the observational data are given in table 4 . for each of the 22 objects observed , we list the type of data taken and the corresponding figure number for the images and/or spectra . we also list the total 2 luminosity from the galaxy for all objects for which we have 2 images , and the total 2 luminosity from the minor - axis emission - line gas for galaxies in which emission - line regions ( elrs ) are evident along the minor axis . the total 2 luminosity from the galaxy was calculated by summing the flux inside rectangular regions enclosing all of the emission - line nebulae from the galaxy . the 2 luminosities of the minor - axis elrs were calculated by summing flux inside rectangular regions around the individual elrs mentioned in sections 4.1 and 4.2 . in the following subsections , we present and discuss our new images and spectra and also note whether other data which has been published is suitable for searching for evidence for minor - axis outflows . seyferts which are good candidates for having such outflows are identified and statistical results for our samples are discussed in section 5 . for each of the galaxies in our complete sample , we searched the literature for published data which could be used to look for signatures of minor - axis outflows . for many of the objects ( ic 1657 , um 319 , mrk 993 , mrk 577 , ark 79 , ngc 1320 , mcg @xmath52 - 27 - 9 , ngc 4602 , eso 103-g35 , ngc 6810 , ic 1417 , ngc 7410 and ngc 7590 ) , the published data was not suitable exceptions are noted in the following subsections . our images for mrk 993 are shown in figure 1a . many elrs are scattered throughout the galactic disk , but no minor - axis emission is evident in our 2 image . we did not find double - peaked line profiles or any evidence for elrs extending out of the disk in our minor axis spectra . no extraplanar emission is noticeable in our 2 image ( figure 1b ) . the spectrum from the position 3.1 ( @xmath31 kpc ) south ( along the minor axis ) of the nucleus may have double - peaked h@xmath1 , [ nii ] and [ s ii ] emission line profiles ( consistent with what is expected from the shell of an wind - blown bubble ) , but the possible substructure in the profiles is nearly the same level of magnitude as the noise . for this reason , we have classified these features as only suggestive of a minor axis outflow . spectra with higher signal - to - noise ( s / n ) ratios would be useful for determining if these components are double peaked emission lines from a wind - blown bubble . our r - band image ( figure 1c ) shows the presence of a companion galaxy @xmath320 to the north along the minor axis . apart from emission from this companion galaxy , we find no extended 2 emission in our long - slit spectra along the minor axis . fabry - perot studies ( e.g. amram 1992 ) show that the kinematics of the emission - line gas are quite complex , but there is no evidence for an outflow from the nucleus . no minor axis emission is noticeable in our 2 image ( figure 1d ) . this galaxy forms a pair with ngc 1321 , which is positioned @xmath31.7 to the north . ngc 1386 is located in the fornax cluster , so we have used the distance to that cluster ( 20 mpc ) in our calculations . in the 2 image ( figure 1e ) , there is an elr with luminosity 3.1 @xmath17 10@xmath22 erg s@xmath7 to the northwest , at a distance of 41 ( 4.0 kpc ) from the nucleus . the continuum emission from the disk extends out to this position , so the elr could lie in the the plane of the galaxy disk . alternatively , the emission could be from gas in a halo cloud which has been ionized by a wind . weaver , wilson & baldwin ( 1991 ) have used long - slit spectroscopy to study the kinematics of the extranuclear gas within @xmath312(@xmath31 kpc ) . the line profiles and line ratios of the elrs surrounding the nucleus suggest that an outflow from the nucleus may be occurring along the _ major _ axis . ulvestad & wilson ( 1984 ) found that the morphology of the nuclear radio continuum emission is slightly extended @xmath3 400 pc toward the southwest along position angle ( p.a . ) although there is good evidence for a nuclear outflow in ngc 1386 , it does not appear to be directed along the minor axis . except for the northwest elr , all of the line emission originates from @xmath91 kpc . more solid evidence is needed to conclude that a galactic scale outflow ( i.e. one blowing out of the galactic disk ) is present in this galaxy . a dust lane separates the line emission which immediately surrounds the nucleus ( see figure 1f ) from the bright ( l@xmath23 } = $ ] 3.6 @xmath17 10@xmath4 erg s@xmath7 ) elr which extends from @xmath35@xmath515 ( [email protected] kpc ) to the northwest , in the direction of the minor axis . a number of ionized filaments of luminosity @xmath310@xmath22 erg s@xmath7 are also present beyond the northwest elr , at distances @xmath2430 ( 4.5 kpc ) . such bright filamentary structures are commonly found in luminous ir galaxies with starburst - driven superwinds ( e.g. heckman , armus & miley 1990 ) . tsvetanov , dopita & allen ( 1995 ) find evidence for outflowing gas with velocities @xmath3200 km s@xmath7 on both sides of the galaxy disk . radio continuum maps of the nuclear region of ngc 2992 show emission extending out to 2 ( 0.3 kpc ) along the minor axis which has the structure of `` striking pair of loops '' ( wehrle & morris 1988 ) . these authors interpret these loops as limb - brightened bubbles or magnetic arches . the bright minor - axis optical elrs and ` figure-8 ' radio morphology suggest that a powerful galactic outflow is occurring in ngc 2992 . our 2 image ( figure 1 g ) shows emission from the disk but no extended emission along the minor axis . no extended minor - axis emission is apparent in our 2 image ( figure 1h ) of ngc 4235 . elrs are noticeable extending from the nucleus out along the _ major _ axis , especially to the northeast ( see also pogge 1989 ) . we did not find double - peaked line profiles or any evidence for elrs extending out of the disk in our minor axis spectra . radio continuum maps of the nuclear region ( ulvestad & wilson 1989 ) are unresolved or very slightly resolved . no extended emission was noticed by hummel , beck & dettmar ( 1991 ) in their large - scale radio map . we did not obtain any new images or spectra of ngc 4388 since there is already good evidence for a galactic outflow in this galaxy . corbin , baldwin & wilson ( 1988 ) and pogge ( 1988 ) have shown that conical structures of ionized gas extend outward from the nucleus , both above and below the disk . these authors argue that some of the line - emitting gas may have been ejected from the nucleus . radio maps of this galaxy ( hummel 1983 ; stone , wilson & ward 1988 ) reveal diffuse emission extending outward from the nucleus , perpendicular to the galactic disk . much of the emission in our 2 image ( figure 1i ) comes from a ring structure in the disk ( buta & de vaucouleurs 1983 ) , but no emission is evident along the minor axis . this seyfert galaxy also houses a strong nuclear starburst . the presence of a superwind in this this galaxy has been discussed in detail by heckman , armus & miley ( 1990 ) , who argue that the wind is driven by the starburst . harnett ( 1989 ) present images of a radio halo in this galaxy , presumably produced by the wind . a bi - symmetric halo of emission - line gas can be seen in our 2 image ( figure 1j ) extending along the minor axis , @xmath310 ( 3 kpc ) on both sides of the nucleus . the h@xmath1+[nii ] luminosity of the extended emission on either side is @xmath32.5 @xmath17 10@xmath25 erg s@xmath7 . unger ( 1987 ) show that radio emission extends @xmath36 west from the nucleus and suggest that it is from material lying out of the plane . the h@xmath1 halo we observe here is probably produced by an outflow from the nuclear region and we consider ic 4329a a good candidate for a large - scale galactic outflow . emission - line nebulae extend along the minor axis , @xmath35(0.6 kpc ) north and south of the nuclear region ( see figure 1k ) . wilson , baldwin & ulvestad ( 1985 ) first noted double - peaked [ o iii ] @xmath265007 and h@xmath27 emission lines in spectra of the elrs @xmath05 north and south of the nuclear region . our spectra from these positions ( see figure 1k ) also show double - peaked h@xmath1 , [ nii ] and [ s ii ] emission lines . a ` loop ' of radio continuum emission extends to the north from the nuclear region ( wehrle & morris 1987 ) . these features imply the presence of a minor - axis wind which is blowing a shell of material northward ( and perhaps southward ) from the nucleus . thus , there is very good evidence for a minor - axis outflow in ngc 5506 . our 2 image of ic 1368 is shown in figure 1l . note that the nuclear source is elongated in the direction of the minor axis and extends @xmath35 ( 1.3 kpc ) on each side of the nucleus . such extended emission - line halos are commonly found in edge - on starburst galaxies with winds , so we have classified ic 1368 as a good candidate for a large - scale outflow . our 2 image of his galaxy shows emission from the disk , but not from regions extending along the minor axis ( figure 1 m ) . no extended emission is present in our 2 image ( figure 1n ) . much of the emission comes from clumpy h ii regions in the disk . for the following objects , there were no published data that is suitable for searching for a large - scale outflow : ugc 3255 , eso 362-g8 , ngc 4117 , ic 5169 and mrk 915 . this galaxy has an elliptical r - band morphology ( see figure 2a ) . a bright elr of luminosity @xmath28 } = $ ] 1 @xmath17 10@xmath25 erg s@xmath7 is noticeable 19.7 ( 7.4 kpc ) from the nucleus in p.a . the location of this elr is not positioned exactly on the minor axis , but the gas is located @xmath34 kpc ( in projection ) out of the disk . this suggests that it has been ejected from the disk . we have therefore classified ngc 513 as a good candidate for a large - scale outflow . we did not obtain images of ugc 3255 . the position of the slit for our minor - axis spectra is shown in a greyscale plot of a b - band image ( digitized survey plate ) in figure 2b . we did not find double - peaked line profiles or any evidence for elrs extending out of the disk in our minor axis spectra . conical elrs can be seen in the 2 image of this galaxy in figure 2c . the northeast cone extents from the nucleus out to @xmath314 ( 4.3 kpc ) along p.a . 65(roughly perpendicular to the major axis ) and has an 2 luminosity of 1.8 @xmath17 10@xmath4 erg s@xmath7 . mulchaey , wilson & tsvetanov ( 1996 ) find the gas in the conical elr to have high [ o iii]5007/h@xmath1 ratios , consistent with photoionization by the agn . the presence of gas so far out of the disk suggests that a large - scale outflow is occurring in eso 362-g8 . the presence of extranuclear elrs in mrk 10 has been previously noted by schulz ( 1982 ) , who found line emission extending westward from the nucleus . we also find extranuclear line emission to be present from our long - slit data . the orientation of the slit ( p.a . 40 ) and a graph of the relative h@xmath1 flux for positions along the slit is shown in figure 2d . emission - line gas is present along the minor axis out to 20(11.3 kpc ) to the northeast from the nuclear region , and out to 10(5.6 kpc ) to the southwest . such emission could be produced by a galactic outflow blowing along the minor axis . however , due to the limited spatial coverage of our long - slit spectra , we classify this evidence as only suggestive . a more complete study of the extranuclear optical emission - line gas in mrk 10 is clearly warranted . our 2 image ( figure 2e ) of this galaxy shows emission from the inner disk but no extended emission along the minor axis . we did not find double - peaked line profiles or any evidence for elrs extending out of the disk in our minor axis spectra . a patchy ring of h ii regions shows up well in our 2 image ( figure 2f ) . the field of view of our ccd is small ( 5 ) compared to the large optical size of the galaxy ( @xmath310 @xmath17 5 ) , so our 2 image is not very useful for looking for emission from extraplanar gas . the morphology of the 2 emission within the stellar ( r - band ) envelope is not elongated along the minor axis . we did not find double - peaked line profiles or any evidence for elrs extending out of the disk in our minor axis spectra . this galaxy has been very well studied , but we did not find any evidence in the literature for a minor axis outflow . the 2 image ( figure 2 g ) shows elrs extending along the minor axis , @xmath36.5 ( 1.3 kpc ) to the northwest and southeast of the nucleus , perpendicular to the bar . the total 2 luminosity from the northwest elrs is @xmath310@xmath25 erg s@xmath7 . the small , bright elr south of the nucleus has a h@xmath1+[nii ] luminosity of @xmath35 @xmath17 10@xmath22 erg s@xmath7 and the remaining southwest elrs emit @xmath310@xmath25 erg s@xmath7 . such emission could be produced by an outflow along the minor axis . however , the projected locations of the the elrs are inside the stellar ( r - band ) envelope , so the elrs may be located in the inner disk of ic 5169 . for this reason , we classify this evidence as only suggestive of a minor - axis outflow . no emission is evident extending along the minor axis in our 2 image ( figure 2h ) .

six of these galaxies show at least one of the following : ( i ) bi - symmetric h halos extending along the minor axis , ( ii ) bright emission - line complexes at distances kpc ( in projection ) out of the disk , and ( iii ) double - peaked emission - line profiles from the gas along the minor - axis , suggesting that a wind - blown bubble is present . 2h+[nii ]

we have launched a search for large - scale ( kpc ) minor - axis outflows in edge - on seyfert galaxies in order to assess their frequency of occurrence and study their properties . here we present optical continuum and 2 line images and/or minor - axis long - slit spectra of 22 edge - on seyfert galaxies . six of these galaxies show at least one of the following : ( i ) bi - symmetric h halos extending along the minor axis , ( ii ) bright emission - line complexes at distances kpc ( in projection ) out of the disk , and ( iii ) double - peaked emission - line profiles from the gas along the minor - axis , suggesting that a wind - blown bubble is present . our results indicate that of seyferts have good evidence for minor - axis galactic outflows . kinetic luminosities of the galactic outflows in our sample seyferts are erg s , assuming all of the observed minor - axis emission is produced by the outflow . these values are , in general ,.1 as large as those for well - studied cases of superwinds in starburst galaxies ( heckman , armus & miley 1990 ) . however , far - infrared luminosities of our sample seyferts are also.1 as large . both starburst - driven superwinds and wide - angled outflows from the active galactic nucleus are possible explanations for the observed large - scale outflows . 2h+[nii ]

astro-ph9512169

c

the results from our observational data are listed symbolically in the last column of table 4 . for most of the objects we classified as good candidates for minor - axis outflows , either double - peaked emission lines are found from regions along the minor axis , or the morphology of the 2 emission resembles that of a halo extending above and below the galaxy disk . in ngc 513 and eso 362-g8 , the nebulae have conical morphologies , similar to ` ionization cones ' observed in some seyfert galaxies ( e.g. pogge 1989 , wilson & tsvetanov 1994 ) . the line emission from the extranuclear gas in these objects could be produced by ionizing radiation from the agn or by a shock from an outflowing jet . however , in both cases , the elrs are found @xmath34 kpc ( in projection ) out of the disk , which is , in general , further out than the typical maximum extent of ionization cones in seyferts ( @xmath32 kpc , wilson & tsvetanov 1994 ) . an obvious possible explanation for how the gas got so far out of the disk is that it was blown out by a minor - axis outflow . thus we consider the six galaxies ngc 2992 , ic 4329a , ngc 5506 , ic 1368 , ngc 513 and eso 362-g8 to be good candidates for having large - scale minor axis outflows . our images and spectra of ark 79 , mrk 10 and ic 5169 are suggestive of a minor axis wind , but are not entirely convincing in and of themselves . therefore , we have not included them as ` good candidates ' when calculating statistics for our samples . further optical studies of the minor axis nebulae in these galaxies would be useful for determining if galactic outflows are present . if we ignore the results in the literature and only consider results from the images and spectra we obtained , we find that for the 14 objects in our representative sample , four ( 29% ) show good evidence for minor axis outflows . including the objects from table 2 , six ( 27% ) of the 22 objects in our extended sample show good evidence for minor axis outflows . as mentioned in section 4.1 , there is evidence in the literature for minor - axis outflows in two additional seyferts in our complete sample ( ngc 4388 and ngc 4945 ) . all objects which show good evidence for minor axis outflows ( from our images and spectra or from the literature ) are marked with an asterisk in tables 1 and 2 . if we include the results from the literature , we find good evidence for minor axis outflows in four ( 29% ) of the 14 objects in our representative sample , six ( 27% ) of the 22 objects in our complete sample , and six ( 27% ) of the 22 objects in our extended sample . the results are consistent : @xmath325@xmath530% of edge - on seyferts show good evidence for large - scale galactic outflows . these results underestimate the `` true '' fraction of seyferts which have minor axis outflows . for many of the objects , data suitable for detecting emission from these outflows ( e.g. h@xmath1 images , long - slit spectra of the minor - axis elrs , deep radio - continuum images , deep x - ray images ) are not available . in addition , our images are only sensitive to surface brightnesses @xmath010@xmath18 erg s@xmath7 @xmath19 arcsec@xmath20 and we have minor axis spectra to search for double - peaked emission lines for only nine of 22 objects observed . detailed kinematic studies of extended emission - line regions in seyferts are very useful for determining if an outflow is present , but such studies have been published for very few objects in our samples . assuming our edge - on samples are unbiased subsamples of seyfert galaxies , our results suggest that large - scale galactic outflows are likely to be present in @xmath0@xmath2 of _ all _ seyfert galaxies . in table 5 , we list all seyfert galaxies known ( by us ) to have good evidence for galactic outflows . evidence comes in the form of optical emission - line nebulae and split emission lines along the minor axis , extended radio continuum emission along the minor axis , and extended x - ray halos along the minor axis . most of the outflows which have been identified are in seyferts with edge - on disks . outflows in only a few of these galaxies ( e.g. ngc 3079 , mrk 231 and ngc 4945 ) have been studied in detail . the question of what powers large - scale outflows in seyferts remains open even for the most well - studied cases . for example , in a very complete kinematic fabry - perot study of the two bi - symmetric wind - blown superbubbles in the nucleus of ngc 3079 , veilleux ( 1994 ) found that either a starburst- or an agn - driven wind was consistent . in the following subsections , we discuss two scenarios for powering the large - scale outflows in seyferts : starburst - driven superwinds and outflows from the active nucleus . superwinds in starburst galaxies have been fairly well studied ( heckman , armus & miley 1990 ; lehnert & heckman 1995 ) , so it is natural to compare properties of large - scale outflows in seyferts with those of superwinds in starburst galaxies . the superwind in the archetypical edge - on starburst galaxy m82 has an 2 luminosity of @xmath310@xmath29 erg s@xmath7 and a kinetic luminosity of 10@xmath30 erg s@xmath7 ( heckman , armus & miley 1990 ) . we can estimate kinetic luminosities for the seyfert outflows by scaling l@xmath31}$ ] for our sample seyferts ( table 4 ) by the ratio of the kinetic luminosity of m82 to the 2 luminosity of its minor - axis elrs . using this method , we find kinetic luminosities @xmath310@xmath32@xmath510@xmath33 erg s@xmath7 ( logarithmic mean 10@xmath34 erg s@xmath7 ) for the seyfert outflows , assuming all of the line emission is produced by the outflow . the implied kinetic luminosities of our seyfert outflows are , in general , a factor @xmath30.1 as large as those of superwinds from heckman , armus & miley ( 1990 ; several @xmath17 10@xmath6 erg s@xmath7 ) . however , the mean far - ir luminosity of our sample ( @xmath35 43.4 @xmath36[erg s@xmath7 ] ) is smaller than that of heckman , armus & miley s sample ( @xmath35 44.9 @xmath36[erg s@xmath7 ] ) by about the same factor , so if the seyfert outflows are powered by nuclear starbursts , smaller kinetic luminosities are to be expected . high rates of massive star formation have been inferred for the nuclear regions of several seyfert galaxies . for example , in ngc 1068 , approximately half of the ir luminosity comes from the agn and the other half comes from the starburst ( balick & heckman 1985 ) . the energy input from a possible starburst is directly proportional to the starburst component of l@xmath38 ( cf . heckman , lehnert & armus 1993 ) . however , for most seyferts , separating the starburst and agn components of l@xmath38 is not straightforward ( cf . telesco 1988 ; however , see also rodriguez - espinosa , rudy & jones 1987 , who claim that star formation produces the bulk of the far - ir emission in seyferts ) . measuring massive - star formation rates from stellar absorption lines is in general , quite difficult to do in seyferts ( cf . diaz 1992 ) . thus , it is not known how common circumnuclear starbursts are in seyferts . baum ( 1993 ) could not distinguish between starburst- or agn - driven winds using their radio data . however , they found that the luminosity of the extranuclear radio emission is comparable to that in starburst galaxies and follows the same radio - ir relation as that of starburst galaxies , suggesting that the large - scale radio emission may be of starburst origin . in order to verify that these galactic outflows are starburst - driven superwinds , one must find evidence for massive stars in the seyfert nuclei and determine if the putative starburst is powerful enough to drive a galactic wind . the agn can certainly provide enough energy to drive a galactic outflow . however , linear nuclear radio sources ( suggestive of a collimated nuclear outflow ) in seyferts are not , in general , oriented along the same position angle as the large - scale diffuse radio emission ( baum 1993 ) . therefore , it is unlikely that the large - scale minor - axis radio emission is from lobes at the end of collimated radio jets , as in powerful radio galaxies ( unless the jet outflow axis precesses ) . on the other hand , if nuclear outflows from the agn are weak , they may lose energy to the interstellar medium in the nuclear region and become poorly - collimated . if the gas continues to flow outward , it may be be diverted toward the minor axis ( where the pressure gradient is lowest ) and continue on as a wide - angled outflow . many different models have been presented for nuclear outflows from agns . theoretical models have been proposed for hydro - magnetic jets which originate from the accretion disk surrounding the black hole , or even from the black hole itself ( cf . blandford 1993 ) . another model ( krolik & begelman 1986 ; balsara & krolik 1993 ) proposes that radiation - driven winds originate at the inner edge of the proposed molecular torus . thus , estimating the amount of kinetic energy being channelled from the agn into the outflow is highly model - dependent .

our results indicate that of seyferts have good evidence for minor - axis galactic outflows . kinetic luminosities of the galactic outflows in our sample seyferts are erg s , assuming all of the observed minor - axis emission is produced by the outflow . these values are , in general ,.1 as large as those for well - studied cases of superwinds in starburst galaxies ( heckman , armus & miley 1990 ) . however , far - infrared luminosities of our sample seyferts are also.1 as large . both starburst - driven superwinds and wide - angled outflows from the active galactic nucleus are possible explanations for the observed large - scale outflows .

we have launched a search for large - scale ( kpc ) minor - axis outflows in edge - on seyfert galaxies in order to assess their frequency of occurrence and study their properties . here we present optical continuum and 2 line images and/or minor - axis long - slit spectra of 22 edge - on seyfert galaxies . six of these galaxies show at least one of the following : ( i ) bi - symmetric h halos extending along the minor axis , ( ii ) bright emission - line complexes at distances kpc ( in projection ) out of the disk , and ( iii ) double - peaked emission - line profiles from the gas along the minor - axis , suggesting that a wind - blown bubble is present . our results indicate that of seyferts have good evidence for minor - axis galactic outflows . kinetic luminosities of the galactic outflows in our sample seyferts are erg s , assuming all of the observed minor - axis emission is produced by the outflow . these values are , in general ,.1 as large as those for well - studied cases of superwinds in starburst galaxies ( heckman , armus & miley 1990 ) . however , far - infrared luminosities of our sample seyferts are also.1 as large . both starburst - driven superwinds and wide - angled outflows from the active galactic nucleus are possible explanations for the observed large - scale outflows . 2h+[nii ]

astro-ph0405260

c

we calculate the velocity components of fornax assuming that the distance to fornax is @xmath67 kpc , and the heliocentric radial velocity is @xmath68 km s@xmath2 ( mateo 1998 ) . we have adopted a standard solar motion of @xmath69 km s@xmath2 ( dehnen & binney 1998 ) with respect to the local standard of rest ( lsr ) . here the @xmath70 component is positive outward from the galactic center , @xmath26 is positive toward galactic rotation , and @xmath71 is positive toward the north galactic pole . the adopted rotation velocity of the lsr is @xmath72 km s@xmath2 , and the solar circle radius is 8.0 kpc . the uncertainties in the derived fornax velocity components are determined based on the uncertainties in the distance , radial velocity and proper motions . we also present the proper motion in the galactic rest frame ( i.e. , with solar and lsr motion subtracted ) , in both equatorial and galactic coordinates . these proper motions and the velocity components are listed in table 3 . the first row for each object lists the proper motion and velocity components for that object , while the second row lists the 1-@xmath53 uncertainty in our measurement of these quantities . the velocity components are in a cylindrical coordinate system , where @xmath73 is positive outward from the galactic center , @xmath74 is positive in the direction of galactic rotation , and @xmath71 is positive toward the north galactic pole . we also list the radial and tangential velocity components , where the radial component is along the direction from the galactic center to the object . along with these , we derive here the same quantities for the fornax proper - motion measurement of p02 , and for the sculptor proper - motion measurement of schweitzer et al . ( 1995 ) . in figure 7 we show density contour plots of fornax as derived from the star counts of the raster scan of plate cd0100 . the fornax globular clusters are also marked . galactic rest frame proper motions are indicated as follows . our proper - motion determination is represented by the shorter arrow ( points ene ) , and its uncertainty is defined by the shaded circle . the longer arrow to the se represents the proper motion as determined by p02 . our proper - motion value indicates a direction of motion closer to the direction of the major axis of the dwarf , while that of p02 is practically perpendicular to the major axis . also , the size of our proper motion is smaller than that of p02 . the position angle of our proper motion is @xmath75 , while that of p02 is @xmath76 . the sculptor dsph is located at a position angle of @xmath77 from fornax . the direction toward sculptor is represented with a gray line in fig . thus , our proper - motion determination indicates that fornax is moving , within errors , along the direction on the sky defined by fornax and sculptor , and away from sculptor ( fig . the position angle of sculptor s proper motion is @xmath78 ( schweitzer et al . 1995 ) , while fornax lies at a position angle of @xmath79 with respect to sculptor . therefore sculptor s direction of motion is some @xmath80 away from the fl@xmath15s@xmath15 plane . we calculate orbital elements by integrating orbits back in time over a period of 20 gyr and using the galactic potential model from johnston , spergel & hernquist ( 1995 ) . the integration time is chosen such that a few orbits are completed , and the orbital elements are averaged over the number of orbits . the uncertainties in the orbital elements are determined from 300 integrations that have initial conditions determined randomly from the uncertainties in the proper motions , radial velocity and distance ( see dinescu , girard & van altena 1999 , dinescu et al . in table 4 we list the orbital parameters for the current fornax absolute proper - motion determination and for that of p02 , and for the sculptor dwarf . the total orbital energy should be regarded as being on a relative scale for comparison between measurements and should not be used as a bound versus unbound criterion for fornax , for example . the orbital inclination is calculated as @xmath81 sin@xmath82 . our proper - motion determination implies a low - eccentricity , polar orbit for the fornax dwarf , with the current location at pericenter . similar integrals of motion for two or more objects indicate membership to the same stream . our measurement for fornax gives @xmath83 , @xmath84 and @xmath85 that are larger than those of sculptor . however , the uncertainties in these quantities do not allow us to confidently rule out the membership of sculptor to a stream that includes fornax , or the proposed fl@xmath15s@xmath15 stream . our estimate of the apocentric radius of fornax is close to the galactocentric radii of leo i ( 250 kpc ) and leo ii ( 205 kpc ) ( mateo 1998 ) , thus reinforcing the hypothesis of the common origin of the fl@xmath15s@xmath15 stream . the sextans dsph with a current galactocentric distance of 86 kpc ( mateo 1998 ) , may qualify as a member of the fl@xmath15s@xmath15 stream . while its location on the sky appears farther away from the orbital plane of fornax ( see figure 9 below ) than those of leo i and leo ii , an overlap of the orbits is within the uncertainties associated with the fornax orbit . the phoenix dsph is located at @xmath86 kpc ( mateo 1998 ) from the galactic center , about twice the apocenter distance of fornax s orbit , and is therefore a rather unlikely member of any daughter stream of the fornax dsph , unless substantial orbital decay occurred for the latter . in contrast to these results , the p02 proper motion measurement for fornax gives a rather eccentric orbit for fornax , with the dsph more likely bound to the local group than to our galaxy . specifically , p02 argue against the membership of fornax to the fl@xmath15s@xmath15 stream . the fornax dsph has a population that consists of predominantly intermediate - age ( @xmath87 gyr ) stars , besides the old , metal - poor stars that are more traditional in dwarf spheroidals ( ggh03 and references therein ) . in addition to these stars , fornax has relatively young stars with ages between 2 gyr and 200 myr ( pont et al . 2004 and references therein ) . stars in fornax have a wide metallicity range , between [ fe / h ] = -2.0 and -0.4 as recently demonstrated by pont et al . more importantly , pont et al . ( 2004 ) determine an age - metallicity relationship which implies that fornax underwent an initial enrichment process up to [ fe / h ] = -1.0 about 3 gyr ago , after which continued star formation that lasted until some 200 myr ago increased the metallicity to [ fe / h ] @xmath88 . the inferred star - formation rate increased substantially over the last 4 gyr ( table 5 in pont et al 2004 ) . given this star - formation history , fornax is expected to have some gas associated with it . however , young ( 1999 ) detected no h i gas within one core radius of the galaxy . specifically , there were no detections at the column density detection limits of @xmath10 @xmath11 at the galaxy center and @xmath12 @xmath11 at one core radius . young ( 1999 ) mentions that there may be undetected h i between the core radius and the tidal radius of fornax . however , if the lack of gas is due to its removal by ram - pressure stripping as fornax moves through a homogeneous intragalactic medium , then this gas is more easily stripped from the least dense regions of the satellite , and these regions are more likely the outskirts rather than the center of the dsph ( ggh03 ) . also , the bright , blue stars in fornax associated with young , main sequence stars ( stetson et al . 1998 ) are located in the central region of the dsph , where there was no h i detection . thus , as pont et al . ( 2004 ) suggest , it seems that fornax is now at a particular moment in its history , just after its `` gas death '' . ggh03 explored whether ram - pressure stripping as fornax moves through a uniform , gaseous halo can explain the lack of gas in fornax . by using the velocity determined by p02 and adopting a gaseous halo density of @xmath89 @xmath90 , ggh03 estimate an upper limit for the fornax gas density of @xmath91 @xmath90 where ram - pressure stripping is efficient . the fornax gas density obtained from this simple , pressure - balance estimation is not that of an environment where stars could have formed recently , as is seen in fornax . therefore the lack of gas in fornax has to be explained by a more powerful gas - removal process than the simple one just described . our lower value of the velocity of fornax compared to that of p02 ( table 3 ) would make even less efficient the ram - pressure stripping caused by its motion through a uniform , low - density gaseous halo . the upper limit for the fornax gas density stated above corresponds to a column density of @xmath92 @xmath11 , if one assumes a uniform density distribution within one core radius . in this estimation , we have used a core radius of @xmath93 ( walcher et al . 2003 ) , which corresponds to 0.6 kpc . from our orbit determination , there may be another plausible explanation for the lack of gas in a system that was capable of producing stars some 200 myr ago . fornax crossed the magellanic plane relatively recently . using the velocity and distance data from van der marel et al . ( 2002 ) for the lmc , we have derived its orbit , and therefore the orientation of the magellanic plane . according to our orbit calculations , fornax crossed the magellanic plane about @xmath94 myr ago , a recent event , considering the 4.5-gyr orbital period of fornax ( table 4 ) . at this crossing , fornax was located @xmath95 kpc from the galactic center , specifically at ( x , y , z ) = ( 5 , -25 , -145 ) kpc ( the sun is at ( 8.0 , 0.0 0.0 ) kpc ) . in figure 8 we show the orbits of the lmc ( dark line ) and of fornax ( gray line ) in the plane of the galactic disk , and the x - z plane perpendicular to the galactic disk . the orbits represent 10-gyr integrations backward in time . the current positions of the lmc and fornax are indicated with filled symbols . we have also marked 200 and 500 myr ago on the orbit of fornax with cross symbols . while in the x - z plot of the orbits , the lmc orbit does not quite reach that of fornax , moderate uncertainties in the orbits due to proper - motion uncertainties easily allow for their actual crossing . it is conceivable that gas from the lmc trails along its orbit beyond what is now known as the ms , a 100@xmath96 tidal filament of neutral hydrogen . the recent n - body / sph simulations of the lmc - galaxy interaction by mastropietro et al . ( 2004 ) show that a large amount of gas ( @xmath97 m@xmath14 ) is lost along the orbit . these simulations include both tidal and ram - pressure stripping . contrary to previous modeling of this interaction , mastropietro et al . ( 2004 ) find that the amount of stripped stars is negligible compared to the amount of stripped gas . the predictions are that the ms forms a great circle on the sky . their figure 2 shows that the lost gas is distributed in the plane of the orbit , and out to distances above and below the galactic plane of @xmath98 kpc . in fact , braun & thilker ( 2004 ) report the detection of a diffuse northern ( @xmath99 ) extension of the ms , that has a column density of @xmath100 @xmath11 . according to the mastropietro et al . ( 2004 ) models , this detection corresponds to the distant , above - the - galactic - plane part of the lmc orbit . thus fornax may have undergone recent , efficient ram - pressure stripping by passing through the denser , inhomogeneous environment of the gas in the magellanic plane , along the orbit of the lmc . whether gas from the lmc in this part of its orbit ( at z = -140 kpc ) has the appropriate density to cause efficient ram - pressure stripping in fornax , remains to be determined from detailed models of the clouds interaction with the galaxy . nevertheless , based on our calculated orbits , the crossing of the magellanic plane took place at a time that coincides with the time when star formation ceased in fornax . to illustrate the geometry , in figure 9 we show the projection on the sky of the entire ( i.e. , one period ) orbit of fornax , and the most recent gyr of the orbit of the lmc . the dark part of fornax s orbit represents the most recent gyr . the current locations of fornax , the lmc , sculptor , leo i , leo ii , sextans and phoenix are indicated with filled circles . the ms is indicated as derived from the h i column density data kindly provided to us by mary putman ( putman et al . 2003 , hereafter p03 ) . in this plot , we highlight the density contour corresponding to n@xmath101 @xmath11 . besides mapping out the large - scale ms structure , p03 also analyze the spatial and velocity distributions of h i clouds in the ms and in the direction of the sculptor group , as cataloged in a previous paper ( putman et al . the sculptor group is an association of galaxies at the south galactic pole ( sgp ) , and at distances ranging from 2 to 4 mpc . roughly half of this group falls on the same line of sight as a part of the ms , namely that section in the vicinity of the sgp . p03 ( see also references therein ) found that there are more clouds in this region than in any other part of the ms . they also found that the distributions of velocity and orientation of the elongated clouds with respect to the ms do not match those of the clouds in the bulk of the ms ( their figures 11 and 14 ) . in addition , they show that the velocity distribution of the clouds in this region of the ms does not match that of the sculptor group galaxies either . unlike distant , extragalactic clouds , these anomalous clouds show diffuse connections between one another , and a likely velocity gradient across the ms ( see their figures 7 and 13 ) . p03 conclude that these `` excess '' clouds ( when compared to the ms cloud distribution ) are more likely associated with some halo material rather than the distant sculptor group . p03 further note that the origin of the clouds may be linked to crossing tidal streams from galactic satellites with polar orbits . this is exactly the type of orbit that we have calculated from our proper - motion measurement of fornax dsph . in figure 10 ( a ) ( left panel ) we show this region of the sky in a gnomonic projection with the sgp at the center of the projection . the orbits of fornax and the lmc are shown . the sculptor , phoenix and fornax dsphs are indicated , and the h i data from p03 are shown , with the n@xmath101 @xmath11 contour highlighted . this panel is to be compared with the density map in p03 ( their figs . 5 and 12 ) , and with the velocity map in p03 ( their fig . 7 ) . a reference feature common to all these figures that can be used to guide the eye , is the bifurcation of the ms at @xmath102 , and @xmath103 . figure 10(b ) is a similar projection in which we show the h i clouds cataloged by putman et al . ( 2002 ) as individual sources . from their catalog we have excluded sources associated with galaxies . each cloud is represented with a line segment that indicates the orientation and size ( major axis ) of the cloud . only elongated clouds ( i.e. , minor / major axis @xmath40 0.7 ) that are small ( i.e. , semi - major axis @xmath104 ) are included in this plot . the putman et al . ( 2002 ) catalog is comprised of clouds with local - standard - of - rest velocities larger than 80 km s@xmath2 in absolute value , a selection that aims to eliminate features associated with the galactic disk h i emission . from fig . 10 ( b ) , one can see that there is an increase in the number of clouds in the sgp region of the ms , specifically near the location on the sky of the sculptor dsph and between @xmath105 to @xmath106 , and @xmath107 . these excess clouds , already mentioned in p03 , are located along the newly determined orbit of fornax . moreover , the orientation of the elongation of these excess clouds is aligned with the orbit of fornax , while the bulk of the clouds along the ms , are aligned with the long axis of the ms . the orientation of the elongation of these two groups of clouds with respect to the long axis of the ms can also be seen in figure 8 of p03 . in addition to the orientation of the clouds , figure 8 of p03 also shows the head - tail structure of the clouds , i.e. , a dense core with diffuse tail structure . p03 note that often the clouds aligned with the ms have the tails point away from the magellanic clouds . from figure 8 of p03 , the clouds in the sgp / sculptor - group region of the ms that have an orientation almost perpendicular to the long axis of the ms have the tails point away from the ms , and , according to our figure 10 ( b ) , away from fornax . therefore the orientation of the elongation and of the head - tail structure of the clouds is similar for these two groups of clouds , provided that for one group the source where they originated is the lmc , and for the other group the source is the fornax dsph . from our orbit calculation , fornax and/or material from fornax has a galactocentric radial velocity ( in the galactic rest frame ) of @xmath108 km s@xmath2 , when it crosses the magellanic plane . this negative , rather low radial velocity indicates that fornax is approaching a turning point in its orbit in this case the pericenter and it is well within the velocity range of the excess clouds discussed in p03 . ( see their fig . 11 , in which the galactic - rest - frame velocities are along the line of sight rather than along the direction to the galactic center , but these directions are very close for objects located at large galactocentric radii . ) therefore we suggest that the excess clouds in the sgp / sculptor - group region of the ms are stripped material from the fornax dsph , as it crossed the magellanic orbit ( fig . according to our orbit , fornax s previous pericenter passage was @xmath109 gyr ago ( tab . 4 ) . since there is a significantly larger intermediate - age ( 4 - 7 gyr , e.g. , ggh03 , tolstoy et al . 2003 ) population than old population in fornax , it is conceivable that the intermediate - age population is the result of the tidal interaction between fornax and our galaxy at the previous pericenter passage of the satellite . between the last pericenter passage and the present time ( which practically coincides with pericenter passage ) , fornax continues to form stars and consumes most of its gas . the recent crossing of the magellanic plane ( and the supposed left - over gas from the lmc ) may have swept away the remaining gas , causing star formation to cease . if fornax is gravitationally bound to the galaxy , then its current velocity is smaller than the escape velocity . by assuming a point - mass galactic gravitational potential , the limit on the escape velocity gives a lower limit for the galactic mass as : @xmath110 where @xmath111 is the galactocentric radius , and @xmath26 is the total velocity of the dsph . by taking @xmath112 kpc , and the total velocity from the values in table 3 we obtain @xmath113 m@xmath14 . the uncertainty in the mass estimate is derived from that in the total velocity . this estimate is in reasonable agreement with recent determinations of the milky way mass from a large sample of halo objects and satellites ( sakamoto , chiba & beers 2003 ) . they find a lower mass limit of @xmath114 m@xmath14 .

the corresponding orbit of fornax is polar , with an eccentricity of 0.27 , and a radial period of 4.5 gyr . fornax s current location is near pericenter . we propose that ram - pressure stripping due to the passage of fornax through a gaseous medium denser than the typical intragalactic medium left behind from the lmc may have caused the end of star formation in fornax .

we have measured the absolute proper motion of the fornax dwarf spheroidal galaxy from a combination of photographic plate material and wfpc2 data that provide a time baseline of up to 50 years . the extragalactic reference frame consists of 8 qso images and 48 galaxies . the absolute proper motion is mas yr and mas yr . the corresponding orbit of fornax is polar , with an eccentricity of 0.27 , and a radial period of 4.5 gyr . fornax s current location is near pericenter . the direction of the motion of fornax supports the notion that fornax belongs to the fornax - leoi - leoii - sculptor - sextans stream as hypothesized by lynden - bell ( 1976 , 1982 ) and majewski ( 1994 ) . according to our orbit determination , fornax crossed the magellanic plane myr ago , a time that coincides with the termination of the star - formation process in fornax . we propose that ram - pressure stripping due to the passage of fornax through a gaseous medium denser than the typical intragalactic medium left behind from the lmc may have caused the end of star formation in fornax . the excess , anomalous clouds within the south galactic pole region of the magellanic stream whose origin has long been debated in the literature as constituents of either the magellanic stream or of the extragalactic sculptor group , are found to lie along the orbit of fornax . we speculate that these clouds are stripped material from fornax as the dwarf crossed the magellanic clouds orbit .

astro-ph0405260

i

we have measured the absolute proper motion of fornax dsph from a combination of photographic plates and @xmath0 wfpc2 images with a time baseline of up to 50 years . a total of 8 qso images and 48 galaxies were used in the correction to absolute proper motion . the uncertainty in each proper - motion direction is 0.16 mas yr@xmath2 . this measurement implies a polar orbit , with a low eccentricity , and with the current location of fornax near pericenter . the motion of fornax supports the notion that fornax belongs to the plane defined by leo i , leo ii , sextans , sculptor and fornax . we also note that the orbit of fornax indicates that the dsph crossed the magellanic plane some 200 myr ago , a time that coincides with the termination of the dsph s star - formation process . it is found that the excess , anomalous h i clouds in the sgp / sculptor - group region of the ms ( p03 ) , are located along the orbit of fornax . the orientation of the elongation of these excess clouds seems to better align with the orbit of fornax rather than with that of the lmc . we thus speculate that these clouds were stripped from fornax , as the dsph crossed the magellanic orbit . we acknowledge funding from @xmath0 archive grant 08739 . srm , did and bk were also supported by nsf career award ast-9702521 , nsf grant ast-0307851 , nasa / jpl contract 1228235 , a cottrell scholar award from the research corporation , and a david and lucile packard foundation fellowship to srm . srm thanks eduardo hardy for loan of his early du pont plates of fornax , allen sandage for loan of the 200-inch fornax plates , oscar duhalde and fernando peralta for assistance during srm s du pont photographic observing runs , and david monet for generating early plate scans of the du pont fornax plates . did thanks mary putman for making available the h i density data for the ms . anderson , j. & king , i. r. 1999 , , 111 , 1095 anderson , j. & king , i. r. 2000 , , 112 , 1360 anderson , j. & king , i. r. 2003 , , 115 , 113 baggett , s et al . 2002 , in @xmath0 wfpc2 data handbook , v 4.0 , ed . b. mobasher , baltimore , stsci bellazzini , m. , ibata , r. , ferraro , f. r. , & testa , v. 2003 , , 405 , 577 braun , r. & thilker , d. a. 2004 , , in press buonanno , r. , corsi , c. e. , castellani , m. , marconi , g. , fusi pecci , f. , & zinn , r. 1999 , , 118 , 1671 chiu , l. -t . g. 1976 , , 88 , 803 cohen , j. 2004 , , in press cudworth , k. m. , & rees , r. f. 1991 , , 103 , 470 dehnen , w. & binney , j. j. 1998 , , 298 , 387 da costa , g. s. & armandroff , t. e. 1995 , , 109 , 2533 dinescu , d. i. , girard , t. m. , & van altena , w. f. 1999 , 117 , 1792 dinescu , d. i. , majewski , s. r. , girard , t. m. , & cudworth , k. m. , 2000 , , 120 , 1892 dinescu , d. i. , majewski , s. r. , girard , t. m. , & cudworth , k. m. , 2001 , , 122 , 1916 frinchaboy , p. m. , majewski , s. r. , crane , j. d. , reid , i. n. , rocha - pinto , h. j. , phelps , r. l. , patterson , r. j. , & muoz , r. r. 2004 , , 602 , l21 grebel , e. k. , gallagher , j. s. & harbeck , d. 2003 , , 125 , 1926 kroupa , p. 1997 , new astronomy 2 , 139 kunkel , w. e. 1979 , , 228 , 718 kunkel w. e. & demers , s. 1976 , roy . obs . bull . 182 , 241 hodge , p. 1961 , , 66 , 83 johnston , k. v , spergel , d. n. , & hernquist , l. 1995 , , 451 , 598 knierman , k. a. , gallagher , s. c. , charlton , j. c. , hunsberger , s. d. , whitmore , b. , kundu , a. , hibbard , j. e. , & zaritsky , d. 2003 , 126 , 1227 lee , j. -f . & van altena , w. f. 1983 , , 88 , 1683 lynden - bell , d. 1976 , , 174 , 695 lynden - bell , d. 1982 , observatory , 102 , 202 mackey , a. d. , & gilmore , g. f. 2003a , , 340 , 175 mackey , a. d. , & gilmore , g. f. 2003b , , 345 , 747 majewski , s. r. 1994 , , 431 , l17 majewski , s. r. , skrutskie , m. f. , weinberg , m. d. , & ostheimer , j. c. 2003 , , 599 , 1082 majewski , s. r. , kunkel , w. e. , law , d. r. , patterson , r. j. , polak , a. a. , rocha - pinto , h. j. , crane , j. d. , frinchaboy , p. m. , hummels , c. b. , johnston , k. v. , rhee , j. , skrutskie , m. f. , & weinberg , m. 2004 , , in press martin , n. f. , ibata , r. a. , bellazzini , m. , irwin , m. j. , lewis , g. f. , & dehnen , w. 2004 , , 348 , 12 martnez - delgado , d. , zinn , r. , carrera , r. & gallart , c. 2002 , , 573 , l19 mastropietro , c. , moore , b. , mayer , l. , stadel , j. , & wadsley , j. 2004 , in asp conf . `` satellites and tidal streams '' , la palma 2003 , ed . f. prada , d. martnez - delgado and t. mahoney , in press mateo , m. 1998 , araa , 36 , 435 mayer , l. governato , f. , colpi , m. , moore , b. , quinn , t. , wadsley , j. , stadel , j. , & lake , g. 2001 , , 559 , 754 piatek , s. , pryor , c. , olszewski , e. w. , harris , h. c. , mateo , m. , minniti , d. , monet , d. g. , morrison , h. , & tinney , c. g. 2002 , , 124 , 3198 pont , f. , zinn , r. , gallart , c. , hardy , e. & winnick , r. 2004 , , in press putman , m. e. , de heiji , v. , staveley - smith , l. , braun , r. , freeman , k. c. , gibson , b. k. , burton , w. b. , barnes , d. g. , banks , g. d. , bhathal , r. , de blok , w. j. g. , boyce , p.j . , disney , m. j. , drinkwater , m. j. , ekers , r. d. , henning , p.a . , jerjen , h. , kilborn , v. a. , knezek , p. m. , koribalski , b. , malin , d. f. , marquarding , m. , minchin , r. f. , mould , j. r. , oosterloo , t. , price , r. m. , ryder , s. d. , sadler , e. m. , stewart , i. , stootman , webster , r. l. & wright , a. e. 2002 , , 123 , 873 putman , m. e. , staveley - smith , l. , freeman , k. c. , gibson , b. k. & barnes , d. g. 2003 , , 586 , 170 saviane , i. , held , e. v. , bertelli , g. 2000 , , 355 , 56 schweitzer , a. e. , cudworth , k. m. , majewski , s. r. , & suntzeff , n. b. 1995 , 110 , 2747 stetson p. , b. , hesser , j. e. , & smecker - hane , t. a. 1998 , , 110 , 533 strader , j. , brodie , j. p. , forbes , d. a. , beasley , m. a. , & huchra , j. p. 2003 , , 125 , 1291 tinney , c. g. , da costa , g. s. , & zinnecker , h. 1997 , 285 , 111 tinney , c. g. 1999 , 303 , 565 tolstoy , e. , venn , k. a. , shetrone , m. , primas , f. , hill , v. , kaufer , a. , & szeifert , t. 2003 , , 125 , 707 valdes , f. 1982 , in instrumentation in astronomy iv , s.p.i.e . proceedings , vol . 331 , p. 465 valdes , f. 1993 , focas user s guide , noao document + ( ftp://iraf / noao.edu / iraf / docs / focas / focasguide.ps.z ) van der marel , r. p. , alves , d. r. , hardy , e. & suntzeff , n. b. 2002 , , 124 , 2639 walcher , c. j. , fried , j. w. , burkert , a. , & klessen , r. s. 2003 , , 406 , 847 yanny , b. , guhathakurta , p. , schneider , d. p. , & bahcall , j. n. 1994 , 435 , l59 young , l. m. 1999 , , 117 , 1758 lcrclcc + + + & & & & & + & & & & & & + + + + ph275b & 09.10.50 & 0.15 & 60 & 103a - e gg11+no . 25 & @xmath117 & @xmath118 + ph805b & 04.09.53 & 23.58 & 30 & 103a - d gg11 & @xmath119 & @xmath120 + ph863b & 13.09.53 & 23.15 & 60 & 103a - d corning 3484 & @xmath121 & @xmath122 + + + + 276 & 18.12.74 & 23.06 & 45 & iiia - j gg385 & @xmath123 & @xmath124 + @xmath125 & 18.12.74 & 20.34 & 60 & iiia - j gg385 & @xmath123 & @xmath124 + 282 & 19.12.74 & 21.53 & 70 & iia - d gg495 & @xmath123 & @xmath124 + @xmath126 & 19.12.74 & 20.17 & 50 & iiia - j gg385 & @xmath123 & @xmath124 + 287 & 20.12.74 & 21.80 & 70 & iia - d gg495 & @xmath123 & @xmath124 + @xmath127 & 20.12.74 & 20.30 & 60 & iiia - j gg385 & @xmath123 & @xmath124 + + + + cd0100 & 12.10.77 & 22.43 & 90 & 103a - d w16 & @xmath128 & @xmath129 + cd0103 & 13.10.77 & 22.60 & 60 & 103a - d w16 & @xmath130 & @xmath129 + cd2644 & 16.08.85 & 23.75 & 60 & 103a - o gg385 & @xmath131 & @xmath132 + cd2677 & 20.08.85 & 23.45 & 60 & 103a - o w2c & @xmath131 & @xmath132 + cd3107 & 02.11.94 & 23.33 & 180 & iia - d gg495 & @xmath133 & @xmath134 + cd3110 & 03.11.94 & 0.07 & 225 & iia - d gg495 & @xmath133 & @xmath134 + cd3302 & 23.01.01 & 20.37 & 120 & iiia - f gg495 & @xmath135 & @xmath136 + + lcclcc + + + & & & & + & & & & & + + cluster 4 & 10.03.95 & 1100 & f814w & @xmath137 & @xmath138 + cluster 3[ngc 1049 ] & 04.06.96 & 120 - 700 & f555w / f814w & @xmath139 & @xmath140 + cluster 2 & 05.06.96 & 120 - 700 & f555w / f814w & @xmath141 & @xmath142 + fornax field[parallel data ] & 25.09.98 & 300 & f606w & @xmath143 & @xmath144 + qso[a+b ] & cluster 4 & 10.03.99 & 160 & f606w & @xmath145 & @xmath146 + fornax field[parallel data ] & 08.03.00 & 400 & f606w & @xmath147 & @xmath148 + lrrrrrrrrr + + + & & & & & & & & & + & & & & + + fornax & 0.36 & 0.07 & -0.13 & 0.34 & 197 & 62 & 123 & -23 & 239 + & @xmath149 & 0.16 & 0.16 & 0.16 & 101 & 102 & 44 & 60 & 93 + + fornax ( p02 ) & 0.26 & -0.37 & 0.32 & 0.32 & 152 & -230 & 116 & -38 & 296 + & @xmath150 & 0.13 & 0.13 & 0.13 & 81 & 82 & 36 & 48 & 79 + + sculptor & 0.36 & 0.43 & -0.47 & -0.30 & 60 & 193 & -88 & 96 & 199 + & @xmath151 & 0.25 & 0.22 & 0.25 & 90 & 87 & 12 & 16 & 87 + rrrrrrrrrrr + + + & & & & & & & & & & + & & & & & & & & + + + & & & & & & & & & & + & & & & & & & & & & + + & & & & & & & & & & + & & & & & & & & & & + + & & & & & & & & & & + & & & & & & & & & & +

we have measured the absolute proper motion of the fornax dwarf spheroidal galaxy from a combination of photographic plate material and wfpc2 data that provide a time baseline of up to 50 years . the extragalactic reference frame consists of 8 qso images and 48 galaxies . the direction of the motion of fornax supports the notion that fornax belongs to the fornax - leoi - leoii - sculptor - sextans stream as hypothesized by lynden - bell ( 1976 , 1982 ) and majewski ( 1994 ) . according to our orbit determination , fornax crossed the magellanic plane myr ago , a time that coincides with the termination of the star - formation process in fornax . the excess , anomalous clouds within the south galactic pole region of the magellanic stream whose origin has long been debated in the literature as constituents of either the magellanic stream or of the extragalactic sculptor group , are found to lie along the orbit of fornax . we speculate that these clouds are stripped material from fornax as the dwarf crossed the magellanic clouds orbit .

we have measured the absolute proper motion of the fornax dwarf spheroidal galaxy from a combination of photographic plate material and wfpc2 data that provide a time baseline of up to 50 years . the extragalactic reference frame consists of 8 qso images and 48 galaxies . the absolute proper motion is mas yr and mas yr . the corresponding orbit of fornax is polar , with an eccentricity of 0.27 , and a radial period of 4.5 gyr . fornax s current location is near pericenter . the direction of the motion of fornax supports the notion that fornax belongs to the fornax - leoi - leoii - sculptor - sextans stream as hypothesized by lynden - bell ( 1976 , 1982 ) and majewski ( 1994 ) . according to our orbit determination , fornax crossed the magellanic plane myr ago , a time that coincides with the termination of the star - formation process in fornax . we propose that ram - pressure stripping due to the passage of fornax through a gaseous medium denser than the typical intragalactic medium left behind from the lmc may have caused the end of star formation in fornax . the excess , anomalous clouds within the south galactic pole region of the magellanic stream whose origin has long been debated in the literature as constituents of either the magellanic stream or of the extragalactic sculptor group , are found to lie along the orbit of fornax . we speculate that these clouds are stripped material from fornax as the dwarf crossed the magellanic clouds orbit .

astro-ph0010058

c

we have presented new hubble space telescope observations of the quasar pair lbqs 0107@xmath0025a , b , along with observations of a third quasar , lbqs 0107@xmath00232 . @xcite found 5 coincident lyman @xmath1 lines in the quasar pair . the new data increase that yield to 12 coincident lines , albeit with a more generous velocity window for declaring a match . the comparisons of the lbqs 0107@xmath0025a , b pair to the third quasar yield 8 and 9 matches , respectively . there are 3 triple matches within a velocity window of 550 km s@xmath26 . the significance of the coincident absorbers is established with a monte carlo simulation that lays down lines randomly in velocity space , with numbers that account for the poisson variance in the number of absorbers seen per sight - line and the varying signal to noise between spectra . simulations of random lines give a distribution of coincident pairs that peaks slightly towards zero velocity difference , with important implications for determining the significance of matches in this ( and other ) experiments . the main results are , ( 1 ) coincident lines within @xmath5v@xmath6@xmath25 200 @xmath3 that are significant at the 90% level for two quasar pairings , ( 2 ) coincident pairs of stronger lines preferentially have small velocity separations , and ( 3 ) a strong absorber that represents a highly significant triple coincidence . the simplest interpretation of the double and triple coincidences is in terms of absorbers with coherence lengths spanning 0.5 to 1 mpc at @xmath27 and extending in two dimensions on the plane of the sky . the correlation between line strengths for the coincident pairs is weak , so the absorbers must be extended but inhomogeneous . it is difficult to distinguish between single , coherent absorbers and clustered but distinct absorbers with a pair experiment . however , the detection of a highly significant match in all three quasars in the asterism indicates that at least one strong absorber has a sheet - like geometry . as more data on multiple quasar sight - lines accumulates , the line matching statistics can be used for an important new measure of the dimensionality of large scale structure at modest redshifts . this research was supported by grant go-06592.01 - 95a from nasa , awarded through the space telescope science institute . development of some of the line - finding and identification software was supported by national science foundation grant ast 98 - 03072 . we acknowledge the referee for helping improve the analysis and presentation of this paper . we thank tom aldcroft and cathy petry for making their spectral analysis packages available to us , and christian drouet daubigny for substantial efforts with the data reduction . we appreciate the efforts of a number of stsci support staff to shepherd this long - running project through to near - completion .

this triple system is unique in providing sensitivity to coherent ly absorption on transverse scales of approximately 1 mpc at 1 . taking into account the equivalent widths of the lines , one of these triple coincidences is significant at the 99.99% confidence level , based on monte carlo simulations with random line placements . matches with strong lines preferentially have small velocity separations . one of the triple coincidences appears to be a strong absorber with a sheet - like , but inhomogeneous , geometry and a coherence length approaching or exceeding 1 mpc .

we have obtained follow - up observations of the quasar pair lbqs 0107a , b and new observations of the nearby quasar lbqs 0107 with the hubble space telescope faint object spectrograph . extended wavelength coverage of lbqs 0107a and b using the g270h grating was also obtained . this triple system is unique in providing sensitivity to coherent ly absorption on transverse scales of approximately 1 mpc at 1 . monte carlo simulations were used to establish the confidence level for matches between absorption features in different lines of sight as a function of velocity separation . pairwise , there are 8 , 9 , and 12 lines that match between spectra . three instances of matches between all three lines of sight were found with velocity separations of less than 550 . two of the pairings have coincident lines within that would occur with less than 10% probability by chance . taking into account the equivalent widths of the lines , one of these triple coincidences is significant at the 99.99% confidence level , based on monte carlo simulations with random line placements . matches with strong lines preferentially have small velocity separations . these same simulations are used to demonstrate that the distribution of matches for a population of absorbers randomly distributed in velocity space is peaked towardv = 0 , which has implications for the statistical significance of matches . one of the triple coincidences appears to be a strong absorber with a sheet - like , but inhomogeneous , geometry and a coherence length approaching or exceeding 1 mpc .

0908.2103

i

the physics of low dimensional quantum magnets is a very interesting and topical area of research . these systems exhibit a broad range of novel physical properties and exotic quantum ground states , ranging from spin - peierls and haldane gap behavior in quasi - one - dimensional systems to high temperature superconductivity in quasi - two - dimensional systems . spin - peierls systems in particular have undergone a recent renaissance due to the discovery of two new , and somewhat unconventional , inorganic spin - peierls compounds , the titanium oxyhalides tiobr and tiocl . spin - peierls behavior arises in quasi - one - dimensional ( 1d ) systems which possess a combination of spin 1/2 magnetic moments , short - range antiferromagnetic interactions , and strong magneto - elastic coupling . at low temperatures these systems undergo a spin - peierls phase transition which is characterized by dimerization of the lattice and the development of a non - magnetic singlet ground state . as the presence of interchain interactions typically drives quasi-1d systems towards long - range magnetic order , only a select family of compounds with particularly strong spin - phonon coupling have been found to exhibit a spin - peierls transition . the first experimental realization of the spin - peierls transition was discovered in organic charge transfer compounds , such as ttf - cubdt@xcite and mem-(tcnq)@xmath7@xcite . it was considerably later that spin - peierls behavior was observed in cugeo@xmath8 , the first inorganic spin - peierls compound ( t@xmath9 @xmath1 14 k)@xcite . tiobr and tiocl , the recently discovered inorganic spin - peierls compounds based on ti@xmath10 , are often referred to as unconventional " spin - peierls systems . unlike standard spin - peierls systems , which undergo a single continuous phase transition at t@xmath9 , the titanium oxyhalides undergo two successive phase transitions upon warming - a first - order transition at t@xmath6 between commensurate and incommensurate spin - peierls states , and a higher - order transition at t@xmath0 between the incommensurate spin - peierls state and a disordered pseudogap state which extends up to t * @xmath1 135 k@xcite . in addition , the titanium oxyhalides are unique among spin - peierls compounds because of their unusually high transition temperatures ( t@xmath6/t@xmath0 @xmath1 65 k/92 k in tiocl@xcite and 27 k/48 k in tiobr@xcite ) and surprisingly large singlet - triplet energy gap ( e@xmath11 @xmath1 430 to 440 k in tiocl@xcite and 150 k in tiobr@xcite ) . the origins and properties of the incommensurate spin - peierls state between t@xmath6 and t@xmath0 have attracted particular attention to these compounds . both tiobr and tiocl crystallize into a feocl - type structure , with an orthorhombic space group of _ pmmn _ at room temperature@xcite . this structure consists of buckled ti - o bilayers in the _ ab_-plane , which are separated by double layers of either br@xmath12 or cl@xmath12 ions and stacked along the _ c_-axis . the additional reduction of effective dimensionality within the ti - o bilayers , from two to one , is believed to arise from ordering of the ti@xmath10 orbital degrees of freedom@xcite . spin - peierls dimerization occurs along the crystallographic _ b_-axis , and is driven by the direct exchange of ti _ _ d__@xmath13 orbitals@xcite . high temperature susceptibility measurements suggest that both tiobr and tiocl can be fit to a s = 1/2 heisenberg chain model , with nearest - neighbor exchange couplings of @xmath1 660 k and 360 k respectively@xcite . in general , tiobr has attracted considerably less attention than its sister compound tiocl . this is largely due to the fact that it is more difficult to grow single crystals of tiobr than tiocl , although it is also more challenging to work with tiobr because it is extremely hygroscopic ( even more so than its isostructural counterpart ) and has substantially lower transition temperatures . all measurements to date seem to suggest that apart from a slight difference in energy scales , the two compounds behave almost identically - they have matching low temperature phase diagrams , and appear to be isostructural in each of the major phases . however , there are subtle differences between the lattice constants of the two materials , perhaps most notably in the ratio of the _ a _ and _ b _ lattice constants which describe the ti - o bilayers . while the room temperature lattice parameters reported for tiobr are _ a _ = 3.78 , _ b _ = 3.49 , and _ c _ = 8.53 @xcite , those of tiocl are _ a _ = 3.79 , _ b _ = 3.38 , and _ c _ = 8.03 @xcite . thus , while the _ a_-axis ( i.e. interchain ) spacing of the two compounds is almost identical , the _ b_-axis ( i.e. intrachain ) spacing is @xmath1 3 to 4% smaller in tiocl . as a result , both the relative and absolute strength of the intrachain interactions are expected to be greater in tiocl , giving rise to physical properties which are more strongly one - dimensional in nature . this appears to be reflected in both the magnitude of the nearest - neighbor exchange coupling and the size of the singlet - triplet energy gap . the critical behavior of spin - peierls systems is a subject which has generated considerable interest and confusion over the past thirty years . widely varying and often contradictory critical exponents have been reported for a number of spin - peierls compounds . early studies of cugeo@xmath8 , the first inorganic spin - peierls system , led to conflicting claims of tricritical@xcite , three - dimensional@xcite , and mean - field - like@xcite critical behavior . subsequent work@xcite has revealed that much of this discrepancy can be attributed to the narrowness of the asymptotic critical region , and it has been shown that the system belongs to a conventional 3d universality class . similarly , while the organic compounds mem-(tcnq)@xmath14 and ttf - cubdt were initially believed to exhibit mean - field - like critical behavior@xcite , more detailed measurements@xcite suggest that these compounds correspond to 3d universality classes as well . the critical behavior of the recently discovered ti - based spin - peierls compounds , tiobr and tiocl , has been less extensively studied but appears similarly enigmatic . to date there has been only one report of critical exponents for these systems , which placed the value of @xmath2 for the continuous transition at t@xmath0 ( between the disordered pseudogap state and the incommensurate spin - peierls state ) between 0.10 @xmath4 0.04 and 0.26 @xmath4 0.09 in tiobr@xcite . similar values of @xmath2 = 0.15@xcite and @xmath2 = 0.25@xcite can be extracted from other x - ray diffraction measurements on tiocl and tiobr , although these results have not been explicitly quoted as critical exponents by the authors . this range of @xmath2 values suggests some form of either quasi-2d or tricritical behavior at t@xmath0 , a result which is somewhat surprising for a phase transition which is known to be driven by inherently three - dimensional spin - phonon interactions . for two compounds which have already been shown to exhibit behavior which significantly differs from the standard spin - peierls scenario , this poses a very interesting question - is the critical behavior of these compounds truly distinct from that of cugeo@xmath8 and the organic spin - peierls systems or is 3d universality one of the fundamental properties of any spin - peierls transition ? the need for a detailed study of the critical behavior of these systems has been further underlined by a recent claim based on symmetry analysis@xcite that the transition at t@xmath0 is intrinsically first order in nature , despite the rather substantial weight of experimental evidence to the contrary@xcite . in this paper we report the first detailed study of the critical properties of tiobr . using an approach which incorporates both standard power law fits and modified power law fits which include a first order correction - to - scaling term , we find that the transition at t@xmath0 can be well described by conventional 3d universality classes . we offer a qualitative comparison which suggests that tiocl also corresponds to a similar universality class , and discuss the potential change in criticality which results when tiocl is doped with non - magnetic sc ions . our results indicate that the asymptotic critical regime in tiobr is quite narrow , providing a natural explanation for the anomalously low values of @xmath2 which have previously been reported in the literature . the ease with which our data can be fit to models of a continuous phase transition clearly contradicts arguments for the first order nature of the spin - peierls transition at t@xmath0@xcite . in addition , we offer evidence that commensurate fluctuations , which inhabit the incommensurate spin - peierls and pseudogap phases of tiocl , are absent in tiobr . we propose that this may reflect the weaker one - dimensionality of the system , and the greater importance of interchain interactions . finally , we observe that the incommensurate and commensurate spin - peierls states in tiobr appear to be shifted in * q*-space with respect to each other . this may be an indication that the structure of the incommensurate spin - peierls state is more complex than previously assumed .

we have performed detailed x - ray scattering measurements on single crystals of the spin - peierls compound tiobr in order to study the critical properties of the transition between the incommensurate spin - peierls state and the paramagnetic state at t 48 k. we have determined a value of the critical exponent which is consistent with the conventional 3d universality classes , in contrast with earlier results reported for tiobr and tiocl . using a simple power law fit function we demonstrate that the asymptotic critical regime in tiobr is quite narrow , and obtain a value of = 0.32 0.03 in the asymptotic limit . we observe no evidence of commensurate fluctuations above t in tiobr , unlike its isostructural sister compound tiocl .

we have performed detailed x - ray scattering measurements on single crystals of the spin - peierls compound tiobr in order to study the critical properties of the transition between the incommensurate spin - peierls state and the paramagnetic state at t 48 k. we have determined a value of the critical exponent which is consistent with the conventional 3d universality classes , in contrast with earlier results reported for tiobr and tiocl . using a simple power law fit function we demonstrate that the asymptotic critical regime in tiobr is quite narrow , and obtain a value of = 0.32 0.03 in the asymptotic limit . a power law fit function which includes the first order correction - to - scaling confluent singularity term can be used to account for data outside the asymptotic regime , yielding a more robust value of = 0.39 0.05 . we observe no evidence of commensurate fluctuations above t in tiobr , unlike its isostructural sister compound tiocl . in addition , we find that the incommensurate structure between t and t is shifted in * q*-space relative to the commensurate structure below t .

astro-ph9811138

i

binaries have long been thought to have a crucial impact on globular cluster dynamics and evolution ( hut et al . 1992 ) , but only recently ( especially with the use of _ hst _ ) have large numbers of them been found in globular cluster cores where they are expected to act as the central energy source that drives cluster expansion . discoveries of binary millisecond pulsars ( e.g. manchester et al . 1991 ) and multiple low - luminosity x - ray sources ( hertz & grindlay 1983 ) have recently been supplemented by discoveries of large numbers of eclipsing binaries in globulars ( e.g. 47 tuc ; edmonds et al . 1996 and kaluzny et al . 1998 ) and a significant population of main sequence main sequence binaries in ngc 6752 ( rubenstein and bailyn 1997 ) . another recent breakthrough has been the discovery of cataclysmic variables ( cvs ) in the cores of globular clusters , using either dwarf nova ( dn ) outbursts in m5 ( oosterhoff 1941 ) , 47 tuc ( paresce & de marchi 1994 ) and ngc 6624 ( shara , zurek & rich 1996 ) , uv excess to recover an old nova in m80 ( shara and drissen 1995 ) or narrow - band h@xmath2 emission . using the latter technique 3 cvs have been reported in ngc 6397 by cool et al . ( 1995 ) and grindlay et al . ( 1995 ; hereafter gc95 ) , and a fourth cv candidate by cool et al . ( 1998 ; hereafter cg98 ) . also , 2 probable cvs have been reported in ngc 6752 by bailyn et al . these cvs appear to be the long - sought optical counterparts of the low - luminosity x - ray sources found in globular cluster cores . in particular , the 3 brightest optical emission line objects in ngc 6397 ( gc95 ) are the probable counterparts of the 3 brightest x - ray sources found by cool et al . ( 1993 ; see also cool et al . 1995 ) . observations of cvs in clusters can be used for a variety of studies including : ( 1 ) cv formation and evolution in low - metallicity environments , ( 2 ) stellar interactions in high - density environments , and ( 3 ) cluster dynamical evolution . probable formation mechanisms for globular cluster cvs include tidal capture and exchange collisions between main sequence ( ms ) stars and white dwarfs ( wds ) , complementing studies of the ms star - ms star interactions that produce blue stragglers . since these formation mechanisms differ from those for field cvs , and the stellar environment is different , it would not be surprising to find systematic differences between globular cluster and field cvs . in particular , gc95 and grindlay ( 1996 ) have suggested that the cvs in ngc 6397 might have a much higher percentage of magnetic wds than field cvs . the dense , collapsed core of ngc 6397 is a prime region to study the effects of stellar interactions because its high central density makes interaction rates large and its relative proximity at 2.2 kpc makes it possible to probe the core with high spatial resolution ( cg98 ) . this paper presents new _ hst_/fos spectra of cv 1 ( from gc95 ) and cv 4 ( from cg98 ) in ngc 6397 . by combining all available spectra for cvs 14 with the photometry of cg98 and comparing with field cvs we show that the cv disks are consistent with those of faint quiescent dne , given their expected periods , but that their 2 4686 lines are unusually strong for dne ( such systems would probably have long recurrence times between outbursts ) . instead , we argue that cvs 13 may be magnetic cvs ( or perhaps old novae ) , and that cv 4 is either a low accretion rate dn or a magnetic cv . it is possible that these objects may even be quiescent lmxbs , although this is unlikely based on detailed comparisons with the x - ray and optical properties ( grindlay 1996 , 1998 ) . in any case we present good evidence that there _ are _ systematic differences between populations of globular cluster and field cvs . along with the 3 previously known classes of uv bright stars in ngc 6397 ( blue stragglers , cvs and wds ) , cg98 have discovered another class of uv bright stars . three faint , hot stars have been found within only @xmath116@xmath3 of the cluster center , all of them non - variable ( unlike the flickering cvs ) . cg98 have argued that these non - flickering ( nf ) stars are unlikely to be cvs , `` normal '' co wds ( recently evolved from single red giants ) , extended horizontal branch stars or field stars , but instead that they are good candidates for low - mass helium wds . helium wds have masses @xmath4 0.49 , and in the field are usually found in binary systems containing either another wd or a neutron star ( marsh , dhillon & duck 1995 , and rappaport et al . these double degenerates are thought to form by roche lobe overflow ( and usually common envelope events ) in primordial binaries containing red giants , if he ignition in the red giant core , a proto helium wd , is avoided ( iben , tutukov and yungelson 1997 discuss detailed formation scenarios ) . several low - mass wds have been found or inferred in open and globular clusters including the helium wd red giant binary s1040 in m67 ( landsman et al . 1997 ) , and the ultra short period x - ray binary systems 4u 1820 - 30 in ngc 6624 ( anderson et al . 1997 ) and star s in ngc 6712 ( anderson et al . 1993 ) . s1040 in m67 probably formed after a subgiant underwent roche lobe overflow in a primordial binary ( landsman et al . 1997 ) , but in denser globular clusters , primordial binary evolution may be less important than interactions involving subgiants or red giants . for example , red giant / wd or red giant / ms star direct collisions should cause a helium wd to be left behind in a binary system ( davies , benz & hills 1991 ) . systems such as 4u 1820 - 30 and star s probably result from either neutron star / red giant collisions ( verbunt 1987 ) or neutron star / ms star capture and delayed mass transfer ( bailyn & grindlay 1987 ) . here , we report the first spectrum of one of the ngc 6397 nfs . the lack of emission lines in the spectrum provides extra evidence against the cv possibility and the log g value presented here argues against a co wd or extreme horizontal branch identification . by comparing with published model atmospheres we determine log g and for the nf and we then compare these parameters ( along with the luminosity ) with wd evolutionary models to show that a low - mass helium wd is , indeed , a plausible explanation for the nf . we also present evidence that the nf spectrum is significantly doppler shifted from the expected wavelength , suggesting that the nf is in a binary system with a massive dark companion .

( 1995 ) we present new evidence that cvs 13 may be dq her systems , as originally suggested by grindlay et al . ( 1995 ) , and we show that cv 4 may either be a dwarf nova or another magnetic system . we also present the first spectrum of a member of a new class of uv bright stars in ngc 6397 ( cool et al . 1998 ) . these faint , hot stars do not vary , unlike the cvs , and are thus denoted as `` non - flickerers '' ( nfs ) . like the cvs ,

we have used the hubble space telescope ( _ hst _ ) and the faint object spectrograph ( fos ) to study faint uv stars in the core of the nearby globular cluster ngc 6397 . we confirm the presence of a 4th cataclysmic variable ( cv ) in ngc 6397 ( hereafter cv 4 ) , and we use the photometry of cool et al . ( 1998 ) to present evidence that cvs 14 all have faint disks and probably low accretion rates . by combining these results with new uv spectra of cv 1 and the published spectra of grindlay et al . ( 1995 ) we present new evidence that cvs 13 may be dq her systems , as originally suggested by grindlay et al . ( 1995 ) , and we show that cv 4 may either be a dwarf nova or another magnetic system . another possibility is that the cvs could be old novae in hibernation between nova eruptions ( shara et al . 1986 ) . we also present the first spectrum of a member of a new class of uv bright stars in ngc 6397 ( cool et al . 1998 ) . these faint , hot stars do not vary , unlike the cvs , and are thus denoted as `` non - flickerers '' ( nfs ) . like the cvs , their spatial concentration is strongly concentrated toward the cluster center . using detailed comparisons with stellar atmosphere models we have determined log g = 6.25 1.0 , and = 17,500 5,000 k for this nf . using these line parameters and the luminosity of the nf we show that the nf spectrum is consistent with a helium wd having a mass of.25 and an age between 0.1 and 0.5 gyr ( depending on the models used ) . the nf spectrum appears to be significantly doppler shifted from the expected wavelength , suggesting the presence of a dark , massive companion , probably a carbon - oxygen ( co ) wd . 2

astro-ph9811138

c

we summarize here the results for cvs 14 : ( 1 ) a 4th cv candidate in ngc 6397 has been spectroscopically confirmed , ( 2 ) uv data for cv 1 implies that it has a red disk when compared with field cvs , ( 3 ) the photometry of cg98 combined with kurucz spectra for the estimated secondaries provide strong evidence that cvs 14 all have faint disks and probably low accretion rates ( consistent with faint quiescent dne ) , ( 4 ) the 24686/ line ratios ( together with the faint disks ) imply that cvs 13 may be dq her systems , ( 5 ) the correlations between the 2/ line ratios for cvs 14 and both ( a ) the continuum ratios between and h@xmath2 and ( b ) @xmath23 ( disk ) provide extra evidence that the 6397 cvs are mainly dq her systems . this is consistent with the finding of verbunt et al . ( 1997 ) that cvs 13 could be dq her systems based on their x - ray and optical fluxes . an alternative explanation is that some of the cvs are old novae in hibernating phases between nova eruptions . we conclude that there may be fundamental differences between populations of globular cluster cvs and field / open cluster cvs , perhaps caused by the different formation mechanism of tidal capture and exchange collisions or perhaps because of the different environment in globular clusters . one possible explanation is that interactions cause stars to rotate more quickly , resulting in stronger magnetic fields than in most field stars , as suggested by gc95 . alternatively , vandenberg , larson & de propris ( 1998 ) have suggested that rapidly rotating cores of giant stars in the metal poor globular cluster m30 might reconcile this cluster s luminosity function with stellar evolutionary theory . similar problems exist in understanding the luminosity function of ngc 6397 , although further study of the theory of vandenberg et al . ( 1998 ) is needed . another possibility is that magnetic wds are formed in globulars from differentially rotating cores in blue stragglers ( grindlay 1996 ) . prospects for further work on the cv data include modeling of the disk for cv 1 , power spectrum analysis of both the time series obtained by cg98 and the sub - exposures for the fos spectra , studies of line profile changes with time and detailed spectral modeling incorporating the cluster s low metallicity . a clear test of the hypothesis that most of the 4 cvs are dq her systems is to search for a stable optical ( or x - ray ) period with @xmath69 ( dq hers usually have @xmath70 ; patterson 1994 ) . because the short fos observations of the cvs are inadequate for this purpose , we shall propose to obtain simultaneous spectra of cvs 1 and 2 using moderate time - resolution ( @xmath71 60s ) spectroscopy in the blue ( using stis with a long slit ) , to directly test the magnetic cv hypothesis and place constraints on the hibernating nova scenario . the results for the nf are : ( 1 ) using detailed comparisons with stellar atmospheres from wesemael et al . ( 1980 ) and kurucz ( 1993 ) we have determined log g = 6.25 @xmath0 1.0 , and = 17,500 @xmath0 5,000 k ( consistent with = 22,000 @xmath0 7,000 k using the photometry of cg98 ) , ( 2 ) by using these line parameters and the luminosity of the nf we have shown that the nf spectrum is consistent with a helium wd having a mass of @xmath10.25 and an age between 0.1 and 0.5 gyr ( depending on the models used ) , and ( 3 ) the nf spectrum appears to be significantly doppler shifted from the expected wavelength , suggesting the presence of a dark , massive companion . the low mass of the nf ( and probably similar or lower masses for the others ) suggest that interactions between degenerate stars and subgiants or faint red giants are more efficient at producing helium wds than interactions involving degenerate stars and brighter red giants . although we have not yet made a rigorous attempt to find evidence for velocity variability of the line for the nf , the prospects from subdividing this low s / n spectrum are poor , especially since almost two thirds of the data for the nf was obtained over just one @xmath142 min time segment . clearly , observations over a longer time are needed to confirm that doppler shift evidence presented above and to study radial velocity variations . use of stis with the long slit would enable two nfs to be observed simultaneously , along with many cluster stars providing an ideal radial velocity reference . observations in the blue would also give excellent coverage of balmer absorption lines ( with the exception of h@xmath2 ) , giving considerably more accurate line parameters , and helping determine whether the luminosity difference between the bright nf and the two fainter ones is mainly because of mass or age differences . we thank r. kurucz , l. althaus and o. benvenuto for models , b. hansen , r. di stefano and f. wesemael for discussions and an anonymous referee for helpful comments . this work was partially supported by nasa grants nag5 - 3808 and hst grant go-06742 ( pde and jeg ) , and nasa grant nag5 - 6404 ( cdb ) . & 4687.04 @xmath0 0.59 & 1.26 @xmath0 0.11 & 5.9 @xmath0 0.5 & 21.0 @xmath0 2.0 & 0.0 @xmath0 2.7 h@xmath72 & 4858.09 @xmath0 0.21 & 3.92 @xmath0 0.16 & 18.0 @xmath0 0.8 & 3.8 @xmath0 5.7 & 15.6 @xmath0 1.6 he i & 5872.91 @xmath0 0.45 & 1.51 @xmath0 0.14 & 6.9 @xmath0 0.7 & 21.6 @xmath0 2.2 & 0.0 @xmath0 2.7 h@xmath2 & 6559.19 @xmath0 0.30 & 4.40 @xmath0 0.18 & 21.0 @xmath0 0.9 & 24.0 @xmath0 1.2 & 0.0 @xmath0 1.6 he ii & 4688.37 @xmath0 0.86 & 1.44 @xmath0 0.16 & 11.2 @xmath0 1.3 & 13.9 @xmath0 12.0 & 23.6 @xmath0 7.1 h@xmath72 & 4862.47 @xmath0 0.17 & 4.19 @xmath0 0.15 & 31.9 @xmath0 1.2 & 20.8 @xmath0 2.0 & 11.1 @xmath0 2.1 he i & 5873.98 @xmath0 0.53 & 1.04 @xmath0 0.10 & 7.6 @xmath0 0.8 & 21.7 @xmath0 2.8 & 0.0 @xmath0 3.2 h@xmath2 & 6563.60 @xmath0 0.39 & 3.94 @xmath0 0.16 & 30.2 @xmath0 1.3 & 30.7 @xmath0 1.5 & 2.1 @xmath0 2.1 he ii & 4685.71 @xmath0 0.81 & 0.53 @xmath0 0.05 & 15.2 @xmath0 1.5 & 26.2 @xmath0 5.5 & 10.6 @xmath0 7.3 h@xmath72 & 4860.73 @xmath0 0.12 & 2.07 @xmath0 0.05 & 59.0 @xmath0 1.6 & 13.8 @xmath0 0.9 & 10.5 @xmath0 0.8 he i & 5874.59 @xmath0 0.37 & 0.53 @xmath0 0.03 & 13.6 @xmath0 1.0 & 18.6 @xmath0 1.5 & 0.0 @xmath0 1.6 h@xmath2 & 6562.94 @xmath0 0.24 & 2.81 @xmath0 0.09 & 71.7 @xmath0 2.8 & 3.1 @xmath0 4.1 & 20.2 @xmath0 1.4 he ii & 4685.60 @xmath0 0.67 & 0.20 @xmath0 0.03 & 12.3 @xmath0 1.8 & 21.0 @xmath0 3.6 & 0.0 @xmath0 4.1 h@xmath72 & 4861.84 @xmath0 0.05 & 2.73 @xmath0 0.03 & 158.0 @xmath0 2.7 & 9.4 @xmath0 0.5 & 8.1 @xmath0 0.4 he i & 5874.78 @xmath0 0.18 & 0.79 @xmath0 0.03 & 29.3 @xmath0 1.4 & 15.0 @xmath0 0.8 & 0.0 @xmath0 1.0 h@xmath2 & 6563.27 @xmath0 0.06 & 3.39 @xmath0 0.04 & 106.7 @xmath0 1.7 & 11.9 @xmath0 0.3 & 6.2 @xmath0 0.4 cv 1 & 5.95 & 5.93 & 0.68 & 5.1 & & 8.5 & 7.6 & 8.5 cv 2 & 7.13 & 7.24 & 0.57 & 4.4 & 9.7 & 8.7 & 8.2 & 8.5 cv 3 & 7.84 & 8.18 & 0.49 & 3.8 & 9.3 & 8.9 & 8.8 & 8.7 cv 4 & 8.41 & 8.53 & 0.45 & 3.6 & 10.9 & 9.9 & 9.9 & 9.3

we confirm the presence of a 4th cataclysmic variable ( cv ) in ngc 6397 ( hereafter cv 4 ) , and we use the photometry of cool et al . ( 1998 ) to present evidence that cvs 14 all have faint disks and probably low accretion rates . by combining these results with new uv spectra of cv 1 and the published spectra of grindlay et al . their spatial concentration is strongly concentrated toward the cluster center . using detailed comparisons with stellar atmosphere models we have determined log g = 6.25 1.0 , and = 17,500 5,000 k for this nf . using these line parameters and the luminosity of the nf we show that the nf spectrum is consistent with a helium wd having a mass of.25 and an age between 0.1 and 0.5 gyr ( depending on the models used ) . the nf spectrum appears to be significantly doppler shifted from the expected wavelength , suggesting the presence of a dark , massive companion , probably a carbon - oxygen ( co ) wd . 2

we have used the hubble space telescope ( _ hst _ ) and the faint object spectrograph ( fos ) to study faint uv stars in the core of the nearby globular cluster ngc 6397 . we confirm the presence of a 4th cataclysmic variable ( cv ) in ngc 6397 ( hereafter cv 4 ) , and we use the photometry of cool et al . ( 1998 ) to present evidence that cvs 14 all have faint disks and probably low accretion rates . by combining these results with new uv spectra of cv 1 and the published spectra of grindlay et al . ( 1995 ) we present new evidence that cvs 13 may be dq her systems , as originally suggested by grindlay et al . ( 1995 ) , and we show that cv 4 may either be a dwarf nova or another magnetic system . another possibility is that the cvs could be old novae in hibernation between nova eruptions ( shara et al . 1986 ) . we also present the first spectrum of a member of a new class of uv bright stars in ngc 6397 ( cool et al . 1998 ) . these faint , hot stars do not vary , unlike the cvs , and are thus denoted as `` non - flickerers '' ( nfs ) . like the cvs , their spatial concentration is strongly concentrated toward the cluster center . using detailed comparisons with stellar atmosphere models we have determined log g = 6.25 1.0 , and = 17,500 5,000 k for this nf . using these line parameters and the luminosity of the nf we show that the nf spectrum is consistent with a helium wd having a mass of.25 and an age between 0.1 and 0.5 gyr ( depending on the models used ) . the nf spectrum appears to be significantly doppler shifted from the expected wavelength , suggesting the presence of a dark , massive companion , probably a carbon - oxygen ( co ) wd . 2

1501.07466

c

within the context of @xmath6 theory , we have described a green s function method for handling radiative effects on false vacuum decay . by this means and employing the thin- and planar - wall approximations , we have been able to calculate analytically and in a straightforward manner both the functional determinant of the quadratic fluctuations about the classical soliton configuration and the first correction to the configuration itself . this green s function method is well suited to numerical evaluation and , as a consequence , should be applicable to potentials of more general form . as such , we anticipate that it may be of particular use when the non - degeneracy of minima is purely radiatively generated . examples of the latter include the spontaneous symmetry breaking of the massless cw model @xcite or the instability of the electroweak vacuum . other applications might include the calculation of corrections to inflationary potentials in the time - dependent inflaton background , for instance in inflection - point or @xmath72-term inflation @xcite , which exploit the flat directions and saddle points of the mssm potential . furthermore , the use of green s functions naturally admits the introduction of finite - temperature effects or extension to non - trivial background spacetimes . green s functions have proved to be central objects within perturbative calculations throughout quantum field theory and it is therefore unsurprising that we find these suitable to treat solitons in @xmath6 theory as well . we take this as an encouragement that further theoretically- and phenomenologically - interesting systematic results on false vacuum decay may be within reach . the authors would like to thank jrgen baacke , daniel litim and holger gies for helpful correspondence and discussions . the work of p.m. is supported by a university foundation fellowship ( tuff ) from the technische universitt mnchen . the work of b.g . is supported by the gottfried wilhelm leibniz programme of the deutsche forschungsgemeinschaft ( dfg ) . both authors acknowledge support from the dfg cluster of excellence origin and structure of the universe .

we introduce a green s function method for handling radiative effects on false vacuum decay . , we take the theory , extended with additional heavier scalars , wherein we calculate analytically both the functional determinant of the quadratic fluctuations about the classical soliton configuration and the first correction to the soliton configuration itself .

we introduce a green s function method for handling radiative effects on false vacuum decay . in addition to the usual thin - wall approximation , we achieve further simplification by treating the bubble wall in the planar limit . as an application , we take the theory , extended with additional heavier scalars , wherein we calculate analytically both the functional determinant of the quadratic fluctuations about the classical soliton configuration and the first correction to the soliton configuration itself .

1504.05296

i

a tiling of the plane is a covering of @xmath2 by a collection of compact subsets , called _ tiles _ , for which two distinct tiles can only meet along their boundaries . the building blocks of a tiling are the _ prototiles _ : a finite set of tiles with the property that every other tile is a translation of some prototile . a tiling is said to be _ nonperiodic _ if it lacks any translational periodicity . one method of producing tilings is via a substitution rule ; a rule that expands each tile , and breaks it into smaller pieces , each of which is an isometric copy of an original tile . a nonperiodic substitution rule gives rise to a dynamical system , called the _ continuous hull _ , that consists of all tilings whose local patterns appear in some finite substitution of a prototile . the continuous hull becomes a dynamical system where the homeomorphism is induced by translation . in order to associate a particularly tractable @xmath0-algebra to a nonperiodic tiling , kellendonk @xcite places punctures in each tile , which he then uses to define a discrete subset of the continuous hull , which we refer to as the _ discrete hull_. in this paper , we define spectral triples on kellendonk s @xmath0-algebra @xmath3 associated to a tiling . the fundamental new ingredients for these spectral triples , are the recently developed fractal dual substitution tilings @xcite . suppose @xmath4 is a nonperiodic substitution tiling with finite prototile set @xmath5 . for each prototile @xmath6 , a fractal dual tiling defines a fractal tree , in fact infinitely many , on a self - similar tiling @xmath7 ; a tiling constructed from the substitution rule on @xmath8 . each of our fractal trees defines a unique fractal path between the punctures of any two tiles in @xmath7 . moreover , each fractal tree on @xmath9 respects the hierarchy of the substitution rule . given a fractal tree on @xmath9 , we apply perron - frobenius theory to the substitution matrix associated to the edges of the fractal dual tiling , to define a length function on each fractal edge in the fractal tree . this extends to a self - similar length function on the entire fractal tree , with scaling factor given by the perron - frobenius eigenvalue @xmath10 . if @xmath11 is the scaling factor for the original tiling , the scaling factor @xmath10 of the fractal tree , is related to the hausdorff dimension @xmath12 of the fractal dual tiling by the formula @xmath13 . the fractal tree is then used to define a length function between any two tiles of @xmath7 using perron - frobenius theory . let @xmath14 denote the fractal length between the punctures of two tiles @xmath15 and @xmath16 in @xmath7 . to each substitution tiling with a fractal dual tiling , we construct spectral triples on kellendonk s @xmath0-algebra @xmath3 , which we now outline . for each @xmath6 , let @xmath17 , with canonical basis @xmath18 , and define an unbounded multiplication operator @xmath19 . we show that @xmath20 is a @xmath1-summable ( positive ) spectral triple . let @xmath21 . for each function @xmath22 , we define an unbounded multiplication operator @xmath23 . then , @xmath24 is also a @xmath1-summable spectral triple . this defines a collection of spectral triples on kellendonk s algebra @xmath3 that each respect the hierarchy of the substitution rule . using operator algebras as the basic framework , alain connes developed noncommutative geometry @xcite , and has shown its significance to many fields of mathematics . in particular , one of the overarching themes of noncommutative geometry is to describe a consistent mathematical model for quantum physics . dynamical systems are particularly well suited to the tools of noncommutative geometry , and provide dynamical invariants in a noncommutative framework . of particular importance to connes program are spectral triples , which typically define a noncommutative riemannian metric on a @xmath0-algebra . a spectral triple @xmath25 consists of a @xmath0-algebra @xmath26 faithfully represented on a separable hilbert space @xmath27 , and a self - adjoint unbounded operator @xmath28 on @xmath27 with compact resolvent , whose commutators with a dense @xmath29-subalgebra of @xmath26 are bounded . the noncommutative topology of tilings has a long history . alain connes initiated the study of substitution tilings in a noncommutative framework by giving a detailed description of a @xmath0-algebra associated with the penrose tiling in his seminal book @xcite . in 1982 , dan shechtman discovered quasicrystals @xcite , a type of material that is neither crystalline nor amorphous . the mathematical theory explaining shechtman s discovery had already been developed in the context of purely mathematical research ; nonperiodic tilings provide an excellent model for quasicrystals . in an attempt to understand the physics of quasicrystals , bellissard defined a crossed product @xmath0-algebra by a family of schrdinger operators . years later , kellendonk defined a discrete version of the continuous hull and constructed a groupoid @xmath0-algebra associated with a tiling @xcite . soon afterwards , anderson and putnam @xcite showed that the continuous hull @xmath30 of a tiling is a smale space , and used this observation to describe the @xmath31-theory of the crossed product @xmath32 . more recently , kellendonk s construction was generalised to tilings with infinite rotational symmetry in @xcite , and the rotationally equivariant @xmath31-theory of these algebras was completely worked out in @xcite . only recently has there been a breakthrough in the noncommutative geometry of tilings . the primary interest in spectral triples on tilings is that the continuous hull of a nonperiodic tiling is not only a topological object , it also has rich geometric structure . the groundbreaking spectral triple for tilings appeared in john pearson s 2008 thesis @xcite , and the subsequent joint paper with bellissard @xcite . these spectral triples were defined on the commutative @xmath0-algebra associated with the hull of a tiling . a few years later , the second author constructed spectral triples on the unstable @xmath0-algebra of a smale space @xcite , which is strongly morita equivalent to kellendonk s algebra . however , in the special case of tiling algebras , this spectral triple essentially measured the euclidean distance between two tilings in the groupoid used to define the @xmath0-algebra , and ignored the substitution system . since bellissard and pearson s seminal result there have been a number of papers on spectral triples of tilings , see for example @xcite . the survey article @xcite explains these constructions and their relationship to one another . we thank the anonymous reviewer for suggesting revisions that greatly improved the exposition .

we introduce a new class of noncommutative spectral triples on kellendonk s-algebra associated with a nonperiodic substitution tiling . these spectral triples are constructed from fractal trees on tilings , which define a geodesic distance between any two tiles in the tiling . we show that each spectral triple is-summable , and respects the hierarchy of the substitution system . to elucidate our results , we construct a fractal tree on the penrose tiling , and explicitly show how it gives rise to a collection of spectral triples .

we introduce a new class of noncommutative spectral triples on kellendonk s-algebra associated with a nonperiodic substitution tiling . these spectral triples are constructed from fractal trees on tilings , which define a geodesic distance between any two tiles in the tiling . since fractals typically have infinite euclidean length , the geodesic distance is defined using perron - frobenius theory , and is self - similar with scaling factor given by the perron - frobenius eigenvalue . we show that each spectral triple is-summable , and respects the hierarchy of the substitution system . to elucidate our results , we construct a fractal tree on the penrose tiling , and explicitly show how it gives rise to a collection of spectral triples .

1410.0007

i

most of our knowledge of the stellar populations of galaxies comes from fitting stellar population synthesis models to their integrated light , as it is prohibitively difficult to characterize individual stars outside of the local volume . these models are commonly used to measure the total stellar masses of galaxies , as well as their ages , elemental abundances , star formation rates , dust content , stellar initial mass function , and other properties ( see the reviews by walcher et al . 2011 ; conroy 2013 , and references therein ) . many of the model ingredients carry significant uncertainties , which translate into uncertainties in derived stellar population parameters . the uncertainties in derived masses , star formation rates , and other parameters can be @xmath3dex or more ( see , e.g. , conroy , gunn , & white 2009 ; mitchell et al . 2013 ) . = 16.5 cm the predictions of stellar population synthesis models have historically been tested with star clusters , as stellar population parameters derived from the integrated light can be compared to those derived from the distribution of stars in the color - magnitude diagram ( cmd ) ( e.g. , worthey 1994 ; bruzual & charlot 2003 ; maraston 2005 ; schiavon 2007 ; conroy et al . 2009 ; thomas , johansson , & maraston 2011 ; nol et al . in fact , models are frequently tuned and calibrated to fit available data from open clusters in the milky way and the magellanic clouds , as well as the ancient , and generally metal - poor , globular clusters . thanks to programs such as the acs nearby galaxy survey treasury ( angst ; dalcanton et al . 2009 ) , some tests can now be done using individual stars in galaxies out to @xmath4mpc ( see , e.g. , girardi et al . 2010 ) . despite advances like these , the performance of the models remains essentially untested in important regions of parameter space . among the most important regimes is that of the metal - rich , old stellar populations which dominate the light of massive early - type galaxies . correctly modeling these stellar populations is critical for many aspects of astrophysics ; examples are the high mass end of the galaxy mass function ( croton et al . 2006 ) and the core mass function ( van dokkum et al . 2014 ) , the masses of central black holes ( van der marel et al . 1998 ) , the production of atomic elements in the universe ( worthey , faber , & gonzalez 1992 ; conroy , graves , & van dokkum 2014 ) , the stellar initial mass function ( van dokkum & conroy 2010 ; conroy & van dokkum 2012b ) , and the physical conditions in the densest star forming regions in the early universe ( krumholz 2011 ; nelson et al . 2014 ) . unfortunately , star clusters in the local group with similar ages and abundance patterns as giant ellipticals are rare ( e.g. , caldwell et al . 2011 ; van dokkum & conroy 2011 ) . we therefore largely rely on a combination of milky way stars and theoretical models to fit the spectra of these galaxies . of particular concern are the red giants that dominate the near - ir light . the spectra of these stars have strong and ubiquitous molecular bands of titanium - oxide ( tio ) and h@xmath5o , which often coincide with spectral features that are used to constrain abundances , ages , and the imf ( see , e.g. , lanon & wood 2000 ; rayner , cushing , & vacca 2009 ) . in this paper we introduce a new method to test the predictions of stellar population synthesis models for old , unresolved stellar populations . the method makes use of the fact that giants are sufficiently rare and luminous that poisson fluctuations in their number cause pixel - to - pixel fluctuations in the surface brightness distribution of nearby early - type galaxies . the existence of these surface brightness fluctuations is well known , and they have been used extensively to measure distances to galaxies : if a galaxy is closer , there are less giant stars in each pixel , and the pixel - to - pixel poisson fluctuations around the mean will therefore be larger ( e.g. , tonry & schneider 1988 ; tonry et al . 2001 ; mei et al . 2005 ; blakeslee et al . 2010 ) . pixels with high and low fluctuations allow us to do an experiment that gives unique information : we can study how the integrated spectrum changes when giants are added or subtracted to the galaxy . this is illustrated in fig . [ demo.fig ] , which shows the different stellar content of pixels with low and high fluctuations . the bright pixel at bottom left has many more luminous giants than the faint pixel at bottom right ; therefore , comparing spectra of pixels with different brightness enables us , in principle , to isolate spectral features of stars on the upper giant branch . furthermore , in the regime of very large fluctuations there will be pixels ( or more appropriately , lines of sight through the galaxy ) whose light has only a small contribution from luminous stars on the rgb and agb . spectroscopy of these pixels can provide information on the integrated light of stars that are still on the main sequence , which is difficult to access in any other way . this method builds on previous studies that compared the fluctuation amplitude in various broad - band filters to predictions from stellar population synthesis models ( e.g. , worthey 1994 ; vazdekis et al . 1997 ; blakeslee , vazdekis , & ajhar 2001 ; liu , graham , & charlot 2002 ; jensen et al . a central conceptual difference with previous work is that we do not use the absolute fluctuation signal in the analysis , which is difficult to measure ( as it requires an accurate distance , a thorough knowledge of the effects of the psf , and a careful treatment of contaminating objects ) . instead , the method relies on the relative change in the spectrum @xmath6 for a given relative change in the total flux @xmath7 . this is a key strength of the method : the distance , psf , and other effects that determine the absolute amplitude of the fluctuations are only relevant in that they set the dynamic range that is probed with the data . a second difference is that we identify the fluctuations of individual pixels rather than their statistical ensemble . here we take a first step toward fluctuation spectroscopy by using imaging through the narrow - band ramp filters in the advanced camera for surveys ( acs ) of hst . we study a regime where the observed fluctuations are dominated by systematic changes in the tio absorption strength with temperature on the upper giant branch . the target is , the most luminous galaxy in the virgo cluster ( with the possible exception of m87 depending on the chosen aperture ) . the main goal of the present paper is to introduce fluctuation spectroscopy as a method to dissect unresolved stellar populations . we also constrain certain aspects of the stellar synthesis model , and we show that more complete tests are possible with future data sets . the paper is organized as follows . in [ obs.sec ] the hst observations are described , with emphasis on the geometric constraints imposed by the ramp filters . in [ analysis.sec ] the variation in the ramp filters is measured as a function of the variation in the broad - band flux of a pixel . in [ model.sec ] we interpret the observed variation in the ramp filters , both in the context of a default isochrone and default population synthesis model and in the context of several variations of this model . the results are summarized in [ conclusions.sec ] .

differential spectroscopy of pixels as a function of fluctuation strength ( `` fluctuation spectroscopy '' ) effectively measures the spectral variation of stars as a function of their luminosity , information that is otherwise difficult to obtain for individual stars outside of the local group . models with ages or metallicities that are significantly different from the integrated - light values do not yield good fits . the current observations constitute a powerful test of the expected luminosities and temperatures of metal - rich giants in massive early - type galaxies . studies of pixels with much larger ( negative ) fluctuations will provide unique information on main sequence stars and the stellar initial mass function .

we introduce a new method to determine the relative contributions of different types of stars to the integrated light of nearby early - type galaxies . as is well known , the surface brightness of these galaxies shows pixel - to - pixel fluctuations due to poisson variations in the number of giant stars . differential spectroscopy of pixels as a function of fluctuation strength ( `` fluctuation spectroscopy '' ) effectively measures the spectral variation of stars as a function of their luminosity , information that is otherwise difficult to obtain for individual stars outside of the local group . we apply this technique to the elliptical galaxy , using hst / acs imaging in six narrow - band ramp filters tuned to spectral features in the range 0.8 m 1.0 m . pixels with% broad - band variations show differential color variations of 0.1% 1.0% in the narrow - band filters . these variations are primarily due to the systematic increase in tio absorption strength with increasing luminosity on the upper giant branch . the data are very well reproduced by the same conroy & van dokkum ( 2012 ) stellar population synthesis model that is the best fit to the integrated light , with residuals in the range 0.03% 0.09% . models with ages or metallicities that are significantly different from the integrated - light values do not yield good fits . we can also rule out several modifications to the underlying model , including the presence of a significant (% of the light ) population of late m giants . the current observations constitute a powerful test of the expected luminosities and temperatures of metal - rich giants in massive early - type galaxies . studies of pixels with much larger ( negative ) fluctuations will provide unique information on main sequence stars and the stellar initial mass function .

1009.3173

i

during the evolution of a cancer disease , a fundamental step for the tumor consists in provoking proliferation of the surrounding blood vessels and migration toward the tumour . this process , called tumoral neo - angiogenesis establishes a proper vascular network which ensures to the tumour supply of nutrients and allow the tumor to grow further than 2 - 3 mm diameter . it is also important in the metastatic process by making possible the spread of cancerous cells to the organism which then can develop in secondary tumors ( metastases ) . thus , an interesting therapeutic strategy first proposed by j. folkman @xcite in the seventies consists in blocking angiogenesis with the goal to starve the primary tumor by depriving it from nutrient supply . this can be achieved by inhibiting the action of the vascular endothelial growth factor molecule either with monoclonal antibodies or tyrosine kinase inhibitors . although the concept of the therapy seems perfectly clear , the practical use of the anti - angiogenic ( aa ) drugs leaves various open questions regarding to the best temporal administration protocols . indeed , aa treatments lead to relatively poor efficacy and can even provoke deleterious effects , especially on metastases @xcite . regarding to these therapeutic failures , it seems that the _ scheduling _ of the drug plays a major role . indeed , as shown in the publication @xcite , different schedules for the same drug can lead to completely different results . moreover , aa drugs are never given in a monotherapy but always combined with cytotoxic agents ( also named chemotherapy ) which act directly on the cancerous cells . again , the scheduling of the drugs seems to be highly relevant @xcite and the optimal combination schedule between these two types of drugs is still a clinical open question . thus , the complex dynamics of tumoral growth and metastatic evolution have to be taken into account in the design of temporal administration protocols for anti - cancerous drugs . + in order to give answers to these questions , various mathematical models are being developed for tumoral growth including the angiogenic process . we can distinguish between two classes of models : mechanistic models ( see for instance @xcite ) try to integrate the whole biology of the processes and comprise a large number of parameters ; on the other hand phenomenological models aim to describe the tumoral growth without taking into account all the complexity levels ( see @xcite for a review and @xcite ) . most of these models deal only with growth of the primary tumor but in 2000 , iwata et al . @xcite proposed a simple model for the evolution of the population of metastases , which was then further studied in @xcite . this model did not include the angiogenic process in the tumoral growth and thus could not integrate a description of the effect of an aa drug . we combined it with the tumoral model introduced by hahnfeldt et al . @xcite which takes into account for angiogenesis . the resulting partial differential equation is part of the so - called structured population dynamics ( see @xcite for an introduction to the theory ) : it is a transport equation with a nonlocal boundary condition . its mathematical analysis is not classical because the structuring variable is two - dimensional ; as far as we know such models have only been studied in the case where one structuring variable is the age and thus has constant velocity ( see @xcite ) . this is not the case in our situation and the theoretical analysis of the model without treatment ( autonomous case ) was performed in @xcite . + in this paper , we present some mathematical and numerical analysis of the model in the non - autonomous case that is , integrating both cytotoxic and aa treatments and with a general growth field @xmath0 satisfying the hypothesis that there exists a positive constant @xmath1 such that @xmath2 where @xmath3 is the normal to the boundary . we first simplify the problem by straightening the characteristics of the equation . we perform some theoretical analysis first at the continuous level ( uniqueness and a priori estimates ) using the theory of renormalized solutions . then we introduce an approximation scheme which follows the characteristics of the equation ( lagrangian scheme ) . the introduction of such schemes in the area of size - structured population equations can be found in @xcite for one - dimensional models . here , we go further in the lagrangian approach by doing the change of variables straightening the characteristics and discretizing the simple resulting equation , in the case of a general class of two - dimensional non - autonomous models . we prove existence of the weak solution to the continuous problem through the convergence of this scheme _ via _ discrete a priori @xmath4 bounds and establish an error estimate in the case of more regular data . + finally , we use this scheme to perform various simulations demonstrating the possible utility of the model . first , as a predictive tool for the number of metastases in order to refine the existing classifications of cancers regarding to metastatic aggressiveness . secondly , the model can be used to test various temporal administration protocols of aa drugs in monotherapy or combined with a cytotoxic agent .

it is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastasis that we analyze first at the continuous level . we present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions + nous introduisons et analysons un modle phnomnologique pour les thrapies anti - angiogniques dans le traitement des cancers mtastatiques . cest une quation de transport structure munie dune condition aux limites non - locale qui dcrit lvolution de la densit de mtastases . au niveau continu , des estimations a priori prouvent lunicit . nous prsentons lanalyse numrique dun schma lagrangien bas sur les caractristiques , do nt la convergence nous permet dtablir lexistence de solutions . nous dmontrons ensuite une estimation derreur et utilisons le modle pour produire des simulations intressantes au regard de possibles applications cliniques . _ ams 2010 subject classification : 35f16 , 65m25 , 92c50 _ * keywords * : anticancer therapy modelling , angiogenesis , structured population dynamics , lagrangian scheme .

we introduce and analyze a phenomenological model for anti - angiogenic therapy in the treatment of metastatic cancers . it is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastasis that we analyze first at the continuous level . we present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions . then we prove an error estimate and use the model to perform interesting simulations in view of clinical applications . + nous introduisons et analysons un modle phnomnologique pour les thrapies anti - angiogniques dans le traitement des cancers mtastatiques . cest une quation de transport structure munie dune condition aux limites non - locale qui dcrit lvolution de la densit de mtastases . au niveau continu , des estimations a priori prouvent lunicit . nous prsentons lanalyse numrique dun schma lagrangien bas sur les caractristiques , do nt la convergence nous permet dtablir lexistence de solutions . nous dmontrons ensuite une estimation derreur et utilisons le modle pour produire des simulations intressantes au regard de possibles applications cliniques . _ ams 2010 subject classification : 35f16 , 65m25 , 92c50 _ * keywords * : anticancer therapy modelling , angiogenesis , structured population dynamics , lagrangian scheme .

1003.5926

i

financial bubbles are generally defined as transient upward acceleration of prices above fundamental value @xcite . however , identifying unambiguously the presence of a bubble remains an unsolved problem in standard econometric and financial economic approaches @xcite , due to the fact that the fundamental value is in general poorly constrained and it is not possible to distinguish between exponentially growing fundamental price and exponentially growing bubble price . to break this stalemate , sornette and co - workers have proposed that bubbles are actually not characterized by exponential prices ( sometimes referred to as `` explosive '' ) , but rather by faster - than - exponential growth of price ( that should therefore be referred to as `` super - explosive '' ) . see @xcite and references therein . the reason for such faster - than - exponential regimes is that imitation and herding behavior of noise traders and of boundedly rational agents create positive feedback in the valuation of assets , resulting in price processes that exhibit a finite - time singularity at some future time @xmath0 . see @xcite for a general theory of finite - time singularities in ordinary differential equations , @xcite for a classification and @xcite for applications . this critical time @xmath0 is interpreted as the end of the bubble , which is often but not necessarily the time when a crash occurs @xcite . thus , the main difference with standard bubble models is that the underlying price process is considered to be intrinsically transient due to positive feedback mechanisms that create an unsustainable regime . furthermore , the tension and competition between the value investors and the noise traders may create deviations around the finite - time singular growth in the form of oscillations that are periodic in the logarithm of the time to @xmath0 . log - periodic oscillations appear to our clocks as peaks and valleys with progressively greater frequencies that eventually reach a point of no return , where the unsustainable growth has the highest probability of ending in a violent crash or gentle deflation of the bubble . log - periodic oscillations are associated with the symmetry of discrete scale invariance , a partial breaking of the symmetry of continuous scale invariance , and occurs in complex systems characterized by a hierarchy of scales . see @xcite for a general review and references therein . recent literatures on bubbles and crashes can be summarized as the following kinds : first , the combined effects of heterogeneous beliefs and short - sales constraints may cause large movements in asset . in this kind of models , the asset prices are determined at equilibrium to the extent that they reflect the heterogeneous beliefs about payoffs . but short sales restrictions force the pessimistic investors out of the market , leaving only optimistic investors and thus inflated asset price levels . however , when short sales restrictions no longer bind investors , then prices fall back down @xcite . while in the second type , the role of `` noise traders '' in fostering positive feedback trading has been emphasized . these models says trend chasing by one class of agents produces momentum in stock prices @xcite . the empirical evidence on momentum strategies can be found in @xcite . after the discussion on bubbles and crashes , the literatures on rebound should be summarized also . on the theoretical side , there are several competing explanations for price decreases followed by reversals : liquidity and time - varying risk . @xcite stresses the importance of liquidity : as more people sell , agents who borrowed money to buy assets are forced to sell too . when forced selling stops , this trend reverses . @xcite shows that it is risky to be a fundamental trader in this environment and that price reversals after declines are likely to be higher when there is more risk in the price , as measured by volatility . on the empirical front concerning the forecast of reversals in price drops , @xcite shows that the simplest way to predict prices is to look at past performance . @xcite shows that price - dividend ratios forecast future returns for the market as a whole . however , these two approaches do not aim at predicting and can not determine the most probable rebound time for a single ticker of the stock . the innovation of our methodology in this respect is to provide a very detailed method to detect rebound of any given ticker . in this paper , we explore the hypothesis that financial bubbles have mirror images in the form of `` negative bubbles '' in which positive feedback mechanisms may lead to transient accelerating price falls . we adapt the johansen - ledoit - sornette ( jls ) model of rational expectation bubbles @xcite to negative bubbles . the crash hazard rate becomes the rally hazard rate , which quantifies the probability per unit time that the market rebounds in a strong rally . the upward accelerating bullish price characterizing a bubble , which was the return that rational investors require as a remuneration for being exposed to crash risk , becomes a downward accelerating bearish price of the negative bubble , which can be interpreted as the cost that rational agents accept to pay to profit from a possible future rally . during this accelerating downward trend , a tiny reversal could be a strong signal for all the investors who are seeking the profit from the possible future rally . these investors will long the stock immediately after this tiny reversal . as a consequence , the price rebounds very rapidly . this paper contributes to the literature by augmenting the evidence for transient pockets of predictability that are characterized by faster - than - exponential growth or decay . this is done by adding the phenomenology and modeling of `` negative bubbles '' to the evidence for characteristic signatures of ( positive ) bubbles . both positive and negative bubbles are suggested to result from the same fundamental mechanisms , involving imitation and herding behavior which create positive feedbacks . by such a generalization within the same theoretical framework , we hope to contribute to the development of a genuine science of bubbles . the rest of the paper is organized as follows . section 2.1 summarizes the main definitions and properties of the johansen - ledoit - sornette ( jls ) for ( positive ) bubbles and their associated crashes . section 2.2 presents the modified jls model for negative bubbles and their associated rebounds ( or rallies ) . the subsequent sections test the jls model for negative bubbles by providing different validation steps , in terms of prediction skills of actual rebounds and of abnormal returns of trading strategies derived from the model . section 3 describes the method we have developed to test whether the adapted jls model for negative bubbles has indeed skills in forecasting large rebounds . this method uses a robust pattern recognition framework build on the information obtained from the calibration of the adapted jls model to the financial prices . section 4 presents the results of the tests concerning the performance of the method of section 3 with respect to the advanced diagnostic of large rebounds . section 5 develops simple trading strategies based on the method of section 3 , which are shown to exhibit statistically significant returns , when compared with random strategies without skills with otherwise comparable attributes . section 6 concludes .

we introduce the concept of `` negative bubbles '' as the mirror ( but not necessarily exactly symmetric ) image of standard financial bubbles , in which positive feedback mechanisms may lead to transient accelerating price falls . to model these negative bubbles , we adapt the johansen - ledoit - sornette ( jls ) model of rational expectation bubbles with a hazard rate describing the collective buying pressure of noise traders . the price fall occurring during a transient negative bubble can be interpreted as an effective random down payment that rational agents accept to pay in the hope of profiting from the expected occurrence of a possible rally . this result is obtained by using a general pattern recognition method that combines the information obtained at multiple times from a dynamical calibration of the jls model . error diagrams , bayesian inference and trading strategies suggest that one can extract genuine information and obtain real skill from the calibration of negative bubbles with the jls model .

we introduce the concept of `` negative bubbles '' as the mirror ( but not necessarily exactly symmetric ) image of standard financial bubbles , in which positive feedback mechanisms may lead to transient accelerating price falls . to model these negative bubbles , we adapt the johansen - ledoit - sornette ( jls ) model of rational expectation bubbles with a hazard rate describing the collective buying pressure of noise traders . the price fall occurring during a transient negative bubble can be interpreted as an effective random down payment that rational agents accept to pay in the hope of profiting from the expected occurrence of a possible rally . we validate the model by showing that it has significant predictive power in identifying the times of major market rebounds . this result is obtained by using a general pattern recognition method that combines the information obtained at multiple times from a dynamical calibration of the jls model . error diagrams , bayesian inference and trading strategies suggest that one can extract genuine information and obtain real skill from the calibration of negative bubbles with the jls model . we conclude that negative bubbles are in general predictably associated with large rebounds or rallies , which are the mirror images of the crashes terminating standard bubbles . keywords : negative bubble , rebound , positive feedback , pattern recognition , trading strategy , error diagram , prediction , bayesian methods , financial markets , price forecasting , econophysics , complex system , critical point phenomena

0706.3737

i

recent experiments @xcite have unravelled a fascinating set of phenomena in atomically thin layer of hexagonally arranged carbon atoms known as graphene . @xcite the quasiparticles of graphene are @xmath0-dimensional massless weyl fermions . @xcite in the context of condensed matter physics their properties are strikingly different from non - relativistic fermions . and phenomena that are hard to realize for the relativistic case , such as the klein paradox or the _ zitterbewegung _ are accessible in graphene . @xcite it is perhaps not an exaggeration to remark that many subtleties and a rich set of phenomenology are waiting to be discovered . a highlight has been the observation of an unconventional quantum hall effect @xcite and the corresponding theoretical development.@xcite in graphene the filling fractions are @xmath1 for magnetic field @xmath2 , where @xmath3 is an integer.@xcite the factor of @xmath4 comes from the two fold spin degeneracy and the two fold nodal degeneracy of the landau levels . the zeeman splitting is negligible compared to the cyclotron frequency and the disorder broadening of the landau levels . the factor of half is due to a zero mode in the landau level spectrum of dirac fermions.@xcite for stronger magnetic fields , @xmath5 , plateaus appear at @xmath6 , where @xmath7 is an integer.@xcite the plateaus at @xmath8 can be explained by the lifting of both the spin and the nodal degeneracies in the lowest landau level ( lll ) , but those at @xmath9 reflect only the removal of spin degeneracy in higher landau levels . the removal of nodal degeneracy requires electron - electron interaction . mechanisms suggested include @xmath10 ferromagnetism@xcite , sublattice symmetry breaking due to short range interactions@xcite and the generation of a mass gap by magnetic catalysis . @xcite @xmath10 quantum hall ferromagnetism predicts plateaus at all odd integer filling fractions . however , apart from @xmath11 , the plateaus at @xmath12 have not yet been observed . the special quantization rules in graphene are explained by the relativistic landau levels , modified perhaps by interactions , but for the existence of hall plateaus the laughlin argument is necessary.@xcite according to this argument the extended states at the center of a landau band are separated by the localized states elsewhere . if the fermi energy falls in the mobility gap , the plateaus are explained by a gauge invariance argument that is remarkably robust . the underlying phenomenon , therefore , is a localization - delocalization ( ld ) transition at the band center.@xcite the conventional integer quantum hall ( iqh ) plateau transition has been widely studied , and it is known that the localization length exponent @xmath13.@xcite can we prove that the same argument applies to graphene , and , if so , does the ld transition belong to the same universality class ? in the absence of a magnetic field , dirac fermions in the presence of disorder have been widely studied in systems as varied as gapless semiconductors , @xcite gapless superconductors , @xcite and iqh plateau transitions . @xcite as compared to nonrelativistic fermions , the localization problem of dirac fermions is richer because of a number of discrete symmetries . more specifically , if the disorder is particle - hole symmetric , for example a random gauge field , the ld transition takes place at zero energy and is reflected in the single particle density of states ( dos ) , in contrast to the conventional metal - insulator transition where the dos is smooth through the ld transition . surprisingly , there is a line of fixed points with continuously varying exponents depending on the disorder coupling constant . @xcite some of the unusual behavior of disordered dirac fermions may be expected to realize in graphene . one such effect that has received considerable attention is the weak ( anti)-localization phenomenon.@xcite however , relativistic landau levels in the presence of disorder have not yet received much attention . @xcite here we provide a reasonably complete study of the possible effects . there is another important reason why ld transitions in the relativistic landau level should be carefully analyzed . in the conventional iqh effect , the spin - degenerate plateau transition corresponds to @xmath14 when it is assumed that the ld transition takes place at a single energy at the band center.@xcite this has led to intense theoretical investigation of the ld transition in the spin - degenerate landau band . @xcite when spin - orbit scattering is included , the ld transition is found to occur at two distinct energies , away from the band center . scaling analysis about these distinct energies provide , once again , that @xmath15 , as in the spin - polarized system . the scaling about a single energy at the band center leads to the effective exponent @xmath16 . one should anticipate a similar discrepancy between the spin and the nodal polarized iqh effect and the fourfold degenerate iqh effect in graphene . for simplicity we shall concentrate on the spin polarized lowest landau level ( lll ) of graphene and analyze the ld transition both in the presence and in the absence of nodal degeneracy . an interesting example of a controlled analytic calculation in the disordered landau level problem is the dos in the lll . this was first computed exactly by wegner @xcite by examining the euler trails of the impurity diagrams for the white noise disorder and was subsequently extended by brezin _ _ @xcite by using a supersymmetric ( susy ) technique . here we also obtain some exact results for the dos in the disordered relativistic lll using susy techniques . the most general model of disorder consists of a random potential , a random mass , a random gauge field and a random internode scattering ; however , the random gauge field leaves the lll unperturbed . after projection to the spin - polarized lll , we study the following hamiltonian : @xmath17 where @xmath18 , @xmath19 represent potential and mass disorders respectively and @xmath20 and @xmath21 describe internode scattering effects . a mass @xmath22 of the fermions have been included to study the effect of the removal of the nodal degeneracy . for simplicity we have omitted the constant zeeman energy . the @xmath23 matrix @xmath24 is the identity matrix and @xmath25 , @xmath26 and @xmath27 are the three pauli matrices . because of a large number of cases involved , it is useful to summarize the results for the ld transition . let @xmath28 , @xmath29 , @xmath30 and @xmath31 denote the widths of the gaussian random distributions corresponding to the random potential , random mass , and random internode scatterings , respectively . the list of possible cases are : 1 . @xmath33 and @xmath34 . 2 . @xmath35 , @xmath36 . 3 . @xmath37 , @xmath38 . 4 . @xmath39 , @xmath40 . @xmath33 , @xmath35 and @xmath41 . 6 . @xmath33 , @xmath37 and @xmath42 . 7 . @xmath33 , @xmath39 and @xmath43 . 8 . @xmath35 , @xmath37 , @xmath44 . 9 . @xmath35 , @xmath39 , @xmath45 . @xmath37 , @xmath39 and @xmath46 . 11 . @xmath33 , @xmath35 , @xmath47 and @xmath48 . @xmath33 , @xmath35 , @xmath49 and @xmath50 . 13 . @xmath33 , @xmath37 , @xmath49 and @xmath51 . 14 . @xmath35 , @xmath37 , @xmath49 and @xmath52 . 15 . @xmath33 , @xmath35 , @xmath47 and @xmath49 . in the cases ( 1 ) and ( 2 ) , when disorder does not mix the two nodes , the ld transitions belong to the conventional iqh universality class with @xmath53 . it is interesting to note that mass disorder produces ld transition in the lll , whereas for zero magnetic field random mass is known to be an irrelevant perturbation for the @xmath0-dimensional dirac fermions .@xcite the hamiltonians for ( 2 ) , ( 3 ) and ( 4 ) involve only a single pauli matrix at a time , related to each other by unitary transformations . thus , ( 2 ) , ( 3 ) and ( 4 ) are equivalent to each other and have @xmath53 . because unitary transformations leave the identity matrix invariant , the same argument implies that ( 5 ) , ( 6 ) and ( 7 ) are equivalent to each other and once again @xmath53 . the cases ( 8) , ( 9 ) and ( 10 ) involve a pair of pauli matrices and are equivalent to each other . in ( 8) the hamiltonian has a discrete symmetry @xmath54 , often called a particle - hole symmetry . the cases ( 9 ) and ( 10 ) have the same discrete symmetry with respect to @xmath26 and @xmath27 . the case ( 10 ) has been analyzed by hikami _ et al._@xcite for a spin degenerate nonrelativistic lll . when @xmath55 , dos diverges at the band center and has two symmetrically located peaks away from it . the ld transition takes place at these three distinct energies . away from the band center the ld transition has the exponent @xmath56 and the transition at the band center corresponds to a different exponent . if @xmath57 , the divergence of the dos at the band center disappears , but the two symmetrically placed peaks away from the band center still exist . we find that the ld transition at these two energies hve continuously varying exponents depending on the ratio @xmath58 . the cases ( 11 ) , ( 12 ) and ( 13 ) are equivalent . the hamiltonians in these cases are respectively the hamiltonians for the cases ( 8) , ( 9 ) and ( 10 ) , augmented by the identity matrix corresponding to the potential disorder . potential disorder breaks the discrete symmetry mentioned above , and there is no divergence of the dos at the band center . the dos is still peaked at two symmetrically placed energies away from the band center . the ld transitions occur at energies away from the band center . if @xmath28 is much smaller than the two remaining coupling constants , @xmath59 follows trends similar to ( 8) , ( 9 ) , and ( 10 ) . if @xmath28 is comparable or larger , we find @xmath60 . in ( 14 ) all three pauli matrices are present . the discrete symmetry of ( 8) , ( 9 ) and ( 10 ) are absent , and the ld transitions take place at two symmetrically placed energies away from the band center . when all the coupling constants are equal , the exponent @xmath61 . depending on the relative strengths of the coupling constants the exponents vary continuously . if any particular coupling constant is significantly larger than the rest , @xmath60 . by adding @xmath28 we obtain ( 15 ) . if @xmath28 is smaller than the rest , the situation is similar to ( 14 ) . if @xmath28 is larger than the rest , @xmath60 . when @xmath63 , the ld transitions occur at two symmetrically placed energies about the band center , and these energies are greater than or equal to @xmath22 . in the absence of internode scattering , the transitions occur at @xmath64 and the exponent @xmath60 . if the strength of the intranode scattering is larger than @xmath22 , the bands at @xmath65 overlap and effectively correspond to the nodally degenerate case . if @xmath46 and only one of the internode couplings is present , the dos diverges at @xmath64 with an exponent of 0.5 and is identically zero for @xmath66 . the ld transitions occur at @xmath64 and have a continuously varying exponent . when the disorder is strong compared to @xmath22 , @xmath60 , and , in the opposite limit , @xmath59 approaches unity . if we include small intranode scattering the situation is similar . if the intranode scattering strength is greater than the internode scattering , @xmath60 . when @xmath67 and both internode couplings are present , the dos diverges at @xmath64 with an exponent @xmath68 . however , the ld transitions occur at energies larger than @xmath69 . we have analyzed a case where @xmath55 . the exponent varies continuously . if the internode scattering strength is larger than @xmath22 , @xmath70 , and in the opposite limit @xmath59 approaches unity . this behavior is stable against intranode scattering if its strength is smaller than both @xmath22 and the internode scattering . if intranode scattering strength is larger than the internode scattering , @xmath60 . our paper is organized as follows : in sec . ii we describe the dirac fermion model . in sec . iii we describe various possible disorders and their forms when projected to the lll . in sec iv we calculate the averaged density of states using supersymmetry . in the sections v , vi , and vii we describe the numerical studies of the ld transition projected to the lowest landau level . section viii is a brief concluding section . in the appendix [ appendixa ] we provide some mathematical details of the density of states calculation . in appendix [ appendixb ] we describe the recursive green function technique used for numerical calculations and finally in appendix [ appendixc ] we outline the procedure of data collapse involved in the finite size scaling of the localization length .

we investigate , analytically and numerically , the effects of disorder on the density of states and on the localization properties of the relativistic two dimensional fermions in the lowest landau level . employing a supersymmetric technique we use a numerical technique to establish the localization - delocalization ( ld ) transition in the lowest landau level . for some types of disorder the ld transition is shown to belong to a different universality class , as compared to the corresponding nonrelativistic problem . the results are relevant to the integer quantum hall plateau transitions observed in graphene .

we investigate , analytically and numerically , the effects of disorder on the density of states and on the localization properties of the relativistic two dimensional fermions in the lowest landau level . employing a supersymmetric technique , we calculate the exact density of states for the cauchy ( lorentzian ) distribution for various types of disorders . we use a numerical technique to establish the localization - delocalization ( ld ) transition in the lowest landau level . for some types of disorder the ld transition is shown to belong to a different universality class , as compared to the corresponding nonrelativistic problem . the results are relevant to the integer quantum hall plateau transitions observed in graphene .

1601.00549

i

boosting is considered as one of the most important ensemble learning methods in the machine learning literature and it is extensively used in several different real life applications from classification to regression ( @xcite ) . as an ensemble learning method ( @xcite ) , boosting combines several parallel running `` weakly '' performing algorithms to build a final `` strongly '' performing algorithm ( @xcite ) . this is accomplished by finding a linear combination of weak learning algorithms in order to minimize the total loss over a set of training data commonly using a functional gradient descent ( @xcite ) . boosting is successfully applied to several different problems in the machine learning literature including classification ( @xcite ) , regression ( @xcite ) , and prediction ( @xcite ) . however , significantly less attention is given to the idea of boosting in online regression framework . to this end , our goal is ( a ) to introduce a new boosting approach for online regression , ( b ) derive several different online regression algorithms based on the boosting approach , ( c ) provide mathematical guarantees for the performance improvements of our algorithms , and ( d ) demonstrate the intrinsic connections of boosting with the adaptive mixture - of - experts algorithms ( @xcite ) and data reuse algorithms ( @xcite ) . although boosting is initially introduced in the batch setting ( @xcite ) , where algorithms boost themselves over a fixed set of training data , it is later extended to the online setting ( @xcite ) . in the online setting , however , we neither need nor have access to a fixed set of training data , since the data samples arrive one by one as a stream ( @xcite ) . each newly arriving data sample is processed and then discarded without any storing . the online setting is naturally motivated by many real life applications especially for the ones involving big data , where there may not be enough storage space available or the constraints of the problem require instant processing ( @xcite ) . therefore , we concentrate on the online boosting framework and propose several algorithms for online regression tasks . in addition , since our algorithms are online , they can be directly used in adaptive filtering applications to improve the performance of conventional mixture - of - experts methods ( @xcite ) . for adaptive filtering purposes , the online setting is especially important , where the sequentially arriving data is used to adjust the internal parameters of the filter , either to dynamically learn the underlying model or to track the nonstationary data statistics ( @xcite ) . specifically , we have @xmath0 parallel running weak learners ( wl ) ( @xcite ) that receive the input vectors sequentially . each wl uses an update method , such as the second order newton s method ( nm ) or stochastic gradient descent ( sgd ) , depending on the target of the applications or problem constraints ( @xcite ) . after receiving the input vector , each algorithm produces its output and then calculates its instantaneous error after the observation is revealed . in the most generic setting , this estimation / prediction error and the corresponding input vector are then used to update the internal parameters of the algorithm to minimize a priori defined loss function , e.g. , instantaneous error for the sgd algorithm . these updates are performed for all of the @xmath0 wls in the mixture . however , in the online boosting approaches , these adaptations at each time proceed in rounds from top to bottom , starting from the first wl to the last one to achieve the `` boosting '' effect ( @xcite ) . furthermore , unlike the usual mixture approaches ( @xcite ) , the update of each wl depends on the previous wls in the mixture . in particular , at each time @xmath1 , after the @xmath2 wl calculates its error over @xmath3 pair , it passes a certain weight to the next wl , the @xmath4 wl , quantifying how much error the constituent wls from @xmath5 to @xmath2 made on the current @xmath3 pair . based on the performance of the wls from @xmath6 to @xmath7 on the current @xmath3 pair , the @xmath4 wl may give a different emphasis ( importance weight ) to @xmath3 pair in its adaptation in order to rectify the mistake of the previous wls . the proposed idea for online boosting is clearly related to the adaptive mixture - of - experts algorithms widely used in the machine learning literature , where several parallel running adaptive algorithms are combined to improve the performance . in the mixture methods , the performance improvement is achieved due to the diversity provided by using several different adaptive algorithms each having a different view or advantage ( @xcite ) . this diversity is exploited to yield a final combined algorithm , which achieves a performance better than any of the algorithms in the mixture . although the online boosting approach is similar to mixture approaches ( @xcite ) , there are significant differences . in the online boosting notion , the parallel running algorithms are not independent , i.e. , one deliberately introduces the diversity by updating the wls one by one from the first wl to the @xmath8 wl for each new sample based on the performance of all the previous wls on this sample . in this sense , each adaptive algorithm , say the @xmath4 wl , receives feedback from the previous wls , i.e. , @xmath5 to @xmath2 , and updates its inner parameters accordingly . as an example , if the current @xmath3 is well modeled by the previous wls , then the @xmath4 wl performs minor update using @xmath3 and may give more emphasis ( importance weight ) to the later arriving samples that may be worse modeled by the previous wls . thus , by boosting , each adaptive algorithm in the mixture can concentrate on different parts of the input and output pairs achieving diversity and significantly improving the gain . the linear online learning algorithms , such as sgd or nm , are among the simplest as well as the most widely used regression algorithms in the real - life applications ( @xcite ) . therefore , we use such algorithms as base wls in our boosting algorithms . to this end , we first apply the boosting notion to several parallel running linear nm - based wls and introduce three different approaches to use the importance weights ( @xcite ) , namely `` weighted updates'',``data reuse '' , and `` random updates '' . in the first approach , we use the importance weights directly to produce certain weighted nm algorithms . in the second approach , we use the importance weights to construct data reuse adaptive algorithms ( @xcite ) . however , data reuse in boosting , such as ( @xcite ) , is significantly different from the usual data reusing approaches in adaptive filtering ( @xcite ) . as an example , in boosting , the importance weight coming from the @xmath2 wl determines the data reuse amount in the @xmath4 wl , i.e. , it is not used for the @xmath2 filter , hence , achieving the diversity . the third approach uses the importance weights to decide whether to update the constituent wls or not , based on a random number generated from a bernoulli distribution with the parameter equal to the weight . the latter method can be effectively used for big data processing ( @xcite ) due to the reduced complexity . the output of the constituent wls is also combined using a linear mixture algorithm to construct the final output . we then update the final combination algorithm using the sgd algorithm ( @xcite ) . furthermore , we extend the boosting idea to parallel running linear sgd - based algorithm similar to the nm case . we start our discussions by investigating the related works in section [ sec : rel_work ] . we then introduce the problem setup and background in section [ sec : problem ] , where we provide individual sequence as well as mse convergence results for the nm and sgd algorithms . we introduce our generic boosted online regression algorithm in section [ sec : bora ] and provide the mathematical justifications for its performance . then , in sections [ sec : brls ] and [ sec : blms ] , three different variants of the proposed boosting algorithm are derived , using the nm and sgd , respectively . then , in section [ sec : analysis ] we provide the mathematical analysis for the computational complexity of the proposed algorithms . the paper concludes with extensive sets of experiments over the well known benchmark data sets and simulation models widely used in the machine learning literature to demonstrate the significant gains achieved by the boosting notion .

in addition , we implement several variants of the proposed generic algorithm . we demonstrate an intrinsic relationship , in terms of boosting , between the adaptive mixture - of - experts and data reuse algorithms . furthermore , we provide theoretical bounds for the computational complexity of our proposed algorithms . we demonstrate substantial performance gains in terms of mean square error over the base learners through an extensive set of benchmark real data sets and simulated examples .

we investigate boosted online regression and propose a novel family of regression algorithms with strong theoretical bounds . in addition , we implement several variants of the proposed generic algorithm . we specifically provide theoretical bounds for the performance of our proposed algorithms that hold in a strong mathematical sense . we achieve guaranteed performance improvement over the conventional online regression methods without any statistical assumptions on the desired data or feature vectors . we demonstrate an intrinsic relationship , in terms of boosting , between the adaptive mixture - of - experts and data reuse algorithms . furthermore , we introduce a boosting algorithm based on random updates that is significantly faster than the conventional boosting methods and other variants of our proposed algorithms while achieving an enhanced performance gain . hence , the random updates method is specifically applicable to the fast and high dimensional streaming data . specifically , we investigate newton method - based and stochastic gradient descent - based linear regression algorithms in a mixture - of - experts setting , and provide several variants of these well known adaptation methods . however , the proposed algorithms can be extended to other base learners , e.g. , nonlinear , tree - based piecewise linear . furthermore , we provide theoretical bounds for the computational complexity of our proposed algorithms . we demonstrate substantial performance gains in terms of mean square error over the base learners through an extensive set of benchmark real data sets and simulated examples .

1601.00549

c

we introduced a novel family of boosted online regression algorithms and proposed three different boosting approaches , i.e. , weighted updates , data reuse , and random updates , which can be applied to different online learning algorithms . we provide theoretical bounds for the mse performance of our proposed methods in a strong mathematical sense . we emphasize that while using the proposed techniques , we do not assume any prior information about the statistics of the desired data or feature vectors . we show that by the proposed boosting approaches , we can significantly improve the mse performance of the conventional sgd and nm algorithms . moreover , we provide an upper bound for the weights generated during the algorithm that leads us to a thorough analysis of the computational complexity of these methods . the computational complexity of the random updates method is remarkably lower than that of the conventional mixture - of - experts and other variants of the proposed boosting approaches , without degrading the performance . therefore , the boosting using random updates approach is an elegant alternative to the conventional mixture - of - experts method when dealing with real life large scale problems . we provide several results that demonstrate the strength of the proposed algorithms over a wide variety of synthetic as well as real data .

we specifically provide theoretical bounds for the performance of our proposed algorithms that hold in a strong mathematical sense . furthermore , we introduce a boosting algorithm based on random updates that is significantly faster than the conventional boosting methods and other variants of our proposed algorithms while achieving an enhanced performance gain .

we investigate boosted online regression and propose a novel family of regression algorithms with strong theoretical bounds . in addition , we implement several variants of the proposed generic algorithm . we specifically provide theoretical bounds for the performance of our proposed algorithms that hold in a strong mathematical sense . we achieve guaranteed performance improvement over the conventional online regression methods without any statistical assumptions on the desired data or feature vectors . we demonstrate an intrinsic relationship , in terms of boosting , between the adaptive mixture - of - experts and data reuse algorithms . furthermore , we introduce a boosting algorithm based on random updates that is significantly faster than the conventional boosting methods and other variants of our proposed algorithms while achieving an enhanced performance gain . hence , the random updates method is specifically applicable to the fast and high dimensional streaming data . specifically , we investigate newton method - based and stochastic gradient descent - based linear regression algorithms in a mixture - of - experts setting , and provide several variants of these well known adaptation methods . however , the proposed algorithms can be extended to other base learners , e.g. , nonlinear , tree - based piecewise linear . furthermore , we provide theoretical bounds for the computational complexity of our proposed algorithms . we demonstrate substantial performance gains in terms of mean square error over the base learners through an extensive set of benchmark real data sets and simulated examples .

1004.1417

i

constructing models of inflation in string theory is an active field , for reviews see e.g. @xcite . because string theory naturally has many dynamical degrees of freedom , multi - field models of inflation are also common . examples are inflation from axions @xcite , tachyons @xcite , m5-branes @xcite or multiple d - branes @xcite to name a few . if many degrees of freedom are present , it is natural for them to decay or stabilize during inflation one after the other . a phenomenological approach to recover some of the effects caused by decaying fields was proposed in @xcite and dubbed staggered inflation . @xcite relies on coarse graining , assuming that many fields decay in any given hubble time , which may or may not be the case in concrete models . in this paper , we set out to investigate a single decay in detail to extract analytically the consequences for cosmological perturbations . as a simple and yet non - trivial framework , we choose the kklmmt @xcite brane inflation @xcite set up . in this proposal , inflation is driven by a brane - antibrane pair , located in a warped throat generated by the background branes and fluxes @xcite . inflation ends when the distance between the mobile brane and the antibrane reaches the string scale and a tachyon is formed . after the brane - antibrane collision , the energy stored in their tensions is released into light closed string modes , which can ignite reheating . we extend this proposal by including two mobile stacks with @xmath1 and @xmath2 branes respectively and @xmath3 antibranes at the tip of the throat . we assume that the stacks are separated from each other so the stack closer to the tip , say stack one , annihilates first during inflation . this collision results in particle production during inflation and a sudden change in the inflationary potential . we would like to examine some effects of the produced particles via the change in the equation of state parameter on the power - spectrum of cosmological perturbations . inflation ends when the remaining stack of @xmath2 branes annihilates with the background s @xmath2 antibranes . this extension does not improve upon the back - reaction and fine - tuning issues of the kklmmt proposal @xcite , but provides a well motivated toy model in string theory . to handle the analysis , we assume that perturbations in the effective field describing the first stack , @xmath4 , are taken over by the radiation bath , decaying quickly after the annihilation event . hence , we focus on perturbations in the remaining field only , @xmath5 . for this simplification to be consistent , we assume that @xmath6 . we derive asymptotic solutions in the two slow - roll regimes before and after the collision for this field , which we match at the collision time . treating the mechanism of tachyon formation and the collision as instantaneous events , we use the israel junction conditions @xcite to provide the matching conditions , which boil down to the continuity of the bardeen potential @xmath7 and the curvature perturbation @xmath8 in the case at hand . it is in these matching conditions that the jump in the equation of state parameter enters . we then compute the power - spectrum of curvature perturbations and find a slightly redder spectrum on scales that were super - horizon at the time of the first stack s annihilation . on sub - horizon scales , we find an oscillatory modulation of the power spectrum . the concrete outline of this paper is as follows : we review and extend the kklmmt setup in sec . [ kklmmt ] before deriving the background , slow - roll solution in sec . [ sec : bgr ] . perturbations are discussed in sec . [ sec : pertub ] , with the matching conditions in sec . [ sec : matching ] and the bogoliubov coefficients in sec . [ sec : bogol ] . these coefficients enable the computation of the power - spectrum in sec . [ sec : powersp ] , which we expand for super- and sub - horizon scales in sec . [ sec : suph ] and sec . [ sec : subh ] . we conclude in sec . [ sec : concl ] .

the stack closest to the bottom of the throat annihilates first with antibranes , resulting in particle production and a change of the equation of state parameter . we find an oscillatory modulation of the power - spectrum for scales within the horizon at the time of the collision , and a slightly redder spectrum on super - horizon scales . we comment on implications for staggered inflation .

we investigate brane inflation driven by two stacks of mobile branes in a throat . the stack closest to the bottom of the throat annihilates first with antibranes , resulting in particle production and a change of the equation of state parameter . we calculate analytically some observable signatures of the collision ; related decays are common in multi - field inflation , providing the motivation for this case study . the discontinuity in enters the matching conditions relating perturbations in the remaining degree of freedom before and after the collision , affecting the power - spectrum of curvature perturbations . we find an oscillatory modulation of the power - spectrum for scales within the horizon at the time of the collision , and a slightly redder spectrum on super - horizon scales . we comment on implications for staggered inflation .

0901.1723

c

in the present work , the ta and the mqt escape process of the ybco josephson junction coupled to the lc circuit has been analyzed by taking into account the anisotropy of the mass and the two - dimensional nature of the phase dynamics . based on the feynman - vernon approach , the effective one - dimensional action is derived by integrating out the degree of freedom of the lc circuit . we found that the coupling to the lc circuit gives negligible reduction for ta escape rate . on the other hand , we also found that the mqt escape rate is considerably reduced due to the coupling between the junction and the lc circuit . more importantly , the temperature dependence of the mqt escape rate for the ybco junction coupled with the lc circuit is quite different from that without the lc circuit . these theoretical results are in an excellent agreement with experimental data of the ybco biepitaxial josephson junction . @xcite therefore we can conclude that _ the anisotropy of the mass and the two - dimensional nature of the potential profile due to the coupling to the lc circuit are quite important and essential to understand macroscopic quantum phenomena and qubit operation in such systems . _ there , however , remain a question , which can not be treated by the present approach . as seen from fig . 5 , the extended circuit model can not explain a hump structure of @xmath225 near 0.1 k. @xcite we note that such a characteristic behavior has been observed in a dc - squid ( superconducting quantum interference device ) system composed only by low-@xmath4 superconductors . @xcite while the deviation between our theory and the experimental data is left for a future problem , it might be attributed to the fact that our model neglects thermal / dynamical population from the quasi - ground state to the excited states in the metastable well . we note that in the nonadiabatic cases ( @xmath237 ) corresponding to the mqt experiment for the ybco biepitaxial junction @xcite more quantum levels due to excitation of the lc circuit are relevant to the decay process than in a simple one - dimensional system . in order to investigate the thermal / dynamical population effect , we have to solve a master equation to obtain population probabilities of each level by the larkin and ovchinnikov theory . @xcite this consideration may explain the anomaly of the escape rate @xmath203 near the crossover temperature . finally we would like to comment advantages of the junction - lc coupling to the qubit and quantum optics applications . the system that we considered in this paper can be regarded as an artificial atom ( the josephson junction ) coupled to the quantized electromagnetic field ( the lc circuit ) . therefore the appearance of several interesting phenomena relating to quantum optics , @xcite e.g. , the vacuum rabi oscillation , @xcite generation of a non - classical state of the lc system , @xcite and laser oscillation @xcite is expected also in the ybco biepitaxial junctions . additionally the lc circuit will act as a quantum information bus . @xcite therefore the entanglement or the coupling between separated high-@xmath4 qubits and eventually a high-@xmath4 version of the circuit - qed system @xcite will be realized in such biepitaxial junctions . these studies will open up the possibility of future applications for high-@xmath4 superconductor materials . we would like to thank j. ankerhold , a. barone , m. fogelstrm , a. a. golubov , d. r. gulevich , g. johansson , j. r. kirtley , t. lfwander , f. lombardi , j. p. pekola , g. rotoli , v. s. shumeiko , and f. tafuri for useful discussions . one of the authors ( s. k. ) would like to thank the applied quantum physics laboratory at the chalmers university of technology for its hospitality during the course of this work . this work was supported by nano - ned program under project no . tcs.7029 , crest ( jst ) , eu nanoxide , eu strep project midas , the swedish research council ( vr ) under the linnaeus center on engineered quantum systems , the swedish research council ( vr ) under the project macroscopic quantum tunneling and coherence in superconductive d - wave junctions , the knut and alice wallenberg foundation , the swedish foundation for strategic research ( ssf ) under the project oxide , and the jsps - rsas scientist exchange program .

we investigate classical thermal activation ( ta ) and macroscopic quantum tunneling ( mqt ) for a ybacuo(ybco ) josephson junction coupled to an lc circuit theoretically . due to the coupling between the junction and the lc circuit , these results are in an excellent agreement with recent experimental data for the mqt and ta rate in a ybco biepitaxial josephson junction .

we investigate classical thermal activation ( ta ) and macroscopic quantum tunneling ( mqt ) for a ybacuo(ybco ) josephson junction coupled to an lc circuit theoretically . due to the coupling between the junction and the lc circuit , the macroscopic phase dynamics can be described as the escape process of a fictitious particle with an mass moving in a _ two - dimensional _ potential . we analytically calculate the escape rate including both the ta and mqt regime by taking into account the peculiar dynamical nature of the system . in addtion to large suppression of the mqt rate at zero temperature , we study details of the temperature dependece of the escape rate across a crossover region . these results are in an excellent agreement with recent experimental data for the mqt and ta rate in a ybco biepitaxial josephson junction . therefore the coupling to the lc circuit is essential in understanding the macroscopic quantum dynamics and the qubit operation based on the ybco biepitaxial josephson junctions .

1204.1319

i

the color glass condensate ( cgc ) formalism has been successfully applied to many processes in high energy collisions involving at least one hadron or nucleus in the initial state . examples are structure functions ( inclusive and diffractive ) in deeply inelastic scattering of electrons on protons or nuclei , and particle production in proton - proton , proton - nucleus and nucleus - nucleus collisions , for a recent review see ref.@xcite . the predicted suppression of @xmath2 for the single inclusive hadron production in deuteron - nucleus ( da ) collisions as well as the disappearance of the away side peak in di - hadron angular correlations in the forward rapidity region of rhic @xcite are two of most robust predictions of the formalism which have been confirmed @xcite , see also refs.@xcite . the cgc formalism has been also successful in providing predictions for the first lhc data @xcite in proton - proton ( pp ) and nucleus - nucleus collisions @xcite . nevertheless , there are more recent , alternative phenomenological approaches which combine nuclear shadowing , transverse momentum broadening and cold matter energy loss to describe the rhic data @xcite . therefore , one needs to consider other observables which may help clarify the underlying dynamics of forward rapidity particle production at small @xmath0 . inclusive prompt photon production @xcite and prompt photon - hadron angular correlations @xcite in the forward rapidity region are two such examples . furthermore , there are advantages to studying prompt photon production as compared to hadron production . it is theoretically cleaner ; one avoids the difficulties involved with description of hadronization of final state quarks and gluons , usually described by fragmentation functions valid at high transverse momentum . also , one does not have to worry about possible initial state - final state interference effects which may be present for hadron production . in case of photon - hadron vs. di - hadron angular correlations , again the underlying theoretical understanding is more robust . unlike di - hadron correlations which involve higher number of wilson lines @xcite , photon - hadron correlations depend only on the dipole cross section properties of which are well understood . both processes have been investigated previously , albeit not in detail and only in a limited kinematic range @xcite , see also refs.@xcite . in this work , we extend the existing results for inclusive prompt photon production by clearly separating the contribution of direct and fragmentation photons . we show that direct photons are more sensitive to gluon saturation effects in the kinematics regions considered . we then investigate the dependence of prompt photon - hadron azimuthal angular correlations on high gluon density effects and show that gluon saturation effects lead to disappearance of the away side peak . the effect is very similar to the disappearance of the away side peak in di - hadron correlations observed in the forward rapidity region of rhic in da collisions @xcite . therefore , a measurement of this correlation at rhic and the lhc would greatly help to clarify the role of cgc in the dynamics of particle production at high energy . the advantage of the cgc formalism over the more phenomenological models is that the cross section for many of these processes have the same common ingredient @xcite , the dipole total cross section ; the imaginary part of the forward scattering amplitude of a quark - antiquark dipole on a proton or nucleus target . its rapidity ( energy ) dependence is governed by the b - jimwlk / bk evolutions equations @xcite and is pretty well - understood . the most recent advances in our understanding of the rapidity dependence of the dipole cross section include the running coupling constant corrections and the full next - to - leading order corrections @xcite . the only input is the dipole profile ( dependence on the dipole size @xmath3 ) at the initial rapidity @xmath4 which is modeled , usually motivated by the mclerran - venugopalan ( mv ) model @xcite . the sensitivity to this initial condition is expected to go away at very large rapidities , see sec . iii and ref.@xcite . this paper is organized as follows ; we consider prompt photon - hadron production cross section in section iia and inclusive prompt photon production in section iib where we describe how to separate the contribution of direct and fragmentation photons . we then present our detailed numerical results and predictions at kinematics appropriate for rhic and the lhc experiments in section iii . we summarize our results in section iv .

we then analyze azimuthal correlations in photon - hadron production in high energy proton - nucleus collisions and obtain a strong suppression of the away - side peak in photon - hadron correlations at forward rapidities , similar to the observed mono - jet production in deuteron - gold collisions at forward rapidity at rhic .

we investigate inclusive prompt photon and semi - inclusive prompt photon - hadron production in high energy proton - nucleus collisions using the color glass condensate ( cgc ) formalism which incorporates non - linear dynamics of gluon saturation at small via balitsky - kovchegov equation with running coupling . for inclusive prompt photon production , we rewrite the cross - section in terms of direct and fragmentation contributions and show that the direct photon ( and isolated prompt photon ) production is more sensitive to gluon saturation effects . we then analyze azimuthal correlations in photon - hadron production in high energy proton - nucleus collisions and obtain a strong suppression of the away - side peak in photon - hadron correlations at forward rapidities , similar to the observed mono - jet production in deuteron - gold collisions at forward rapidity at rhic . we make predictions for the nuclear modification factor and photon - hadron azimuthal correlations in proton(deuteron)-nucleus collisions at rhic and the lhc at various rapidities .

1204.1319

i

we have investigated prompt photon production and prompt photon - hadron azimuthal angular correlations in proton - proton and proton - nucleus collisions using the color glass condensate formalism . we have provided predictions in the kinematic regions appropriate to rhic and the lhc experiments . we have shown that single inclusive and direct prompt photon production cross section in p(d)a collisions at forward rapidities at both rhic and the lhc is suppressed , as compared to normalized production cross section in proton - proton collisions . at rhic , a good portion of the predicted suppression is due to the projectile being a deuteron rather than a proton . this suppression is larger at the lhc compared to rhic which is even more impressive given that the projectile at the lhc is a proton . we showed that direct photon production is most affected by gluon saturation effects in the target nucleus than the fragmentation photons . however , at the lhc energies at forward rapidities the nuclear modification suppression for direct , fragmentation and inclusive prompt photon production is rather similar . we showed that the nuclear modification factor @xmath90 for inclusive prompt photon production at rhic and the lhc is a sensitive probe of small - x dynamics . we note that our results based on gluon saturation dynamics and using the color glass condensate formalism are different from those coming from the collinear factorization @xcite . therefore , @xmath90 measurement at rhic and the lhc is a crucial test of different factorization schemes , see also refs.@xcite for other observables . we have also studied prompt photon - hadron azimuthal angular correlations in kinematic regions which can be probed by rhic and the lhc experiments . it is shown that the away side peak in photon - hadron angular correlation goes away as one lowers the final state particle s momenta , very similarly to the disappearance of the away side peak in di - hadron correlations in forward rapidity da collisions at rhic . at fixed transverse momenta , the suppression of the away side peak gets stronger as one goes to larger rapidities ( more forward ) or higher energy or denser system as expected , due to stronger saturation effects in the target nucleus . presently , we are not aware of any alternative approach which leads to this novel phenomenon . note that in contrast to the nuclear modification factor for prompt photon , the prompt photon - hadron azimuthal angular correlation defined via eq.([az ] ) is free from the isospin effect , and can be considered as a cleaner probe of saturation effect . finally , we emphasize that prompt photon - hadron azimuthal angular correlations suffers from much less theoretical uncertainties as compared to di - hadron azimuthal angular correlations and thus a measurement of this correlation would go a long way toward establishing the dominance of gluon saturation effects at small @xmath25 . it will be interesting to see what the predictions of pqcd - motivated models @xcite are for photon - hadron azimuthal angular correlations . in these models one usually needs to combine models of higher twist shadowing , the cronin effect and cold matter energy loss in order to describe the data on single inclusive hadron production and di - hadron azimuthal angular correlations . the advantage of the cgc formalism is that the same framework can be used to describe nuclear shadowing of structure functions @xcite at small @xmath0 and includes transverse momentum broadening ( the cronin effect ) @xcite . it does not however include cold matter energy loss due to longitudinal momentum transfer between the projectile and the target which may be important at the very forward rapidities . it is not clear at the moment how to calculate this effect from first principles qcd . even though this energy loss itself is small , due to steepness of the production cross section at forward rapidity , it can suppress the cross section significantly . the purpose of this appendix is to define the kinematics and derive the needed relations between various light - cone energy fractions which appear in the production cross sections used . this is slightly different from the standard relations used in production cross sections based on collinear factorization theorems of pqcd . we first consider scattering of a quark on the target where a photon and a quark are produced , depicted in fig . 1 , q(p ) a ( p_a)(k ) q(l ) x , where @xmath11 is a label for the multi - gluon state , described by a classical field representing a proton or nucleus target . in the standard pqcd ( leading twist ) kinematics , only one parton from the target interacts . this is not the case here since the target is described by a classical gluon field representing a multi - gluon state with intrinsic momentum rather than an individual gluon with a well defined energy fraction @xmath25 and zero transverse momentum . nevertheless , since most of the gluons in the target wave function have momentum of order @xmath148 , one can think of the state describing the target as being labeled by a ( four ) momentum @xmath149 . in this sense , the gluons in the target collectively carry fraction @xmath25 of the target energy and have intrinsic transverse momentum denoted @xmath150 . this also means that there is no integration over @xmath25 in our case unlike the collinearly factorized cross sections in pqcd ( this basically corresponds to setting @xmath25 equal to the lower limit of @xmath25 integration in pqcd cross sections ) . we thus have @xmath151 where @xmath152 are the momenta of the incoming projectile , target and the produced hadron respectively . ( pseudo)-rapidities of the produced quark and photon are related to their energies via @xmath153 imposing energy - momentum conservation at the partonic level via @xmath154 and using leads to @xmath155 the above relations and ( and the on mass shell condition ) can be used to derive the following expressions for the energy fractions @xmath156 . we obtain , @xmath157 where the final hadron transverse momentum and rapidity are denoted by @xmath27 and @xmath158 , and we used @xmath159 . note that light - cone momentum fraction @xmath25 appears in the dipole forward scattering amplitude @xmath19 whereas @xmath13 is the fraction of the projectile proton ( deuteron ) carried by the incident quark , see . to derive an expression for the lower limit of @xmath31 integration in , we note that @xmath160 . using the relation between the minus components of the four momenta given above , we get x_q = k^- + . the minimum value of @xmath31 occurs when @xmath13 is maximum , i.e. , @xmath161 . we then have z_f^min = q^- - k^- , which can be written in terms of the transverse momenta and rapidities of the final state hadron and photon as z_f^min = e^_h 1 - e^_. we now consider the kinematics of single inclusive photon production cross section . the cross section is obtained from by integrating over the final state quark momenta . this requires some care as we have now explicitly separated direct and fragmentation photons in . again using eqs.([a1 ] , [ a2 ] , [ a31 ] ) , we obtain the following relation , x_g=(k_te^-_+ ) , [ xg1 ] where opposite to , we avoided to introduce @xmath158 and @xmath31 . one can use the energy - momentum delta functions in to obtain the following relation , where the parameter @xmath114 is the fraction of energy of parton carried away by photon and it is defined as follows , z = e^_. in case of direct photons with transverse momentum @xmath52 , one should shift momentum @xmath36 in ( this is how we obtained the expersion ) . assuming that @xmath162 , we get [ a6 ] |x_g = , where we have now used @xmath58 to denote the light cone momentum fraction of the target carried by gluons for production of direct photons so as to distinguish it from the momentum fraction involved in production of fragmentation photons . in the later case , the integration variable @xmath43 has been shifted twice . implementing the shifts in and noting that the @xmath43 integration in the fragmentation photon production cross section is dominated by its singularity at @xmath163 we get , for fragmentation photons , x_g=. we are grateful to javier albacete for useful communications and for providing us with the latest tables for the numerical solution of rcbk equation . we would also like to thank william brooks and raju venugopalan for useful discussions . we acknowledge and thank barbara jacak , john lajoie and richard seto for helpful discussions about phenix detector capabilities . is supported in part by the doe office of nuclear physics through grant no . de - fg02 - 09er41620 , from the `` lab directed research and development '' grant ldrd 10 - 043 ( brookhaven national laboratory ) , and from the city university of new york through the psc - cuny research program , grant 64554 - 00 42 . the work of a.h.r is supported in part by fondecyt grants 1110781 . f. gelis , e. iancu , j. jalilian - marian and r. venugopalan , ann . nucl . part . * 60 * , 463 ( 2010 ) [ arxiv:1002.0333 ] ; 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we investigate inclusive prompt photon and semi - inclusive prompt photon - hadron production in high energy proton - nucleus collisions using the color glass condensate ( cgc ) formalism which incorporates non - linear dynamics of gluon saturation at small via balitsky - kovchegov equation with running coupling . for inclusive prompt photon production , we rewrite the cross - section in terms of direct and fragmentation contributions and show that the direct photon ( and isolated prompt photon ) production is more sensitive to gluon saturation effects . we make predictions for the nuclear modification factor and photon - hadron azimuthal correlations in proton(deuteron)-nucleus collisions at rhic and the lhc at various rapidities .

we investigate inclusive prompt photon and semi - inclusive prompt photon - hadron production in high energy proton - nucleus collisions using the color glass condensate ( cgc ) formalism which incorporates non - linear dynamics of gluon saturation at small via balitsky - kovchegov equation with running coupling . for inclusive prompt photon production , we rewrite the cross - section in terms of direct and fragmentation contributions and show that the direct photon ( and isolated prompt photon ) production is more sensitive to gluon saturation effects . we then analyze azimuthal correlations in photon - hadron production in high energy proton - nucleus collisions and obtain a strong suppression of the away - side peak in photon - hadron correlations at forward rapidities , similar to the observed mono - jet production in deuteron - gold collisions at forward rapidity at rhic . we make predictions for the nuclear modification factor and photon - hadron azimuthal correlations in proton(deuteron)-nucleus collisions at rhic and the lhc at various rapidities .

0908.4129

i

the most important factor that determines whether a massive star can form or not is its mass accretion rate ( larson & starrfield 1971 ; for recent reviews , see mckee & ostriker 2007 ; zinnecker & yorke 2007 ) . it follows from the fact that the outward radiative force on the accretion flow onto a forming massive star increases rapidly with the stellar mass . if the mass accretion rate is too low , there would be insufficient ram pressure to overcome the radiation pressure near the dust sublimation radius , and the infall would be choked . in the spherical model of wolfire & cassinelli ( 1987 ) , the required minimum accretion rate ranges from @xmath4 to @xmath5 for stars in the mass range @xmath6 , although the requirement can be relaxed somewhat if the accretion flow is flattened , by , e.g. , magnetic support ( nakano 1989 ) or rotation ( jijina & adams 1996 ) . in addition to overcoming the radiation pressure , a high accretion rate can also greatly modify the internal structure and appearance of a growing massive star ( e.g. , hosokawa & omukai 2009 ) . the associated high accretion luminosity may help heat up the region surrounding the protostar , perhaps suppressing the potential fragmentation that may adversely affect massive star formation at the early stages ( krumholz & mckee 2008 ) . a high mass accretion rate may not be difficult to achieve in principle , given that most , if not all , massive stars are thought to form in dense , massive , cluster - forming clumps ( mckee & ostriker 2007 ; zinnecker & yorke 2007 ) . for example , a parsec - sized dense clump of @xmath7 would have an average density of @xmath8 g @xmath9 , corresponding to a global free fall time @xmath10 myr . the ratio of the clump mass and free - fall time yields a characteristic accretion rate @xmath11 ( e.g. , cesaroni 2005 ) which , if channeled to a single object , would have a sufficiently large ram pressure to overcome the radiation pressure from even the most massive stars . in practice , the mass accretion rate onto any individual star will be reduced relative to the characteristic free - fall rate by several factors , such as the turbulence , magnetic fields , protostellar outflows , and radiative feedback . these factors are included in our simulations , except the last one . supersonic turbulence is observed ubiquitously in dense clumps of star cluster and massive star formation ( e.g. , garay 2005 ) . the turbulence is expected to reduce the mass accretion rate onto any individual star relative to @xmath12 in at least two ways . first , it resists the global collapse , thereby reducing the total amount of gas that collapses into stars per unit time . second , it fragments the clump material into many centers of collapse , creating a cluster of stars each accreting at a fraction of the total rate . these effects of the turbulence are difficult to quantify analytically ; numerical simulations are required ( mac low & klessen 2004 ) . for example , using sph simulation with sink particles , bonnell , bate & vine ( 2003 ) found that a dense turbulent clump of @xmath7 in mass and 0.5 pc in radius ( corresponding to @xmath13 ) produced a cluster of about 400 stars . in their simulation , the most massive star ( of 27 ) formed from an average accretion rate of order @xmath4 , much smaller than the global free - fall rate . in this paper , we will explore the effects of the turbulence on the stellar mass accretion further with a grid - based code , enzo , including adaptive mesh refinement ( amr ) and sink particles . the grid - based code also enables us to quantify , in addition , the effects of magnetic fields , which are generally difficult to treat in sph ( see , however , price & bate 2008 ) . there is ample observational evidence for magnetic fields in regions of massive star formation . in the nearest region of active massive star formation , omc1 , the well - ordered polarization vectors of submillimeter dust continuum leave little doubt that the ( slightly pinched ) magnetic field is dynamically important ( e.g. , vaillancourt et al . a cn zeeman measurement yields a line - of - sight field strength of 0.36 mg , corresponding to a magnetic energy density that is higher than the turbulent energy density and a mass - to - flux ratio ( before geometric correction ) that is 4.5 times higher than the critical value @xmath14 ( falgarone et al . the mass - to - flux ratio is close to the median value inferred by falgarone et al . for a sample of a dozen or so high - mass star forming regions where the cn zeeman measurements are made . their best estimate for the mean dimensionless mass - to - flux ratio ( in units of the critical value ) is @xmath15 after geometric corrections , although it can be uncertain by a factor of 2 in either direction . a goal of our calculations is to determine how a magnetic field of this magnitude affects the stellar mass accretion rate , using an mhd version of the enzo code ( wang & abel 2009 ) . the third element that we consider in this paper are protostellar outflows , which are routinely observed around forming stars of both low and high masses ( see the review by richer et al . their effects are expected to be particularly important in the dense clumps of active cluster formation , where many stars are formed close together in both space and time ( li & nakamura 2006 ; norman & silk 1980 ) . a case in point is the dense clump associated with the reflection nebula ngc 1333 in the perseus molecular cloud , which is sculpted by dozens of outflows detectable in co , optical forbidden lines and h@xmath16 emission ( sandell & knee 2001 ; walawender et al . 2008 ; maret et al . the outflows appear to inject enough momentum into the dense clump to replenish the turbulence dissipated in this region ( see , however , maury et al . 2009 for a discussion of ngc 2264 , where the current generation of active outflows appear incapable of supporting the cluster - forming clump ) . it is possible that a good fraction , perhaps the majority , of the cluster members are formed during the time when the clump turbulence is driven by protostellar outflows ( nakamura & li 2007 , matzner 2007 , carroll et al . 2008 , swift & welch 2008 ) . we will improve on the previous outflow feedback simulations of nakamura & li ( 2007 ) by including sink particles , making the outflow injection more continuous , and dramatically increasing the numerical resolution . these improvements enable us to evaluate the effects of the outflows on the accretion rates onto individual stars , especially massive stars , which are the focus of this paper . we will describe the properties of the lower mass cluster members formed in our simulations , including their mass distribution and spatial clustering , in a companion paper . the effects of radiative feedback , ignored in our current calculations , are discussed in [ limitation ] . the rest of the paper is organized as follows . in [ method ] , we describe the numerical method and simulation setup . these are followed by two result sections , focusing first on the global star formation history and clump dynamics ( [ global ] ) and then on the massive stars ( [ massivestars ] ) . we find that the massive stars in our simulations are formed through neither the collapse of pre - existing 0.1 pc - sized turbulent cores nor competitive accretion ; their formation is controlled to a large extent by the clump dynamics , which are found to be regulated strongly by the collective outflow feedback from all accreting stars and , to a lesser extent , by a moderate magnetic field . in [ discussion ] , we discuss this new scenario of outflow - regulated clump - fed " ( orcf for short ) massive star formation and contrast it with the existing scenarios . the last section contains a brief summary .

the calculations are carried out using a block structured adaptive mesh refinement code that solves the ideal mhd equations including self - gravity and implements accreting sink particles . the need for large - scale feeding makes the massive star formation prone to regulation by outflow feedback , which directly opposes the feeding processes . we conclude that the massive star formation in our simulated turbulent , magnetized , parsec - scale clump is outflow - regulated and clump - fed ( orcf for short ) . , we discuss the properties of the lower mass cluster members formed along with the massive stars , including their mass distribution and spatial clustering .

we investigate massive star formation in turbulent , magnetized , parsec - scale clumps of molecular clouds including protostellar outflow feedback using three dimensional numerical simulations of effective resolution . the calculations are carried out using a block structured adaptive mesh refinement code that solves the ideal mhd equations including self - gravity and implements accreting sink particles . we find that , in the absence of regulation by magnetic fields and outflow feedback , massive stars form readily in a turbulent , moderately condensed clump of ( containing initial jeans masses ) , along with a cluster of hundreds of lower mass stars . the massive stars are fed at high rates by ( 1 ) transient dense filaments produced by large - scale turbulent compression at early times , and ( 2 ) by the clump - wide global collapse resulting from turbulence decay at late times . in both cases , the bulk of the massive star s mass is supplied from outside a 0.1 pc - sized core " that surrounds the star . in our simulation , the massive star is clump - fed rather than core - fed . the need for large - scale feeding makes the massive star formation prone to regulation by outflow feedback , which directly opposes the feeding processes . the outflows reduce the mass accretion rates onto the massive stars by breaking up the dense filaments that feed the massive star formation at early times , and by collectively slowing down the global collapse that fuel the massive star formation at late times . the latter is aided by a moderate magnetic field of strength in the observed range ( corresponding to a dimensionless clump mass - to - flux ratio a few ) ; the field allows the outflow momenta to be deposited more efficiently inside the clump . we conclude that the massive star formation in our simulated turbulent , magnetized , parsec - scale clump is outflow - regulated and clump - fed ( orcf for short ) . an important implication is that the formation of low - mass stars in a dense clump can affect the formation of massive stars in the same clump , through their outflow feedback on the clump dynamics . in a companion paper , we discuss the properties of the lower mass cluster members formed along with the massive stars , including their mass distribution and spatial clustering .

0908.4129

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massive stars form quickly in our simulated parsec - scale clump in the absence of any magnetic field or outflow feedback ( see model hd ) . they are fueled by high mass accretion rates from either the dense filaments that are formed by turbulent compression or the clump - wide collapse due to the global turbulence dissipation . in both cases , the dense material that is depleted onto the massive star is constantly replenished . the replenishment is illustrated in the left panel of fig . [ starcore ] , where the mass of the most massive object is plotted as a function of time , along with the mass of the gas within a core " of 0.1 pc in diameter around the object ; the size was chosen to coincide with the fiducial value that mckee & tan ( 2003 ) used to define their turbulent cores . " it is clear that the core " so defined has an initial mass that is well below the final mass of the most massive object , and thus can not supply all of the mass of the object . as the object gains mass , the mass of the core " stays roughly constant or even increases ( rather than decreases ) , which demands that the core mass be replenished or fed from the surrounding clump . we are thus motivated to term this model the clump - fed massive star formation " model . our `` clump - fed massive star formation '' model ( cf model for short ) contains elements of the two widely discussed scenarios for massive star formation in the literature : the turbulent core model of mckee & tan ( 2003 ) and competitive accretion model of bonnell et al . it has in common with the turbulent core model in that the mass accretion rate onto the massive star is not primarily determined by the star itself , but rather by the properties of the pre - existing gas that produces the seed of the star in the first place and that continues to feed the stellar growth ; in other words , if the massive star were to be removed prematurely , another seed would be produced in its place and grow to a high mass . it is the properties of the fueling gas that determine the stellar mass accretion rate and thus the stellar mass . mckee & tan envisioned this gas to be a pre - existing massive turbulent core . it collapses to form the massive star , with a mass accretion rate that depends on the core structure . for example , if the turbulent core has a density profile of @xmath34 , the mass accretion rate would increase linearly with time @xmath115 ( mckee & tan 2003 ) . in our cf model , the pre - existing gas is the cluster - forming clump , which produces the transient dense material that feeds the massive star at a high rate through two mechanisms : ( 1 ) the collapse of the dense filaments produced by turbulent compression , as already emphasized by banerjee et al . ( 2006 ) , and ( 2 ) global collapse , driven by the turbulence decay in our simulations , but can in principle be caused by an external compression as well . the first mechanism depends on the detailed properties of the initial turbulence in the clump , which are not well constrained observationally . the second mechanism depends on the dissipation of ( supersonic ) turbulence that is inevitable , and should be more robust . our unregulated cf model has in common with the competitive accretion model in that a massive star can form even in the absence of a pre - existing turbulence - supported massive core and that the global gravitational potential and dynamics of the clump play an important , even the dominant , role in massive star formation . the latter is especially true at late times , when the global collapse feeds mass at a high rate to the compact region near the bottom of the potential well , where a large number of stars ( including massive stars ) are already present . in the absence of stellar feedback , competition for this clump - fed material in the crowded region is unavoidable . the most massive object tends to grow the fastest , mainly because it typically locates closest to the center of the potential , as emphasized by bonnell et al . although the numerical results of our grid - based amr hydro simulations are in broad agreement with those of sph simulations of bonnell et al . ( 2003 ) , we differ from their interpretation of the results regarding the formed stars , particularly as it relates to massive star formation . when a massive star is formed , the vast majority of the clump mass remains in the gas . the high accretion rates of the massive stars at late times of our hydro simulation derive directly from the global gas collapse . even if there were no stars near the center of the collapse ( or more likely the mass accretions onto individual stars are terminated by the stellar feedback ) , ( other ) massive stars can still form from scratch , as long as the collapse delivers mass to the center at a high enough rate . so we argue it is predominantly the structure and dynamics of the gaseous component that set the relevant physics in forming the massive stars rather than the properties of the stars made previously . a moderately strong magnetic field ( corresponding to the observationally inferred dimensionless mass - to - flux ratio of a few ) does not qualitatively change the clump - fed picture for massive star formation by itself . as discussed in [ mhd ] , the magnetic field has relatively little effect on the high mass accretion rate onto the most massive object induced by the initial turbulent compression and filament formation . indeed , it is conducive to filament formation by guiding the converging flows to collide along the field lines . the magnetic field does slow down the global collapse - induced rapid accretion by a modest factor of a few . the basic ingredients of the cf model remain , however , as can be seen from the middle panel of fig . [ starcore ] . specifically , the initial core mass is still much less the final mass of the most massive object , and most of the mass that goes into the object still needs to be replenished or fed from the surrounding clump . we conclude that the feeding processes for massive star formation are only weakly regulated by the magnetic field , perhaps because the field is only moderately strong ( i.e. , the clump is moderately supercritical ) , and it resists the feeding passively rather than actively ( unlike the outflows , see below ) . the magnetic field does change the dynamical coupling between different parts of the clump , an important aspect of cluster and massive star formation that we plan to return to in a future investigation . massive star formation through rapid accretion of the mass that is fed from outside the small region surrounding the forming star is particularly vulnerable to outflow feedback . this is because the feeding is directly opposed by the feedback . in the case of the rapid accretion fed by turbulent compression and filament formation , the filament is quickly chopped up into small segments by the outflows driven by the stars formed in it ( see the outflow movie in the electronic version of the paper ) . the outflows also slow down any further mass accumulation in the filament after star formation is initiated . as a result , this mode of turbulent compression - fed massive star formation is strongly regulated , perhaps even choked off completely , by outflow feedback . in the case of the rapid accretion fed by global collapse , the infall is countered by the outflows on all scales , especially on the global clump scale . the additional global support provided by the outflow feedback can reduce the total star formation rate by a large factor . this reduction affects the formation of all cluster members , especially the massive stars . this is because the massive stars receive a larger fraction of the collapse - fed material , and are thus more sensitive to the change of global clump dynamics . they also tend to complete their formation toward the end of cluster formation ( even though their seeds tend to be among the first objects to form ) , making them more prone to the accumulative influence of multiple generations of outflows that precede their eventual formation . since the outflows are believed to be driven by the release of gravitational binding energy from mass accretion in one form or another ( konigl & pudritz 2000 ; shu et al . 2000 ) , and most of the accreted mass goes to low - mass ( rather than high - mass ) stars for a salpeter - like imf , a large fraction if not the bulk of the outflow feedback should come from the low - mass stars . in this sense , the formation of low - mass stars in a dense clump can profoundly influence the formation of massive stars in the same clump , through their feedback on the clump dynamics . whether massive stars eventually form or not in a dense clump depends on the extent to which all the outflows in the clump collectively regulate the global collapse and slow down the star formation . if the total star formation rate is reduced , for example , below the fiducial minimum rate for massive star formation , @xmath116 , no massive stars would form at all . in the opposite extreme where the outflows are weak and the feedback is not strong enough to reverse the global collapse , stars ( especially massive stars ) would form quickly , as in our pure hydro simulation . the degree of outflow regulation will depend on the properties of the outflows , including their strengths and degrees of collimation , both of which are somewhat uncertain . what we have demonstrated explicitly through numerical simulation is that for well - collimated jets of reasonable strength the outflow feedback can prevent rapid global collapse , and keep the total star formation rate an order of magnitude below the characteristic free - fall rate . massive stars do eventually form in our simulation that includes outflow feedback . it demonstrates that outflows can strongly regulate massive star formation , but do not necessarily quench it completely , especially in dense massive clumps with a high characteristic free - fall rate @xmath12 . for such clumps , even when the bulk of the clump material is supported , a small fraction can still percolate down the global gravitational potential well , feeding the formation of massive stars near the center at a high enough rate . the fact that our outflow - regulated massive star formation remains clump - fed rather than core - fed is illustrated in the right panel of fig . [ starcore ] . as in the hd and mhd models that do not have outflow feedback , the mass of the 0.1 pc - sized `` core '' that surrounds the most massive object in the wind model is initially smaller than the final mass of the object , and does not decrease monotonically as the object accretes . again , the bulk of the accreted stellar material must come from outside the `` core , '' which is an essential feature of our new scenario of outflow - regulated clump - fed ( orcf ) massive star formation . in this picture , the parsec - scale cluster - forming clump , rather than a 0.1 pc - sized turbulent core , is the basic unit for massive star formation . as pointed out by bonnell et al . ( 2007 ) , a potential drawback of the turbulent core model is that massive , turbulence - supported , cores tend to fragment into many stars rather than collapse monolithically , although radiative feedback from the rapidly accreting massive stars can reduce the level of fragmentation ( krumholz & mckee 2008 ) . fragmentation is expected to be less of a problem in our clump - fed picture of massive star formation , since the material near the forming massive stars does not have to be supported by a strong turbulence ; it is typically in a state of rapid collapse that feeds the growing massive stars at a high rate , even though the clump as a whole may remain supported by ( possibly outflow - driven ) turbulence and , perhaps to a lesser extent , magnetic fields . if the parsec - scale dense clumps are indeed the basic units of massive star formation , how they form in the first place becomes an important problem that deserves close theoretical and observational attention . massive stars play a dominant role in galaxy formation and evolution . our orcf scenario suggests a rough criterion for their formation that can be used in global galaxy formation simulations that reach the scale of the cluster forming clumps but do not resolve their internal structure . the criterion is based on a threshold for mass accretion rate . a high mass accretion rate is needed not only to overcome the radiation pressure ( wolfire and cassinelli 1987 ) and quench the development of hii region ( walmsley 1995 ) , but also to satisfy observational constraints on the time scale of massive star formation . wood & churchwell estimated an age of @xmath117 years for uc hii regions , which probably represent a relatively late stage of massive star formation , when the bulk of mass accretion has completed and the mass accretion rate becomes too low to trap the hii region ( churchwell 2002 ) . the majority of the stellar mass may be accreted during the hot core ( and perhaps hypercompact hii ) phase , which lasts for a time of order @xmath118 years or less ( kurtz et al . the relatively short time scale is also consistent with the dynamical times estimated for massive molecular outflows ( which are presumably driven by rapid mass accretion during the main accretion phase , as in the case of low mass stars ; e.g. , bontemps et al . 1996 ) , which are typically of order @xmath118 years or less ( e.g. , zhang et al . if the time scale for massive star formation is indeed @xmath117 yrs or less , to form a star of 10 , a stellar mass accretion rate of @xmath119 or more would be needed . a minimum requirement for massive star formation in a clump is that the characteristic free - fall rate @xmath12 of the clump be greater than @xmath120 . the actual requirement will be more stringent . the accretion rate onto massive stars @xmath121 is related to the characteristic free - fall rate @xmath12 of the dense clump by two factors : @xmath122 , where @xmath123 is the actual rate of star formation normalized to the characteristic rate @xmath89 , and @xmath124 the fraction of the stellar mass accretion onto massive stars . we estimate the characteristic free - fall rate using the clump mass divided by the free - fall time at the average density @xmath125 ( where @xmath126 is the clump mass in units of @xmath127 and @xmath128 the clump radius in units of parsec ) , which yields @xmath129/yr for a @xmath130 clump of 1 pc in radius , consistent with the value obtained in our reference model of non - turbulent collapse . the most uncertain factor in the above equation is perhaps @xmath123 , the star formation rate compared to the characteristic free - fall rate . it depends on the extent to which the clump is supported globally . decaying turbulence can provide significant global support within a turbulence decay time , when @xmath123 can be significantly below unity . unless the star formation is terminated in one decay time , @xmath123 will eventually increase to a value not far from unity , as demonstrated in our hd model . a moderate magnetic field does not change the global support fundamentally , reducing @xmath123 by a factor of only a few ( see model mhd ) . together with the magnetic field , protostellar outflows can reduce @xmath123 by an order of magnitude , to values of order @xmath131 . the value of @xmath123 may range from about 0.1 ( before the virial turbulence decays away or after it is replenished ) to close to unity ( after the turbulence has decayed in the absence of magnetic support and turbulence replenishment ) . krumholz & tan ( 2007 ) argued that the star formation efficiency per free fall time is of order @xmath92 or less , implying @xmath132 . nakamura & li ( 2007 ) found a similarly low value for the well - studied nearby clump of active cluster formation ngc 1333 . based on these results , we choose @xmath133 as the fiducial value . a smaller @xmath123 would make it more difficult to form massive stars . the value for the remaining factor @xmath124 can be constrained both observationally and numerically . if the salpeter slope is universal for the upper part of the imf , then about 1/3 of the stellar mass must reside in stars more massive than 10 m@xmath134 ( assuming a lower cut - off at 0.3 @xmath135 ) . in this case , @xmath136 , which is similar to the ratios obtained in our simulations , according to tables 2 - 4 . to be conservative , we assume that all of the massive star accretion rate , @xmath137 , goes to a single star . if more than one massive star are fed at this rate , the requirement for massive star formation would be more stringent . taken together , the above considerations yield the following mass accretion rate for a massive star : @xmath138 which has to exceed @xmath139 for massive star formation to actually occur ( @xmath140 is the critical mass accretion rate for massive star formation in units of @xmath116/yr ) . this yields a rough condition on the ratio of the mass and radius of the clump for massive star formation : @xmath141 the significance of the above condition is that , if the fraction of the total stellar mass going into massive stars ( @xmath124 ) is constrained by observations , then whether a dense clump of a given mass and size ( and thus given @xmath12 ) can form massive stars or not boils down to the total star formation rate , @xmath142 . it depends on the clump dynamics , which is sensitive to the outflow feedback . the above condition is consistent with , for example , the sample of massive star forming clumps associated with water masers of plume et al . ( 1997 ) , which has a mean virial mass @xmath143 and mean radius @xmath144 . their ratio of 7.6 is comfortably above the fiducial value of @xmath145 in equation ( [ condition ] ) , indicating that massive stars can form , even when the total rate of star formation is an order of magnitude below the characteristic free - fall rate . a small value for the product @xmath146 ( @xmath147 ) may be the reason for the massive star formation to occur predominantly in those special regions of molecular clouds the massive dense clumps that are both massive and compact . the most severe limitation of the current work is perhaps the neglect of radiative feedback . radiative heating changes the clump fragmentation behavior , especially close to the forming stars ( krumholz et al . 2007 ; bate 2009 ) . this effect was mimicked to some extent by the relatively large sink particle merging distance adopted in our simulations ( with a length of 5 cells or @xmath7 au ) , which suppresses fragmentation on the small ( mostly disk ) scale . furthermore , if our orcf scenario is correct , the formation of massive stars may be more sensitive to the global clump dynamics ( which are less affected by the radiative heating ) than the gas properties close to the stars . nevertheless , we believe that the formation of massive stars will benefit from the suppression of fragmentation by radiative heating , especially near the bottom of the gravitational potential well of the clump , where the thermal jeans mass is formally smaller than the typical stellar mass . on small scales , radiative pressure may slow down the mass accretion onto individual massive stars somewhat , although the accretion may be enhanced to some extent by non - ideal mhd effects , such as ambipolar diffusion , which are not included in our ideal mhd calculations . another effect that we neglected was the hii region driven by the massive star s uv radiation . the expansion of hii regions provides a way to remove the clump gas , and perhaps terminate the cluster formation . it needs to be included in future simulations that aim to model the entire history of cluster formation . such studies may also need to include massive star winds , which are observed to have dramatic effects in some regions ( e.g. the carina nebula , see smith & brooks 2008 for a review ) . they are the main alternative to the hii regions as the means for terminating the cluster formation . a further limitation is the periodic boundary condition used in our simulation . it precludes any communication between the cluster - forming clump and its surrounding environment . if there is energy injection into the dense clump from the ambient medium , the externally supplied energy may aid the outflows in regulating the cluster and massive star formation . large - scale external compression may , on the other hand , lead to rapid clump collapse and massive star formation . in this case , the feeding of massive stars may extend beyond the parsec - scale clump , and the massive star formation may simply be part of the rapid clump formation .

the massive stars are fed at high rates by ( 1 ) transient dense filaments produced by large - scale turbulent compression at early times , and ( 2 ) by the clump - wide global collapse resulting from turbulence decay at late times . in both cases , the bulk of the massive star s mass is supplied from outside a 0.1 pc - sized core " that surrounds the star . in our simulation , the massive star is clump - fed rather than core - fed . an important implication is that the formation of low - mass stars in a dense clump can affect the formation of massive stars in the same clump , through their outflow feedback on the clump dynamics . in a companion paper

we investigate massive star formation in turbulent , magnetized , parsec - scale clumps of molecular clouds including protostellar outflow feedback using three dimensional numerical simulations of effective resolution . the calculations are carried out using a block structured adaptive mesh refinement code that solves the ideal mhd equations including self - gravity and implements accreting sink particles . we find that , in the absence of regulation by magnetic fields and outflow feedback , massive stars form readily in a turbulent , moderately condensed clump of ( containing initial jeans masses ) , along with a cluster of hundreds of lower mass stars . the massive stars are fed at high rates by ( 1 ) transient dense filaments produced by large - scale turbulent compression at early times , and ( 2 ) by the clump - wide global collapse resulting from turbulence decay at late times . in both cases , the bulk of the massive star s mass is supplied from outside a 0.1 pc - sized core " that surrounds the star . in our simulation , the massive star is clump - fed rather than core - fed . the need for large - scale feeding makes the massive star formation prone to regulation by outflow feedback , which directly opposes the feeding processes . the outflows reduce the mass accretion rates onto the massive stars by breaking up the dense filaments that feed the massive star formation at early times , and by collectively slowing down the global collapse that fuel the massive star formation at late times . the latter is aided by a moderate magnetic field of strength in the observed range ( corresponding to a dimensionless clump mass - to - flux ratio a few ) ; the field allows the outflow momenta to be deposited more efficiently inside the clump . we conclude that the massive star formation in our simulated turbulent , magnetized , parsec - scale clump is outflow - regulated and clump - fed ( orcf for short ) . an important implication is that the formation of low - mass stars in a dense clump can affect the formation of massive stars in the same clump , through their outflow feedback on the clump dynamics . in a companion paper , we discuss the properties of the lower mass cluster members formed along with the massive stars , including their mass distribution and spatial clustering .

0908.4129

i

we have carried out amr - mhd simulations of massive star formation in dense , turbulent , parsec - scale clumps of cluster star formation including sink particles and outflow feedback . we find that , without regulation by magnetic fields and outflows , massive stars form quickly . they are fed at a high rate first by the converging flows in the initial turbulence and later by the global collapse induced by turbulence decay . a moderate magnetic field alone does not affect these feeding processes much . they are greatly modified , however , by a combination of protostellar outflows and magnetic fields . the outflows break up the turbulent compression - produced dense filaments that feed the massive stars at early times and stall the global collapse that fuel the massive star formation at later times . the outflow feedback is enhanced by a magnetic field , which links different parts of the clump together ; the coupling makes the deposition of the outflow momenta in the clump more efficient . the magnetically - aided outflow feedback can in principle reduce the total rate of star formation below the critical mass accretion rate for massive star formation and suppress the massive star formation completely . in practice , whether massive stars form in a dense clump or not depends on the properties of the clump ( particularly its mass and size ) and the degree of magneto - outflow regulation of its star formation ( see equation [ [ condition ] ] ) . for parsec - scale clumps of order @xmath7 , we have demonstrated explicitly through numerical simulations that the formation of massive stars is clump - fed and outflow - regulated . additional simulations and analysis are needed to determine whether this new scenario of outflow - regulated clump - fed massive star formation is applicable to more massive and/or more compact dense clumps . in a companion paper , we will explore the effects of the outflow feedback on the lower mass cluster members . walawender , j. , bally , j. , francesco , j. d. , jrgensen , j. , & getman , k. 2008 , handbook of star forming regions , volume i : the northern sky asp monograph publications , vol . 4 . edited by bo reipurth , p.346 llllll hd - a1 & 61.1 & 0.96 & 4 & ( 0.66 , 0.40 , 0.48 ) & + hd - a2 & 22.6 & 1.36 & 1 & ( 0.66 , 0.40 , 0.48 ) & + hd - a3 & 10.1 & 2.03 & 1 & ( 0.68 , 0.41 . 0.48 ) & + hd - b1 & 21.3 & 1.11 & 1 & ( 0.74 , 0.48 , 0.33 ) & + hd - b2 & 15.8 & 1.72 & 1 & ( 0.74 , 0.48 , 0.33 ) & + hd - all & 131 & & 8 & & 137 stars , 350 ; 37% massive + mhd - a1 & 12.3 & 1.05 & 1 & ( 0.41 , 0.34 , 0.51 ) & + mhd - a2 & 46.7 & 1.35 & 2 & ( 0.44 , 0.38 , 0.52 ) & + mhd - b1 & 14.6 & 2.30 & 1 & ( 0.51 , 0.65 , 0.36 ) & + mhd - all & 73.6 & & 4 & & 86 stars , 165 ; 45% massive + wind - all & 0 & & 0 & & 72 stars , 69.7 ; no massive stars + llllll mhd - a1 & 15.0 & 1.05 & 1 & ( 0.32 , 0.45 , 0.51 ) & + mhd - a2 & 110 & 1.35 & 2 & ( 0.44 , 0.40 , 0.51 ) & + mhd - a3 & 12.5 & 3.13 & 1 & ( 0.46 , 0.41 , 0.51 ) & + mhd - b1 & 45.8 & 2.30 & 1 & ( 0.46 , 0.65 , 0.39 ) & + mhd - all & 183 & & 5 & & 121 stars , 337 ; 54% massive + wind - a1 & 16.9 & 1.16 & 1 & ( 0.38 , 0.42 , 0.50 ) & + wind - b1 & 10.5 & 2.29 & 1 & ( 0.45 , 0.68 , 0.42 ) & + wind - all & 27.4 & & 2 & & 123 stars , 134 ; 20% massive + llllll wind - a1 & 46.4 & 1.16 & 1 & ( 0.47 , 0.36 , 0.51 ) & + wind - a2 & 11.8 & 1.34 & 1 & ( 0.43 , 0.33 , 0.47 ) & + wind - b1 & 16.7 & 2.29 & 1 & ( 0.49 , 0.67 , 0.44 ) & + wind - b2 & 12.0 & 2.31 & 1 & ( 0.51 , 0.67 , 0.43 ) & + wind - all & 86.9 & & 4 & & 183 stars , 250 ; 35% massive +

we investigate massive star formation in turbulent , magnetized , parsec - scale clumps of molecular clouds including protostellar outflow feedback using three dimensional numerical simulations of effective resolution . we find that , in the absence of regulation by magnetic fields and outflow feedback , massive stars form readily in a turbulent , moderately condensed clump of ( containing initial jeans masses ) , along with a cluster of hundreds of lower mass stars . the outflows reduce the mass accretion rates onto the massive stars by breaking up the dense filaments that feed the massive star formation at early times , and by collectively slowing down the global collapse that fuel the massive star formation at late times . the latter is aided by a moderate magnetic field of strength in the observed range ( corresponding to a dimensionless clump mass - to - flux ratio a few ) ; the field allows the outflow momenta to be deposited more efficiently inside the clump .

we investigate massive star formation in turbulent , magnetized , parsec - scale clumps of molecular clouds including protostellar outflow feedback using three dimensional numerical simulations of effective resolution . the calculations are carried out using a block structured adaptive mesh refinement code that solves the ideal mhd equations including self - gravity and implements accreting sink particles . we find that , in the absence of regulation by magnetic fields and outflow feedback , massive stars form readily in a turbulent , moderately condensed clump of ( containing initial jeans masses ) , along with a cluster of hundreds of lower mass stars . the massive stars are fed at high rates by ( 1 ) transient dense filaments produced by large - scale turbulent compression at early times , and ( 2 ) by the clump - wide global collapse resulting from turbulence decay at late times . in both cases , the bulk of the massive star s mass is supplied from outside a 0.1 pc - sized core " that surrounds the star . in our simulation , the massive star is clump - fed rather than core - fed . the need for large - scale feeding makes the massive star formation prone to regulation by outflow feedback , which directly opposes the feeding processes . the outflows reduce the mass accretion rates onto the massive stars by breaking up the dense filaments that feed the massive star formation at early times , and by collectively slowing down the global collapse that fuel the massive star formation at late times . the latter is aided by a moderate magnetic field of strength in the observed range ( corresponding to a dimensionless clump mass - to - flux ratio a few ) ; the field allows the outflow momenta to be deposited more efficiently inside the clump . we conclude that the massive star formation in our simulated turbulent , magnetized , parsec - scale clump is outflow - regulated and clump - fed ( orcf for short ) . an important implication is that the formation of low - mass stars in a dense clump can affect the formation of massive stars in the same clump , through their outflow feedback on the clump dynamics . in a companion paper , we discuss the properties of the lower mass cluster members formed along with the massive stars , including their mass distribution and spatial clustering .

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since the prediction of radio ( paczyski & rhoads 1993 ) and optical transients ( mszros & rees 1997 ) associated with grbs , more than 100 afterglows have been observed ( including @xmath0-ray transients ) . good monitoring in all three frequency domains has been achieved for about 20 afterglows ; the radio , optical , and @xmath0-ray flux was observed to decay as a power - law , @xmath8 ( @xmath9 ) , confirming the expectations . for 10 of these well - observed afterglows 980519 , 990123 , 990510 , 991216 , 000301c , 000926 , 010222 , 012111 , 020813 , 030226 the optical light - curve decay exhibits a steepening at about 1 day after the burst , with an increase @xmath10 in the temporal index as low as 0.4 ( afterglow 991216 ) and as high as 1.8 ( afterglow 000301c ) . optical light - curve breaks have or may have been observed in other afterglows ; they are not included in the sample of afterglows modelled in this work because those afterglows have been adequately monitored at only one optical frequency . with the exception of the afterglow 010222 , for which one , late ( 10 days ) measurement suggests that a break occurred also in the @xmath0-ray light - curve , currently available @xmath0-ray observations do not extend sufficiently before and after the optical break time to prove that the light - curve break is achromatic . within the measurement uncertainties , a single power - law fits well the decay of all adequately monitored @xmath0-ray afterglows : 990123 , 990510 , 991216 , 000926 ( and 010222 until the last measurement ) . breaks , in the form of peaks , have been observed in the radio emission of all 10 afterglows above , usually at @xmath11 days after the burst , often occurring after the optical light - curve break . given that the radio and optical breaks are not simultaneous , they can not both arise from the dynamics of the afterglow , the structure of the grb ejecta , or some property of the circumburst medium ( cbm ) , as these mechanisms should yield achromatic breaks . furthermore , given that , before their respective breaks , the radio emission rises while the optical falls - off , these temporal features can not be due to the passage of the same afterglow continuum break through the observing band . with the possible exception of the afterglow 990123 , there is no evidence for an evolution ( softening ) of the optical continuum across the light - curve break for the above 10 afterglows ( panaitescu 2005 ) . furthermore , the only spectral feature whose passage could yield the large steepening @xmath10 observed in some cases the peak of the forward shock ( fs ) continuum should yields a rising or flat optical light - curve before the break , contrary to what is observed . therefore , it is the radio peak which should be attributed to a spectral break crossing the observing domain . that spectral break should be the injection frequency @xmath12 , which , for reasonable shock microphysical parameters , should reach the radio at around 10 days . indeed , for the afterglow 991208 , there is observational evidence ( galama 2000 ) that the peak of the afterglow continuum crosses the 10100 ghz domain at that time . further evidence for the passage of a spectral break through radio is provided by that the peak time of the radio flux of the afterglow 030329 increases with decreasing observing frequency ( frail 2005 ) . today , the generally accepted reason for the optical light - curve break is the narrow collimation of the grb ejecta . as predicted by rhoads ( 1999 ) , if the grb ejecta are collimated , then the afterglow light - curve should exhibit a steepening when the jet begins to expand sideways . more than half of the steepening @xmath10 is due by the finite angular opening of the jet : as the grb remnant is decelerated ( by sweeping - up of the cbm ) and the relativistic doppler beaming of the afterglow emission decreases , an ever increasing fraction of the emitting surface becomes visible to the observer ; when the jet edge is seen , that fraction can not increase any longer and the afterglow emission exhibits a faster decay ( panaitescu , mszros & rees 1998 ) . because it arises from the blast wave dynamics , a light - curve break should also be present at radio wavelengths at the same time as the optical break . however , radio observations before 1 day are very scarce and strongly affected by galactic interstellar scintillation ( goodman 1997 ) until after 10 days , thus they can not disentangle the jet - break from that arising from the passage of the fs peak frequency . another mechanism for the optical light - curve breaks has been proposed by rossi , lazzati & rees ( 2002 ) and zhang & mszros ( 2002 ) : if grb outflows are endowed with an angular structure ( non - uniform distribution of the ejecta kinetic energy with direction ) , as first proposed by mszros , rees & wijers ( 1998 ) , then a steepening of the afterglow decay would arise when the brighter , outflow symmetry axis becomes visible to the observer . in this model , the stronger the angular structure is , the larger the break magnitude @xmath10 should be . a third mechanism for breaks rests on the proposal of paczyski ( 1998 ) and rees & mszros ( 1998 ) that the fs energizing the cbm could be refreshed by the injection of a substantial energy through some delayed ejecta which were released at the same time with the grb - producing ejecta , but had a smaller lorentz factor , or were ejected sometime later , and which catch up with the decelerating fs during the afterglow phase . fox ( 2003 ) have proposed that the early ( 0.0030.1 day ) , slow decay of the optical emission of the afterglow 021004 is caused by such an injection process . in this scenario , when the energy injection episode ends , the fs deceleration becomes faster and the afterglow emission should exhibit a steepening . note the various origins of the afterglow light - curve break in each model . in the * jet * model , the break is caused by the changing outflow dynamics when the jet starts to spread and by the outflow s geometry . in the * structured outflow ( so ) * model the origin is , evidently , the outflow s anisotropic surface brightness . for both these models , special relativity effects play an important part . in the * energy injection ( ei ) * model , the break originates in the altered outflow dynamics at the time when the energy injection subsides . the purpose of this work is to compare the ability of these three models in accommodating + @xmath13 the shape of the light - curve breaks observed in the optical emission of the afterglows 980519 , 990123 , 990510 , 991216 , 000301c , 000926 , 010222 , 012111 , 020813 , 030226 and + @xmath14 the relative intensity of the radio , optical , and @xmath0-ray emissions of these afterglows , + for either a uniform ( homogeneous ) cbm , or one with a @xmath1 density radial stratification , as expected if grbs progenitors are massive stars ( woosley 1993 , paczyski 1998 ) . for the first task above , we performed an analytical test of the models ( see table 2 of panaitescu 2005 ) , based on comparing + @xmath13 the pre- and post - break optical light - curve decay indices , @xmath15 and @xmath16 , + @xmath14 those in the @xmath0-rays , + @xmath17 the slopes @xmath18 and @xmath19 of the power - law optical and @xmath0-ray continua ( @xmath20 and @xmath21 ) , and + @xmath22 the optical to@xmath0-ray spectral energy distribution ( sed ) slope , @xmath23 , + with the relations among them expected for each model . we note that , in the framework of the relativistic fireballs ( mszros & rees 1997 ) , the optical and @xmath0-ray decay indices and sed slopes are tightly connected , as only one continuum feature , the cooling frequency @xmath24 ( sari , narayan & piran 1998 ) , can be between these domains at the times when observations were usually made ( 0.1100 days ) , and that the sed slope increases by a fixed amount , @xmath25 , across this spectral break . including the radio afterglow emission in the analytical test of the three break models is less feasible and often unconstraining . first , that the afterglow radio flux is modulated by diffractive and refractive interstellar scintillation makes it difficult to determine accurately the radio sed slope ( see figs . 4 and 5 of frail , waxman & kulkarni 2000a for the best monitored radio afterglow 970508 ) . second , after the injection frequency has fallen below the radio ( during the decay phase of the radio light - curve ) , we do not expect , in general , any spectral break to be between radio and optical , hence the radio and optical light - curve indices should be the same . this is , indeed , the case for most afterglows ; nevertheless , there are a few troubling exceptions : over 12 decades in time , the radio emission of the afterglows 991208 , 991216 , 000926 , and 010222 exhibits a much shallower decay than that observed at optical wavelengths at the same time or prior to the radio decay . an analytical investigation of the various possible ways to decouple the radio and optical light - curves ( panaitescu & kumar 2004 ) has led to the conclusion that , the anomalous radio decay is due to a contribution from the reverse shock to the radio emission . however , radio observations provide an indirect constraint on them because the flux and epoch of the radio peak determine the fs synchrotron peak flux , injection frequency , and self - absorption frequency . these three spectral properties constrain the afterglow parameters pertaining to the outflow dynamics ( energy per solid angle , jet initial opening , medium density ) and emission ( magnetic field strength , typical post - shock electron energy ) , parameters which determine the shape and epoch of the optical light - curve break , as well as the location of the cooling frequency . the best way to take into account the constraints arising from the radio emission and to test fully the three break models is to calculate numerically the afterglow dynamics and emission , and to fit all the available measurements . data fitting also allows the determination of the various model parameters .

we investigate numerically the ability of three models ( jet , structured outflow , energy injection ) to accommodate the optical light - curve breaks observed in 10 grb afterglows ( 980519 , 990123 , 990510 , 991216 , 000301c , 000926 , 010222 , 011211 , 020813 , and 030226 ) , as well as the relative intensities of the radio , optical , and-ray emissions of these afterglows .

we investigate numerically the ability of three models ( jet , structured outflow , energy injection ) to accommodate the optical light - curve breaks observed in 10 grb afterglows ( 980519 , 990123 , 990510 , 991216 , 000301c , 000926 , 010222 , 011211 , 020813 , and 030226 ) , as well as the relative intensities of the radio , optical , and-ray emissions of these afterglows . we find that the jet and structured outflow models fare much better than energy injection model in accommodating the multiwavelength data of the above 10 afterglows . for the first two models , a uniform circumburst medium provides a better fit to the optical light - curve break than a wind - like medium with a stratification . however , in the only two cases where the energy injection model may be at work , a wind medium is favoured ( an energy injection is also possible in a third case , the afterglow 970508 , whose optical emission exhibited a sharp rise but not a steepening decay ) . the best fit parameters obtained with the jet model indicate an outflow energy of ergs and a jet opening of . structured outflows with a quasi - uniform core have a core angular size of and an energy per solid angle of , surrounded by an envelope where this energy falls - off roughly as with angle from the outflow axis , requiring thus the same energy budget as jets . circumburst densities are found to be typically in the range , for either model . we also find that the reverse shock emission resulting from the injection of ejecta into the decelerating blast wave at about 1 day after the burst can explain the slowly decaying radio light - curves observed for the afterglows 990123 , 991216 , and 010222 . 2nu^2 _ 0_e__0 3cm^-3 5310 ^ 53 gamma - rays : bursts - ism : jets and outflows - radiation mechanisms : non - thermal - shock waves

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in this work we expand our previous investigation ( panaitescu & kumar 2003 ) of the * jet model * to four other grb afterglows for which an optical light - curve break was observed : 010222 ( for which radio observations were not available at the time of our previous modelling ) , 011211 , 020813 , and 030226 . we also note that , here , we have not employed a broken power - law electron distribution to explain both the slower decaying radio emission and the faster falling - off optical light - curve observed for some afterglows ( 991216 and 000301c ) . our prior conclusion that a homogeneous circumburst medium provides a better fit to the broadband afterglow emission than environments with a wind - like stratification stands ( table 1 ) . for afterglows with a sharp steepening @xmath10 of the optical light - curve decay ( 990510 , 000301c , 011211 , and 030226 ) , this is due to that the transition between the jet asymptotic dynamical regimes ( spherical expansion at early times and lateral spreading afterward ) occurs faster for a homogeneous medium than for a wind ( kumar & panaitescu 2000 ) . for the afterglows with shallower breaks , a wind medium ( as expected if the grb progenitor is a massive star ) provides an equally good fit as ( or , at least , not much worse than ) a homogeneous medium . for the acceptable fits ( table 2 ) obtained with the jet model and for a uniform medium , the jet initial kinetic energy , @xmath140 , is between 2 and 6 @xmath141 ergs , the initial jet opening angle , @xmath26 , is between @xmath114 and @xmath142 ( with 000926 an outlier at @xmath143 ) , and the medium density , @xmath29 , between 0.05 and 1 @xmath144 ( with 000926 an outlier , again , at @xmath145 ) . for a wind , @xmath140 has about the same range , @xmath26 ranges from @xmath114 to @xmath146 , while the wind parameter @xmath79 is between 0.1 and 2 . 70% of the 64 galactic wr stars analyzed by nugis & lamers ( 2000 ) have a @xmath79 parameter in this range ; for the rest @xmath147 . we note that the @xmath140 resulting from our numerical fits is uncertain by a factor 2 , @xmath26 by about 30% , @xmath29 by almost one order of magnitude , and @xmath79 by a factor of 2 . although the inferred wind density parameter @xmath79 is in accord with the measurements for wr stars a uniform medium is instead favoured by the fits to the afterglow data . this is an interesting issue for the established origin of long bursts in the collapse of massive stars . wijers ( 2001 ) has proposed that the termination shock resulting from the interaction between the wind and the circumstellar medium could homogenize the wind . the numerical hydrodynamical calculations of garcia - segura , langer & mac low ( 1996 ) show that , for a negligible pressure @xmath148 of the circumstellar medium ( about @xmath149 ) , the termination shock of the rsg wind has a radius of 10 pc , outside a shell of uniform density is form . however , this radius is much larger than the distance of about 1 pc where the afterglow emission is produced . chevalier , li & fransson ( 2004 ) made the case that , if the burst occurred in an intense starburst region , where the interstellar pressure is about @xmath150 , then the shocked rsg wind would form bubble of uniform density of about @xmath151 extending from 0.4 to 1.6 pc , in accord with the fit densities and the blast - wave radius @xmath152^{1/4}$ ] pc , resulting from equation ( [ gs0 ] ) . the * structured outflow model * involving an energetic , uniform core , surrounded by a power - law envelope ( equation [ [ eq ] ] ) which impedes the lateral spreading of the core , retains most of the ability of the jet model to yield a steeply decaying optical light - curve after the core ( or its boundary ) becomes visible to an observer located outside the core opening ( or within it ) , while accommodating , at the same time , the observed slope of the optical spectral energy distribution ( sed ) . this is so because , in both models , more than half of the increase @xmath10 in the light - curve power - law decay index is due to the finite opening of the bright(er ) ejecta . for a jet , the remainder of the steepening @xmath10 is caused by the lateral spreading . for a structured outflow , an extra contribution to the steepening , which can lead to a @xmath10 even larger than that produced by a jet , results if the observer is located outside the core opening . for a uniform medium , we find that the structured outflow model provides a better fit than the jet model for 6 of the 10 afterglows analyzed here ( table 1 ) . for a wind , the former model works better for three afterglows , fits of comparable quality being obtained for the other six . only the afterglow 990510 is better explained with a jet , for either type of circumburst medium . within the framework of structured outflows , 8 out of 10 afterglows are better fit with a uniform medium than with a wind , which is partly due to that , just as for a jet , the light - curve steepening is sharper if the medium is uniform ( panaitescu & kumar 2003 ) . for the `` acceptable '' fits ( @xmath96 ) obtained with the so model , the ejecta kinetic energy per solid angle in the core , @xmath27 , ranges from 0.5 to 3 @xmath153 for either type of medium , with an uncertainty of a factor 3 . the angular opening of the core , @xmath74 , is between @xmath154 and @xmath155 for a homogeneous medium , and about @xmath155 for a wind ( 991216 being an outlier at @xmath154 ) , with an uncertainty less than 50% . the structural parameter @xmath75 ( equation [ [ eq ] ] ) , which characterizes the energy distribution in the outflow envelope , is found to be between 1.5 and 2.7 for a uniform medium , and between 1.0 and 2.3 for a wind ( with 000926 being an outlier at @xmath156 ) . these values are consistent with that proposed by rossi ( 2002 ) , @xmath157 , to explain the quasi - universal jet energy resulting in the jet model . for structured outflows , the ejecta kinetic energy contained within an opening of twice the location of the observer ( relative to the outflow symmetry axis ) , @xmath51 , ranges from 1 to 4 @xmath141 ergs , for either type of medium . hence , the energy budget required by the structured outflow model is very similar to that of the jet model . the best fit medium densities obtained with the structured outflow model are similar to those resulting for a jet . we find that the * energy injection model * , where a light - curve decay steepening is attributed to the cessation of energy injection in the forward shock , can be at work only in two afterglows , 990123 and 020813 . the major shortcoming of the ei model is that , in order to explain the steep fall - off of the optical light - curve after the break with a spherical outflow , an electron distribution that is too soft ( an index @xmath89 too large ) is required to accommodate the relative intensities of the radio and @xmath0-ray emissions . low density solutions ( @xmath158 , @xmath159 ) , for which the @xmath0-ray emission is mostly synchrotron , yield a cooling frequency that is too low , resulting in model @xmath0-ray fluxes underestimating the observations by a factor of at least 10 . high density solutions ( @xmath160 , @xmath161 ) , for which the @xmath0-ray is mostly inverse compton scatterings , produce a forward shock peak flux that is too large , which leads to model radio fluxes overestimating the data by a factor of 10 . we note that , due to adiabatic cooling , the grb ejecta electrons which were energized by the reverse shock during the burst , do not contribute significantly to the afterglow radio emission at days after the burst . numerically , we find that , if the microphysical parameters are the same for both the reverse and forward shocks , then the 1 day radio flare of the afterglow 990123 can not be explained with the emission from the grb ejecta electrons , as proposed by sari & piran ( 1999 ) , as the synchrotron emission from these electrons peaks in the radio earlier than 0.1 day , regardless of how relativistic is the reverse shock . for the reverse shock emission to be significant at 1 day after the burst , there must be some other ejecta catching up with the decelerating outflow at that time or the assumption of equal microphysical parameters for both shocks must be invalid ( panaitescu & kumar 2004 ) . furthermore , the optical emission from the ejecta electrons is below that observed at 100 s ( akerlof 1999 ) by a factor 5 for a wind and a factor 50 for a uniform medium . a delayed injection of ejecta , carrying less kinetic energy than that already existing in the forward shock ( not altering the forward shock dynamics ) , may be at work in the afterglows 990123 , 991216 , and 010222 , whose radio decay is substantially slower than that observed in the optical after the break . as shown by us ( panaitescu & kumar 2004 ) , such a decoupling of the radio and optical emissions can not be explained by models based on a single emission component ( forward shock ) and require the contribution of the reverse shock [ 0123jet+ei ] , [ 1216jet+ei ] , and [ 0222jet+ei ] , illustrate that the sum of the reverse and forward shock emissions yields a slower decaying radio emission , consistent with the observations . however , for the forward shock peak flux to be as dim as observed in the radio after 10 days , when the forward shock peak frequency decreases to 10 ghz , an extremely tenuous medium is required : @xmath162 or @xmath163 . the former might be compatible with a massive star progenitor if grbs occur in the `` superbubble '' blown by preceding supernovae exploding in the same molecular cloud ( scalo & wheeler 2001 ) , while the latter points to a progenitor with a low mass and low metallicity or , otherwise , to a small mass - loss rate and high wind speed during the last few thousand years before the collapse , when the environment within 1 pc is shaped by the stellar wind . as a final conclusion , we note that the structured outflow model is a serious contender to the jet model in accommodating the broadband emission of grb afterglows with optical light - curve breaks . in both models , the best fit parameters describing the ejecta kinetic energy jet opening & energy or core opening & energy density along the outflow symmetry axis have narrow distributions , hinting to a possible universality of these parameters .

we find that the jet and structured outflow models fare much better than energy injection model in accommodating the multiwavelength data of the above 10 afterglows . for the first two models , a uniform circumburst medium provides a better fit to the optical light - curve break than a wind - like medium with a stratification . structured outflows with a quasi - uniform core have a core angular size of and an energy per solid angle of , surrounded by an envelope where this energy falls - off roughly as with angle from the outflow axis , requiring thus the same energy budget as jets . circumburst densities are found to be typically in the range , for either model . we also find that the reverse shock emission resulting from the injection of ejecta into the decelerating blast wave at about 1 day after the burst can explain the slowly decaying radio light - curves observed for the afterglows 990123 , 991216 , and 010222 . 2nu^2 _

we investigate numerically the ability of three models ( jet , structured outflow , energy injection ) to accommodate the optical light - curve breaks observed in 10 grb afterglows ( 980519 , 990123 , 990510 , 991216 , 000301c , 000926 , 010222 , 011211 , 020813 , and 030226 ) , as well as the relative intensities of the radio , optical , and-ray emissions of these afterglows . we find that the jet and structured outflow models fare much better than energy injection model in accommodating the multiwavelength data of the above 10 afterglows . for the first two models , a uniform circumburst medium provides a better fit to the optical light - curve break than a wind - like medium with a stratification . however , in the only two cases where the energy injection model may be at work , a wind medium is favoured ( an energy injection is also possible in a third case , the afterglow 970508 , whose optical emission exhibited a sharp rise but not a steepening decay ) . the best fit parameters obtained with the jet model indicate an outflow energy of ergs and a jet opening of . structured outflows with a quasi - uniform core have a core angular size of and an energy per solid angle of , surrounded by an envelope where this energy falls - off roughly as with angle from the outflow axis , requiring thus the same energy budget as jets . circumburst densities are found to be typically in the range , for either model . we also find that the reverse shock emission resulting from the injection of ejecta into the decelerating blast wave at about 1 day after the burst can explain the slowly decaying radio light - curves observed for the afterglows 990123 , 991216 , and 010222 . 2nu^2 _ 0_e__0 3cm^-3 5310 ^ 53 gamma - rays : bursts - ism : jets and outflows - radiation mechanisms : non - thermal - shock waves

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the black - hole candidate grs 1915 + 105 is one of the most studied x - ray sources in our galaxy due to its remarkably rich phenomenological diversity across the entire electromagnetic spectrum except the visible band . it was first detected in 1992 with the watch instrument on - board the granat satellite ( castro - tirado , brandt , & lund 1992 ) . in contrast with other transient x - ray sources , it has never been switched off since detection . its optical counter - part has not been detected due to a very high line - of - sight absorption ( @xmath026 magnitude , chaty et al . 1996 ) . in the absence of optical observations , the binary parameters as well as the nature of the companion were unknown till 2001 . finally nine years after its detection , greiner et al . ( 2001 ) , by near - infrared spectroscopic observations with vlt , established it as a low mass x - ray binary ( lmxb ) system with a k - m iii type companion star of mass [email protected] m@xmath2 . the black hole mass was determined to be 14@xmath14 m@xmath2 which is the largest mass known so far for any black hole candidate in an x - ray binary . grs 1915 + 105 achieved the status of micro - quasar much earlier in 1994 when mirabel & rodriguez ( 1994 ) detected episodes of superluminal ejections from this source , first time in any galactic source . observations of many such episodes of superluminal ejections during the past eight years make grs 1915 + 105 distinct among other micro - quasars in our galaxy . apart from huge superluminal radio flares , grs 1915 + 105 also shows various other types of radio emission like radio oscillations ( pooley & fender 1997 ) and extended periods of steady , flat spectrum radio emission known as radio `` plateau '' states ( fender et al . these radio `` plateau '' states are particularly interesting due to their association with the large radio flares . it is found that the `` plateau '' states are almost always followed by large radio flares with steep spectrum ( hannikainen et al . 1998 ; fender et al . 1999 ; klein - wolt et al . 2002 ) , though so far there is no satisfactory explanation for this observed association . the true glory of this source came into notice after the launch of nasa s _ rossi x - ray timing explorer ( rxte ) _ in 1996 . pointed observations with rxte - pca showed extremely rich and exciting morphology in the x - ray intensity patterns ( greiner , morgan , & remillard 1996 ; morgan , remillard , & greiner 1997 ; muno , morgan , & remillard 1999 ) . similar diversity in the x - ray emission from this source was also observed with the _ indian x - ray astronomy experiment ( ixae ) _ ( paul et al . 1997 , 1998 ; yadav et al . belloni et al . ( 2000 ) carried out a detailed analysis of all the rxte pointed observations in 1996 - 97 and classified the complex diversity of the x - ray emission exhibited by this source into 12 classes on the basis of light curves and hardness ratios ( one more variability class was identified later on - see klein - wolt et al . 2002 ; naik , rao & chakrabarti 2002 ) . they also put an important step forward in understanding the complexity of this source by showing that all the variability classes occur because of repeated transitions of the source in three basic states . they showed that the transitions between these three states , named as states a , b , and c , can be very fast i.e. within a few seconds . the states a and b are characterized by a soft spectrum with the total luminosity being low and high , respectively . the state c is characterized by a hard spectrum and the presence of strong quasi periodic oscillations ( qpo ) in the power density spectrum . this source is probably the best example for a strong connection between the accretion disk , manifested in the x - ray band , and the jet , manifested in the radio / ir band , in a black hole system ( pooley & fender 1997 ; eikenberry et al . 1998 ; 2000 ; mirabel et al . 1998 ) . study of the correlated behavior of the source in the x - ray and the radio / ir wave bands plays a very important role in the endeavor of understanding this source and many attempts have been made so far to relate the x - ray emission characteristics with the episodes of various types of radio emission . muno et al . ( 2001 ) studied representative observations in detail and showed that the properties of the qpo , like frequency , phase - lag , coherence etc . are correlated with the radio emission . rau & greiner ( 2003 ) showed that the properties of accretion disk are not correlated with the radio emission . naik & rao ( 2000 ) showed that the radio emission is high only during three variability classes : @xmath3 , @xmath4 and a sub - class of @xmath5 ( @xmath6/@xmath7 or @xmath8 . ) into four sub - classes @xmath9 , @xmath10 , @xmath11 and @xmath12 based on their order of occurrence . out of these four sub - classes only @xmath6 and @xmath7 show high radio emission . however , later more such occurrences of class @xmath5 have been observed during which the radio emission is high . thus , instead of numbered sub - classes , class @xmath5 can be divided into two generic sub - classes radio - quiet ( @xmath13 ) and radio - loud ( @xmath8 ) . the sub - class @xmath8 corresponds to the radio `` plateau '' states . ] they suggested that the radio emission is associated with the soft x - ray dips ( short periods of state a ) observed in the classes @xmath3 and @xmath4 , apart from the sub - class @xmath8 . naik et al . ( 2001 ) detected similar dips in the x - ray light curve during the presence of a large radio flare indicating their association with large radio flares . klein - wolt et al . ( 2002 ) studied all simultaneous observations of the source by rxte and ryle telescope and showed that the radio emission is associated with only state c and not with states a or b. they also found an one - to - one relation between series of long ( @xmath14 100 s ) , well separated state c intervals and radio oscillation events . they suggested a scenario , according to which the long uninterrupted state c intervals are associated with continuous jets which give `` plateau '' radio emission , whereas if the state c intervals are well separated by other states then the radio oscillation events are observed . a different picture , however , emerges when the association of the radio emission with the different sub - classes of @xmath5 ( state c ) are examined in detail ( see discussion in section [ scenario ] for more details on this ) . the sub - classes of class @xmath5 can be divided into two different types of hard states : radio - loud hard state ( i.e. @xmath15 ) and radio - quiet hard state ( i.e. @xmath16 ) ( vadawale et al . 2001b ; trudolyubov 2001 ) . by a detailed spectral study of rxte observations of the source belonging to the two types of hard states , vadawale et al . ( 2001b ) showed that the wide band x - ray spectrum of state @xmath16 consists of two components : a multicolor disk - blackbody and a comptonized component whereas the wide band x - ray spectrum of state @xmath15 consists of three components : a multicolor disk - blackbody , a comptonized component and a power - low . they further showed that the additional power - law component can be modeled as due to synchrotron radiation in x - rays , coming from the base of a continuous jet which is present only during the @xmath15 states . this three - component picture gets further support from other results such as : only the comptonized component is responsible for the low - frequency qpo ( rao et al . 2000 ) and both the qpo as well as the comptonized component are absent during the soft dips ( short state a periods ) observed in class @xmath4 ( vadawale et al . 2001a ) . it should be noted that the radio - loud hard state also occurs as a part of other variability classes like @xmath4 and @xmath3 . hence we will refer it generically as @xmath15 , whereas the particular sub - class of class @xmath5 during which the radio emission is high , will be referred as @xmath8 . in this paper we explore the association of the radio `` plateau '' states with large superluminal radio flares and try to envisage a scenario to explain this association as well as the various types of radio emission observed from this source . since there are not many detailed studies of such episodes of superluminal jet emissions , in the first part of the paper we present a detailed study of a complete sequence of flare morphology described , sequentially , by a small flare , `` plateau '' state , a disturbed accretion disk and a superluminal jet . we report the observations of the source with _ giant meter - wave radio telescope ( gmrt ) _ at 1.28 ghz when the source exhibits a flare which turned out to be a pre - plateau flare . we also present the results of a detailed analysis of all the pointed rxte observations during this flare cycle which confirm the three - component x - ray spectral description of the pre - flare `` plateau '' state . in order to confirm the three - component description during all occurrences of the `` plateau '' state , we further carry out similar analysis of representative pointed rxte observations prior to all huge radio flares identified in the gbi monitoring data on this source . finally we summarize the results and propose a phenomenological model for different types of radio emission from this source .

we investigate the association between the radio `` plateau '' states and the large superluminal flares in grs 1915 + 105 and propose a qualitative scenario to explain this association . to investigate the properties of the source during a superluminal flare , we present gmrt observations during a radio flare which turned out to be a pre - plateau flare as shown by the contemporaneous ryle telescope observations . a major superluminal ejection this episode , thus has all the three types of radio emission : a pre - plateau flare , a `` plateau '' state and superluminal jets . we detect a strong correlation between the average x - ray flux during the `` plateau '' state and the total energy emitted in radio during the subsequent radio flare . this picture can explain all types of radio emission observed from this source in terms of its x - ray emission characteristics .

we investigate the association between the radio `` plateau '' states and the large superluminal flares in grs 1915 + 105 and propose a qualitative scenario to explain this association . to investigate the properties of the source during a superluminal flare , we present gmrt observations during a radio flare which turned out to be a pre - plateau flare as shown by the contemporaneous ryle telescope observations . a major superluminal ejection was observed at the end of this `` plateau '' state ( dhawan et al . 2003 ) , associated with highly variable x - ray emission showing x - ray soft dips . this episode , thus has all the three types of radio emission : a pre - plateau flare , a `` plateau '' state and superluminal jets . we analyze all the available rxte - pca data during this episode and show that : ( 1 ) the pre - flare `` plateau '' state consists of a three - component x - ray spectra which includes a multicolor disk - blackbody , a comptonized component and a power - law and ( 2 ) the compton cloud , which is responsible for the comptonizing component , is ejected away during the x - ray soft dips . we investigate all the available monitoring data on this source and identify several candidate superluminal flare events and analyze the contemporaneous rxte pointed observations . we detect a strong correlation between the average x - ray flux during the `` plateau '' state and the total energy emitted in radio during the subsequent radio flare . we find that the sequence of events is similar for all large radio flares with a fast rise and exponential decay morphology . based on these results , we propose a qualitative scenario in which the separating ejecta during the superluminal flares are observed due to the interaction of the matter blob ejected during the x - ray soft dips , with the steady jet already established during the `` plateau '' state . this picture can explain all types of radio emission observed from this source in terms of its x - ray emission characteristics .

1504.04898

i

we investigate using rydberg atom interactions to deterministically synthesize collective quantum states that can be strongly coupled to an optical cavity for applications in quantum information science , quantum optics and the production of quantum light fields . the method enables a single or several collective excitations to be prepared in a high - finesse optical cavity . the number of excitations is precisely controlled so that photon number states can be produced using the coupled atoms - cavity system . the system we describe in this paper differs from typical jaynes - cummings ( jc ) and tavis - cummings ( tc ) physics in that strong atom - atom interactions play a key role in the initial state preparation , which is the focus of this paper . rydberg atoms have many exotic properties . for example , rydberg atoms are large , interact strongly with one another , have relatively long lifetimes , and can be manipulated with external electric and magnetic fields @xcite . particularly important to the work presented in this paper , the interactions between ultracold rydberg atoms can be larger than typical frequency stabilized laser spectral bandwidths and kinetic energies at distances of over @xmath2 m @xcite . the interactions can be manipulated easily with electric fields , relative to valence states @xcite . there is a broad range of behavior that can be induced when the multi - level character of the interactions is taken into account . rydberg atom blockade is a result of the strong interactions between rydberg atoms . in rydberg atom blockade , the long range interactions between rydberg atoms suppress multiple excitations in a volume in which the interactions are large enough to shift the excitation laser out of resonance with the rydberg atom transition frequency @xcite . it has been realized over the last 15 years that rydberg atom blockade is useful for a host of applications , particularly in quantum optics and quantum information science . rydberg atom blockade can be used to control quantum dynamics and prepare interesting quantum states @xcite . rabi oscillations have been observed in effective two - level ultracold rydberg atoms @xcite demonstrating long coherence times and collective behavior . collective rabi oscillations on rydberg transitions have even been observed in a thermal rubidium ( rb ) vapor on a time scale below @xmath3ns @xcite . atoms contained in cavities , both optical and microwave , have been important systems for investigating the quantum - classical boundary in physics . the ability to entangle atoms with light presented by cavity quantum electrodynamics has also served as a model system for applications in quantum information science @xcite . a cavity quantum electrodynamical system with a single excitation or controlled number of excitations is useful both for fundamental studies @xcite and applications that use quantum behavior , particularly those involving quantum entanglement @xcite . entangled states can be created between distant atoms in one cavity or separate cavities @xcite . trapping of a single atom in a high - finesse optical cavity has been achieved @xcite . however , it is technically challenging to couple the light in the cavity to a single atom because of the small absorption cross - section @xcite . the problem of small absorption cross - sections can be handled by using an atomic ensemble , where light more strongly interacts with collective atomic states . in this paper , we theoretically show that one can excite collective @xmath0 atom superposition states using rydberg atom interactions that can be strongly coupled to a high - finesse cavity . we observe @xmath4 enhancement of the rabi oscillations within the cavity showing that the collective state can be realized @xcite and analyze the decay mechanisms that affect this interacting many - body system . collectively enhanced cooperativity factors help to improve the efficiency of photon generation out of the cavity . the efficiency can be improved by increasing the number of atoms . we also show that by chirping the laser excitation pulses in time , the single atom rydberg blockade effect can be suppressed and we can create two rydberg excitations within the blockade radius that are coupled to the cavity . we use a four - level diamond type atomic scheme as shown in fig . [ fig:1](b ) . one side of the diamond is used to collectively excite the atoms to the rydberg level using a pair of @xmath1-pulses or a pair of counter - intuitive stimulated raman adiabatic passage ( stirap ) pulses with rabi frequencies @xmath5 and @xmath6 . by using a laser pulse , @xmath7 , and the single atom cavity coupling strength , @xmath8 , the state of the collective atoms - cavity system can be controlled . rydberg atom blockade plays an important role in this process , since we are interested in cases where a single or controlled finite number of coherently shared excitation(s ) are produced in a collection of @xmath9 state rb atoms . the @xmath0 interacting atoms - cavity system is within the reach of experimental realization @xcite . the system can be used to prepare single photons using a single excitation and more complex quantum light fields by preparing multiple excitations in the cavity . recently , a jc model in the optical domain has been proposed for investigating rydberg blockaded atomic ensembles in a cavity . the transmission through the cavity was studied numerically by monte - carlo simulation @xcite . in contrast to this work and others , our studies resemble a pumping scheme for inverting the population of a laser , except the upper state of the lasing transition is prepared in a collective state . the pumping scheme is similar to a raman or superradiant laser and work done on low atom number masers and micromasers . however , for these types of lasers and masers , the atoms are coherent but non - interacting @xcite . our approach is useful for single photon generation @xcite , as well as the generation of other types of quantum light fields , and coherent optical manipulation for quantum information processing @xcite . the collective atoms - cavity system can also be important for generating unique quantum states such as superposition states of the atomic ensemble @xcite . the approach does not require phase matching and it may be easier to use this system than those based on phase matching to create more elaborate quantum light fields @xcite . creating arbitrary quantum light fields remains an important challenge for quantum optics , so it is useful to explore a wide range of different strategies . the method that we explore in this paper may have technological and experimental advantages because the collective state is prepared on a set of transitions which have significantly different excitation wavelengths , @xmath10 nm for all transitions in rb , than the cavity mode to which it is coupled . the cavity output can be filtered and detected with low background .

we investigate the coherent manipulation of interacting rydberg atoms placed inside a high - finesse optical cavity for the deterministic preparation of strongly coupled light - matter systems . one side of the diamond is used to excite the atoms into a collective ` superatom ' rydberg state using either-pulses or stimulated raman adiabatic passage ( stirap ) pulses . the upper transition on the other side of the diamond we use numerical simulation to show that non - classical states of light can be generated and that the state that is coupled to the cavity field is a collective one . we also investigate how different decay mechanisms affect this interacting many - body system . we also analyze our system in the case of two rydberg excitations within the blockade volume . the simulations are carried out with parameters corresponding to realizable high - finesse optical cavities and alkali atoms like rubidium .

we investigate the coherent manipulation of interacting rydberg atoms placed inside a high - finesse optical cavity for the deterministic preparation of strongly coupled light - matter systems . we consider a four - level diamond scheme with one common rydberg level for interacting atoms . one side of the diamond is used to excite the atoms into a collective ` superatom ' rydberg state using either-pulses or stimulated raman adiabatic passage ( stirap ) pulses . the upper transition on the other side of the diamond is used to transfer the collective state to one that is coupled to a field mode of an optical cavity . due to the strong interaction between the atoms in the rydberg level , the rydberg blockade mechanism plays a key role in the deterministic quantum state synthesis of the atoms in the cavity . we use numerical simulation to show that non - classical states of light can be generated and that the state that is coupled to the cavity field is a collective one . we also investigate how different decay mechanisms affect this interacting many - body system . we also analyze our system in the case of two rydberg excitations within the blockade volume . the simulations are carried out with parameters corresponding to realizable high - finesse optical cavities and alkali atoms like rubidium . pacs numbers : : 32.80.ee , 42.50.ex , 37.30.+i , 42.50.

hep-th9805171

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the description of certain charged black holes as d - branes in string theory implies a connection between the low - energy gauge dynamics on the brane and the low energy supergravity in spacetime . recently , maldacena has proposed decoupling limits in which the brane gauge dynamics is dual to string theory on the near - horizon anti - de sitter geometry of the corresponding black hole @xcite . a more precise definition of this duality was developed in @xcite . we associate to the string compactification on @xmath6 a conformal field theory living on a space conformal to the @xmath7-dimensional boundary @xmath8 of the ads factor . to each field @xmath9 there is a corresponding local operator @xmath10 in the conformal field theory . the relation between string theory in the bulk and field theory on the boundary is : @xmath11 here @xmath12 is the effective action in the bulk , @xmath13 is the field @xmath9 restricted to the boundary , and @xmath14 is the time - ordering symbol in the field theory on @xmath8 . the expectation value on the right hand side is taken in the boundary field theory , with @xmath13 treated as a source term . in the classical supergravity limit , given a boundary field we solve for the corresponding bulk field and use it to relate the bulk effective action to boundary correlation functions . in euclidean ads this proposal used the absence of normalizable solutions to the field equations , and the resulting unique extension of a boundary field @xmath13 into the bulk @xcite . we are interested in issues of spacetime causal structure and dynamics , so we would also like a hamiltonian formulation of the bulk theory in lorentzian signature ads spaces . the standard construction of quantum field theory depends on the existence of a complete set of normalizable modes , which is in tension with the unique extendibility of ads boundary conditions into the bulk . indeed , several consistent quantizations have been found @xcite , involving particular choices of boundary conditions for ads spacetimes and the resulting set of normalizable modes . on the other hand , the bulk - boundary correspondence demands the ability to tune the boundary conditions in order to describe the appropriate boundary correlation functions . in this paper we resolve these tensions by arguing that the bulk - boundary correspondence as formulated in @xcite demands the inclusion of both normalizable and non - normalizable modes . the former propagate in the bulk and correspond to physical states while the latter serve as classical , non - fluctuating backgrounds and encode the choice of operator insertions in the boundary theory . we begin in sec . [ sec : review ] by reviewing the computation of boundary correlation functions , and providing a prescription for computing the bulk effective action in a hamiltonian formulation . we will argue that specifying the boundary conditions involves turning on non - normalizable modes which do not fluctuate . including such non - fluctuating modes may seem strange , but several well - known examples exist in other contexts : a classic example is a field theory which undergoes spontaneous symmetry breaking , and more recent related examples arise in @xcite . normalizable solutions to the wave equation are then used in the mode expansion of operators and the construction of a fock space . the resulting hilbert space of states is identified with the hilbert space of the boundary theory @xcite . in sec . [ sec : norm ] we make this more explicit by studying solutions to the wave equation for free scalars of arbitrary mass . we find that for general masses , the field equations have both normalizable and non - normalizable solutions and the latter couple to the boundary . in sec . [ sec : ads3 ] we specialize to @xmath0 , whose bulk isometry group and boundary conformal group are both @xmath15 . we show that the normalizable modes transform in unitary irreducible representations of @xmath16 while the non - normalizable modes transform in non - unitary reducible representations which contain a highest weight module . the normalizable and non - normalizable highest weight representations are built on states with @xmath1 weights @xmath17 . is the inverse of the cosmological constant of @xmath0 . ] interesting subtleties arise for small masses and for integral @xmath18 . we carry out the analysis in both global and poincar coordinates in order to discuss conformal field theories both on the cylinder and the plane . the latter case has some curious features because poincar coordinates only cover a patch of the global spacetime . we conclude the paper with a discussion of the utility and limitations of the bulk - boundary correspondence for describing bulk spacetime physics via the boundary gauge theory .

we investigate the details of the bulk - boundary correspondence in lorentzian signature anti - de sitter space . operators in the boundary theory couple to sources identified with the boundary values of non - normalizable bulk modes . such modes do not fluctuate and provide classical backgrounds on which bulk excitations propagate . normalizable modes in the bulk arise as a set of saddlepoints of the action for a fixed boundary condition . they fluctuate and describe the hilbert space of physical states . we discuss the group properties of mode solutions in both global and poincar coordinates and their relation to different expansions of operators on the cylinder and on the plane . finally , we discuss the extent to which the boundary theory is a useful description of the bulk spacetime . # 1([#1 ] ) * bulk vs. boundary dynamics * * in anti - de sitter spacetime * * vijay balasubramanian , per kraus and albion lawrence * .5 cm __lyman laboratory of physics , harvard university _ _ _ cambridge , ma 02138 , usa

we investigate the details of the bulk - boundary correspondence in lorentzian signature anti - de sitter space . operators in the boundary theory couple to sources identified with the boundary values of non - normalizable bulk modes . such modes do not fluctuate and provide classical backgrounds on which bulk excitations propagate . normalizable modes in the bulk arise as a set of saddlepoints of the action for a fixed boundary condition . they fluctuate and describe the hilbert space of physical states . we provide an explicit , complete set of both types of modes for free scalar fields in global and poincar coordinates . for , the normalizable and non - normalizable modes originate in the possible representations of the isometry group for a field of given mass . we discuss the group properties of mode solutions in both global and poincar coordinates and their relation to different expansions of operators on the cylinder and on the plane . finally , we discuss the extent to which the boundary theory is a useful description of the bulk spacetime . # 1([#1 ] ) * bulk vs. boundary dynamics * * in anti - de sitter spacetime * * vijay balasubramanian , per kraus and albion lawrence * .5 cm __lyman laboratory of physics , harvard university _ _ _ cambridge , ma 02138 , usa _ .5 cm _ california institute of technology _ _ pasadena , ca 91125 , usa _ # 1#2

astro-ph0604063

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galaxy environment has a fundamental role in the evolutionary paths followed by galaxies . it is well known that galaxy populations change according to the environment in which they are found . the most classical evidence of such environmental dependence is the morphology - density relation ( e.g. * ? ? ? * ; * ? ? ? the fraction of galaxies with distinct morphological types ( essentially spirals , lenticulars and ellipticals ) correlates strongly with the local galaxy density , with high - density environments being populated preponderantly by early - type galaxies . this is related to the dependence of the fraction of star - forming galaxies with the environment , based in the presence or not of emission lines , such as h@xmath2 and , in galaxy spectra ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? such dependence is also intrinsically related to the reduced gaseous content of galaxies in denser regions @xcite . recent studies have found that the star formation rate ( sfr ) of galaxies is the most sensitive parameter to galaxy environment , declining strongly in high - density regions of galaxy clusters ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , whereas structural parameters are less affected by environment @xcite . the relation environment - sfr has also an additional dependence on galaxy luminosity , being steeper for fainter galaxies @xcite . however , when one restricts the analysis to star - forming galaxies the median sfr of this class of objects seems to be unaffected by environment , although the fraction of such galaxies decreases with increasing local density @xcite . the most plausible way to account for these trends is to assume that galaxy properties ( mainly those related to star formation and gas properties ) are affected by environment through well known physical mechanisms acting on galaxies . this path , linked directly to the environment , gives origin to a _ nurture _ perspective for galaxy evolution . in fact , several physical mechanisms were already proposed and studied to account for the evolutionary trends discussed above . interactions between the intragalactic and intergalactic medium , including gas removal and evaporation ( _ ram pressure stripping _ ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and the suppression of the accretion of gas - rich materials in the neighbourhood of the galaxy ( _ starvation _ ; * ? ? ? * ; * ? ? ? * ) , are typical mechanisms claimed to affect star formation properties of galaxies infalling onto denser regions . another path by which galaxy evolution proceeds is related to the initial conditions established during the formation epoch of galaxies , which could , in principle , account for the relations between galaxy properties and environment . this path gives origin to a _ nature _ perspective driving galaxy evolution . as expected from a biased galaxy formation scenario ( e.g. * ? ? ? * ) , massive galaxies are formed earlier preferentially in high - density regions ; in opposition , low mass galaxies would be formed later with a smooth distribution in the density field . thus , in this scenario there is , naturally , an expected relation between age of formation ( or mass ) and environmental density . in fact , hierarchical galaxy formation models successfuly reproduce the morphology - density relation ( e.g. * ? ? ? * ) , demonstrating that it is present even if the physical mechanisms mentioned above are not considered . additionally , studies based on high - redshift galaxies ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * and others ) and also on local galaxies ( kauffmann et al . 2003a ; heavens et al . 2004 ; mateus et al . 2006 , hereafter seagal ii ) have revealed that the existence of a ` downsizing ' in galaxy formation is extremely important in analysis involving the star formation properties of galaxies . these results suggest that massive galaxies have stopped to form stars at earlier times , with low mass systems comprising a large fraction among galaxies with ongoing star formation . these trends are also recovered by recent high - resolution simulations ( e.g. * ? ? ? * ) and semi - analytic models for galaxy formation ( e.g. * ? ? ? * ; * ? ? ? . however , the physical origin of the downsizing is still a subject of debate ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . here we will shed some light into the discussion concerning galaxy formation and evolution by investigating the role of environment on the stellar population properties of galaxies in the nearby universe . other works have increased our understanding on this issue through distinct approaches ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . in this paper , we will use the results of the application of a spectral synthesis method to a volume limited sample of sdss galaxies . this method is able to recover important physical properties of galaxies from their spectra , including mean stellar ages , mean stellar metallicities and stellar masses , among others . the details of such approach were discussed by cid fernandes et al . ( 2005 ) ( hereafter seagal i ) and its results have been recently used in seagal ii , where we have studied the bimodality of the galaxy population . in this work we show that the relations between galaxy properties and environment , well characterised by the age density relation , are distinct when we divide galaxies according to luminosity or stellar mass . this is a result of the different mass - to - light ( @xmath3 ) ratios of galaxies in distinct environments . in dense regions galaxies of same luminosity tend to have higher @xmath3 ratios . we argue that a natural path emerges from these results but via a nurture way in the sense that massive galaxies are formed preferentially in high - density regions ( where the evolution was accelerated ) in the high-@xmath4 universe ( when the star formation rate was high ) , since their stellar populations also tend to be the oldest ones and they inhabit the densest regions we observe in the local universe . the paper is organised as follows . section 2 describes the data used in this work , the galaxy sample definition and a brief overview of the spectral synthesis method used in our analysis . section 3 describes some parameters related to star formation activity in galaxies that will be discussed in this work , and section 4 defines the environmental parameter , namely the projected local galaxy density . in section 5 we investigate the environmental dependence of the stellar population properties of galaxies . finally , in section 6 we discuss the implications of our findings in the context of galaxy evolution , and in section 7 we summarise the main results of this work .

physical quantities related to the stellar content of galaxies are derived from a spectral synthesis method applied to a volume - limited sample containing more than 60 thousand galaxies ( ; ) , extracted from the data release 4 of the sloan digital sky survey ( sdss ) . density relation is distinct when we divide galaxies according to luminosity or stellar mass .

we investigate the environmental dependence of stellar population properties of galaxies in the local universe . physical quantities related to the stellar content of galaxies are derived from a spectral synthesis method applied to a volume - limited sample containing more than 60 thousand galaxies ( ; ) , extracted from the data release 4 of the sloan digital sky survey ( sdss ) . mean stellar ages , mean stellar metallicities and stellar masses are obtained from this method and used to characterise the stellar populations of galaxies . the environment is defined by the projected local galaxy density estimated from a nearest neighbour approach . we recover the star formation density relation in terms of the mean light - weighted stellar age , which is strongly correlated with star formation parameters derived from h . we find that the age density relation is distinct when we divide galaxies according to luminosity or stellar mass . the relation is remarkable for galaxies in all bins of luminosity . on the other hand , only for an intermediate stellar mass interval ( associated to a transition in galaxy properties ) the relation shows a change in galaxy properties with environment . such distinct behaviours are associated to the large stellar masses of galaxies with the same luminosity in high - density environments . in addition , the well known star formation density relation results from the prevalence of massive systems in high - density environments , independently of galaxy luminosity , with the additional observed downsizing in galaxy formation , in which the star formation is shifted from massive galaxies at early times to low - mass galaxies as the universe evolves . finally , our results support that a natural path for galaxy evolution proceeds _ via _ a nurture way , in the sense that galaxy evolution is accelerated in denser environments , that took place mainly at high - redshifts . galaxies : evolution galaxies : formation galaxies : fundamental parameters galaxies : stellar content stars : formation [ firstpage ]

astro-ph0604063

i

in this fourth paper of the seagal collaboration , we have shed some light on the discussion about the environmental dependence of galaxy properties in the local universe . we based our analysis on the stellar population properties of galaxies in a volume - limited sample drawn from the sdss data release 4 . the application of a spectral synthesis method to the data produces robust estimators for mean stellar ages , mean stellar metallicities and stellar mass , which have been used in this work to characterise the stellar populations of galaxies . the environment is defined by the local galaxy density estimated from a nearest neighbour approach , and by the distance to cluster centres obtained from a public catalogue of sdss clusters . the main approach used in this study is the comparison of the relations between galaxy properties and environment for galaxies divided in intervals of luminosity and stellar mass . we summarise our main findings below : 1 . we recover the star formation density relation in terms of the mean light - weighted stellar age , @xmath31 , which is strongly correlated with star formation parameters derived from h@xmath2emission line . 2 . we confirm that high - density environments are populated by a large fraction of massive galaxies with old stellar populations , in opposition to low - density regions , dominated by low - mass galaxies actively forming stars . we also note that galaxies with intermediate stellar masses have constant fractions along the range of densities covered by our sample . the transition in galaxy fraction occurs at @xmath65 @xmath66 mpc@xmath67 , corresponding to 23 virial radii from cluster centres . the environmental dependence of @xmath31 is distinct when we divide galaxies according to luminosity or stellar mass . the relation between mean age and local density is remarkable for galaxies in all bins of luminosity . on the other hand , only for a intermediate stellar mass interval ( associated to a transition in galaxy properties ) the relation shows a change in galaxy properties . for low - mass galaxies , the relation slightly increases along the density range , but showing low values of @xmath31 characteristic of late - type galaxies in all environments . the most massive galaxies also show a slight change in the median values of @xmath31 as galaxy density increases , but their values are higher everywhere . we find that the distinct behaviours of the _ age density relation _ for galaxies divided by luminosity or stellar mass are associated to the large stellar mass of galaxies with the same luminosity in dense environments . in other words , the well known star formation density relation results from the prevalence of massive systems in high - density environments , independently of galaxy luminosity , in addition to the observed downsizing in galaxy formation , where the star formation is shifted from massive galaxies at early times to low - mass ones as the universe evolves . a principal component analysis of our parameter set reveals that the local galaxy density is the primary responsible for the total variance present in our data , whereas the mean light - weighted stellar age of galaxies is the second one . this result reflects that the age density relation is the main driver of the environmental dependence observed in some galaxy properties . the mean stellar metallicity of less massive / luminous galaxies increases in high - density regions , indicating that even low - mass galaxies in dense environments tend to be more evolved than their counterparts in low - density regions . our results support that a natural path for galaxy evolution proceeds _ via _ a nurture way mainly at high - redshifts : massive galaxies have been formed in denser regions and evolved in an accelerated way , contrasting with a more _ unsocial _ life of low - mass galaxies preferentially inhabiting low density regions of the universe . in this work , the concept of ` nature via nurture ' ( see * ? ? ? * for a genetic view of this expression ) in the scenario of galaxy evolution was advocated in order to summarise the results obtained here related to the environmental dependence of galaxy properties in the local universe . many steps are needed towards a comprehensive view of the processes which have guided galaxy formation and evolution , mainly those related to the properties of the stellar content of galaxies in high redshifts . we expect to contribute further to these issues in other papers of this series on semi - empirical analysis of galaxies .

mean stellar ages , mean stellar metallicities and stellar masses are obtained from this method and used to characterise the stellar populations of galaxies . the environment is defined by the projected local galaxy density estimated from a nearest neighbour approach . we recover the star formation density relation in terms of the mean light - weighted stellar age , which is strongly correlated with star formation parameters derived from h . we find that the age the relation is remarkable for galaxies in all bins of luminosity . on the other hand , only for an intermediate stellar mass interval ( associated to a transition in galaxy properties ) the relation shows a change in galaxy properties with environment . such distinct behaviours are associated to the large stellar masses of galaxies with the same luminosity in high - density environments . in addition , the well known star formation density relation results from the prevalence of massive systems in high - density environments , independently of galaxy luminosity , with the additional observed downsizing in galaxy formation , in which the star formation is shifted from massive galaxies at early times to low - mass galaxies as the universe evolves . finally , our results support that a natural path for galaxy evolution proceeds _ via _ a nurture way , in the sense that galaxy evolution is accelerated in denser environments , that took place mainly at high - redshifts .

we investigate the environmental dependence of stellar population properties of galaxies in the local universe . physical quantities related to the stellar content of galaxies are derived from a spectral synthesis method applied to a volume - limited sample containing more than 60 thousand galaxies ( ; ) , extracted from the data release 4 of the sloan digital sky survey ( sdss ) . mean stellar ages , mean stellar metallicities and stellar masses are obtained from this method and used to characterise the stellar populations of galaxies . the environment is defined by the projected local galaxy density estimated from a nearest neighbour approach . we recover the star formation density relation in terms of the mean light - weighted stellar age , which is strongly correlated with star formation parameters derived from h . we find that the age density relation is distinct when we divide galaxies according to luminosity or stellar mass . the relation is remarkable for galaxies in all bins of luminosity . on the other hand , only for an intermediate stellar mass interval ( associated to a transition in galaxy properties ) the relation shows a change in galaxy properties with environment . such distinct behaviours are associated to the large stellar masses of galaxies with the same luminosity in high - density environments . in addition , the well known star formation density relation results from the prevalence of massive systems in high - density environments , independently of galaxy luminosity , with the additional observed downsizing in galaxy formation , in which the star formation is shifted from massive galaxies at early times to low - mass galaxies as the universe evolves . finally , our results support that a natural path for galaxy evolution proceeds _ via _ a nurture way , in the sense that galaxy evolution is accelerated in denser environments , that took place mainly at high - redshifts . galaxies : evolution galaxies : formation galaxies : fundamental parameters galaxies : stellar content stars : formation [ firstpage ]

cond-mat0106546

i

vortex motion is the principle mechanism for resistive losses in type ii superconductors . vortices also provide valuable information about the nature of low lying excitations in the superconducting state . in clean @xmath1-wave bcs superconductors the low - lying excitations in the core are the bound states of caroli , de gennes and matricon @xcite . these excitations have superconducting as well as normal metallic properties . for example , these states are the source of circulating supercurrents in the equilibrium vortex core , and they are strongly coupled to the condensate by andreev scattering @xcite . furthermore , the response of the vortex core states to an electromagnetic field is generally very different from that of normal electrons . however , in the dirty limit , @xmath2 , the the bardeen - stephen model @xcite of a normal - metal spectrum with the local drude conductivity in the core provides a reasonable description of the dissipative dynamics of the vortex core . the opposite extreme is the `` superclean limit '' , @xmath3 , in which the quantization of the vortex - core bound states must be taken into account . in this limit a single impurity and its interaction with the vortex core states must be considered . electromagnetic response is then controlled by selection rules governing transition matrix elements for the quantized core levels and the level structure of the core states in the presence of an impurity @xcite . in the case of d - wave superconductors in the superclean limit , _ nodes _ in the spectrum of bound states lead to a finite dissipation from landau damping for @xmath4 @xcite . the superclean limit is difficult to achieve even for short coherence length superconductors ; weak disorder broadens the vortex core levels into a quasi - continuum . we investigate the intermediate - clean regime , @xmath5 , where the discrete level structure of the vortex - core states is broadened and the selection rules are broken due to strong overlap between the bound state wave functions . however , the vortex core states remain well defined on the scale of the superconducting gap , @xmath6 . in this regime we can take advantage of the power of the quasiclassical theory of nonequilibrium superconductivity @xcite . the energy required to maintain a net charge density of order an elementary charge per particle within a coherence volume ( or coherence area in two dimensions ) is much larger than the condensation energy . thus , charge accumulation in the vortex core is strongly suppressed . in order to reduce the coulomb energy associated with the charge accumulation an internal electrochemical potential , @xmath7 , develops in response to an external electric field . this potential produces an internal electric field , @xmath8 , which is the same order of magnitude as the external field . even though the external field may vary on a scale that is large compared to the coherence length , @xmath9 , the internal field develops on the coherence length scale . the source of the internal field is a charge density that accumulates inhomogeneously over length scales of order the coherence length . it is necessary to calculate the induced potential self consistently from the spatially varying order parameter , spectral function and distribution function for the electronic states in the vicinity of the vortex core . an order of magnitude estimate shows that to produce an induced field of the order of the external field , the dynamically induced charge is of order @xmath10 , where @xmath11 is the typical energy scale set by the strength of the external field . this charge density accumulates predominantly in the vortex core region and creates a dipolar field around the vortex core . for a pinned vortex the charge accumulates near the interface separating the metallic inclusion from the superconductor . disorder plays a central role in the dissipative dynamics of the mixed state of type ii superconductors . impurities and defects are a source of scattering that limits the mean free path of carriers , thus increasing the resistivity . defects also provide ` pinning sites ' that inhibit vortex motion and suppresses the flux - flow resistivity . however , for _ a.c . _ fields even pinned vortices are sources for dissipation . the magnitude and frequency dependence of this dissipation depends on the electronic structure and dynamics of the core states of the pinned vortex . in the analysis presented below we consider vortices in the presence of pinning centers . we model a pinning center as a normal metallic inclusion which is coupled to the electronic states of the superconductor through a highly transmitting interface . in this model the charge dynamics of the electronic states near the interface between the pinning region and superconductor plays an important role in the electromagnetic response of the core . in the next section we provide a short summary of the nonequilibrium quasiclassical equations , including the transport equations for the quasiparticle distribution and spectral functions , constitutive equations for the order parameter , impurity self - energy and electromagnetic potentials . in section [ sec : electronic_structure ] we present calculations for the the electronic structure of vortices for superconductors with both @xmath1-wave and @xmath12-wave pairing symmetry . the results are based on self - consistent calculations of the order parameter and impurity self energy . for @xmath1-wave superconductors , impurity scattering leads to inhomogeneous broadening of the vortex core bound states , as well as bands of impurity states within the gap . in the case of @xmath12-wave pairing the core states are further broadened by coupling between bound states and the continuum states through impurity scattering . we also discuss the structure of doubly quantized vortices and vortices bound to mesoscopic size metallic inclusions . in the case of the doubly quantized vortex there are two branches of zero - energy bound states centered at finite impact parameter from the vortex center . this leads to a unique signature of a doubly quantized vortex : currents in the core circulate opposite to the supercurrents outside the core . section [ sec : nonequilibrium_response ] summarizes calculations of the vortex core dynamics for @xmath1-wave vortices in the presence of impurity scattering . we describe the charge dynamics of the vortex core for both pinned and unpinned vortices , and calculate the local a.c . conductivity that results from the coupled dynamics of the order parameter collective mode and the quasiparticle bound states in the vortex core . we discuss energy transport by the core states and the absorption features in the conductivity spectrum , which we interpret in terms of absorption within the bound - state band centered at the fermi level and resonant transitions involving the bound and continuum states .

we discuss the electronic structure of singly and doubly quantized vortices for both s - wave and d - wave pairing symmetry . we consider the intermediate clean regime , where the vortex - core bound states are broadened into resonances with a width comparable to or larger than the quantized energy level spacing , and calculate the response of a vortex core to an _ a.c . we then obtain the dynamical conductivity , spatially resolved in the region of the core , for external frequencies in the range , . we also calculate the dynamically induced charge distribution in the vicinity of the core . . presented at the 2000 workshop on _ microscopic structure and dynamics of vortices in unconventional superconductors and superfluids _ , held at the _ max planck institute for the physics of complex systems _ in dresden .

we investigate the equilibrium and nonequilibrium properties of the core region of vortices in layered superconductors . we discuss the electronic structure of singly and doubly quantized vortices for both s - wave and d - wave pairing symmetry . we consider the intermediate clean regime , where the vortex - core bound states are broadened into resonances with a width comparable to or larger than the quantized energy level spacing , and calculate the response of a vortex core to an _ a.c . _ electromagnetic field for vortices that are pinned to a metallic defect . we concentrate on the case where the vortex motion is nonstationary and can be treated by linear response theory . the response of the order parameter , impurity self energy , induced fields and currents are obtained by a self - consistent calculation of the distribution functions and the excitation spectrum . we then obtain the dynamical conductivity , spatially resolved in the region of the core , for external frequencies in the range , . we also calculate the dynamically induced charge distribution in the vicinity of the core . this charge density is related to the nonequilibrium response of the bound states and collective mode , and dominates the electromagnetic response of the vortex core . presented at the 2000 workshop on _ microscopic structure and dynamics of vortices in unconventional superconductors and superfluids _ , held at the _ max planck institute for the physics of complex systems _ in dresden .

1503.07147

r

* the length is sufficient to characterize the exponential growth of each cell*. various techniques have been put forth to analyze cell morphology gathered from single cell images @xcite . recent work on image analysis of single cells has attempted to optimize two problems : separation of distinct ( but potentially overlapping ) cells and accurate determination of the edge of each cell @xcite . because crowding is not an issue in our setup , we could focus solely on constructing an algorithm to delineate each cell contour accurately and precisely . as shown in fig . 1a , b and described in the methods section , we first segment each cell using pixel - based edge detection similar to @xcite , then perform spline interpolation to determine the cell contour at sub - pixel resolution . the sequence of such images for each single cell constitutes a trajectory in time @xmath3 that serves as the basis for quantitative analysis . division events are then detected in an automated fashion using custom python code , and used to divide time trajectories for each cell into individual generations . all data shown here were obtained by observing 260 single _ c. crescentus _ cells perfused in complex medium ( peptone - yeast extract ; pye ) at 31@xmath4c over the course of 2 days ( corresponding to 9672 separate generations ) . under these conditions , the mean population growth rate and division time remain constant , so we treat the trajectories of individual generations as members of a single ensemble . in other words , we segment each cell trajectory by generation and take the resulting initial frame ( i.e. , immediately following division ) as @xmath5 minutes . in order to average over the ensemble , we then bin quantitative information according to time since division , @xmath3 , normalized by the respective division time @xmath6 . the normalized time , @xmath7 , serves as a cell - cycle phase variable . for our quantitative analysis , we focus on a set of three intuitive and independent parameters that characterize cell shape at each stage of growth : length @xmath8 , width @xmath9 , and radius of curvature @xmath10 ( fig . 1c ) . they are calculated directly from each splined contour as follows ( see also supplementary fig . 1 ) : * we define the length , @xmath11 , as the pole - to - pole distance along the contour of the cell medial axis at the normalized time @xmath12 ( fig . 2a ) . * we assign a single radius of curvature , @xmath13 , to each cell based upon the best - fit circle to the medial axis ( fig . although stalked ( @xmath14 ) and swarmer ( @xmath15 ) portions may be described by different radii of curvature toward the end of the cell cycle , the average radius obtained by averaging the contributions of each portion yields the same value , i.e. , @xmath16 ( see supplementary fig . 2c ) . * we define the width , @xmath17 as the length of the perpendicular segment spanning from one side of the cell contour to the other at each position @xmath18 along the medial axis , which runs from @xmath19 at the stalked pole to @xmath20 at the swarmer pole . furthermore , we spatially averaged the width over positions along the medial axis , @xmath21 , to obtain a characteristic width at each time point ( fig . 2c ) . the mean division time is @xmath22 min , where @xmath23 indicates a population average . we find that @xmath24 increases exponentially with time constant @xmath25 min , essentially the same time constant that we previously observed for the cross - sectional area @xcite , while @xmath26 and @xmath27 remain approximately constant for @xmath28 and each shows a dip for @xmath29 when cell constriction becomes prominent . the sharp rise in @xmath27 seen for @xmath30 results from independent alignment of the stalked and swarmer portions with the microfluidic flow as they become able to move independently ( i.e. , fluctuate easily about the plane of constriction ) . these observations confirm the assumptions in @xcite that the length is sufficient to describe the growth of cell size . moreover , we can track the dynamics of the spanning angle , @xmath31 , using the relation @xmath32 . * mechanical model for cell shape and growth*. there are many details of cell growth and shape that require interpretation . for example , it is not obvious _ a priori _ that growth should be almost exclusively longitudinal . therefore , we have developed a minimal mechanical model that can explain these observations . we parametrize the geometry of the cell wall by a collection of shape variables @xmath33 , where @xmath34 , @xmath35 , and @xmath36 are the parameters introduced above ( fig . as the cell grows in overall size , we postulate that the rate of growth in the shape parameter @xmath37 is proportional to the net decrease in cell wall energy , @xmath38 , per unit change in @xmath37 @xcite . assuming linear response , the configurational rate of strain , @xmath39 , is proportional to the corresponding driving force @xmath40 , in analogy with the constitutive law of newtonian flow @xcite : @xmath41 where the constant @xmath42 describes the rate of irreversible flow corresponding to the variable @xmath37 . according to equation , exponential growth occurs if @xmath43 is constant , whereas @xmath37 reaches a steady - state value if @xmath44 along with the condition @xmath45 . it thus remains to specify the form of @xmath46 . for a _ c. crescentus _ cell of total volume @xmath47 and surface area @xmath48 , our model for the total energy in the cell wall is given by @xmath49 where @xmath50 is a constant pressure driving cell wall expansion ; @xmath51 is the tension on the surface of the cell wall ; @xmath52 is the energy required to maintain the cell width ; @xmath53 represents the mechanical energy required to maintain the crescent cell shape ; @xmath54 is the energy driving cell wall constriction . traditionally @xmath50 was taken to be the turgor pressure @xcite ; while the importance of the turgor pressure has recently been questioned @xcite , an effective pressure must still arise from the synthesis and insertion of peptidoglycan strands that constitute the cell wall . we note that a purely elastic description of cell wall mechanics would lead to a curvature - dependent surface tension @xcite . however , if growth is similar to plastic deformation , the tension is uniform @xcite . the effective tension in our model depends on the local surface curvatures through the energy terms @xmath52 and @xmath53 , that describe harmonic wells around preferred values of surface curvatures . the mechanical energy for maintaining width is given by @xmath55 where the constant @xmath56 is the preferred radius of curvature , @xmath57 is the bending rigidity and @xmath58 is a differential area element @xcite . contributions to @xmath57 can come from the peptidoglycan cell wall as well as membrane - associated cytoskeletal proteins like mreb , mrec , rodz , etc . , which are known to control cell width @xcite . in addition to maintaining a constant average width , _ c. crescentus _ cells exhibit a characteristic crescent shape , which relies on expression of the intermediate filament - like protein crescentin @xcite . although the mechanism by which crescentin acts is not known , various models have been proposed , including modulation of elongation rates across the cell wall @xcite and bundling with a preferred curvature @xcite . we assume the latter and write the energy for maintaining the crescent shape as @xmath59 where @xmath60 is the arc - length parameter along the crescentin bundle attached to the cell wall , @xmath61 is the local curvature , @xmath62 is the preferred radius of curvature , @xmath63 is the contour length , and @xmath64 is the linear bending rigidity . equation accounts for the compressive stresses generated by the crescentin bundle on one side of the cell wall , leading to a reduced rate of cell growth , according to equation . as a result , the cell wall grows differentially and maintains a non - zero curvature of the centerline . in the absence of crescentin ( @xmath65 ) , our model predicts an exponential decay in the cell curvature that leads to a straight morphology , consistent with previous observations @xcite . finally , one must also account for the energy driving cell wall constriction . constriction proceeds via insertion of new peptidoglycan material at the constriction site . this process leads to the formation of daughter pole caps @xcite . we take constriction to be governed by an energy of the form @xmath66 , where @xmath67 is the surface area of the septal cell wall , and @xmath68 is the energy per unit area released during peptidoglycan insertion . * there exists an optimal cell geometry for a given mechanical energy*. to apply the model introduced above ( equations and ) to interpreting the data in fig . 2 , we assume a minimal cell geometry given by a toroidal segment with uniform radius of curvature @xmath13 , uniform cross - sectional width @xmath21 and the spanning angle @xmath69 . to this end , we estimate as many mechanical parameters as we can from the literature and then determine the rest by fitting our experimentally measured values . turgor pressure in gram - negative bacteria has been measured to be in the range @xmath70 mpa @xcite . we use a value for the effective internal pressure close to the higher end of the measured values for turgor pressure , @xmath71 mpa , in order to account for peptidoglycan insertion . we estimate the surface tension as @xmath72 nn@xmath73 m ( see supplementary model section ) and multiply it by the cell surface area @xmath74 to obtain the cell wall surface energy . first , we neglect cell constriction ( setting @xmath75 ) and assume that the crescentin structure spans the length of the cell wall ( excluding the endcaps ) @xcite , with a contour length @xmath76 . the mechanical properties of mreb and crescentin are likely similar to those of f - actin and intermediate filaments , respectively @xcite . however , due to a lack of direct measurements , we obtain the mechanical parameters @xmath57 and @xmath64 by fitting the model to the experimental data . as desired , we find that the total energy @xmath46 has a stable absolute minimum at particular values of the cross - section diameter @xmath77 and the centerline radius @xmath10 , given by solution of @xmath78 ( see supplementary fig . 4 ) . the measured values are @xmath79 m and @xmath80 m ( @xmath28 ) , and , as indicated by the red solid curves in fig . 2b , c , the model reproduces them with @xmath81 nn@xmath82 m and @xmath83 nn@xmath82m@xmath84 . while the fitted value for @xmath64 is numerically close to the estimate based on the known mechanical properties of intermediate filaments ( @xmath85 nn@xmath82m@xmath84 ) , the value for @xmath57 is much higher than the bending rigidity of mreb bundles ( see supplementary information ) . this indicates that @xmath57 is only determined in part by mreb and can have contributions from the cell wall . given stable values for @xmath77 and @xmath10 , growth is completely described by the dynamics of the angle variable @xmath69 . consequently , we write the total energy in the scaling form @xmath86 , with @xmath87 the energy density along the longitudinal direction . the condition for growth then becomes @xmath88 , such that the energy is minimized for increasing values of @xmath69 . from our experimental data , the angle spanned by the cell centerline increases by an amount @xmath89 during the entire cycle . using our parameter estimates and fitting the data in fig . 2 , we obtain a numerical value for the energy density @xmath90 nn@xmath82 m . we relate the angle dynamics to the length by @xmath91 where @xmath92 ( @xmath88 ) is the rate of longitudinal growth , which can be interpreted as resulting from remodeling of peptidoglycan subunits with a mean current @xmath93 , across the cell surface area @xmath94 . from an exponential fit to the data for cell length ( fig . 2a ) , we obtain @xmath95 ( nn @xmath82 m min)@xmath96 , which gives us an estimate of the friction coefficient , @xmath97 nn @xmath82m@xmath96 min , associated with longitudinal growth ; e.g. , mreb motion that is known to correlate strongly with the insertion of peptidoglycan strands @xcite . our results are consistent with previous observations of _ c. crescentus _ cells with arrested division but continued growth @xcite . * constriction begins early and proceeds with the same time constant as exponential growth*. having characterized the dynamics of growth , we now turn to constriction at the division plane . as mentioned above , we obtain the experimental width at each point along each cell s medial axis . the typical width profile is non - uniform along its length , exhibiting a pronounced invagination near the cell center ( with width @xmath98 ; fig . this invagination , which ultimately becomes the division plane , is readily identifiable early in the cell cycle , even before noticeable constriction occurs . we discuss the kinetics of constriction in this section , and focus on its location later in the manuscript . as shown in fig . 3a ( black points ) , @xmath99 progressively decreases towards zero until pinching off at @xmath100 . due to the limited spatial resolution of our imaging ( phase contrast microscopy ) , the pinch - off process occurring for @xmath30 could not be captured , but @xmath99 at earlier times ( i.e. , @xmath101 ) is precisely determined as a function of @xmath12 . to model the dynamics of constriction , we assume as in ref . @xcite ( fig . 3a , inset ) : ( i ) the shape of the zone of constriction is given by two intersecting and partially formed hemispheres with radii @xmath102 ; and ( ii ) constriction proceeds by completing the missing parts of the hemisphere such that the newly formed cell wall surface maintains the curvature of the pre - formed spherical segments . as a result , a simple geometric formula is obtained that relates the width of the constriction zone , @xmath98 , to the surface area @xmath103 of the newly formed cell wall , @xmath104 where @xmath105 is the maximum surface area achieved by the caps as the constriction process is completed , i.e. , when @xmath106 . we assume that the addition of new cell wall near the division plane initiates with a rate , @xmath107 , and thereafter grows exponentially with a rate , @xmath108 , according to , @xmath109 subject to the initial condition @xmath110 . the first term on the right - hand side of equation follows from equation , using @xmath103 as the shape variable , after incorporating the constriction energy @xmath111 . the rate of septal peptidoglycan synthesis , @xmath108 , is thus directly proportional to the energy per unit area released during constriction , @xmath68 . the solution , @xmath112 , can then be substituted into equation to derive the time - dependence of @xmath98 , whose dynamics is controlled by two time scales : @xmath113 and @xmath114 . fitting equation with the data for @xmath99 , we obtain @xmath115 min and @xmath116 min . the fitted values for the time constants controlling constriction dynamics ( @xmath113 and @xmath114 ) are remarkably similar to that of exponential cell elongation ( @xmath117 min ) . this shows that septal growth proceeds at a rate comparable to longitudinal growth . therefore , one of the main conclusions that we draw is that cell wall constriction ( fig . 3a ) is controlled by the same time constant as exponential longitudinal growth ( fig . 2a ) . having determined the dynamics of @xmath98 , we compute the average width across the entire cell @xmath21 using the simplified shape of the constriction zone as shown in fig . 3a ( inset ) . the resultant prediction ( blue solid curve in fig . 2c ) is in excellent agreement with the experimental data and captures the dip in @xmath26 seen for @xmath118 . constriction also leads to a drop in the average radius of curvature of the centerline , as shown by the experimental data in fig . in the supplementary material we derive a relation between the centerline radius of curvature @xmath13 and the minimum width @xmath98 , given by @xmath119 , predicting that cell curvature increases at the same rate as @xmath98 drops . using this relation , we are able to quantitatively capture the dip in @xmath27 seen for @xmath118 ( solid blue curve in fig . 2b ) without invoking any additional fitting parameters . * origin of the asymmetric location of the primary invagination*. we now consider the position of the division plane and its interplay with cell shape . as shown in fig . 3b , the distance of the width minimum from the stalked pole ( @xmath120 ) increases through the cell cycle at the same rate as the full length of the growing cell ( @xmath11 ) , such that their ratio remains constant with time - averaged mean @xmath121 . the presence of the primary invagination early in the cell cycle is reiterated in fig . 3c , which shows the width profile constructed by ensemble - averaging over each cell at the timepoint immediately following division . in addition to the width minimum @xmath98 , there are two characteristic maxima near either pole , @xmath122 and @xmath123 , respectively ( fig . 3c , inset ) . as evident in fig . 3c , the stalked pole diameter @xmath124 is on average larger than its swarmer counterpart @xmath125 ( also see supplementary fig . we show that the asymmetric location of the invagination ( and the asymmetric width profile ) can originate from the distinct mechanical properties inherent to the pole caps in _ c. crescentus_. the shapes of the cell poles can be explained by laplace s law that relates the pressure difference , @xmath50 , across the cell wall to the surface tensions in the stalked or the swarmer pole , @xmath126 . the radii of curvature of the poles then follow from laplace s law @xmath127 where the superscript ( @xmath128 ) denotes the stalked or the swarmer pole . thus a larger radius of curvature in the poles has to be compensated by a higher surface tension to maintain a constant pressure difference @xmath50 . assuming that the poles form hemispheres , we have @xmath129 . our data indicate that the early time ratio for @xmath130 ( @xmath131 ) shows a strong positive correlation with the ratio @xmath132 , with an average value @xmath133 ( see supplementary fig 3a ) . laplace s law then requires that the stalked pole be mechanically stiffer than the swarmer pole ; @xmath134 . this observation suggests that the asymmetry in the lengths of the stalked and swarmer parts of the cell depends upon different mechanical properties of the respective poles . to quantitatively support this claim , we investigate an effective contour model for the cell shape . to this end , we assume that the fluctuations in cell shape relax more rapidly than the time scale of growth . this separation of timescales allows us to derive the equation governing the cell contour by minimizing the total mechanical energy ( equation ) . from the solution we compute the resultant width profile for the entire cell ( see supplementary model section ) . as shown in fig . 3d , the model with asymmetric surface tensions of the poles causes the primary invagination to occur away from the cell mid - plane . the spatial location of the invagination relative to the cell length depends linearly on the ratio @xmath135 . symmetry is restored for @xmath136 , as shown in fig . 3d ( blue dashed curve ) . we note that a gradient in @xmath51 along the cell body would imply differences in longitudinal growth rates between the stalked and the swarmer portions of the cell ( eq . ) . our data exclude this possibility since both @xmath120 and @xmath137 grow at the same rate @xmath138 , as evidenced by the constancy of their ratio ( fig . 3b and supplementary fig . because _ c. crescentus _ does not exhibit polar growth , the _ polar stiffness model _ is consistent with the observed uniformity in longitudinal growth rate . in addition , the non - uniformity in cell width comes from the differences in mechanical response in the cell wall due to preferential attachment of crescentin along the concave sidewall . for a cres mutant cell ( where @xmath65 ) , our model predicts a uniform width profile before the onset of constriction . * cell shape evolution during wall constriction*. the experimental width profiles show that the growing and constricting cells typically develop a second minimum in width ( fig . these secondary invaginations are observed in both the stalked and swarmer portions of single cells in the predivisional stage ( @xmath139 ) , although they are more common in the stalked portions ( fig . we show here that these secondary minima become the primary minima in each of the daughter cells . to study the dynamics of the development of the secondary minimum we introduce a new quantity , @xmath140 , defined as the distance from the stalked pole to the secondary minimum in the stalked part ( see fig . 5c , inset ) we find that the ratio @xmath141 has a mean value of @xmath142 0.55 at later points in the cell cycle ( fig . 5b ) , equal to the constant ratio maintained by the distance from the stalked pole to the primary minimum , @xmath143 . in fact the kymograph of width profiles ( shown over 2 generations for a representative single cell ) in fig . 5c demonstrates that the predivisional secondary invaginations are inherited as primary invaginations after division . this mechanism provides continuity and inheritance of the invaginations across generations and is an intrinsic element of the mechanism for cell division in _ c. crescentus_. to quantitatively explain the experimental width profiles during constriction , we use our mechanical model to determine the instantaneous cell shape by minimizing the total energy ( equation ) at the specified time points ( see supplementary model section ) . to take constriction into account , we impose the constraint that @xmath144 , where @xmath145 is determined by equations and . in addition , we assume non - uniform materials properties in the cell wall by taking the tension in the cell poles ( @xmath146 ) and the septal region to be higher than the rest of the cell . as constriction proceeds and @xmath145 decreases , we compute the shape of the cell contours ( fig . 4c ) and the corresponding width profiles ( fig . the computed width profiles faithfully reproduce the secondary invaginations , which become more pronounced as the daughter pole caps become prominent . an example of the experimental width profiles is shown in fig . 4b at evenly - spaced intervals in time for a single generation , and the corresponding model width profiles are shown in fig . we note that the experimental cell contours in the predivisional stage ( @xmath30 ) bend away from the initial midline axis and develop an alternate growth direction ( fig . 4a , blue contour ) . these bend deformations are induced by the microfluidic flow about the pinch - off plane ; the cells become increasingly `` floppy '' as the constriction proceeds .

furthermore , we find that the asymmetry in the division plane location is inherited from the previous generation . bacteria take forms resembling spheres , spirals , rods , and crescents . super - resolution imaging is now revealing the internal positions of associated proteins . however , due to the inherently stochastic nature of molecular processes , understanding how these proteins act collectively to exert mechanical stresses and modulate the effects of turgor pressure and other environmental factors requires complementary methods such as high - throughput , quantitative optical imaging . we previously addressed this issue by engineering a _ c. crescentus _ strain in which cell adhesion is switched on and off by a small molecule ( and inducible promoter ) , allowing measurements to be made in a simple microfluidic device . c. crescentus _ cells grow exponentially in size and divide upon reaching a critical multiple (.8 ) of their initial sizes . , we use more advanced image analysis methods to extract cell shape contours from these data . specifically , we identify natural variables for tracking cell dynamics , and develop a minimal mechanical model that shows how longitudinal growth can arise from an isotropic pressure . this important finding can be understood in terms of an intuitive geometric model that relates the constriction dynamics to the kinetics of the growth of septal cell wall . we further suggest that the site of constriction can arise from differences in materials properties of the poles and show that it is established in the previous generation i.e . , the location of the site of division can be predicted before formation of the divisome .

we investigate the intergenerational shape dynamics of single _ caulobacter crescentus _ cells using a novel combination of imaging techniques and theoretical modeling . we determine the dynamics of cell pole - to - pole lengths , cross - sectional widths , and medial curvatures from high accuracy measurements of cell contours . moreover , these shape parameters are determined for over 250 cells across approximately 10000 total generations , which affords high statistical precision . our data and model show that constriction is initiated early in the cell cycle and that its dynamics are controlled by the time scale of exponential longitudinal growth . based on our extensive and detailed growth and contour data , we develop a minimal mechanical model that quantitatively accounts for the cell shape dynamics and suggests that the asymmetric location of the division plane reflects the distinct mechanical properties of the stalked and swarmer poles . furthermore , we find that the asymmetry in the division plane location is inherited from the previous generation . we interpret these results in terms of the current molecular understanding of shape , growth , and division of _ c. crescentus_. cell shape both reflects and regulates biological function . the importance of cell shape is exemplified by bacteria , which rely on specific localization of structural proteins for spatiotemporal organization . bacteria take forms resembling spheres , spirals , rods , and crescents . these shapes are defined by cell walls consisting of networks of glycan strands cross - linked by peptide chains to form a thin peptidoglycan meshwork . super - resolution imaging is now revealing the internal positions of associated proteins . these include cytoskeletal proteins such as mreb , a homolog of actin , intermediate filament - like bundles of cres ( crescentin ) , and ftsz , a homolog of tubulin . however , due to the inherently stochastic nature of molecular processes , understanding how these proteins act collectively to exert mechanical stresses and modulate the effects of turgor pressure and other environmental factors requires complementary methods such as high - throughput , quantitative optical imaging . multigenerational imaging data for bacterial cells can now be obtained from microfluidic devices of various designs . still , a common limitation of most devices is that the environmental conditions change throughout the course of the experiment , particularly as geometric growth of the population results in crowding of the experimental imaging spaces . we previously addressed this issue by engineering a _ c. crescentus _ strain in which cell adhesion is switched on and off by a small molecule ( and inducible promoter ) , allowing measurements to be made in a simple microfluidic device . this technology allows imaging generations of growth of an identical set of 250500 single cells distributed over fields of view . thus cell density is low and remains constant . these studies afforded sufficient statistical precision to show that single _ c. crescentus _ cells grow exponentially in size and divide upon reaching a critical multiple (.8 ) of their initial sizes . satisfaction of a series of scaling laws predicted by a simple stochastic model for exponential growth indicates that these dynamics can be characterized by a single time scale . in this paper , we use more advanced image analysis methods to extract cell shape contours from these data . the resulting geometric parameters , together with mathematical models , provide insights into growth and division in _ c. crescentus _ and the plausible role of cell wall mechanics and dynamics in these processes . specifically , we identify natural variables for tracking cell dynamics , and develop a minimal mechanical model that shows how longitudinal growth can arise from an isotropic pressure . we then examine the dynamics of cell constriction and unexpectedly find that it is governed by the same time constant as exponential growth . this important finding can be understood in terms of an intuitive geometric model that relates the constriction dynamics to the kinetics of the growth of septal cell wall . we further suggest that the site of constriction can arise from differences in materials properties of the poles and show that it is established in the previous generation i.e . , the location of the site of division can be predicted before formation of the divisome . we relate our results to the known dynamics of contributing molecular factors and existing models for bacterial growth and division .

1503.07147

c

the consistent propagation of a specific shape through the processes of growth and division relies upon an intricate interplay between the controlled spatiotemporal expression and localization of proteins , and cytoskeletal structural elements . the high statistical precision of our measurements allows us to gain new insights into cell morphology . from precise determination of cell contours over time , we observe that a typical cell width profile is non - uniform at all times with a pronounced primary invagination appearing during the earliest stages of the cell cycle . during cell constriction , the decrease in the minimum width is governed by the same time constant as exponential axial growth ( fig . furthermore , the location of the primary invagination divides the cell contour into its stalked and swarmer compartments , such that the ratio of the length of the stalked part @xmath147 to the total pole - to - pole length @xmath11 remains constant during the cycle with a mean value @xmath148 ( fig . these observations and our mechanical model lead to two important conclusions : first , _ the dynamics of cell wall constriction and septal growth occur concomitantly _ , and second , _ the asymmetric location of the primary invagination can be explained by the differences in mechanical properties in the stalked and swarmer poles_. a corollary of the first conclusion is that the size ratio threshold at division occurs naturally without requiring a complex timing mechanism @xcite . in addition to the primary septal invagination , the cell contours exhibit a pronounced secondary invagination during the predivisional stages ( fig . remarkably , the secondary invaginations develop at a precise location relative to the total length of the stalked compartments , @xmath149 ( fig . the data thus allow a third conclusion : _ these secondary invaginations are inherited as primary invaginations in each of the daughter cells , directing the formation of the division plane in the next generation_. thus , through consistent and controlled nucleation of invaginations across generations , _ c. crescentus _ cells maintain a constant ratio of the sizes of stalked and swarmer daughter cells . our experimental observations and the parameters in the cell shape model can be related to the current molecular understanding for gram - negative bacteria , in particular _ c. crescentus_. before the onset of noticeable constriction , cell shape is dictated by the mechanical properties of the peptidoglycan cell wall in addition to various shape - controlling proteins such as mreb , mrec , rodz and cres . single molecule tracking studies have revealed that mreb forms short filamentous bundles anchored to the inner surface of the cell wall and moves circumferentially at a rate much faster than the rate of cell growth @xcite . _ in vitro _ experiments show that mreb filaments can induce indentation of lipid membranes , suggesting that they may have a preferred radius of curvature @xcite . thus on time scales comparable to cell growth , @xmath52 is determined in part by the energy cost of adhering mreb bundles to the cell wall ( see supplementary model section ) . bacterial cell division is driven by a large complex of proteins , commonly known as divisomes that assemble into the z - ring structure near the longitudinal mid - plane of the cell @xcite . the z - ring contains ftsz protofilaments that are assembled in a patchy band - like structure @xcite . ftsz protofilaments are anchored to the cell membrane via ftsa and zipa , and play a crucial role in driving cell wall constriction @xcite . during constriction , the divisome proteins also control peptidoglycan synthesis and direct the formation of new cell wall via the activity of penicillin - binding proteins ( pbps ) @xcite . thus the divisome plays a two - fold role by concomitantly guiding cell wall constriction and growth of the septal peptidoglycan layer . according to our model the constriction of the cell wall is driven by the synthesis of septal cell wall at a rate @xmath108 ( @xmath150 ) , which can be directly related to the activity of pbps triggered by the divisome assembly . furthermore , in our model it is sufficient that the divisome guide the curvature of cell wall growth in the septal region ( see fig . 3a , inset ) . while the mechanism behind the precise asymmetric location of the division plane in _ c. crescentus _ cells is not well understood , it is likely that the atpase mipz helps division site placement by exhibiting an asymmetric concentration gradient during the predivisional stage @xcite . mipz activity inhibits ftsz assembly ; as a result of polar localization of mipz , z - ring assembly is promoted near the mid - cell @xcite . our cell shape model suggests that the early time asymmetric location of the primary invagination , which develops into the division plane , is controlled by the differences in surface tensions maintained in the poles . the presence of this invagination at @xmath151 , as inherited from the secondary invaginations in the previous generation , aids in z - ring assembly at the site of the invagination . the curvature - sensing capability of the z - ring may be enabled by the minimization of the ftsz polymer conformational energy that is determined by the difference between cell surface curvature and ftsz spontaneous curvature @xcite . a higher tension in the stalked pole can be induced by asymmetric localization of polar proteins , such as popz , early in the cell cycle . experiments have shown that popz localizes to the stalked pole during the initial phase of the cell cycle and increasingly accumulates at the swarmer pole as the cell cycle proceeds @xcite . consistent with this observation , our data show that the correlation between the pole sizes ( determined by the ratio of surface tension to pressure ) and the stalked and swarmer compartment lengths tend to disappear later in the cycle ( supplementary fig . 3 ) , as cell constriction proceeds . a recent experimental study also demonstrates that molecular perturbation of clp proteases can destroy the asymmetry of cell division in _ c. crescentus _ @xcite , suggesting the interplay of subcellular protease activity with the physical properties of the cell wall . earlier theoretical models have predicted that a small amount of pinch - off force from the z - ring ( @xmath152 pn ) is sufficient to accomplish division by establishing a direction along which new peptidoglycan strands can be inserted @xcite . in contrast , our data combined with the mathematical model allows the interpretation that _ the early time asymmetric invagination in the cell wall can set the direction for the insertion of new peptidoglycan strands_. constriction results from exponential growth of surface area in the septum ( at the same rate as longitudinal extension ) . the instantaneous cell shape is determined by minimizing the energy functional at given values of the cell size parameters . finally , from our estimate of the cell wall energy density @xmath87 ( @xmath153 nn@xmath82 m ) , we predict that a net amount @xmath154 nn@xmath82 m of mechanical energy is used by the peptidoglycan network for cell wall growth . for a _ c. crescentus _ cell of surface area @xmath155m@xmath84 , layered with glycan strands of length @xmath15 nm and cross - linked by peptide chains with maximally stretched length @xmath14 nm @xcite , there are roughly @xmath156 peptidoglycan subunits . thus on average , each peptidoglycan subunit can consume mechanical energy of @xmath12.4@xmath157 nn@xmath82 m , or @xmath10.6 @xmath158 at a temperature @xmath159c . cell wall remodeling and insertion of new peptidoglycan material can likely create defects in the peptidoglycan network @xcite . one thus expects cellular materials properties to change over time , as a result of these molecular scale fluctuations . although we neglect such variations in our mean field model , it nonetheless quantitatively captures the average trends in cell shape features . in future work we plan to more closely connect the energy terms of the continuum model with molecular details .

moreover , these shape parameters are determined for over 250 cells across approximately 10000 total generations , which affords high statistical precision . our data and model show that constriction is initiated early in the cell cycle and that its dynamics are controlled by the time scale of exponential longitudinal growth . based on our extensive and detailed growth and contour data , we develop a minimal mechanical model that quantitatively accounts for the cell shape dynamics and suggests that the asymmetric location of the division plane reflects the distinct mechanical properties of the stalked and swarmer poles . we interpret these results in terms of the current molecular understanding of shape , growth , and division of _ c. crescentus_. cell shape both reflects and regulates biological function . the importance of cell shape is exemplified by bacteria , which rely on specific localization of structural proteins for spatiotemporal organization . these include cytoskeletal proteins such as mreb , a homolog of actin , intermediate filament - like bundles of cres ( crescentin ) , and ftsz , a homolog of tubulin . still , a common limitation of most devices is that the environmental conditions change throughout the course of the experiment , particularly as geometric growth of the population results in crowding of the experimental imaging spaces . this technology allows imaging generations of growth of an identical set of 250500 single cells distributed over fields of view . thus cell density is low and remains constant . these studies afforded sufficient statistical precision to show that single _ satisfaction of a series of scaling laws predicted by a simple stochastic model for exponential growth indicates that these dynamics can be characterized by a single time scale . in this paper the resulting geometric parameters , together with mathematical models , provide insights into growth and division in _ c. crescentus _ and the plausible role of cell wall mechanics and dynamics in these processes . we then examine the dynamics of cell constriction and unexpectedly find that it is governed by the same time constant as exponential growth . we relate our results to the known dynamics of contributing molecular factors and existing models for bacterial growth and division .

we investigate the intergenerational shape dynamics of single _ caulobacter crescentus _ cells using a novel combination of imaging techniques and theoretical modeling . we determine the dynamics of cell pole - to - pole lengths , cross - sectional widths , and medial curvatures from high accuracy measurements of cell contours . moreover , these shape parameters are determined for over 250 cells across approximately 10000 total generations , which affords high statistical precision . our data and model show that constriction is initiated early in the cell cycle and that its dynamics are controlled by the time scale of exponential longitudinal growth . based on our extensive and detailed growth and contour data , we develop a minimal mechanical model that quantitatively accounts for the cell shape dynamics and suggests that the asymmetric location of the division plane reflects the distinct mechanical properties of the stalked and swarmer poles . furthermore , we find that the asymmetry in the division plane location is inherited from the previous generation . we interpret these results in terms of the current molecular understanding of shape , growth , and division of _ c. crescentus_. cell shape both reflects and regulates biological function . the importance of cell shape is exemplified by bacteria , which rely on specific localization of structural proteins for spatiotemporal organization . bacteria take forms resembling spheres , spirals , rods , and crescents . these shapes are defined by cell walls consisting of networks of glycan strands cross - linked by peptide chains to form a thin peptidoglycan meshwork . super - resolution imaging is now revealing the internal positions of associated proteins . these include cytoskeletal proteins such as mreb , a homolog of actin , intermediate filament - like bundles of cres ( crescentin ) , and ftsz , a homolog of tubulin . however , due to the inherently stochastic nature of molecular processes , understanding how these proteins act collectively to exert mechanical stresses and modulate the effects of turgor pressure and other environmental factors requires complementary methods such as high - throughput , quantitative optical imaging . multigenerational imaging data for bacterial cells can now be obtained from microfluidic devices of various designs . still , a common limitation of most devices is that the environmental conditions change throughout the course of the experiment , particularly as geometric growth of the population results in crowding of the experimental imaging spaces . we previously addressed this issue by engineering a _ c. crescentus _ strain in which cell adhesion is switched on and off by a small molecule ( and inducible promoter ) , allowing measurements to be made in a simple microfluidic device . this technology allows imaging generations of growth of an identical set of 250500 single cells distributed over fields of view . thus cell density is low and remains constant . these studies afforded sufficient statistical precision to show that single _ c. crescentus _ cells grow exponentially in size and divide upon reaching a critical multiple (.8 ) of their initial sizes . satisfaction of a series of scaling laws predicted by a simple stochastic model for exponential growth indicates that these dynamics can be characterized by a single time scale . in this paper , we use more advanced image analysis methods to extract cell shape contours from these data . the resulting geometric parameters , together with mathematical models , provide insights into growth and division in _ c. crescentus _ and the plausible role of cell wall mechanics and dynamics in these processes . specifically , we identify natural variables for tracking cell dynamics , and develop a minimal mechanical model that shows how longitudinal growth can arise from an isotropic pressure . we then examine the dynamics of cell constriction and unexpectedly find that it is governed by the same time constant as exponential growth . this important finding can be understood in terms of an intuitive geometric model that relates the constriction dynamics to the kinetics of the growth of septal cell wall . we further suggest that the site of constriction can arise from differences in materials properties of the poles and show that it is established in the previous generation i.e . , the location of the site of division can be predicted before formation of the divisome . we relate our results to the known dynamics of contributing molecular factors and existing models for bacterial growth and division .

hep-th0606238

i

string theory suggests that our universe is not actually four - dimensional , but in fact a submanifold ( brane ) embedded into a higher - dimensional spacetime ( bulk ) . braneworld gravity and cosmology , especially based on the proposal by randall and sundrum @xcite , has developed a lot in the literature in the codimension one context @xcite . string theory ; however , suggests that there are as many as six or seven extra dimensions and thus , one may consider braneworld models with higher codimensions . recently , codimension two braneworld has been investigated eagerly , because it may give a more _ natural _ resolution of the cosmological constant problem than the codimension one case does , namely the vacuum energy of the brane may affect only the extra dimensions , not the geometry on the brane , see e.g. , @xcite . the basic nature of gravity and cosmology in codimension two braneworld has been reviewed , e.g. , in ref . @xcite ( see also references therein ) . the stability of the extra dimensions is one of the most significant issues in braneworld models with two branes . the interbrane distance between the branes appears as a scalar degree of freedom in the four - dimensional effective theory and affects the geometry and cosmology on the brane . for instance , in rs - type codimension one brane models , this modulus , called the radion , behaves as a scalar degree of freedom in an effective brans - dicke gravity @xcite . several stabilization mechanisms have been discussed in the rs model , both by classical dynamics @xcite and quantum corrections to the bulk vacuum state @xcite . stability of the extra dimensions is also a significant issue in higher codimensions . in this paper , we focus on the issue of quantum mechanical stabilization of the modulus in codimension two braneworld . various codimension two braneworld solutions with two branes have been found , where the compact extra dimensions are supported by the dynamics of flux fields @xcite . solutions with warped compact extra dimensions have also been found @xcite , especially in the context of six - dimensional supergravity theory @xcite . in this paper , we focus on the solution discussed by aghababaie et al . in @xcite . similar warped solutions have been recently discussed in @xcite , in the context of six - dimensional einstein - maxwell theory . in these two - brane models , the magnetic flux plays an essential role in order to obtain regular warped solutions . by regular " we mean that singularities which are stronger than conical ones are not permitted . the branes are situated at the conical defects , whose tensions are determined by the conical deficit angles . in warped brane models the conical defects correspond to the horizons of the bulk geometry and thus , the deficit angles depend on the parameters of the bulk geometry , e.g. , the mass and charge . by the tension - deficit relations , if the brane tensions are fixed , then part of bulk geometry is also fixed . in the models discussed in @xcite , the bulk geometry is also completely determined . however , in the model we shall consider here @xcite , which is based on six - dimensional supergravity , only the warp factor is fixed by the classical analysis . thus , to fix the size of the extra dimensions , quantum corrections of the bulk field should be taken into account . in this paper , we consider such a supersymmetric warped flux compactification model . we shall consider the perturbations of a massless scalar field on this brane background and calculate the effective potential of the volume modulus , focusing on whether or not one - loop quantum corrections can stabilize the absolute size of the extra dimensions . due to the scale invariance of the background field theory , the form of the modulus effective potential is almost completely fixed and therefore we only need to evaluate the sign of the coefficient of the logarithmic term in the effective potential to investigate the possibility of volume stabilization . this is directly related to the appropriate heat kernel coefficient , which is composed of contributions from both the bulk and the conical branes . the paper is organized as follows : in sec . ii , we present a warped flux compactification model that is based on an einstein - maxwell - dilaton theory with a non - vanishing scalar field potential . in sec . iii , we consider the perturbation of a massless , minimally coupled bulk scalar field in order to derive the modulus effective potential and then investigate whether or not the effective potential has a minimum . as a result , the stability of the modulus is determined by the appropriate heat kernel coefficient . then , we present results for our analysis of the heat kernel coefficients and we also discuss the _ rigidity _ of the stabilization , i.e. , is the modulus mass stable against kk perturbations . in the actual investigation of stability , rather than the original six - dimensional model , we consider a four - dimensional counterpart , because of the difficulties associated with evaluating the uv contributions from the conical branes . then , we make some suggestions for the original six - dimensional model . in sec v , we discuss phenomenological implications relating to the hierarchy of the fundamental energy scales and the effective vacuum energy realized on the brane . in sec . vi , we summarize this paper and discuss possible extensions of our present analyses . in appendix a , we introduce the four - dimensional version of the warped flux compactification solution and consider the nature of the massless scalar field perturbations on such a background , including quantum effects . in appendix b , we show the conformal invariance of the @xmath0 heat kernel coefficient . in appendix c we use the conformal invariance of the @xmath1 heat kernel coefficient on the cone to find the smeared coefficient @xmath2 , which is required for the cocycle function . in appendix d we apply the wkb method to give an estimate for the zeta function in four dimensions , which contributes to the mass scale of the modulus .

we investigate the stability of the extra dimensions in a warped , codimension two braneworld that is based upon an einstein - maxwell - dilaton theory with a non - vanishing scalar field potential . hence , we discuss the one - loop effective potential of the volume modulus for a massless , minimally coupled scalar field . given the scale invariance of the background solution , the form of the modulus effective potential can _ only _ be determined from the sign of the logarithmic term in the effective potential that depends on the renormalization scale . this term can be evaluated via heat kernel analysis and we show that in most cases the volume modulus is stabilized . in the actual evaluation , due to a lack of knowledge of the uv contributions from the conical branes in a six - dimensional spacetime , we consider its four - dimensional counterpart . we find that one - loop corrections in this model appear to alleviate some of these problems .

we investigate the stability of the extra dimensions in a warped , codimension two braneworld that is based upon an einstein - maxwell - dilaton theory with a non - vanishing scalar field potential . the braneworld solution has two 3-branes , which are located at the positions of the conical singularities . for this type of brane solution the relative positions of the branes ( the shape modulus ) are determined via the tension - deficit relations , if the brane tensions are fixed . however , the volume of the extra dimensions ( the volume modulus ) is not fixed in the context of the classical theory , implying we should take quantum corrections into account . hence , we discuss the one - loop effective potential of the volume modulus for a massless , minimally coupled scalar field . given the scale invariance of the background solution , the form of the modulus effective potential can _ only _ be determined from the sign of the logarithmic term in the effective potential that depends on the renormalization scale . this term can be evaluated via heat kernel analysis and we show that in most cases the volume modulus is stabilized . in the actual evaluation , due to a lack of knowledge of the uv contributions from the conical branes in a six - dimensional spacetime , we consider its four - dimensional counterpart . we then go on to discuss the mass scale of the modulus itself and find that it becomes comparable to the gravitational scale for mild degrees of warping , when the renormalization scale is set nominally to the gravitational scale . then , we make some suggestions on the original six - dimensional model . finally , we close this article , after discussing some phenomenological implications relating to the hierarchy problem of the fundamental energy scales and the smallness of the effective vacuum energy on the brane . we find that one - loop corrections in this model appear to alleviate some of these problems .

1512.01162

r

in our discussion of the ground state configurations we first present the different structural archetypes that we could identify with our ea - approach . we then present the diagram of states : it provides information on the @xmath10-ranges where the respective structures are the energetically most stable ones ; we further discuss how the thermodynamic properties and the order parameters of our systems vary over a representative range of @xmath10 . [ [ structures - with - one - preferred - orientation ] ] structures with one preferred orientation + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + for @xmath10-values both considerably larger or smaller than unity ( i.e. , by a factor of @xmath118 ) , the particles tend to align parallel to each other in case of strong anisotropy : they accomplish this by forming tilted rows , characterized by a high density of particles along these lines ; these arrangements are denoted as _ parallel displaced_-configurations ( `` pd '' ; see figure [ fig : systems_quadrupolar_snap1 ] ) . since quadrupolar particles avoid a head - to - tail arrangement , neighboring rows repel each other , inducing thereby large gaps between these lanes ; the parallel offset between neighboring rows can be very sensitive to small changes in @xmath10 , leading to a slight modulation of the boops as functions of @xmath10 ( to be discussed below ) . an interesting special case of this structure is observed for a vanishing quadrupolar moment ( i.e. , @xmath119 ) , where particles form a distorted hexagonal lattice , denoted as the _ parallel_-configuration ( `` p '' ; see top left panel of figure [ fig : systems_quadrupolar_snap1 ] ) . [ [ structures - with - two - preferred - particle - orientations ] ] structures with two preferred particle orientations + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + here the preferred structural arrangements are throughout _ herringbone_-configurations ( `` hb '' ) where particles form alternating , parallel lanes , each of them being characterized by a specific particle orientation : in figure [ fig : systems_quadrupolar_snap2 ] particles pertaining to different lanes are colored red and blue , respectively . the relative orientation between neighboring particles depends in a highly sensitive manner on @xmath10 . apart from two special cases ( that are encountered for @xmath10-values very close to unity and which will be discussed below ) two different versions of the hb - configurations emerge from a closer analysis of the obtained structures : * for @xmath10-values somewhat closer to unity , we observe a rather dense structure , which we denote hb@xmath120-configuration ( see panels in the central column of figure [ fig : systems_quadrupolar_snap2 ] ) ; * for @xmath10-values that differ more strongly from unity , particles arrange in densely - populated rows of alternating orientation ( see panels in the right column of figure [ fig : systems_quadrupolar_snap2 ] ) . since neighboring rows repel each other , this structure has a lower overall density which we therefore denote as hb@xmath121 . the two special cases of the hb structure mentioned above are observed for @xmath10-values very close to unity where neighboring particles prefer strict mutual orthogonal orientations with respect to their nearest neighbors . ( i ) for large @xmath122- and small @xmath123-values , a perfect arrangement of mutually orthogonally oriented particles with an underlying square pattern can be observed , denoted as the _ square t_-configuration ( `` t@xmath124 '' ; see left panel of figure [ fig : systems_quadrupolar_snap2 ] ) . ( ii ) further , a closely related arrangement has been identified which is now based on an underlying hexagonal pattern ; it is denoted as the _ hexagonal t_-configuration ( `` t@xmath125 '' ; see bottom left panel of figure [ fig : systems_quadrupolar_snap2 ] ) ; for this particular configuration a mutually perfect orthogonal orientation of nearest neighbors can only be realized for @xmath126 . [ [ structures - with - three - preferred - particle - orientations ] ] structures with three preferred particle orientations + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + a very interesting phenomenon observed in our system is the occurrence of structures where particles arrange in three preferred orientations , characterized by a vanishing nematic order parameter @xmath108 . the _ spatial _ particle arrangement is here irrespective of the values of @xmath127 and @xmath123 reminiscent of a _ trihexagonal _ tiling , @xcite consisting of regular hexagons that are connected by triangles ; we thus denote it as the `` th''-configuration ( see figure [ fig : systems_quadrupolar_snap3 ] where also the hexagons and the triangles are highlighted ) . throughout , the relative angle between the orientations of neighboring particles is @xmath128 , reflected in the order parameter which assumes a value of @xmath129 ( see figure [ fig : ea_2_1 ] ) . we note that the occurrence of the th - configuration strongly depends on the choice of @xmath122 and @xmath123 ; in some cases , this particle arrangement is not observed at all ( see figure [ fig : ea_02_01 ] ) . in contrast , variants of the -configuration can almost always be observed in some range of @xmath10 ( see discussion below ) . [ [ more - complicated - structures ] ] more complicated structures + + + + + + + + + + + + + + + + + + + + + + + + + + + using the ea - approach we also identify more complicated structures , not conforming to the mechanisms described above . these structures require a larger number of particles per cell and turn out to be stable only within very small ranges of @xmath10 ( see subsec . [ subsubsec : diagram_states ] ) . while we observe several different variants of such particle configurations , they share a common feature , namely a mesh - like lattice , where chains of particles undulate back and forth ( see figure [ fig : systems_quadrupolar_snap4 ] ) . we denote them as _ branched _ structures ( `` b '' ) . we now discuss the diagram of states which summarizes the occurrence of the previously identified archetypes of ground state configurations of our system for selected values of @xmath122 and @xmath123 as we vary @xmath10 . since most of the interesting features of our systems can already be captured in the diagram of states obtained for @xmath130 and @xmath131 , we focus from now onwards on this particular set of parameters : we present data for the enthalpy and for a selection of appropriate order parameters introduced in subsec . [ subsec : order_parameters ] , that help to identify the respective structures . the filling fraction @xmath132 , which is also displayed in the following figures , is defined as @xmath133 . at this point we remind the reader that the _ shape _ ( and thus the orientation of the particles ) is invariant under the transformation @xmath134 while the relative orientations of the quadrupolar moments for the cases @xmath10 and @xmath21 are mutually orthogonal : with this symmetry in mind , we can easily disentangle the impact of @xmath122 and @xmath123 on the structure formation by comparing the relevant physical properties for the cases @xmath10 and @xmath21 . these properties are displayed for @xmath130 and @xmath131 in figure [ fig : ea_2_1 ] along with a color - coded , horizontal bar ( above this panel ) which indicates these @xmath10-ranges where the respective particle configurations are the energetically most favorable ones . on a qualitative level we observe that the enthalpy curve is continuous over the entire investigated @xmath10-range ; however , it shows kinks at particular values of the aspect ratio which provide a first evidence for the occurrence of discontinuous transitions between the ground state configurations . the specific enthalpy , @xmath135 , shows a pronounced local minimum at @xmath12 ( i.e. , for circular particle shapes ) : here the t - configuration is dominant , verified by the fact that in this @xmath10-region @xmath136 and @xmath137 . in addition , we observe @xmath138 and @xmath139 , indicating thereby a relative orthogonal orientation of neighboring particles . in contrast , for more anisometric particle shapes ( i.e. , small and large @xmath10-values ) , the enthalpy rapidly decays to rather small values ; actually @xmath40 tends to minus infinity for @xmath140 and @xmath141 as the quadrupoles start to overlap and the repulsive soft core shrinks as @xmath142 . for small and large @xmath10-values the formation of parallel rows is energetically most favorable and pd - configurations are observed . here the nematic order parameter @xmath108 is the appropriate quantity to characterize the emerging structure : indeed , @xmath108 assumes in these @xmath10-regions the value 1 , indicating that a single orientation prevails . in contrast , for the two intermediate @xmath10-ranges , where the enthalpy assumes local maxima the ground state configurations for @xmath10 and @xmath21 are distinctively different ; for these @xmath10-values we observe the formation of more complex structures , reflected by a rather intricate variation of the different order parameters with @xmath10 : ( i ) _ increasing _ first @xmath10 beyond the region where the t - configuration is stable , the system changes after a very narrow @xmath10-region where the hb@xmath143-structure occurs via a discontinuous _ structural _ transition ( identified by a jump in @xmath132 ) into the th - configuration ; the latter one is characterized by @xmath138 , @xmath144 and @xmath145 which provides evidence that the difference in orientation angles between nearest neighbors is @xmath128 . upon further increasing @xmath10 we pass again a very narrow interval where a branched structure is stable and we eventually reach again via a discontinuous structural transition the hb@xmath121-structure ; for this configuration none of the order parameters assume any characteristic value . eventually we identify for even larger @xmath10-values the aforementioned pd - structure . ( ii ) _ decreasing _ , on the other hand , the value of @xmath10 beyond the range where the t - structure is stable , we observe hb - configurations : first the one with the larger density ( i.e. , the hb@xmath143-structure ) and then the hb@xmath121-structure . the shape of @xmath113 ( see figure [ fig : ea_2_1 ] ) indicates that the transition between hb@xmath146 and hb@xmath121 ( and also the subsequent transition to the pd - structure ) is of first order , i.e. , at some point the relative orientation of neighboring particles is discontinuous . at this point it should be mentioned that @xmath132 and the order parameters do not necessarily behave in the same manner as the system changes from one structure to the other : some order parameters or @xmath132 may change abruptly , indicating a first order phase transition , while the other parameters change continuously . as an example we refer the reader to the transition hb@xmath121 @xmath147 pd for @xmath148 . another interesting feature emerges as we compare the curves of the order parameters shown in figure [ fig : ea_2_1 ] obtained for the parameters @xmath149 , with the corresponding data calculated for the parameter sets @xmath150 and @xmath151 , shown in figures [ fig : ea_02_01 ] and [ fig : ea_20_10 ] , respectively . the corresponding curves reveal striking similarities , suggesting that appropriate scaling relations of the order parameters via the values of the quadrupole moment and the pressure hold for the respective ground states . in contrast ( and interestingly ) , the enthalpy curves obtained for the different sets of data differ rather substantially in magnitude . we will discuss a possible background scenario of these observations in more detail in appendix [ sec : reduction of parameter space for hard particles ] . there we will show that indeed a scaling relation for the enthalpy of a systems of _ hard _ , quadrupolar particles can be derived ( see appendix [ sec : reduction of parameter space for hard particles : ground state ] ) . however , it seems that the softness of our particles remember that we consider in this contribution particles with a _ soft _ ( albeit rather steep ) core leads to a breakdown of this scaling law . this feature is presumably due to the fact that a simultaneous scaling of the quadrupole moment and of the pressure also induces a change of the density . to take into account this effect properly , we suggest in appendix [ sec : phenomenological enthalpy scaling for non - hard particles at ground state ] an empirical scaling law for the ground state enthalpy of a system of soft ellipsoidal particles and provide numerical evidence for its justification . in the current subsection , we analyze the md results that we have obtained for all considered aspect ratios @xmath10 and a set of reduced temperatures @xmath90 . as previously mentioned , the ground state configurations that we have obtained with the help of the ea algorithm for a variety of aspect ratios , serve now as initial configurations for the md simulations . corresponding snapshots for the most interesting and most representative configurations , obtained after equilibrating the system , are presented in figure [ fig : systems_quadrupolar_mdsnap ] . before starting the investigations , it is worth to briefly consider typical values of @xmath122 , @xmath123 in experimental systems . as an example , we consider the quadrupolar gay - berne model of benzene proposed by golubkov _ et al . _ we use their quadrupole strength , @xmath152 , and their spherical diameter , @xmath153 ( the latter value is based on the gay - berne contact distance ) . using the surface tension of water ( the 2d equivalent of pressure ) defined in ref . , @xmath154 at @xmath155 , we arrive at the ratio @xmath156 however , since the point quadrupole approximation is known to overestimate the interaction strength for narrow interparticle configurations @xcite due to the singularity in @xmath157 [ see eq . ] , we consider here a reduced value of @xmath158 instead of @xmath159 . with this choice we hope to cover not only benzene molecules , but also other quadrupolar molecules . by identifying @xmath131 with @xmath160 , we arrive at the following energy scale @xmath161 . in the following , we present md simulation results for the parameter pairs @xmath162 , and @xmath163 . we start with a detailed investigation of the structure at @xmath130 , @xmath131 and different temperatures . the md simulations reveal that the structures predicted for vanishing temperature remain stable also at low temperature ( @xmath164 , see panels in the second column of figure [ fig : systems_quadrupolar_mdsnap ] ) . as @xmath90 increases monotonously , defects start to form ( see panels in the third column of figure [ fig : systems_quadrupolar_mdsnap ] ) : the most common of these is a slight wave - like modulation of previously straight lines . finally , once the temperature has been raised above a certain threshold value ( see panels in the fourth column of figure [ fig : systems_quadrupolar_mdsnap ] ) , the crystalline order is rapidly lost . the corresponding transition temperatures depend strongly on @xmath10 : configurations with @xmath165 ( t@xmath166-configuration ) and @xmath10 far from unity ( pd - configuration ) turn out to be the most stable ones : in this situation , particles can approach very closely and exert thus a strongly attractive quadrupole - quadrupole interaction ; these ordered structures break up only at temperatures as high as @xmath167 and @xmath168 , respectively . in contrast , the rather complicated b - configurations melt already at temperatures as low as @xmath169 ( with @xmath170 ) . in order to investigate and to locate the transition of the system from the ordered to the disordered regime , we focus in the following on the reduced potential energy , @xmath171 , and the reduced system area , @xmath172 , ( in units of @xmath6 and @xmath5 , respectively ) . figure [ fig : upotentialvolume ] depicts @xmath173 and @xmath172 as functions of the reduced temperature @xmath90 for all considered values of the aspect ratio @xmath10 . upon increasing the temperature , @xmath171 progressively decreases in magnitude and finally approaches zero , reflecting the diminishing role of particle interactions . at the same time , the area @xmath172 increases . interestingly , we observe along this process that both @xmath174 and @xmath175 show discontinuous changes within very small temperature intervals for all @xmath10-values investigated ; these `` jumps '' are found for both quantities at approximately the same temperature . we attribute these observations to the occurrence of a first order phase transition . the temperatures that delimit these intervals are marked in figure [ fig : upotentialvolume ] by contour lines as functions of @xmath10 . only for @xmath176 no such discontinuity in @xmath177 could be resolved ; this fact can be related to the finite size of the temperature grid . intentionally , we have not evaluated the susceptibility , since it is well established that energy fluctuations are not correctly reproduced within the berendsen scheme . @xcite we now arrive at the discussion of the previously defined boops @xmath106 and @xmath107 [ see eq . ] ; they are displayed in figure [ fig : psi4psi6 ] . as already shown in figure [ fig : ea_2_1 ] , we find for all our ground state configurations intervals in @xmath10 where at least one of the two parameters does not vanish . considering now the temperature dependence of these quantities , we observe for all @xmath10-values investigated a discontinuous change of both @xmath106 and @xmath107 ( if not zero in the ground state ) at exactly the same temperatures where a discontinuous change in @xmath172 was observed . to analyze the structure of the system at finite temperatures on an even more quantitative level , we have calculated in addition various coefficients of the pair distribution function in an expansion in terms of rotational invariants . to be more specific , we use a two - dimensional version of the three - dimensional coefficient functions of the pair distribution function,@xcite i.e. @xmath178 where the @xmath179 are rotational invariants . here we focus on the coefficients @xmath180 , @xmath181 , and @xmath182 defined via the following two - dimensional rotational invariants : @xmath183 the function @xmath180 corresponds to the familiar pair correlation function . the other functions , @xmath182 and @xmath181 , describe , in addition , a local orientational order of the particles . similar to 3d systems @xcite we can interpret these coefficients as follows : @xmath181 provides information about the conditional probability density of a particle ( relative to the bulk probability density ) whose orientation axis is aligned in parallel ( positive value ) or orthogonal ( negative value ) to the orientation axis of a considered particle ; @xmath182 describes the conditional probability density of a particle ( again , relative to the bulk probability density ) positioned along or aside the axis of a considered particle . in the panels of figure [ fig : gxxxofrk21 ] , we present numerical results for these three functions for @xmath184 ( see also the corresponding snapshots shown in the panels in the bottom row of figure [ fig : systems_quadrupolar_mdsnap ] ) . for all three correlation functions the first peak is located at around @xmath185 : this position does not exactly mark the face - to - face alignment of the particles ( which occurs at @xmath186 ) and thus provides evidence for a slightly shifted parallel configuration , induced by the quadrupole ( see snapshots shown in the panels of the bottom row in figure [ fig : systems_quadrupolar_mdsnap ] ) . for @xmath168 , we observe a rapid decay of @xmath180 towards unity for large particle distances @xmath187 : the crystalline order has completely vanished , reflected by the missing peaks for larger @xmath187-values . since at low temperatures all particles are oriented in the same direction , @xmath181 is equivalent to @xmath180 ; however , as the temperature attains @xmath168 , we observe that for large @xmath187-values the orientational order is lost and thus @xmath181 vanishes already at @xmath188 . finally , @xmath182 oscillates around zero in the ordered phase for low temperatures ( @xmath189 ) due to the fact that @xmath182 is by definition not able to contribute to the overall particle density . for @xmath190 , @xmath182 completely vanishes for large @xmath187-values ( @xmath191 ) : obviously , a loss of orientational order occurs for @xmath190 . this temperature threshold , which can be interpreted as a melting temperature , agrees fairly well with the temperature where the discontinuous changes in @xmath177 and @xmath175 ( see figure [ fig : upotentialvolume ] ) and in the boops ( see figure [ fig : psi4psi6 ] ) were observed . concluding , we note that related investigations carried out for other @xmath10-values led to analogous conclusions about the corresponding melting temperature . panel ( a ) , @xmath181 panel ( b ) , and @xmath182 panel ( c ) for @xmath184 and various temperatures ( as labeled).,width=321 ] these observations motivate investigations on a _ melting curve _ that separates the ordered from the disordered phase as we increase the temperature . this line is displayed in figure [ fig : meltingdiagramp1qsqrt2 ] for all considered aspect ratios @xmath10 . we emphasize that these data represent only an estimate for the true , two - phase coexistence lines characterizing a first - order transition . for the latter , one would also expect the occurrence of a hysteresis , i.e. , the observation of two different curves , depending on whether the system is heated up or cooled down from a low or a high - temperature state , respectively . we briefly come back to this issue below . that separates the ordered phase ( at low temperatures ) from the disordered phase ( at high temperatures ) ; for details cf . text . data along on the line correspond to results obtained for disordered state points.,width=321 ] another interesting feature of the melting curve that can be observed is that it exhibits some degree of symmetry in shape when exchanging @xmath10 and @xmath21 ( see figure [ fig : meltingdiagramp1qsqrt2 ] ) . of course , we would not expect full symmetry since the electrostatic properties for the cases @xmath10 and @xmath21 are different ( see bottom panels in figure [ fig : model ] ) . from the data we can conclude that for particles with large eccentricities the melting occurs at higher temperatures than for @xmath10-values close to unity . given the large amount of numerical calculations required to construct the melting line in figure [ fig : meltingdiagramp1qsqrt2 ] , which was calculated for one particular set of parameters , @xmath192 , it would be obviously desirable and helpful to have a scaling relation at hand which allows to easily obtain ( or to extrapolate ) corresponding melting lines for other parameter sets . in appendix [ sec : reduction of parameter space in the hard limit at finite temperature ] we show that such a relation does indeed exist for _ hard _ particles . this relation states that the probability to encounter a microscopic configuration of the many - particle system in phase space is invariant under the simultaneous transformations @xmath193 , @xmath194 , @xmath195 , with @xmath196 being a scaling factor . however , in this contribution we consider _ soft _ particles ( even though characterized by a rather harsh repulsion , see eq . ) . nevertheless , as we discuss in appendix [ sec : scrutinizing the melting curve ] , it is also possible for the system at hand to provide via a suitably adapted scaling law a rough estimate of the location of the melting line at scaled parameters . finally and for the sake of completeness , we now discuss our investigations on the melting transition as obtained in a cooling process ( `` simulated annealing '' ) . the central question that we address is whether the ground state structures can be reproduced at least locally with md simulations starting from a disordered phase at higher temperatures . to this end we performed simulations at @xmath130 and several values of @xmath10 , initializing the system with random particle positions and orientations and cooling it down gradually . the initial pressure and temperature were set to @xmath197 and @xmath198 , respectively ; the initial box - shape is quadratic with a side length of @xmath199 . within the first @xmath200 md steps we linearly decreased the pressure and the temperature down to @xmath131 and @xmath201 , respectively . the simulations extended in total over @xmath202 md steps . for the other simulation parameters we refer the reader to sec . [ subsec : md ] . ( panel ( a ) ) for a system with @xmath203 at a temperature @xmath201 , pressure @xmath131 , and quadrupole strength @xmath130 after a melting ( snapshot in panel ( b ) ) and a cooling procedure ( snapshot in panel ( c ) ) . for the color code of the snapshots see inset in figure [ fig : systems_quadrupolar_mdsnap].,width=321 ] our data provide evidence that the predicted ground state could be obtained via this simulated annealing process only for very few state points . in general , the formation of ordered structures via such a process is hampered and delayed by frustration effects , especially for @xmath10-values far from unity , where particles encounter due to their elongated shapes difficulties to rotate . as an example we discuss the pair correlation function @xmath180 , obtained for @xmath203 ( i.e. , a value close to unity ) and depicted in figure [ fig : k08](a ) . we observe a coincidence in the peak positions of @xmath180 , but not in their heights . we interpret this deviation as an artefact of the crystallite structure appearing after cooling ( see figure [ fig : k08](b ) and ( c ) ) . this might be a consequence of the lack of long - range order in 2d systems .

, we first examine the ground state structures as we vary the aspect ratio of the particles and the pressure . interestingly , we find , besides the intuitively expected t - like configurations , a variety of complex structures , characterized with up to three different particle orientations . in an effort to explore the impact of thermal fluctuations , we observe that ground state structures formed by particles with a large aspect ratio are in particular suited to withstand fluctuations up to rather high temperatures .

we investigate the structural properties of a two - dimensional system of ellipsoidal particles carrying a linear quadrupole moment in their center . these particles represent a simple model for a variety of uncharged , non - polar conjugated organic molecules . using optimization tools based on ideas of evolutionary algorithms , we first examine the ground state structures as we vary the aspect ratio of the particles and the pressure . interestingly , we find , besides the intuitively expected t - like configurations , a variety of complex structures , characterized with up to three different particle orientations . in an effort to explore the impact of thermal fluctuations , we perform constant - pressure molecular dynamics simulations within a range of rather low temperatures . we observe that ground state structures formed by particles with a large aspect ratio are in particular suited to withstand fluctuations up to rather high temperatures . our comprehensive investigations allow for a deeper understanding of molecular or colloidal monolayer arrangements under the influence of a typical electrostatic interaction on a coarse - grained level . authors who have contributed equally to the research

hep-th9511220

i

matrix models provide an arena in which the notion of integrability is realized as noncritical string theory . at the same time , they produce efficient computation of some quantities which would be very formidable in the continuum framework . computation of macroscopic loop amplitudes@xcite @xcite demonstrates this fact most explicitly : the boundary condition which is hard to solve in the continuum framework @xcite turns out to be related to the most natural quantity in matrix models . let us begin with recalling this . a crude correspondence of matrix models with path integrals of noncritical strings tells us that the connected part of the correlator given by averaging over matrix integrals of the product of singlet correlators < < tr ^q_1 tr ^q_2 tr ^q_n > > _ n , conn is an n - punctured surface swept by a noncritical string . to turn these punctures into holes of a macroscpic size , one first introduces a fixed loop length at the i - th boundary by @xmath15 . we are naturally led to consider the limiting procedure _ n ( _ 1 , _ 2 , _ q_i , a 0 , _ n < < tr ^q_1 tr ^q_2 tr ^q_n > > _ n , conn which defines the macroscopic @xmath0-loop amplitude . here @xmath16 is the renormalized string coupling and @xmath17 is an auxiliary parameter which plays the role of a cutoff . an equivalent and more efficient procedure is to consider the correlator consisting of the product of @xmath0-resolvents @xmath18 , to pick its most singular piece and finally to carry out the inverse laplace transforms over @xmath19 s . this in turn means [ eq : procedure ] a_n ( _ 1 , _ 2 , _ n ) = ( _ j=1^n l_j^-1 ) _ a0 _ n < < _ i=1^n tr > > _ n , conn . here , @xmath20 denotes the inverse laplace transform with respect to @xmath21 such that @xmath22 and @xmath23 denotes the critical value of @xmath19 . in this paper , we will carry out this procedure in depth at the @xmath24 critical point realized by the symmetric potential of the two - matrix model . here @xmath25 . in the next section , we evaluate the connected part of the correlator consisting of the product of @xmath0-resolvents for large @xmath26 just mentioned above and derive a general formula for this object in the continuum planar limit . we exploit the planar solution to the heisenberg algebra and its parametrization provided by @xcite . our formula contains a term distinguishable from others , namely the one which is expressible as the total @xmath27 derivatives . here @xmath3 denotes the renormalized cosmological constant . this structure is familiar from the case of pure two - dimensional gravity . this term is , however , found to be supplemented , for @xmath28 , by an increasing number of other terms with @xmath0 . this latter structure testifies to the existence of interactions which can not be captured by the naive notion of operator product expansion for microscopic loop operators : the macroscopic loop operator will be expanded by these . for that reason , these interactions may be referred to as contact interactions . in section iii , we consider the @xmath27 @xmath29 term . we are successful in representing this terms as the summations over @xmath30 indices with its summand in a form of @xmath0 factorized products . these summations are found to conform to the fusion rules and the crossing symmetry for the dressed primaries of the unitary minimal conformal field theory @xcite . using the formula for the inverse laplace transform found in @xcite , [ eq : inverse ] l^-1 [ ] = - k_k / m ( m ) - _ k / m ( m ) . we determine the complete form for this part of the amplitude in terms of the boundary lengths @xmath2 @xmath31 . the answer reads as & & a_n^ fusion ( _ 1 , _ 2 , _ n ) + & & = - ( ) ^n-2 ( ) ^n-3 . the case @xmath32 has been briefly reported in @xcite . in section iv , we consider the remaining pieces in the formula which represent the residual interactions of loops . for the case @xmath5 and the case @xmath6 , we have succeeded in expressing these in terms of the convolution of modified bessel functions and their derivatives . we , therefore , obtain the complete answer for @xmath33 and the one for @xmath34 , which are eq . ( [ eq : n=4answer ] ) and eq . ( [ eq : n=5answer ] ) respectively . although it is not unlikely that one can determine the full amplitude this way for arbitrary @xmath0 , the proof remains elusive . we will finish with a few remarks concerning with the properties of these residual interactions . in appendix a , we derive a set of recursion relations which are used to evaluate the formula in section iii . these recursion relations relate the expression of the terms appearing in the @xmath0-resolvent to those in the @xmath7-resolvent . these define , therefore , the @xmath0-loop amplitude in terms of @xmath7-loop amplitude through the inverse laplace transforms albeit being implicit .

this is found to be supplemented by an increasing number of other terms with which represent residual interactions of loops . we reveal the nature of these interactions by explicitly determining them as the convolution of modified bessel functions and their derivatives for the case and the case . we derive a set of recursion relations which relate the terms in the-resolvents to those in the-resolvents .

we investigate the structure of the macroscopic-loop amplitude obtained from the two - matrix model at the unitary minimal critical point . we derive a general formula for the-resolvent correlator at the continuum planar limit whose inverse laplace transform provides the amplitude in terms of the boundary lengths and the renormalized cosmological constant . the amplitude is found to contain a term consisting of multiplied by the product of modified bessel functions summed over their degrees which conform to the fusion rules and the crossing symmetry . this is found to be supplemented by an increasing number of other terms with which represent residual interactions of loops . we reveal the nature of these interactions by explicitly determining them as the convolution of modified bessel functions and their derivatives for the case and the case . we derive a set of recursion relations which relate the terms in the-resolvents to those in the-resolvents . = -.5 in = 1.5ex plus 1pt = 11 addtoresetequationsection normalsizesetsizexiipt plus3pt minus3pt@ plus3pt plus3.5pt minus0pt # 1@underline#1 twosidetrue @=12 0.0 in 0.0 in 6.0 in 8.5 in .75 in = 11

astro-ph9906355

c

we have invoked star formation triggered by cloud - cloud collisions to explain global star formation rates in disk galaxies and circumnuclear starbursts . previous theories based on the growth rate of gravitational perturbations ignore the dynamically important presence of magnetic fields . theories based on triggering by spiral density waves fail to explain star formation in systems without such waves . furthermore , observations suggest gas and stellar disk instabilities are decoupled . star formation resulting from cloud collisions has been proposed in the past ( e.g. scoville et al 1986 ) , but rejected because of supposedly long collision timescales . however , gammie et al ( 1991 ) show the collision rate of self - gravitating particles in a differentially rotating disk is much larger than that of particles in a box . collision rates are enhanced because particles collide at the shear velocity of encounters with initial impact parameters of order two tidal radii ( typically a few hundred parsecs for gmcs ) . gravitational focusing further increases the cross - section . also , the small scale height of gmcs implies essentially two dimensional interactions in the plane of the disk , increasing the collision rate relative to that for three dimensions . we calculate collision timescales short enough to allow a viable theory of collision induced star formation to be considered . in summary , in this model , self - gravitating gas disks fragment into bound gas clouds . this process is driven either by gravitational , thermal or parker instabilities , or the influence of stellar spiral density waves on the gas . these bound clouds , either atomic or molecular , are relatively long - lived , being supported by static and turbulent magnetic pressure . the latter may be produced by dynamically - regulated low mass star formation ( mckee 1999 ) . we hypothesize a fraction of cloud collisions lead to compression of localized regions of the clouds . these regions , if magnetically supercritical , collapse rapidly to form stars , including high mass ob stars . the bulk of galactic disk stars are thought to form via this `` burst''-mode ( lada et al 1993 ) . thus , the rate limiting step for star formation is not the formation of bound clouds , but the compression of these , or parts of these , in cloud - cloud collisions . therefore at any particular time , most of the bound gas is not actively undergoing star formation . specifically , we have considered an idealized , single mass population of gravitationally bound gas clouds , orbiting in an axisymmetric , thin disk . using the result of gammie et al ( 1991 ) for the cloud velocity dispersion , we predict radial gas distributions , dependent on the toomre @xmath6 stability parameter ( equation [ radialgas ] ) . applying our principal hypothesis , that cloud collisions trigger the majority of disk star formation , using the collision cross - section results of gammie et al ( 1991 ) and with the assumption star formation self - regulates ( @xmath17 ) , we predict enhanced cloud collision rates and a sfr law of the form @xmath231 ( equation [ sfr3 ] ) . for flat rotation curves ( @xmath73 ) , this result is in agreement with the disk averaged data of k98 ( figure [ fig : ken2 ] ) . although uncertain , our estimates of the total sfr in the milky way and for typical starburst systems are consistent with observations . we predict a b - band tully - fisher relation of the form @xmath232 , in agreement with observations ( burstein et al 1995 ; strauss & willick 1995 ) . this theory is to be further scrutinized to discriminate between it and other star formation mechanisms . to this end we have proposed several tests . we predict statistically enhanced sfrs in regions of large negative circular velocity gradients , where the shear rate is increased , and regions of increased cloud velocity dispersion . similarly , decrements are predicted in regions of large positive circular velocity gradients , which reduce the amount of shear . future observations ( e.g. martin & kennicutt 2000 ) of sfr , gas and circular velocity profiles of large samples of disk galaxies should allow for statistically significant tests of our proposed sfr law , and in particular the dependence on the circular velocity gradients and cloud velocity dispersion . however , these tests will be complicated by possible variations in the likelihood of collision induced star formation with collision velocity . the results of numerical simulations may be necessary to account for this effect . we also predict star formation efficiency , @xmath90 , linearly averaged , decreases with increasing cloud mass as @xmath233 . figure [ fig : eff ] shows model predictions for @xmath90 , logarithmically averaged over its distribution , and comparison to observations . larger and deeper surveys of hii regions and gmcs , including their atomic components , are required to improve the significance of this test . undoubtedly our model is an extremely simplified description of the actual star formation process . we have presented an idealized theory in which all star formation is triggered by cloud collisions , however other processes , such as spontaneous star formation , self - triggering and triggering by density waves undoubtedly operate at some level . for the results of the collision induced theory to be valid , we require that the majority of ( high mass ) star formation is initially triggered by this process . the basic theory needs modification where there is a tight correlation of star formation with large scale density waves , allowing for the duration clouds spend in the density wave , and the degree of spatial concentration . the theory can be improved by numerical calculation of collision rates in a many body system , rather than relying on simple two body interaction rates . numerical simulation of cloud collisions ( e.g. klein & woods 1998 ) may provide insight into the details of how a magnetically supercritical region can be produced from the collision of two magnetically subcritical clouds . the parameter space for the outcome of collisions with different initial conditions is also being probed by simulation ( klein , private communication ) . these simulations will constrain the probability , @xmath92 , for star formation to result from typical cloud - cloud collisions . this theory can be applied to analytic models ( e.g. shore & ferrini 1995 ; silk 2000 ) and simulations ( e.g. curir & mazzei 1998 ; weil , eke & efstathiou 1998 ) of disk galaxy formation and evolution , for comparison to cosmological sfr data . we thank chris mckee for many hours of stimulating discussion and much input . we also thank leo blitz , andrew cumming , alex filippenko , rob kennicutt , richard klein , chris matzner , antonio parravano , evan scannapieco , joe silk and an anonymous referee for helpful comments . bertoldi , f. , & mckee , c.f . 1992 , , 395 , 140 + binney , j. , gerhard , o.e . , stark , a.a . , bally , j. , & uchida , k.i . 1991 , , 252 , 210 + blitz , l. 1990 , _ the evolution of the interstellar medium _ , ed . blitz l. , asp press : san francisco , 273 + blitz , l. , & williams , j.p . 1999 , proc . : _ the physics of star formation and early stellar evolution ( crete ii ) _ , astro - ph/9903382 + block , d.l . , bertin , g. , stockton , a. et al 1994 , , 288 , 365 + burkert , a. & lin , d.n.c . 1999 , submitted to + clemens , d.p . 1985 , , 295 , 422 + curir , a. , & mazzei , p. 1998 , new astr . , 4 , 1 + das , m. , & jog , c.j . 1996 , , 462 , 309 + downes , d. , wilson t.l . , bieging , j. & wink , j. 1980 , , 40 , 379 + downes , d. , & solomon , p.m. 1998 , , 507 , 615 + elmegreen , b.g . 1985 , in _ protostars & planets ii _ , eds , black , d. , & matthews , m. , university of arizona press , tucson , 33 + elmegreen , b.g . 1989 , , 338 , 178 + elmegreen , b.g . 1991 , , 378 , 139 + elmegreen , b.g . 1993 , , 411 , 170 + elmegreen , b.g . 1994 , , 425 , l73 + elmegreen , b.g . & clemens , c. 1985 , , 294 , 523 + elmegreen , b.g . , & lada , c.j . 1977 , , 214 , 725 + elmegreen , d.m . , & elmegreen , b.g . 1986 , , 311 , 554 + field , g.b . , & saslaw , w.c . 1965 , , 142 , 568 + franco , j. , shore , s.n . , & tenorio - tagle , g. , , 436 , 795 + gammie , c.f . 1996 , , 462 , 725 + gammie , c.f . , ostriker , j.p . , & jog , c.j . 1991 , , 378 , 565 + greaves , j.s . , & white , g.j . 1991 , , 248 , l27 + grosbol , p.j . , & patsis , p.a . 1998 , , 336 , 840 + gsten , r. , & mezger , p.g . 1982 , vistas astr . , 26 , 159 + hasegawa , t. , sato , f. , whiteoak , j.b . , & miyawaki , r. 1994 , , 429 , l77 + heiles , c. , goodman , a.a . , mckee , c.f . , & zweibel , e.g. 1993 in _ protostars and planets iii _ , eds , levy , e.h . , & lunine , j.i . , university of arizona press , tucson , 279 + ho , l.c . , filippenko , a.v . , & sargent , w.l.w . 1997 , , 487 , 591 + ikuta , c. & sofue , y. 1997 , , 49 , 323 + jog , c.j . & solomon , p.m. 1984 , , 276 , 114 + jog , c.j . 1996 , , 278 , 209 + kenney , j. 1997 , iau symp . , 184 + kennicutt , r.c . 1989 , , 344 , 685 + kennicutt , r.c . 1998 , , 498 , 541 + klein , r.i . , & woods , d.t . 1998 , , 497 , 777 + knapp , g.r . , stark , a.a . , & wilson , r.w . 1985 , , 90 , 254 + kuno , n. , nakai , n. , handa , t. , & sofue , y. 1995 , , 47 , 745 + kuno , n. , tosaki , t. , nakai , n. , & nishiyama , k. 1997 , , 49 , 275 + kwan , j. , & valdes , f. 1987 , , 315 , 92 + lada , e.a . , strom , k.m . & myers , p.c . in _ protostars and planets iii _ , eds , levy , e.h . , & lunine , j.i . , university of arizona press , tucson , 245 + larson , r.b . 1981 , , 194 , 809 + larson , r.b . 1988 , in _ galactic and extragalactic star formation _ , pudritz & m. fich , dordrecht : kluwer , 435 + larson , r.b . 1992 , in _ star formation in stellar systems _ , ed . g. tenorio - tagle , m. prieto , & f. sanchez , cambridge : cambridge univ . press , 125 + lattanzio , j.c . , monaghan , j.j . , pongracic , h. , & schwarz , m.p . 1985 , , 215 , 125 + liszt , h.s . , & burton , w.b . 1996 , in _ unsolved problems of the milky way _ , eds . blitz , l. , & teuben , p. , kluwer : dordrecht + martin , c.l . , & kennicutt , r.c . 2000 , in preparation + mccall , m.l . , & schmidt , f.h . 1986 , , 311 , 548 + mckee , c.f . 1999 , conf . proc . : _ the physics of star formation and early stellar evolution ( crete ii ) _ , astro - ph/9901370 + mckee . c.f . , & williams , j.p . 1997 , , 476 , 144 + mestel , l. 1985 , in _ protostars & planets ii _ , eds , black , d. , & matthews , m. , university of arizona press , tucson , 320 + moriarty - schieven , g.h . , andersson , b .- g . , & wannier , p.g . 1997 , , 475 , 642 + myers , p.c . , & goodman , a.a . 1991 , , 373 , 509 + oort , j.h . 1954 , , 12 , 177 + pandey , a.k . , paliwal , d.c . , & mahra , h.s . 1990 , , 362 , 165 + quirk , w.j . 1972 , , 176 , l9 + sakamoto , k. 1996 , , 471 , 173 + sanders , d.b . , clemens , d.p . , scoville , n.z . , & solomon , p.m. 1986 , , 60 , 1 + schmidt , m. 1959 , , 129 , 243 + scoville , n.z . , sanders , d.b . , & clemens , d.p . 1986 , , 310 , l77 + scoville , n.z . , yun , m.s . , clemens , d.p . , sanders , d.b . , & waller , w.h . 1987 , , 63 , 821 + seiden , p.e . , & schulman , l.s . 1990 , adv . , 39 , 1 + shore , s.n . , & ferrini , f. 1995 , fund . phys . , 16 , 1 + silk , j. 1997 , , 481 , 703 + silk , j. 2000 , , submitted + solomon , p.m. , rivolo , a.r . , barrett , j. , yahil , a. 1987 , , 319 , 730 + spitzer , l. 1978 , _ physical processes in the interstellar medium _ , wiley : new york + stark , a.a , & brand , j. 1989 , , 339 , 763 + taniguchi , y. , & ohyama , y. 1998 , , 509 , l89 + thornley , m.d . , & mundy , l.g . 1997a , , 484 , 202 + thornley , m.d . , & mundy , l.g . 1997b , , 490 , 682 + toomre , a. 1964 , , 139 , 1217 + truelove , j.k . , klein , r.i . , mckee , c.f . , holliman , j.h . , howell , l.h . , & greenough , j.a . 1997 , , 489 , l179 + ungerechts , h. , & thaddeus , p. 1987 , , 63 , 645 + wada , k. , & norman , c. 1999 , , 516 , l13 + wang , b. , & silk , j. 1994 , , 427 , 759 + weil , m.l . , eke , v.r . , & efstathiou , g. 1998 , , 300 , 773 + williams , j.p . , & maddalena , r.j . 1996 , , 464 , 247 + williams , j.p . , & mckee , c.f . 1997 , , 476 , 166 + wiseman , j. , & ho , p.t.p . 1994 , in _ asp conf . 65 , clouds , cores and low mass stars _ , ed . clemens & r. barvainis , san francisco : asp , 396 + wiseman , j. , & ho , p.t.p . 1996 , , 382 , 139 + womack , m. , ziurys , l.m . , & sage , l.j . 1993 , , 406 , l29 + wyse , r.f.g . 1986 , , 311 , l41 + wyse , r.f.g . , & silk , j. 1989 , , 339 , 700 + cccc @xmath56 & obs./magnetic critical mass & @xmath234 & @xmath235 + @xmath10 & observation & @xmath236 & @xmath237 + @xmath9 & observation & @xmath238 & @xmath239 + @xmath63 & @xmath240 & @xmath241 & @xmath241 + @xmath62 & observation & @xmath242 & @xmath243 + @xmath244 & alfven velocity & @xmath245 & uncertain + @xmath246 & @xmath247 & @xmath248 & @xmath249 + @xmath250 & @xmath251 & @xmath252 & @xmath253 + cccc orbital period , @xmath254 & @xmath255 & @xmath256 & @xmath257 + free - fall , @xmath46 & @xmath258 & @xmath259 & @xmath260 + atomic to molecular , @xmath20 & @xmath261 & @xmath262 & @xmath263 + ambipolar diffusion , @xmath45 & @xmath264 & @xmath265 & @xmath266 + collision , @xmath89 & @xmath267 & @xmath268 & @xmath269 + destruction , @xmath270 & williams & mckee ( 1997 ) & @xmath271 & uncertain + lifetime , @xmath272 & @xmath273 & @xmath274 & @xmath275 + alfven crossing , @xmath276 & @xmath277 & @xmath278 & uncertain + impact time , @xmath279 & @xmath280 & @xmath281 & @xmath282 +

we invoke star formation triggered by cloud - cloud collisions to explain global star formation rates of disk galaxies and circumnuclear starbursts . previous theories based on the growth rate of gravitational perturbations ignore the dynamically important presence of magnetic fields . theories based on triggering by spiral density waves fail to explain star formation in systems without such waves . furthermore , observations suggest gas and stellar disk instabilities are decoupled . following gammie , ostriker & jog ( 1991 ) , the cloud collision rate is set by the shear velocity of encounters with initial impact parameters of a few tidal radii , due to differential rotation in the disk . this , together with the effective confinement of cloud orbits to a two dimensional plane , enhances the collision rate above that for particles in a three dimensional box . we predict a b - band tully - fisher relation : , also consistent with observations . as additional tests , we predict enhanced star formation in regions with relatively high shear rates , and lower star formation efficiencies in clouds of higher mass .

we invoke star formation triggered by cloud - cloud collisions to explain global star formation rates of disk galaxies and circumnuclear starbursts . previous theories based on the growth rate of gravitational perturbations ignore the dynamically important presence of magnetic fields . theories based on triggering by spiral density waves fail to explain star formation in systems without such waves . furthermore , observations suggest gas and stellar disk instabilities are decoupled . following gammie , ostriker & jog ( 1991 ) , the cloud collision rate is set by the shear velocity of encounters with initial impact parameters of a few tidal radii , due to differential rotation in the disk . this , together with the effective confinement of cloud orbits to a two dimensional plane , enhances the collision rate above that for particles in a three dimensional box . we predict . for constant circular velocity ( ) , this is in agreement with recent observations ( kennicutt 1998 ) . we predict a b - band tully - fisher relation : , also consistent with observations . as additional tests , we predict enhanced star formation in regions with relatively high shear rates , and lower star formation efficiencies in clouds of higher mass . subject headings : galaxies : starburst and spiral ism : clouds stars : formation

1612.06409

c

@xcite measured a center time for kepler-13ab s eclipse that was very close to being half of an orbital period away from the transit center time , with a displacement of @xmath134s . as they noted , due to the light travel time across the diameter of kepler-13ab s orbit , for a perfectly circular orbit one would expect the eclipse time to actually be delayed by @xmath135s . the apparent earliness of the eclipse implies a slightly eccentric orbit , and is what drives the non - zero value of @xmath64 listed in table [ tab : broadbandpriors ] . as described in section 3.1.1 , we used the predicted eclipse time from @xcite as a prior on our broadband fitting process . since our observations poorly sample the predicted eclipse ingress and egress ( i.e. , figure [ niceplot ] ) , this prior on @xmath62 dominates in our fits and we simply recover it in the posterior distribution for @xmath62 from our mcmc fitting . in our adopted fit , we therefore find that the eclipse center time is @xmath136s earlier than the transit center time plus exactly half the orbital period , which as we expected is effectively identical to the value measured by @xcite . to determine how well our hst / wfc3 can independently constrain the eclipse center time , we conducted an additional broadband fit using no prior on the eclipse center . this gave @xmath137 , which is @xmath138s earlier than the transit center time plus exactly half the orbital period . the large uncertainties on this timing offset make it consistent with the expectations from both @xcite and the perfectly circular case , so our observations are not able to meaningfully determine the eccentricity of kepler-13ab s orbit . one complication in interpreting the optical eclipse depth for kepler-13ab is the relatively high amount of reflected light expected from the planet . specifically , the eclipse depth from reflected light alone should be @xmath139ppm , where @xmath140 is the spherical albedo of the dayside at a particular wavelength . since the kepler - band eclipse measured by @xcite is @xmath141ppm , it is possible though unlikely that the optical eclipse is entirely due to reflected light . for our nir observations , the theoretical expectation is that hot jupiters at @xmath142k should have dayside geometric albedos of effectively zero at these wavelengths @xcite . we therefore did not consider possible signatures of reflected light in our wfc3 spectra , and excluded the kepler eclipse point from our evaluation of our thermal emission models . based on those thermal emission models that assume the wfc3 and further nir data contain no reflected light , we calculate that kepler-13ab should have an eclipse 143ppm deep in the kepler bandpass . the difference between this prediction for the thermal emission and the observed depth of @xmath141ppm implies that kepler-13ab has a spherical albedo of @xmath143 in the kepler bandpass . this is substantially lower than the value found by @xcite , @xmath144 , almost entirely because our models of the planetary thermal emission are higher in the optical . our measured geometric albedo and the expectations from @xcite are thus both consistent with our assumption that the wfc3 and other nir eclipse depths contain no substantial components from reflected light . this is in line with what one would expect from other measurements of hot jupiters eclipses , most of which have @xmath145 in the kepler bandpass @xcite . note , though , that the unknown thermal emission components , and the lower stellar insolation in the @xcite sample make this only a general comparison . indeed , the high stellar insolation that kepler-13ab receives makes it possible that kepler-13ab may have different reflective properties compared to these cooler planets . one way to test this would be to observe an optical eclipse spectrum for the planet . in the case that kepler-13ab has a substantial optical albedo , the optical eclipse spectrum would be a combination of the reflectance spectrum ( expected to increase towards the blue , e.g. * ? ? ? * ) , and the thermal emission spectrum ( expected to decrease towards the blue ) , which would make the observed eclipse spectrum relatively flat . as described in the introduction , the lack of clear stratospheric temperature inversions for planets cooler than approximately 3000k led @xcite to recently suggest that that tio / vo driven inversions may only be present in the atmospheres of extremely hot giant planets . @xcite s spectrally - resolved observations of the @xmath146-band eclipse of the transiting brown dwarf kelt-1b ( 3200k ) showed a monotonically decreasing tp profile . due to the high surface gravity of kelt-1b ( 22 times that of jupiter ) , this led them to suggest that surface gravity also plays a role in the presence of a thermal inversion in hot jupiters . specifically , they argued that this was evidence for the cold - trap methods of sequestering tio / vo described by @xcite and @xcite . briefly , both @xcite and @xcite describe a process of tio / vo gas particles condensing and gravitationally settling out of the upper atmosphere . @xcite envisioned this as a `` vertical '' cold - trap , where tio / vo gas on the dayside of a hot jupiter randomly crosses the condensation boundary in the atmosphere , condenses , and falls into the planetary interior . @xcite considered a `` day - night '' cold - trap , where tio / vo molecules condense on the cooler night side of a hot jupiter , and also settle into the interior . in both cases the efficiency of a cold - trap is determined by the interplay of the rate of gravitational settling and the strength of some vertical lofting mechanism to bring tio / vo condensates back into the upper atmosphere where they can re - vaporize . both analyses found that under reasonable assumptions these two cold - traps should be able to deplete a hot jupiter s stratosphere of gas - phase tio / vo . in the cases of both kepler-13ab and kelt-1b , the dayside temperature profiles both remain too hot at depth to allow for a vertical cold - trap to exist . down to pressures of @xmath147 bar , at no point do either of these profiles cross cooler than the tio or vo condensation curves , which vary between approximately 2200k at @xmath147 bar down to approximately 1600k at @xmath148 bar . the most recent modeling of such a process was done by @xcite , who found that a vertical cold - trap of tio / vo was mostly effective in planets with equilibrium temperatures less than 1900k , which is several hundred degrees cooler than the planets we consider . if a cold - trap process is occurring in these atmospheres - and in the atmospheres of the other extremely hot giant planets - it is very probably caused by a day - night cold - trap . to first order , the rate of gravitational settling in a hot jupiter s atmosphere will be given by the free - fall timescale within that atmosphere . this will be the scale height of the atmosphere divided by the free - fall terminal velocity of condensates , @xmath149 here @xmath150 is the atmospheric temperature , @xmath151 is the mean molecular weight of the atmosphere , @xmath152 is the gravitational acceleration , @xmath153 is the particle radius , @xmath154 is the particle density , @xmath155 is the atmospheric density , and @xmath156 is the viscosity of the gas . if we make the assumption that mean molecular weight and viscosity of hot jupiters atmospheres , as well as the condensate and atmospheric density , are all effectively the same , then the free - fall timescale goes as @xmath157 typically , turbulent diffusion is treated as the dominant vertical lofting mechanism for condensates in the upper portion of a hot jupiter s atmosphere , but the exact efficiency of this process is poorly understood . by analogy to molecular diffusion , the efficiency of vertical mixing is parameterized by the effective diffusion coefficient , @xmath158 @xcite . unlike the molecular diffusion coefficient , however , the value of @xmath158 is the result of inherently chaotic processes that are difficult to model . while mixing length theory can be used to derive analytic estimates for @xmath158 ( e.g. , * ? ? ? * ) in the convective regions of a hot jupiter s atmosphere , these estimates are not appicable to the the upper , radiative , portion of the atmosphere probed by eclipse observations . this make the precise value of @xmath158 difficult to predict , and typical values of @xmath158 used in brown dwarf modeling can cover three to four orders of magnitude ( e.g. , * ? ? ? if we make the assumption that the efficiency of vertical mixing is approximately the same in all hot jupiters atmospheres , then for fixed values of @xmath153 , the condensate size , cold - traps will therefore be less efficient in hotter atmospheres with higher values of @xmath150 , but dramatically more efficient as surface gravity increases . 0.00 in ) from the results of @xcite on hd 189733b . based on existing observations , the red shaded region roughly corresponds to parameter space we would expect to see inverted or isothermal atmospheres , while the blue shaded region should have decreasing tp profiles . the middle purple region is ambiguous , owing to the range of allowable particle sizes . note that it is entirely possible that the mean condensate size changes over this parameter space , or varies individually by planet.,title="fig : " ] -0.0 in though more detailed modeling is necessary to precisely assess the role of cold - trap processes in kepler-13ab s atmosphere , let us proceed from the conclusion in @xcite that for particle sizes greater than `` a few microns '' a day - night cold trap is capable of depleting gas - phase tio / vo in hd 189733b s atmosphere . using the scaling in equation ( [ eq:4120 ] , we may extrapolate from this point to other temperatures and surface gravities , and compare against the other hot jupiters with spectrally - resolved nir emission measurements . based on their 1.1@xmath0 m to 1.7@xmath0 m emission and the modeling in their respective papers , we categorized the other planets with spectrally - resolved nir eclipse observations as having an inverted tp profile ( wasp-33b ) , an isothermal profile ( wasp-12b , wasp-103b ) , or as being ambiguous ( wasp-19b @xcite , wasp-4b @xcite , tres-3b @xcite , and corot-2b @xcite ) . of these three ambiguous planets , tres-3b and corot-2b both show wfc3 spectra consistent with both an isothermal and decreasing tp profile . the temperatures for the isothermal models of both ( 1800k and 1780k , respectively ) are very close to the condensation temperature of tio / vo . depending upon the exact temperature structure of their atmospheres , it is therefore possible that tio and vo have condensed out of their upper atmospheres independently of any possible cold - trap mechanisms . for wasp-4b , the wfc3 measured spectrum agrees with both a 2000k isothermal model and a carbon - rich , monotonically decreasing , model . wasp-19b was observed from the ground by @xcite , and their emission spectrum is not precise enough to distinguish the temperature structure of the planet . we categorized kepler-13ab as having a monotonically decreasing tp profile , as well as kelt-1b . extrapolating from hd 189733 b according to equation ( [ eq:4120 ] ) , we then plotted these eight planets alongside the limits of where we would expect cold - traps to inhibit inversions for particle sizes of @xmath159 m , @xmath160 m , and @xmath161 m . as shown in figure [ logglogt ] , this set of classifications and predictions relatively well represents the planets with hst / wfc3 observations of their dayside emission . in the shaded red region , where we would expect the atmospheres to be inverted or isothermal for reasonable particle sizes , are wasp-33b , wasp-12b , and wasp-103b similarly , both kepler-13ab and kelt-1b lie in the region where we would expect to see decreasing tp profiles assuming the condensate particles grow larger than @xmath159 m . we note that @xcite have also considered the efficiency of cold - traps , but instead choose to compare vertical terminal velocities to vertical mixing velocities to determine if a condensate sinks into the planetary interior , without considering the atmospheric scale height . based on numerical simulations of the vertical mixing velocity in planets cooler than 1750k , this leads @xcite to estimate that the efficiency of cold - trap processes should be roughly independent of temperature , and should scale inversely with condensate size and surface gravity . this nicely contrasts with our equations [ eq:4110 ] and [ eq:4120 ] , which propose a different scaling . which of these is correct - if any - would therefore provide us with good insight into the dominant processes with hot jupiters atmospheres , and could indicate whether vertical mixing velocities are roughly constant , as we have assumed , or if they vary coherent;y with planetary properties , as assumed by @xcite . currently , the global maximum size for condensate particles in the atmospheres of extremely hot jupiters with daysides near 3000k is poorly constrained by atmospheric models . based on the rayleigh scattering signatures seen in transmission spectra the maximum particle size at high altitudes along the planetary limb appears to be on the order of 0.1@xmath0 m @xcite . but 3d models of hd 187933 b s ( @xmath162k ) atmosphere by @xcite show a wide range of possible particle sizes as a function of longitude , latitude , and depth within the atmosphere . @xcite recently analyzed kepler - band albedo estimates from eclipse measurements made by @xcite , in an effort to constrain condensate properties on planetary daysides and at higher pressures than those probed by transmission observations . @xcite found that an average condensate size of 0.1@xmath0 m was able to replicate the reflective properties of the cooler planets ( @xmath163k ) , but that the two hotter planets in the @xcite data set near @xmath164k required a larger average condensate size . what the condensate size is in a hot jupiter with a dayside near 3000k has , therefore , not been extensively modeled . based on the toy model diagrammed in figure ( [ logglogt ] ) , with more spectrally - resolved observations of hot jupiters daysides , it may be possible to observationally constrain the general condensate size in these planets atmospheres by mapping out where stratospheric temperature inversion occur in extremely hot jupiters . though this assumes that cold - traps are the dominant mechanism to inhibit inversion , it will also be necessary to determine if one can even speak of single `` condensate size '' for all hot jupiters . to more adequately assess the role that cold - traps play in hot jupiters atmospheres , we therefore need more two- or three - dimensional atmosphere models , such as those in @xcite and @xcite , that include the variation of temperature structure as a function of longitude and latitude , models of particle and condensate growth processes within hot jupiters atmospheres , and we need spectrally - resolved observations of more systems to validate the results of both .

we measure a broadband ( 1.1 m to 1.65 m ) eclipse depth ofppm , and are able to measure the emission spectrum of the planet at with an average precision of 70ppm . our observations do not well sample either the eclipse ingress or egress , and so we are not able to provide meaningful constraints on the eclipse timing offset observed by . , we suggest that the apparent lack of an inversion is due to cold - trap processes in the planet s atmosphere . using a toy - model for where cold - traps should inhibit inversions , and observations of other planets in this temperature range with measured emission spectra

we observed two eclipses of the kepler-13a planetary system , on ut 2014 april 28 and ut 2014 october 13 , in the near - infrared using wide field camera 3 on the hubble space telescope . by using the nearby binary stars kepler-13bc as a reference , we were able to create a differential light curve for kepler-13a that had little of the systematics typically present in hst / wfc3 spectrophotometry . we measure a broadband ( 1.1 m to 1.65 m ) eclipse depth ofppm , and are able to measure the emission spectrum of the planet at with an average precision of 70ppm . our observations do not well sample either the eclipse ingress or egress , and so we are not able to provide meaningful constraints on the eclipse timing offset observed by . we do find that our observations , combined with those of give an average dayside brightness temperature of 3000k , and are consistent with a non - inverted , monotonically decreasing vertical temperature profile at 2.4 . we exclude an isothermal profile and an inverted profile . we also find that the dayside emission of kepler-13ab appears generally similar to an isolated m7 brown dwarf at a similar effective temperature . due to the relatively high mass and surface gravity of kepler-13ab , we suggest that the apparent lack of an inversion is due to cold - trap processes in the planet s atmosphere . using a toy - model for where cold - traps should inhibit inversions , and observations of other planets in this temperature range with measured emission spectra , we argue that with more detailed modeling and more observations we may be able to place useful constraints on the size of condensates on the daysides of hot jupiters .

1105.4563

i

@xmath0one hundred years ago , in 1911 , toeplitz obtained a deep result on eigenvalues of infinite matrices of the form @xmath1 . we say that @xmath2 is an eigenvalue of @xmath3 if the matrix @xmath4 does not have a bounded inverse , where @xmath5 denotes the infinite - dimensional identity matrix . toeplitz proved that , interestingly , the set of eigenvalues is the same as the image set @xmath6\}$ ] , where @xmath7 note that @xmath8 is the fourier transform of the sequence @xmath9 . for a finite @xmath10 matrix @xmath11 , its eigenvalues are approximately equally distributed ( in the sense of hermann weyl ) as @xmath12 , where @xmath13 are the fourier frequencies . see the excellent monograph by @xcite for a detailed account . covariance matrix is of fundamental importance in many aspects of statistics including multivariate analysis , principal component analysis , linear discriminant analysis and graphical modeling . one can infer dependence structures among variables by estimating the associated covariance matrices . in the context of stationary time series analysis , due to stationarity , the covariance matrix is toeplitz in that , along the off - diagonals that are parallel to the main diagonal , the values are constant . let @xmath14 be a stationary process with mean @xmath15 , and denote by @xmath16 $ ] , @xmath17 , its autocovariances . then @xmath18 is the autocovariance matrix of @xmath19 . in the rest of the paper for simplicity we also call ( [ eqsgnd28238 ] ) the covariance matrix of @xmath19 . in time series analysis it plays a crucial role in prediction [ @xcite , @xcite ] , smoothing and best linear unbiased estimation ( blue ) . for example , in the wiener kolmogorov prediction theory , one predicts @xmath20 based on past observations @xmath21 if the covariances @xmath22 were known , given observations @xmath23 , the coefficients of the best linear unbiased predictor @xmath24 in terms of the mean square error @xmath25 are the solution of the discrete wiener hopf equation @xmath26 where @xmath27 and @xmath28 , and we use the superscript @xmath29 to denote the transpose of a vector or a matrix . if @xmath22 are not known , we need to estimate them from the sample @xmath23 , and a good estimate of @xmath30 is required . as another example , suppose now @xmath31 and we want to estimate it from @xmath23 by the form @xmath32 , where @xmath33 satisfy the constraint @xmath34 . to obtain the blue , one minimizes @xmath35 subject to @xmath34 , ensuring unbiasedness . note that the usual choice @xmath36 may not lead to blue . the optimal coefficients are given by @xmath37 , where @xmath38 ; see @xcite . again a good estimate of @xmath39 is needed . given observations @xmath40 , assuming at the outset that @xmath41 , we can naturally estimate @xmath30 via plug - in by the sample version @xmath42 to judge the quality of a matrix estimate , we use the operator norm . the term `` operator norm '' usually indicates a class of matrix norms ; in this paper it refers to the @xmath43 operator norm or spectral radius defined as @xmath44 is a real vector , and @xmath45 denotes its euclidean norm . for the estimate @xmath46 in ( [ eqscovd29945 ] ) , unfortunately , because too many parameters or autocovariances are estimated and the signal - to - noise ratios are too small at large lags , this estimate is not consistent . @xcite showed that @xmath47 in probability . in section [ secinconsistency ] we provide a precise order of magnitude of @xmath48 and give explicit upper and lower bounds . the inconsistency of sample covariance matrices has also been observed in the context of high - dimensional multivariate analysis , and this phenomenon is now well understood , thanks to the results from random matrix theory . see , among others , @xcite , @xcite and @xcite . recently , there is a surge of interest on regularized covariance matrix estimation in high - dimensional statistical inference . we only sample a few works which are closely related to our problem . @xcite , @xcite and @xcite studied the banding and/or tapering methods , while @xcite and @xcite considered the regularization by thresholding . in most of these works , convergence rates of the estimates were established . however , none of the techniques used in the aforementioned papers is applicable in our setting since their estimates require multiple independent and identically distributed ( i.i.d . ) copies of random vectors from the underlying multivariate distribution , though the number of copies can be far less than the dimension of the vector . in time series analysis , however , it is typical that only one realization is available . hence we shall naturally use the sample autocovariances . in a companion paper , @xcite established a systematic theory for @xmath49 and @xmath50 deviations of sample autocovariances . based on that , we adopt the regularization idea and study properties of the banded , tapered and thresholded estimates of the covariance matrices . @xcite and @xcite applied the banding and tapering methods to the same problem , but here we shall obtain a better and optimal convergence rate . we shall point out that the regularization ideas of banding and tapering are not novel in time series analysis and they have been applied in nonparametric spectral density estimation . in this paper we use the ideas in @xcite and @xcite together with wu s ( @xcite ) recent theory on stationary processes to present a systematic theory for estimates of covariance matrices of stationary processes . in particular , we shall exploit the connection between covariance matrices and spectral density functions and prove a sharp convergence rate for banded covariance matrix estimates of stationary processes . using convergence properties of periodograms , we derive a precise order of magnitude for spectral radius of sample covariance matrices . we also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse . as a main technical tool , we develop a large deviation type result for quadratic forms of stationary processes using @xmath51-dependence approximation , under the framework of causal representations and physical dependence measures . the rest of this article is organized as follows . in section [ secinconsistency ] we introduce the framework of causal representation and physical dependence measures that are useful for studying convergence properties of covariance matrix estimates . we provide in section [ secinconsistency ] upper and lower bounds for the operator norm of the sample covariance matrices . the convergence rates of banded / tapered and thresholded sample covariance matrices are established in sections [ secbanding ] and [ secthresholding ] , respectively . we also conduct a simulation study to compare the finite sample performances of banded and thresholded estimates in section [ secsimulation ] . some useful moment inequalities are collected in section [ sec6 ] . a large deviation result about quadratic forms of stationary processes , which is of independent interest , is given in section [ secld ] . section [ secconclude ] concludes the paper . we now introduce some notation . for a random variable @xmath52 and @xmath53 , we write @xmath54 if @xmath55 , and use @xmath56 as a shorthand for @xmath57 . to express centering of random variables concisely , we define the operator @xmath58 as @xmath59 . hence @xmath60 . for a symmetric real matrix @xmath61 , we use @xmath62 and @xmath63 for its smallest and largest eigenvalues , respectively , and use @xmath64 to denote its operator norm or spectral radius . for a real number @xmath65 , @xmath66 denotes its integer part and @xmath67 . for two real numbers @xmath68 , set @xmath69 and @xmath70 . for two sequences of positive numbers @xmath71 and @xmath72 , we write @xmath73 if there exists some constant @xmath74 such that @xmath75 for all @xmath76 . the letter @xmath77 denotes a constant , whose values may vary from place to place . we sometimes add symbolic subscripts to emphasize that the value of @xmath77 depends on the subscripts .

we obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes . a precise order of magnitude is derived for spectral radius of sample covariance matrices . we also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse . as our main tool , we implement toeplitz [ _ math . ann . _ * 70 * ( 1911 ) 351376 ] idea and relate eigenvalues of covariance matrices to the spectral densities or fourier transforms of the covariances . we develop a large deviation result for quadratic forms of stationary processes using approximation , under the framework of causal representation and physical dependence measures . .

we obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes . a precise order of magnitude is derived for spectral radius of sample covariance matrices . we also consider a thresholded covariance matrix estimator that can better characterize sparsity if the true covariance matrix is sparse . as our main tool , we implement toeplitz [ _ math . ann . _ * 70 * ( 1911 ) 351376 ] idea and relate eigenvalues of covariance matrices to the spectral densities or fourier transforms of the covariances . we develop a large deviation result for quadratic forms of stationary processes using approximation , under the framework of causal representation and physical dependence measures . .

cond-mat0507458

i

the survival of ferromagnetic ordering under the disruption of frozen random fields @xcite and the onset of spin - glass ( sg ) order in systems characterized by random competing interactions @xcite are two central problems in the statistical mechanics of systems with quenched randomness . when properly rephrased , these two problems turn out to relate to core problems in other , quite different disciplines . insight into these two closely related problems in any given system is obtained from the corresponding phase diagram as a function of the physical parameters , such as temperature and disorder strength . finite - connectivity mean - field sg models @xcite and their _ p_-spin counterpart @xcite are important for two distinct reasons . firstly , despite being mean - field in nature , they are believed to share common properties with finite - dimensional spin - glass systems @xcite . secondly , the statistical mechanics of sg model systems with fixed finite connectivity relates to the study of various hard computational problems . in the last two decades the analysis of finite - connectivity sg systems has also offered new tools for understanding the very nature of several optimization problems _ and _ improve algorithmic performances @xcite . in this paper we first obtain the phase diagram of finite - connectivity mean - field sg models . we then investigate the relation between features of the phase diagram and the performance of low density parity check ( ldpc ) codes , analyzing the effects induced by the replica symmetry breaking ( rsb ) nature of solutions obtained for these finite - connectivity sg models @xcite . in order to answer these questions , we exploit the relation between finite - connectivity sg systems and a class of exactly solvable models ; we employ an efficient computational method that has been shown to be quite effective for understanding several features of finite - dimensional sg @xcite . we will consider a generalized model unifying the frameworks for a few distinct problems . particular attention will be given to two special cases : a ) the bethe sg which has been extensively studied under both replica symmetric ( rs ) and rsb anstze @xcite and recently considered in its ferromagnetically biased version @xcite . b ) gallager ( ldpc ) error - correcting codes @xcite . while the former is well known within the statistical physics community , many in this community are less familiar with the latter and its links to the physics of disordered systems . reliable transmission of information in noisy conditions is one of the basic problems of modern communication technology . correspondingly , one of the central problems of information theory is channel coding . methods to achieve reliable information transmission rely on the introduction of structured redundancy to the original message in order to compensate for corruption due to noise . shannon derived rigorous bounds on the level of redundancy ( the code rate ) required to enable error - free communication for a given channel noise @xcite . however , shannon s theorems are non - constructive and do not offer a practical coding scheme . different methods , based on various redundancy construction recipes , have been proposed over the years @xcite . despite the fact that error - correcting codes are now widely used in a variety of applications , current performances of most methods are significantly below shannon s bound . one family of error - correcting codes that have been shown to provide close - to - optimal performances is that of gallager s ldpc codes @xcite . in these codes the structured redundancy is introduced through parity checks of boolean sums of randomly sampled message bits . the relation between the parity - check error - correcting codes and sg models , and consequently between quite different disciplines as statistical physics and information theory , has been pointed to in the seminal work of sourlas @xcite . decoding in ldpc codes corresponds to a class of sg models defined by an underlying lattice geometry that reflects the low density character of the code construction . the importance of this very last point , that made the above correspondence useful and of practical relevance was not understood until recently @xcite . methods developed in the statistical mechanics of diluted sg under the rs anstz have been successfully employed to compute macroscopic properties of such systems for different parameter values ; reasonable agreement with observed decoding bounds have been reported @xcite . to our knowledge however , the only phase diagram that has been evaluated for ldpc codes is in the limit of large coordination / large multi - spin interaction numbers @xcite , which also relates to the phase diagram of the random energy model ( rem ) @xcite . in the following section we introduce the class of ising spin systems to be analyzed and its links to the bethe sg and ldpc decoding problems this will be followed by section [ sec : rs ] where we review the rs equations and the corresponding solutions are obtained using a computational method adopted from the study of @xmath5-dimensional hierarchical models . as part of this section we will present the method and briefly discuss the relation between finite - connectivity sg and @xmath5-dimensional hierarchical models . in section [ sec : rsb ] we introduce the equations behind the rsb theory of finite - connectivity sg studied here and present results obtained for the bethe sg problem and ldpc error - correcting codes under two different transmission channels : the binary erasure channel ( bec ) and the binary symmetric channel ( bsc ) . in section [ sec : disc ] we discuss the results obtained and point to future research directions .

we obtain phase diagrams of regular and irregular finite connectivity spin - glasses . contact is firstly established between properties of the phase diagram and the performances of low density parity check codes ( ldpc ) within the replica symmetric ( rs ) anstz . + pacs numbers : 89.90+n , 89.70+c,05.50+q +

we obtain phase diagrams of regular and irregular finite connectivity spin - glasses . contact is firstly established between properties of the phase diagram and the performances of low density parity check codes ( ldpc ) within the replica symmetric ( rs ) anstz . we then study the location of the dynamical and critical transition of these systems within the one step replica symmetry breaking theory ( rsb ) , extending similar calculations that have been performed in the past for the bethe spin - glass problem . we observe that , away from the nishimori line , in the low temperature region , the location of the dynamical transition line change within the rsb theory , in comparison with the ( rs ) case . for ldpc decoding over the binary erasure channel we find , at zero temperature and rate an rs critical transition point located at while the critical rsb transition point is located at , to be compared with the corresponding shannon bound . for the binary symmetric channel ( bsc ) we show that the low temperature reentrant behavior of the dynamical transition line , observed within the rs anstz , changes within the rsb theory ; the location of the dynamical transition point occurring at higher values of the channel noise . possible practical implications to improve the performances of the state - of - the - art error correcting codes are discussed . + pacs numbers : 89.90+n , 89.70+c,05.50+q +

astro-ph0208210

i

although of fundamental importance to stellar astrophysics , precise measurements of angular radii are generically difficult to acquire routinely and in a model - independent way . classical direct methods of measuring stellar radii include lunar occultations , interferometry , and eclipsing binaries . lunar occultation measurements yield precise angular radii ( see richichi et al . 1999 and references therein ) , but the number of stars to which this technique can be applied is limited . the number of direct measurements using interferometers has recently increased dramatically with advent of , e.g. the palomar testbed interferometer ( van belle et al . 1999a , colavita et al . 1999 ) , and the navy prototype optical interferometer ( armstrong et al . 1998 , nordgren et al . 1999 ) , and is likely to continue to increase as more technologically advanced interferometers come online . unfortunately , both lunar occultation and interferometric angular diameter measurements have traditionally been primarily limited to nearby , evolved stars . angular radii of main - sequence stars can be determined using detached eclipsing binaries ( i.e. popper 1998 ) , however the large amount of data ( both photometric and spectroscopic ) required to yield accurate radii determinations makes this method prohibitive . thus , of the @xmath17 direct , precise angular diameter measurements compiled by van belle ( 1999 ) , the overwhelming majority , @xmath18 , are of evolved stars . finally , it will be difficult to acquire a large sample of angular radii determinations of stars with metallicity considerably smaller than solar using these methods , due to the paucity of metal - poor stars in the local neighborhood . here we present a method , based on a suggestion by paczyski ( 1998 ) , of measuring angular radii of stars that overcomes some of the difficulties inherent in the classical methods . this method employs the extraordinary angular resolution provided by caustics in gravitational microlensing events , and as such is yet another in the growing list of applications of microlensing to the study of stellar astrophysics ( see gould 2001 for a review ) . the original suggestion of paczyski ( 1998 ) was to invert the method of gould ( 1994 ) for measuring the relative source - lens proper motion @xmath19 in microlensing events . if the lens transits the source in a microlensing event , precise photometry can be used to determine the time it takes for the lens to transit one source radius , @xmath20 , where @xmath1 is angular radius of the source . an estimate of @xmath1 , using an empirical color - surface brightness relation , together with a measurement of the flux of the source , can then be used to estimate @xmath19 , which gould ( 1994 ) argued could be used to constrain the location of the lens . however , as paczyski ( 1998 ) pointed out , it is possible to independently measure the angular einstein ring radius of the lens , @xmath21 by making precise astrometric measurements of the centroid shift of the source during the microlensing event using , i.e. , the _ space interferometry mission _ ( sim ) . here @xmath22 is the mass of the lens , @xmath23 is defined by , @xmath24 , and @xmath25 , @xmath26 , and @xmath27 are the distances between the observer - source , observer - lens , and lens - source , respectively . since @xmath28 , by combining the measurement of @xmath5 with the einstein timescale @xmath3 of the event determined from the light curve , it is possible to measure @xmath1 for the source stars of microlensing events . we show that , with reasonable expenditure of resources , it should be possible to measure angular radii of a significant sample ( @xmath29 ) of giant stars in the bulge to an accuracy of @xmath30 , or @xmath10 main - sequence stars to an accuracy of @xmath31 . limb - darkening determinations should also be possible for the majority of the sources , and most will be relatively metal poor as compared to those for which angular radii determinations are currently available . although measurements of @xmath1 can be made using single - lens events , in [ sec : bvs ] we argue that this method is better suited to caustic - crossing binary - lens events , which are more common , easier to plan for , and considerably less resource - intensive than source - crossing single - lens events . we describe in some detail the basic method of measuring @xmath1 for the source stars of caustic - crossing binary - lens events in [ sec : method ] , including a discussion of the expected errors on the individual parameters that enter into the measurement . we discuss various subtleties , complications , and extensions to the method in [ sec : discussion ] , and also present an estimate of the number of @xmath1 measurements that might be made in this way . finally , we summarize and conclude in [ sec : conclusion ] .

the method combines comprehensive ground - based photometry of caustic - crossing bulge microlensing events , with a handful of precise ( ) astrometric measurements of the lensed star during the event , to measure the angular radius of the source , . adopting parameters appropriate to the _ space interferometry mission _ ( sim ) , we find that minutes of sim time is required to measure to accuracy for giant sources in the bulge . for main - sequence sources , can be measured to accuracy in hours .

we outline a method by which the angular radii of giant and main sequence stars located in the galactic bulge can be measured to a few percent accuracy . the method combines comprehensive ground - based photometry of caustic - crossing bulge microlensing events , with a handful of precise ( ) astrometric measurements of the lensed star during the event , to measure the angular radius of the source , . dense photometric coverage of one caustic crossing yields the crossing time scale . less frequent coverage of the entire event yields the einstein timescale and the angle of source trajectory with respect to the caustic . the photometric light curve solution predicts the motion of the source centroid up to an orientation on the sky and overall scale . a few precise astrometric measurements therefore yield , the angular einstein ring radius . then the angular radius of the source is obtained by . we argue that the parameters , and , and therefore , should all be measurable to a few percent accuracy for galactic bulge giant stars using ground - based photometry from a network of small ( 1m - class ) telescopes , combined with astrometric observations with a precision of to measure . we find that a factor of times fewer photons are required to measure to a given precision for binary - lens events than single - lens events . adopting parameters appropriate to the _ space interferometry mission _ ( sim ) , we find that minutes of sim time is required to measure to accuracy for giant sources in the bulge . for main - sequence sources , can be measured to accuracy in hours . thus , with access to a network of 1m - class telescopes , combined with 10 hours of sim time , it should be possible to measure to for giant stars , or to for main sequence stars . we also discuss methods by which the distances and spectral types of the source stars can be measured . a byproduct of such a campaign is a significant sample of precise binary - lens mass measurements . # 1 # 1equation ( [ # 1 ] )

astro-ph0208210

c

our goal in [ sec : method ] was to capture the essence of the method of measuring @xmath1 , and the discussions were therefore somewhat oversimplified , and glossed over several important points . in particular , we concentrated on fold caustic crossing binary - lens events toward the bulge , whereas measurements of @xmath1 should be possible in other , rarer , types of events , such as cusp - crossings and single - lens events , and possibly events toward the magellanic clouds . we also ignored various higher - order effects which could , in principle , complicate the measurements . we therefore briefly discuss some of these complications and extensions . we also discuss the prospects for measuring the spectral type of the source , and also its distance , in order to convert from angular radius @xmath1 to physical radius @xmath36 . finally , we present an example observing campaign aimed at measuring angular radii for a significant sample of sources , outlining the resources required , and estimating the number of @xmath1 measurements that might be made per year for such a campaign . although we have focussed on fold caustic - crossing binary - lens events toward the bulge , it is important to emphasize that @xmath1 can , in principle , be measured for other types of caustic - crossing events such as cusp - crossing events , single - lens events , and all types of caustic - crossing events toward the magellanic clouds . indeed , in [ sec : errors ] we discussed examples in the literature of a single - lens and two cusp - crossing events for which a @xmath11 measurement of @xmath1 would have been feasible . in general , isolated cusp crossings , such as in macho 98-blg-28 , can not be predicted in advance , and thus planning for such events is difficult , if not impossible . however , one will still have some advance warning of those cusp events which occur just after or in place of second fold caustic crossings . for such events , sufficient photometric coverage of the crossing should routinely be possible . in all cases , it is more difficult to disentangle the information arising from the cusp itself with the information from the global light curve . this generally implies that the analysis of these light curves will be more complicated , however this does not necessarily preclude an accurate measurement of @xmath1 . single - lens events are less desirable simply because they require a factor of @xmath9 times more astrometric observing time to achieve the same fractional accuracy in @xmath5 as binary - lens events . since the astrometric observations are likely to be the most limited resource , this makes single lens events considerably less attractive . if it were possible to measure angular radii of stars in the magellanic clouds ( mcs ) , this would be quite interesting , due to the metal - poor nature of the stars . unfortunately , there are several major hindrances to measuring @xmath1 for a substantial number of stars in the mcs . first , the event rates toward both the mcs are small , and a large number of stars must be monitored just to detect a few events per year . therefore , the number of caustic - crossing events is quite low . to date , there have been only two caustic crossing events toward the mcs : macho 98-smc-1 , which we discussed in [ sec : errors ] , and macho lmc-9 . these events have source magnitudes of @xmath142 ( afonso et al . 2000 ) and @xmath143 ( alcock et al . 2000a ) , respectively , which brings up a second difficulty : sim can not follow source stars fainter than @xmath144 , so these two events could not have been used to measure the angular radii of their source stars . in fact , even if the entire lmc were monitored for microlensing , only @xmath65 event per year would have @xmath145 , and this event would be from an evolved star . the probability of a caustic - crossing event ( either binary or single lens ) is smaller by at least an order of magnitude . the paucity of events and faintness of the source stars might be circumvented if sufficiently rapid target of opportunity times are available . in this case , it might be possible to use intrinsically fainter source stars , for which caustic - crossing event will be more common , and measure the astrometric displacement during the brief period of time when the source is highly magnified as it crosses the caustic . the maximum magnification of a source of dimensionless size @xmath146 crossing a fold caustic is @xmath147 . for main - sequence sources , @xmath148 , or more than three magnitudes , and thus sources with @xmath149 can briefly be brightened to sim detectability . for example , the source star of macho 98-smc-1 was brighter than @xmath150 for about 7 hours during the second caustic crossing . finally , even if the source does attain a sufficient brightness to be measurable by sim , it remains to be seen whether the centroid varies sufficiently during this time to provide an accurate measurement of @xmath5 . this is especially difficult in light of the fact that typical value of @xmath5 for self - lensing events toward the mcs are only an order of magnitude larger than sim s accuracy ( paczy ' nski 1998 , gould & salim 1999 ) . in summary , it appears that it will be quite difficult to measure angular radii of stars in the mcs using this method , especially if the majority of the events seen toward these targets are due to self - lensing ( sahu 1994 ) . the method we have presented here is only interesting if it can feasibly be used to make precise @xmath1 measurements for a large number of sources with reasonable expenditure of resources . since the requisite astrometric instruments are likely to be the most limited resource , it is crucial that accurate and unambiguous determinations of @xmath5 be generically possible using a few astrometric measurements , when combined with the photometric light curve solution . we have explained how a complete photometric solution _ generally _ leads to a prediction for the astrometric centroid shift up to an unknown scale @xmath5 and orientation @xmath90 on the sky . however , this is true only under a number of simplifying assumptions , including uniform motion of the observer , source , and lens , dark lenses , isolated sources , and unique global solutions . if one or more of these assumptions are violated , then the prediction for shape of the astrometric curve may not be unique , and thus the measurement of @xmath5 may be compromised . we therefore discuss each of these complications and under what conditions they may be important . binary lenses are characterized by two quantities : @xmath81 , the mass ratio , and @xmath42 , the instantaneous projected separation in units of @xmath5 . it has been demonstrated both theoretically ( dominik 1999a ) and observationally ( afonso et al . 2000 , albrow et al . 2002 ) that certain limiting cases of binary lenses can exhibit extremely similar observable properties . in particular , dominik ( 1999 ) showed that the binary - lens equation can be approximated by an single lens with external shear , or chang - refsdal ( cr ) lens ( chang & refsdal 1979,1984 ) , near the individual masses for widely - separated binaries ( @xmath151 ) , and near the secondary ( least massive ) lens when @xmath152 . furthermore , near the center - of - mass of a close binary , the lens equation is well - approximated by a quadrupole lens , and both the quadrupole lens and cr - lens can exhibit extremely similar magnifications when the quadrupole moment is equated to the shear ( albrow et al . 2002 ) . thus there can exist multiple degenerate solutions to an observed photometric light curve , even with extremely accurate photometry . however the astrometric behavior of these degenerate solutions is very similar both in the shape and overall scale of the astrometric curves , at least for the close / wide degeneracy ( gould & han 2000 ) . therefore this degeneracy should not affect the determination of @xmath5 using the prediction from the light curve . it is likely that the other intrinsic denegeracies will also not affect the determination of @xmath5 , since the degeneracy arises from the lens equation itself , and thus affects both the photometric and astrometric curve in the same manner . note that it is important that the normalization of @xmath5 be consistent for the two degenerate solutions . for example , consider the case of the close / wide degeneracy in macho 98-smc-1 ( afonso et al 2000 , gould & han 2000 ) . if one normalizes to the total mass of the binary , the close solution implies a value of @xmath153 , whereas the wide solution has @xmath154 . since the astrometric curves are essentially identical ( both in shape and scale ) , one might therefore suspect the inversion of this process would yield two equally likely values of @xmath1 that differed by a factor of @xmath155 of course , this ` ambiguity ' is wholly artificial , and arises because the value of @xmath156 for the wide binary is normalized to the entire mass of the binary , whereas the lensing effects are basically caused by the least massive lens , since @xmath157 . normalizing to the mass of the single lens , @xmath158 , where here @xmath159 , and thus @xmath160 , essentially identical to the close - binary solution . note that as @xmath42 approaches unity , the identification of the ` proper ' @xmath5 normalization becomes more nebulous , since the lenses can no longer be considered independent . however , the degeneracies also become less severe as @xmath161 . dominik ( 1999b ) has also shown that poorly - sampled binary lens light curve can also yield distinct degenerate solutions . note that these solutions are ` accidental ' in the sense that they do not arise from degeneracies in the lens equation itself . thus han et al . ( 1999 ) found that such degenerate photometric light curves yield astrometric curves which are widely different . such degeneracies would prohibit the measurement of @xmath5 using a few astrometric measurements . therefore well - sampled photometric light curves are essential for reliable measurements of @xmath1 . if the two observers are displaced by a significant fraction of @xmath162 , the angular einstein ring radius projected onto the observer plane , then the source position @xmath88 as seen by the two observers will be significantly different . since sim will be in an earth - trailing orbit , it will drift away from the earth at a rate of @xmath163 . thus after 2.5 years ( half way through the sim mission ) , it will be displaced from the earth by @xmath164 , which corresponds to a displacement in the einstein ring of , @xmath165 where @xmath166 is the angle between the the line of sight and the earth - sim vector . for typical bulge parameters , @xmath167 and therefore @xmath168 . this implies that both the magnification @xmath82 and the centroid shift @xmath169 will be significantly different ( at a given time ) as seen from the earth and sim . since the value of @xmath170 is not known _ a priori _ , @xmath171 can not be predicted from the ground - based photometry alone , and must be estimated from the astrometric data itself . fortunately , sim will likely have excellent photometric capabilities ( see gould & salim 1999 ) , and thus the relative magnifications between the light curves from the ground and sim will provide additional constraints . indeed , in our monte carlo simulations , we assumed that the astrometric observer was displaced by @xmath172 from the earth , and simultaneously fit for both @xmath5 and @xmath170 ( among other parameters ) , and found that @xmath5 could still be constrained quite accurately . this is because the information about @xmath170 comes primarily from the photometry , while the information about @xmath5 comes primarily from the astrometry . therefore , the two parameters are not degenerate . note that a ` byproduct ' of these measurements is a determination of the total mass of the binary lens ( gould & salim 1999 ; han & kim 2000 ; graff & gould 2002 ) there are two additional parallax effects . one is due to the motion of the earth ( or sim ) around the sun , and will become significant on timescales that are a substantial fraction of a year , which corresponds to many @xmath3 for typical bulge events . there is also a second order effect that arises from the difference in projected velocities between the earth and sim . this effect is @xmath173 , where @xmath174 is the transverse velocity of the lens projected on the observer plane , and is @xmath175 for typical bulge self - lensing events . since the velocities and positions of the earth and sim will be known , both of these effects can easily be included in the fit for the microlensing parallax , and so do not present any additional difficulties . with its planned 10 meter baseline , sim will have a resolution of @xmath176 , sufficient to resolve the majority of unassociated nearby stars that are blended with the source in ground - based photometry ( han & kim 1999 ) . since the photometric blending is well - constrained in binary - lens events , unambiguous prediction of the unblended astrometric behavior of the source is possible . thus , blending will typically not affect the measurement of @xmath5 . however , luminous lenses and companions to the source star with separations @xmath177 will not be automatically resolved by sim ( jeong , han & park 1999 ) . dalal & griest ( 2001 ) have shown that , using two pointings , this limit may be lowered to @xmath178 , however it is essentially impossible to resolve multiple sources with separations below this limit ( e.g. binary source companions ) . in these cases , all that will be measured is the total centroid of all the sources in the resolution element . the centroid in the presence of luminous lenses , @xmath179 , is related to the centroid in the absence of blending , @xmath85 , by @xmath180 \left(1 + \frac{f_t}{a}\right)^{-1 } , \label{eqn : dbpclt}\ ] ] where @xmath181 is the sum of the flux of all unlensed sources ( blends ) relative to @xmath182 , the baseline flux of the lensed source , @xmath82 is the magnification of the source , and @xmath183 is the centroid of the blends relative to the origin of the lens . from , it is clear blending is more complicated in astrometric microlensing than in photometric microlensing : whereas photometric blending can be described by one parameter , the blend fraction @xmath184 , astrometric blending requires two additional parameters , the centroid of light of the blend @xmath183 . a special case of astrometric blending is bright lens blending . in the single lens case , this eliminates the blend location parameters , the location of the centroid of light is the moving lens ( i.e. @xmath185 ) . in bright binary lens blending , only one parameter is eliminated , the centroid of light is somewhere on the lens axis between the two stars in the lens . however , it will generally not be known _ a priori _ which case one is dealing with , and therefore @xmath183 must be included as a parameter in the astrometric fit . blending is problematic because it effectively ` dilutes ' the astrometric shift between two points in the lightcurve , which is qualitatively similar to the effect of changing @xmath5 . if the event is not well covered , these two effects can be quite degenerate . in order to determine how degenerate blending is with the @xmath5 , we have included in our monte carlo simulations a fixed amount of blended light of @xmath186 , and @xmath187 . we assume that @xmath184 is known ( i.e. from photometry ) , but @xmath183 is not . the results are shown in figure 2 . we find that , if the blending fraction is close to 1 , then the two effects are nearly degenerate , and our fractional uncertainty in @xmath5 increases by two orders of magnitude to of order unity . however , for @xmath188 , the median error increases by less than a factor of two . in most cases , the blending will be known to be small from the photometric data . in these cases , the fractional uncertainty in @xmath5 will not be seriously degraded . the few events with known large blending can be easily jettisoned from the sample . the photometric effects of lens rotation in binary microlensing events has been explored theoretically by dominik ( 1998 ) and has been detected in event macho 1997-bul-41 ( albrow et al . the astrometric effects of rotating binary - lenses have not been explored , and it is therefore difficult to draw any general conclusions as to the importance of this effect . however , to the extent that it is detectable in the photometric light curve , lens rotation poses no difficulties , as its astrometric effect should be predictable from the global solution . effects that are photometrically undetectable but astrometrically significant are potentially problematic . the amount that a binary - lens rotates during @xmath3 is given by , @xmath189 where @xmath190 , and assuming circular , face - on orbits . because the caustic cross - section is maximized for binaries with separations of order @xmath5 , the majority of detected caustic - crossings will have @xmath191 ( baltz & gondolo 2001 ) . therefore , for typical events , the effects of binary rotation should be small if astrometric observations are closely spaced with respect to the event timescale @xmath3 . this is generally also advantageous for the accurate recovery of @xmath5 ( see [ sec : thetae ] ) . in this paper , we have emphasized the measurement of the angular radius @xmath1 , rather than the physical radius , @xmath36 . however , it may also be interesting to measure @xmath36 for some events . in order to do this , the distance to the source star must be measured independently . fortunately , the astrometric accuracy needed to measure @xmath1 is generally sufficient to measure the parallax @xmath192 of the source stars , @xmath193 in order to measure @xmath36 to a similar accuracy as @xmath1 ( @xmath11 ) , @xmath192 must be measured to somewhat better accuracy , which implies an astrometric error of @xmath194 . for sim and an @xmath113 source , this is achievable with @xmath195 hours of integration , which is considerably more time than is needed for the @xmath1 measurement alone . however , it is important to note that these measurements can be made after the microlensing event is over . therefore , it should be possible to employ ground - based interferometers for the measurement of @xmath192 , rather than spend precious sim resources , at least for brighter sources . a measurement of @xmath1 is essentially useless if the spectral type and luminosity class of the source is not known . the source stars of microlensing events can be typed in two ways . the first is to simply measure the color and apparent magnitude of the source . this information is generally acquired automatically from the fit to the photometric data of the microlensing event . by positioning the source star on a color - magnitude diagram of other stars in the field , one can generally type the source to reasonable accuracy . the primary pitfalls of this method are differential reddening and projection effects ( i.e. the source may in the foreground or background of the bulk of the stars in the field ) . a more robust way of typing the source star is to acquire spectra . this is best done when the source is highly magnified as it crosses a caustic , as this minimizes the effects of blended light and increases the signal - to - noise . thus such measurements require target - of - opportunity observations . for highly - magnified events , spectra with @xmath196 per resolution element can be achieved with exposure times of tens of minutes for low - resolution spectra ( lennon et al . 1996 ) , or a couple of hours for high - resolution spectra ( minniti et al . 1998 ) , using 8 m or 10m - class telescopes . although low - resolution spectra are sufficient for accurate + spectral typing , high resolution spectra are desirable for a number of other applications , including resolution of the atmosphere of the source star ( gaudi & gould 1999 , castro et al . 2001 , albrow et al . 2001b ) , detailed abundance analysis ( minniti et al . 1998 ) , and detection of a luminous lens ( mao , reetz , & lennon 1998 ) . note also that as a byproduct , true space velocities of a sample of stars in the bulge will be obtained by combining the proper motions and parallaxes of the sources acquired from astrometric measurements with radial velocities determined from the spectra . in this section , we review the requirements for measuring @xmath1 for the source stars of galactic bulge microlensing events , and outline the resources needed for a campaign aimed at measuring @xmath1 for a significant number of sources . the first requirement is a large sample of caustic - crossing binary - lens events from which to choose targets , which in turn requires an even larger sample of microlensing events . a large sample is important in that it ensures that only interesting and promising sources and events are followed . currently , both the ogle and moa collaborations monitor many millions of stars in the galactic bulge . both reduce their data real - time , enabling them to issue ` alerts , ' notification of ongoing microlensing events ( udalski et al . 1994 , bond et al . 2002a).ftp / ogle / ogle3/ews / ews.html ( ogle ) and http://www.roe.ac.uk/@xmath15iab/alert/alert.html ( moa ) . ] combined , these two collaborations should alert about @xmath197 events per year ( with the majority of alerts from ogle ) . extrapolating from previous results ( alcock et al . 2000a , udalski et al . 2000 ) , approximately @xmath14 of these will be caustic - crossing binaries , or 25 events per year . figure 3 shows the cumulative distribution of apparent ( i.e.uncorrected for redenning ) @xmath132 magnitudes of the 438 independent bulge microlensing alerts in 2002 for which baseline magnitudes were available . of these events , 382 ( @xmath198 ) were alerted by ogle , 61 ( @xmath199 ) were alerted by moa , and 5 were alerted by both collaborations . for the typical colors of sources in the bulge ( @xmath200 ) , only about @xmath201 of the alerts have @xmath202 , and thus would have been accessible to sim . the boundary between dwarfs and giants will occur at an apparent magnitude that depends on the color of the source , the distance to the source , and the reddening . however , for definiteness we will simply assume that the boundary between giants and main sequence stars occurs at roughly @xmath203 . with this assumption , we can therefore expect that approximately @xmath204 of all alerted events will be due to giant stars . therefore , we can expect approximately @xmath205 of all alerts , or @xmath206 events ( assuming 500 alerts ) , to be caustic crossing events with giant sources , and @xmath207 , or @xmath208 events , to be caustic crossing events with main sequence sources , @xmath209 of which will be bright enough to monitor with sim .- magnitude of the source . in fact , deviations from the single - lens form will generally be easier to detect in brighter sources , however this bias is likely to be relatively small for caustic - crossing events , which generally exhibit dramatic and easily - detectable deviations from the point lens form . this may seem in contradiction with the fact that none of the five events toward the bulge presented in table 1 are main sequence sources . however , this almost certainly a selection effect : bright binary - lens events are currently preferentially monitored by the follow - up collaborations , in order to achieve higher signal - to - noise during the second caustic crossing . ] these numbers are likely to remain valid at least for the next several years . however , in the more distant future , and in particular by the time sim is launched , it is likely that the next generation of microlensing survey collaborations will have come online . thus we can expect that , when sim time is operational , a considerably larger sample of caustic - crossing events will be available . survey - type experiments are needed to discover microlensing events toward the bulge , and survey - quality data is generally sufficient to uncover the caustic - crossing nature of the target events . however , as we discussed in [ sec : dt ] , more accurate and densely - sampled photometry is generally needed during the caustic crossing in order to measure @xmath2 . currently , there are several collaborations with dedicated ( or substantial ) access to 1 - 2 m class telescopes distributed throughout the southern hemisphere that closely monitor alerted microlensing events with the goal of discovering deviations from the single - lens form , with emphasis on search for extrasolar planets ( albrow et al . 1998 , rhie et al . 2000 , tsapras et al . 2001 , bond et al . these collaborations have also been quite successful in predicting and monitoring binary - lens caustic crossings . it seems likely that these collaborations , or similar ones , will still be in place when the next generation of interferometers , or even sim , come online . in our monte carlo simulations we derived the expected precisions @xmath210 assuming that the photometric errors were dominated by photon statistics , and that a total of @xmath110 photons where collected over the entire exposure time for each event this corresponds to total exposure time of @xmath211 for sim on an @xmath113 source . we assume the fractional photometric uncertainty is @xmath114 , and that the astrometric uncertainty was related to the photometric uncertainty via the expression , @xmath212 , with @xmath213mas , as appropriate for sim . since we assumed that the photometric and astrometric errors are given simply by photon statistics , it is trivial to scale our results for other total exposure times @xmath214 and source brightnesses assuming the characteristics of sim : @xmath215 , and @xmath216 . for the purposes of planning observations , and providing an order - of - magnitude estimate for the number of angular radii that can be measured for a given amount of sim time , it is useful to derive an expression for the exposure time required to achieve a given median photometric precision . to be conservative , we assume that the blending is small , but non - negligible . specifically , we adopt the median error found for the monte carlo simulations assuming a blend fraction of @xmath217 , which is @xmath218 . then , @xmath219 thus , for giant sources ( @xmath220 ) , @xmath221 minutes are required to achieve @xmath14 precision , whereas for main - sequence sources ( @xmath222 ) , @xmath223 hours are required for @xmath14 precision , or @xmath224 hours for @xmath16 precision . we have focussed here primarily on astrometric observations with sim because its capabilities are well - suited to this application . the basic requirements to be able to measure @xmath5 accurately for the events we have discussed are relatively high astrometric precisions , @xmath225 , and high sensitivity ( via , i.e. large apertures ) , as the sources we are considering are faint , @xmath226 . these faint sources are inaccessible to current ground - based interferometers . upcoming large - aperture , ground - based interferometers , such as the very large telescope interferometer or the keck interferometer , should be able to achieve the requisite astrometric precisions on all of the bright ( @xmath227 ) giant events . if the target microlensing source happens to have a bright star within the isoplanatic angle , it may be possible to employ phase referencing to extend sensitivity to very faint @xmath228 sources . this would allow one to measure @xmath5 for main - sequences sources from the ground as well . finally , it may be possible to determine @xmath5 from single - epoch measurements of the visibility and/or closure phase ( delplancke , g ' orski , & richichi 2001 , dalal & lane 2003 ) . in this way , sensitivity could plausibly be extended to main - sequences sources by making carefully - timed interferometric measurements of the source when it is highly - magnified during a caustic crossing . however , it is not clear if there exists enough structure in the image positions during this time to extract @xmath5 . this remains an interesting topic for future study . non - targeted space - based astrometric surveys , such as the global astrometric interferometer for astrophysics , are generally not well - suited to this application , due to the relatively sparse sampling of the source stars . finally , access to target - of - opportunity time on 8 - 10 m class telescopes would allow for accurate spectral typing of the source stars . several nights per bulge season would likely be adequate to type the @xmath229 caustic - crossing events per year . however , more time would be required to perform some of the auxiliary science discussed in [ sec : dos ] , such as resolution of the source - star atmospheres . thus , by combining alerts from survey collaborations , with comprehensive ground - based photometry from follow - up collaborations with access to dedicated ( or semi - dedicated ) 1m - class telescopes , and a modest allocation of a total 10 hours of sim time , it should be possible to measure the angular radii of @xmath29 giant stars in the bulge to @xmath14 , or @xmath10 main sequence stars to @xmath16 . several nights of target - of - opportunity time on @xmath230 m telescopes should allow for accurate spectral typing of the sources via high or low - resolution spectroscopy .

thus , with access to a network of 1m - class telescopes , combined with 10 hours of sim time , it should be possible to measure to for giant stars , or to for main sequence stars . a byproduct of such a campaign is a significant sample of precise binary - lens mass measurements .

we outline a method by which the angular radii of giant and main sequence stars located in the galactic bulge can be measured to a few percent accuracy . the method combines comprehensive ground - based photometry of caustic - crossing bulge microlensing events , with a handful of precise ( ) astrometric measurements of the lensed star during the event , to measure the angular radius of the source , . dense photometric coverage of one caustic crossing yields the crossing time scale . less frequent coverage of the entire event yields the einstein timescale and the angle of source trajectory with respect to the caustic . the photometric light curve solution predicts the motion of the source centroid up to an orientation on the sky and overall scale . a few precise astrometric measurements therefore yield , the angular einstein ring radius . then the angular radius of the source is obtained by . we argue that the parameters , and , and therefore , should all be measurable to a few percent accuracy for galactic bulge giant stars using ground - based photometry from a network of small ( 1m - class ) telescopes , combined with astrometric observations with a precision of to measure . we find that a factor of times fewer photons are required to measure to a given precision for binary - lens events than single - lens events . adopting parameters appropriate to the _ space interferometry mission _ ( sim ) , we find that minutes of sim time is required to measure to accuracy for giant sources in the bulge . for main - sequence sources , can be measured to accuracy in hours . thus , with access to a network of 1m - class telescopes , combined with 10 hours of sim time , it should be possible to measure to for giant stars , or to for main sequence stars . we also discuss methods by which the distances and spectral types of the source stars can be measured . a byproduct of such a campaign is a significant sample of precise binary - lens mass measurements . # 1 # 1equation ( [ # 1 ] )

astro-ph0208210

c

we have outlined a method to measure the angular radii @xmath1 of giant and main sequence source stars of fold caustic - crossing binary microlensing events toward the galactic bulge . our method to measure @xmath1 consists of four steps . first , survey - quality data can be used to discover and alert caustic - crossing binary - lensing events . such data is sufficient to characterize the event timescale @xmath3 and the angle @xmath4 of source trajectory with respect to the caustic . dense sampling of one of the caustic crossings yields the caustic - crossing timescale @xmath231 . the global solution to the binary - lens light curve yields a prediction for the trajectory of the centroid of the source up to an unknown angle @xmath90 , and the scale , @xmath5 . thus a few , precise astrometric measurements during the course of the event yield @xmath5 . the angular source radius is then simply given by @xmath6 . we argued , based on past experience with modeling binary - lens events , that the parameters @xmath231 , @xmath4 , and @xmath3 should be measurable to a few percent accuracy , provided one caustic - crossing is densely and accurately sampled , and the entire event is reasonably well - covered . we then performed a series of monte carlo experiments that demonstrated that astrometric measurements during the course of the binary - lens event should allow for the determination of @xmath5 to @xmath232 accuracy , assuming photon - limited statistics and a total of 60,000 photons per event . this is a factor of @xmath9 fewer photons than are required to measure @xmath5 to the same precision in single - lens events and corresponds to an exposure time of @xmath233 hour with sim on an @xmath113 source . therefore , it should be possible to measure @xmath1 for a significant sample of giant and main - sequence stars in the bulge with reasonable expenditure of resources . we would like to thank neal dalal for helpful conversations . we would also like to thank the anonymous referee for useful comments and suggestions . this work was supported by nasa through a hubble fellowship grant from the space telescope science institute , which is operated by the association of universities for research in astronomy , inc . , under nasa contract nas5 - 26555 , by jpl contract 1226901 , and by the science research center ( src ) of the korean science and engineering foundation ( kosef ) .

we outline a method by which the angular radii of giant and main sequence stars located in the galactic bulge can be measured to a few percent accuracy . dense photometric coverage of one caustic crossing yields the crossing time scale . less frequent coverage of the entire event yields the einstein timescale and the angle of source trajectory with respect to the caustic . the photometric light curve solution predicts the motion of the source centroid up to an orientation on the sky and overall scale . a few precise astrometric measurements therefore yield , the angular einstein ring radius we argue that the parameters , and , and therefore , should all be measurable to a few percent accuracy for galactic bulge giant stars using ground - based photometry from a network of small ( 1m - class ) telescopes , combined with astrometric observations with a precision of to measure . we find that a factor of times fewer photons are required to measure to a given precision for binary - lens events than single - lens events .

we outline a method by which the angular radii of giant and main sequence stars located in the galactic bulge can be measured to a few percent accuracy . the method combines comprehensive ground - based photometry of caustic - crossing bulge microlensing events , with a handful of precise ( ) astrometric measurements of the lensed star during the event , to measure the angular radius of the source , . dense photometric coverage of one caustic crossing yields the crossing time scale . less frequent coverage of the entire event yields the einstein timescale and the angle of source trajectory with respect to the caustic . the photometric light curve solution predicts the motion of the source centroid up to an orientation on the sky and overall scale . a few precise astrometric measurements therefore yield , the angular einstein ring radius . then the angular radius of the source is obtained by . we argue that the parameters , and , and therefore , should all be measurable to a few percent accuracy for galactic bulge giant stars using ground - based photometry from a network of small ( 1m - class ) telescopes , combined with astrometric observations with a precision of to measure . we find that a factor of times fewer photons are required to measure to a given precision for binary - lens events than single - lens events . adopting parameters appropriate to the _ space interferometry mission _ ( sim ) , we find that minutes of sim time is required to measure to accuracy for giant sources in the bulge . for main - sequence sources , can be measured to accuracy in hours . thus , with access to a network of 1m - class telescopes , combined with 10 hours of sim time , it should be possible to measure to for giant stars , or to for main sequence stars . we also discuss methods by which the distances and spectral types of the source stars can be measured . a byproduct of such a campaign is a significant sample of precise binary - lens mass measurements . # 1 # 1equation ( [ # 1 ] )

1504.07337

i

stars in galaxies and dark matter in the universe can be modeled in phase - space as self - gravitating collisionless fluids obeying the vlasov - poisson equations : @xmath5 where @xmath6 represents the phase - space density at position @xmath7 and velocity @xmath8 , @xmath9 is the gravitational potential , and @xmath10 is the gravitational constant . in general , these equations do not have simple analytical solutions . they are therefore often solved numerically . the most widely used numerical scheme is the @xmath2-body approach and there exist many different implementations , which mainly differ from each other in the way poisson equation is solved ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * for reviews on the subject ) . the @xmath2-body method attempts to sample the phase - space density by an ensemble of dirac functions that represent particles interacting with each other through gravitational force . in order to avoid numerical artefacts due to the @xmath11 divergence of the force at small distances , the gravitational potential is usually replaced by an effective one so that the force is smoothed at scales smaller than a softening parameter @xmath12 . this procedure corresponds to assuming that the particles are clouds of size @xmath13 interacting with each other . approximating the phase - space density with macro - particles , however , has its own limitation . in particular , the close @xmath2-body encounter is one of the most notable sources of numerical artefacts , in addition to more subtle collective effects induced by the discrete nature of the distribution of the particles ( see , e.g. * ? ? ? * ; * ? ? ? ? * ; * ? ? ? * ; * ? ? ? of course , the time integration scheme and the way to solve the poisson equation numerically are well - known sources of errors , even though not particular to the @xmath2-body method . there are several previous studies that discussed the limitations of the @xmath2-body results , including underestimating strong numerical artefacts , particularly in the cold case where the initial velocity dispersion is null ( see , e.g. , * ? ? ? * ; * ? ? ? * ) , and long - term nonlinear resonant modes induced by the discrete nature of the particles ( see , e.g. , * ? ? ? * ; * ? ? ? we also note that it is not yet obvious that the fine inner structure of dark matter halos is completely understood from physical and even numerical points of view , despite numerous intensive convergences studies of the @xmath2-body approach ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? it is therefore highly desired to develop alternative numerical methods to the traditional @xmath2-body approach so that one can understand better its validity and fundamental limitations . in the cold case , relevant to the current paradigm of cold dark matter scenario , the phase - space distribution function is supported by a three - dimensional sheet evolving in six - dimensional phase - space , which can be partitioned in a continuous way with an ensemble of tetrahedra as proposed in recent works ( see , e.g. , * ? ? ? * ; * ? ? ? unfortunately , the increasing complexity of the structure of the system during evolution requires more and more sampling elements , and the computational cost becomes prohibitive after several dynamical time - scales . in this article , we consider the warm case , in which the system presents a non - negligible initial local velocity dispersion component relative to gravitational potential energy . in this case , the phase - space distribution function has to be sampled on a 6-dimensional mesh , which makes again the computational cost very high . therefore , we shall restrict to spherical systems , hence reducing the actual number of dimensions of the dynamical setup to three . there exist many methods to solve the vlasov - poisson equations in the warm case , mainly developed in plasma physics . one of the most famous solvers is the splitting algorithm of @xcite and its numerous extensions ( see , e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * but this list is far from complete ) . this algorithm , that we shall adopt below , exploits directly the liouville theorem : the phase - space density @xmath14 is conserved along motion . then the equations of the dynamics during each time step are divided into `` drift '' and `` kick '' parts according to hamiltonian dynamics and are solved backwards : @xmath15 where @xmath16 is computed from @xmath17 . in practice the phase - space distribution function is sampled on a mesh , and each step is performed by using tracer particles located at mesh sites and following the equations of motion split as above . resampling of @xmath17 , @xmath18 and finally the phase - space distribution function at the next time step is performed by using an interpolation , e.g. based on the spline method . the splitting scheme was applied for the first time in astronomy in early 1980 s , to one dimensional systems @xcite , galactic disks @xcite and spherical systems @xcite . nevertheless , it has been almost forgotten since then except for a few contributions ( e.g. , * ? ? ? * ; * ? ? ? * ) that include a recent preliminary investigation of the algorithm in full 6-dimensional phase - space @xcite . as mentioned above , however , solving fully six - dimensional phase - space problems with sufficient accuracy is still very unrealistic now . in this article , therefore , we focus on spherical systems , where phase - space is only three dimensional : the three coordinates of interest are the radial position @xmath19 , the radial velocity @xmath20 and the angular momentum @xmath21 . following earlier works performed in the framework of one dimensional gravity ( see , e.g. , * * ) , we carry out a detailed comparison between an @xmath2-body code , gadget @xcite , and an improved version of the splitting algorithm implementation by @xcite , vlasolve . our goal is to check how well the particle distribution in gadget traces the phase - space density obtained from vlasolve , and to see how the results depend on various parameters of the simulations , in particular the number of particles in the @xmath2-body simulations and the spatial resolution in the vlasov code . we would however like to emphasize here that the purpose of this article is not to compare the performance of the two codes from the view - point of computational cost . while a fairly good physical insight is obtained through visual inspection of the resulting phase - space density plots , we also present a more quantitative comparison . to do so , we introduce correlators and entropic estimators based on a likelihood approach , ans ask whether the @xmath2-body simulations can be considered as local poisson realizations of the vlasov code phase - space density . because of our restrictive choice of the geometry of the system , it is important to simulate spherical configurations that are known to be stable against small anisotropic perturbations induced by the shot noise of the particles . indeed , we shall use the public treecode gadget without any specific modification to enforce spherical dynamics . although an alternative approach consisting in enforcing pure radial dynamics in gadget ( see , e.g. , * ? ? ? * ) may facilitate comparisons with the vlasov code , we do not adopt this approach in order to avoid any possible subtle biases in the analyses . in this respect , the hnon sphere @xcite is particularly suited for our purpose since it is known to preserve well its spherical nature during the course of dynamics even when being simulated with a @xmath2-body technique and , in particular , it is not prone to radial orbit instability ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? in this configuration , the initial phase - space distribution function is isotropic and gaussian distributed in velocity space and given by @xmath22 with @xmath23 , the total mass of the system . in the simulations discussed in this article , we work in units where @xmath24 , and the initial radius of the hnon sphere and its total mass are chosen to be @xmath25 which fixes @xmath26 in equation ( [ eq : henons ] ) once the virial ratio is given . we shall consider `` warm '' and `` cold '' settings , which correspond to the initial virial ratio @xmath27 of @xmath28 and @xmath29 , respectively , where @xmath30 and @xmath31 are the total kinetic and potential energy of the system . the two classes of initial conditions exhibit distinct features , in particular concerning the metastable state to which the system relaxes through phase mixing . the warm system builds a core - halo structure , with the halo displaying a power - law profile @xmath32 ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? in contrast , the cold system develops a more concentrated smaller core ( see , e.g. , * ? ? ? * ; * ? ? ? * ) , but never reaches a strictly stationary regime because a significant fraction of the mass acquires positive energy and escapes from the system ( see , e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? this article is organized as follows . in [ sec : thesimus ] we describe our vlasov solver , vlasolve . section [ sec : gadpres ] provides information about the @xmath2-body runs and the parameters used in gadget . in [ sec : sphericity ] , we check that the @xmath2-body simulations stay indeed spherical during evolution . section [ sec : visu ] presents a visual inspection of the phase - space density , which is followed by a quantitative statistical analysis in [ sec : statana ] . finally , [ sec : discussion ] summarizes and discusses our present results .

is well preserved by the-body simulations , visual and quantitative comparisons are performed . in particular we introduce new statistics , correlators and entropic estimators , based on the likelihood of whether-body simulations actually trace randomly the vlasov phase - space density . -1 cm [ firstpage ] gravitation methods : numerical galaxies : kinematics and dynamics dark matter

we perform a detailed comparison of the phase - space density traced by the particle distribution in gadget simulations to the result obtained with a spherical vlasov solver using the splitting algorithm . the systems considered are apodized hnon spheres with two values of the virial ratio , and . after checking that spherical symmetry is well preserved by the-body simulations , visual and quantitative comparisons are performed . in particular we introduce new statistics , correlators and entropic estimators , based on the likelihood of whether-body simulations actually trace randomly the vlasov phase - space density . when taking into account the limits of both the-body and the vlasov codes , namely collective effects due to the particle shot noise in the first case and diffusion and possible nonlinear instabilities due to finite resolution of the phase - space grid in the second case , we find a spectacular agreement between both methods , even in regions of phase - space where nontrivial physical instabilities develop . however , in the colder case , , it was not possible to prove actual numerical convergence of the-body results after a number of dynamical times , even with particles . -1 cm [ firstpage ] gravitation methods : numerical galaxies : kinematics and dynamics dark matter

1504.07337

c

in this paper we have compared the phase - space distribution function traced by the particle distribution in gadget simulations to the results obtained with our new vlasov code vlasolve for spherical systems , an improved version of the splitting algorithm of @xcite . for the specific comparison , we have chosen ( apodized ) hnon spheres , which are known to be insensitive to radial orbit instability and in particular to preserve the spherical nature of the system . the latter property is confirmed from simulations run with three - dimensional @xmath2-body codes . we considered two values of the initial virial ratio of the spheres , @xmath66 and @xmath3 , corresponding to `` warm '' and `` cold '' configurations , respectively . we have plotted detailed structures of the phase - space distribution functions varying the spatial / mass resolution of the numerical code in a systematic fashion . we have conducted further a quantitative analysis by introducing two new statistical tools . the first one is of entropic nature and corresponds to the log - likelihood quantifying to which extent the @xmath2-body results represent a local poisson sampling of the vlasov phase - space density . the second tool is a correlator of order @xmath117 , proportional to the integral over phase - space of the product between the vlasov phase - space density raised to the power @xmath117 and the particle distribution function . the overall conclusion is that both the vlasov and @xmath2-body methods agree remarkably well with each other , both from the visual and statistical points of view , if sufficient resolution is employed . given the completely different numerical approaches to collisionless dynamics , this is not trivial at all , and the degree of agreement that we have shown for the first time is perhaps even better than what had been expected before . this is reassuring for numerous previous results that have been almost exclusively obtained from the @xmath2-body method . nevertheless there are still unsolved subtle issues in details : * when performing a visual inspection of the phase - space distribution function in the cold case , @xmath3 , although still good at the coarse level , we find that the level of agreement between the @xmath2-body and the vlasov codes worsens at small scales after a few dynamical times . this is mainly due to collective effects induced by the shot noise of the particles in the @xmath2-body simulations ( and not to close particle encounters ) . even with @xmath4 particles , we are not able to prove numerical convergence of the @xmath2-body results . the comparison at this level , however , is made difficult by the fact that the vlasov code is significantly diffusive , which might prevent the development of a variety of physical unstable modes . * while the statistical tools do not provide as rich and intuitive information as visual inspection , they identify some subtle effects . in particular , when taking into account general trends due to diffusion in the vlasov code , significant for @xmath3 , we notice that the match between gadget and vlasolve worsens with time , then improves . the degree of the mismatch increases , and it shows up earlier , when reducing the number of particles in the @xmath2-body simulation . again , this may be ascribed to collective effects due to the shot noise of the particles . nevertheless , the very good match between the gadget simulations with @xmath105 and @xmath4 particles may suggest that convergence is nearly reached in terms of number of particles and information theory , even if it is not fully proved . it is worth mentioning again that the collective effect mentioned above is not related to @xmath2-body relaxation , but rather results from random poisson fluctuations . this can be formulated as follows ( see * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * for similar arguments ) : a given particle at some distance @xmath19 from the center of the system feels a force proportional to the number @xmath188 of particles inside the sphere of radius @xmath19 . poisson fluctuations imply thus that there is a relative error of order of @xmath189 on this force . importantly , the inner number of particles @xmath188 changes with time with random fluctuations around the mean behavior : these fluctuations can be considered as a correlated random walk . indeed , because of the finite velocity dispersion , particles cross both inwards and outwards the frontier of the sphere of radius @xmath19 . a larger velocity dispersion weakens the amount of correlation , thus makes the errors on the force more random , which should have a fuzzy effect on the phase - space density , similarly as collisional relaxation : this is what we can expect for @xmath66 and as observed on fig . [ fig:0v5_allj ] . on the contrary , a smaller velocity dispersion makes the error on the force more _ systematic _ which should induce coherent distortions of the phase - space density : this is what we can expect for @xmath3 and confirmed by visual inspection of fig . [ fig:0v1_all ] . this effect has non - trivial consequences on the energy spectrum of the particles , particularly in cold configurations @xcite . it certainly explains as well the deviations between vlasolve and gadget observed when measuring the statistical estimators defined in this paper . according to @xcite , this _ collective _ effect is dominant over @xmath2-body relaxation , and , as confirmed by our detailed numerical tests in appendix [ app : instab ] , is not significantly influenced by softening . note as well that shot noise creates anisotropies in the system , i.e. deviations from spherical symmetry that may be eventually amplified . @xcite argue that this effect is subdominant compared to the radial component of the noise - induced perturbation when considering the collapse of an homogeneous sphere . although their calculation is performed only prior to collapse and in the cold case , we believe that the conclusion still remains valid for the kind of initial conditions studied in this paper , as suggested by our numerical experiments that seem to preserve well spherical symmetry . clearly , the collective effect due to particle shot noise is a real problem for simulations of close to cold spherical systems when it comes to examine fine structures of the phase - space density . we were not able to prove convergence of the phase - space density in the @xmath3 case even for an @xmath4 particle simulation . notably , this may have non - trivial consequences on the fine structure of simulated dark matter halos , where numerical convergence in terms of number of particles might not have been reached yet despite the numerous intensive studies . indeed , convergence toward the continuous limit might be much slower than expected , hence giving the false impression that it is achieved .

we perform a detailed comparison of the phase - space density traced by the particle distribution in gadget simulations to the result obtained with a spherical vlasov solver using the splitting algorithm . the systems considered are apodized hnon spheres with two values of the virial ratio , and . after checking that spherical symmetry however , in the colder case , , it was not possible to prove actual numerical convergence of the-body results after a number of dynamical times , even with particles .

we perform a detailed comparison of the phase - space density traced by the particle distribution in gadget simulations to the result obtained with a spherical vlasov solver using the splitting algorithm . the systems considered are apodized hnon spheres with two values of the virial ratio , and . after checking that spherical symmetry is well preserved by the-body simulations , visual and quantitative comparisons are performed . in particular we introduce new statistics , correlators and entropic estimators , based on the likelihood of whether-body simulations actually trace randomly the vlasov phase - space density . when taking into account the limits of both the-body and the vlasov codes , namely collective effects due to the particle shot noise in the first case and diffusion and possible nonlinear instabilities due to finite resolution of the phase - space grid in the second case , we find a spectacular agreement between both methods , even in regions of phase - space where nontrivial physical instabilities develop . however , in the colder case , , it was not possible to prove actual numerical convergence of the-body results after a number of dynamical times , even with particles . -1 cm [ firstpage ] gravitation methods : numerical galaxies : kinematics and dynamics dark matter

hep-ph0409274

i

how is electroweak symmetry broken ? the most important theoretical clue we have is the hierarchy problem , the problem of understanding the smallness of the weak scale compared to much higher scales in physics such as the planck scale . perhaps the most elegant solution of the hierarchy problem is dynamical electroweak symmetry breaking @xcite . this is the idea that the scale of electroweak symmetry breaking is determined by a new strong interaction scale . this naturally explains the smallness of the electroweak scale , since the strong interaction scale is given in terms of uv quantities by _ ew~_uv e^-g_c^2/g_uv^2 , where @xmath8 is the strength of the coupling in the uv and @xmath9 is the critical value where electroweak symmetry is broken . for @xmath10 , the electroweak scale is naturally exponentially small compared to @xmath11 . this mechanism is already realized in nature in the strong interaction sector , explaining why the qcd scale is naturally small compared to higher scales . this paradigm for electroweak symmetry breaking makes the general prediction that the electroweak symmetry breaking sector is strongly coupled at the tev scale . within a few years , the lhc will definitively settle the fundamental question of whether electroweak symmetry breaking sector is weakly or strongly coupled . until the lhc turns on , we must rely on indirect constraints . dynamical electroweak symmetry breaking faces a number of potential difficulties . first , strong interactions at the tev scale can ruin the agreement of the standard model with precision electroweak data . however , if the physics that breaks electroweak symmetry is a strongly coupled theory with no large or small parameters , ` dimensional analysis ' ( nda ) gives an estimate for the peskin - takeuchi @xmath7 and @xmath12 parameters s_nda ~ , t_nda ~. for comparison , the value of the @xmath7 parameter from scaled - up qcd is @xcite s_qcd ~0.3 . these are rough estimates , and are comparable to the size of the current 95% confidence level bounds @xcite . these do not rule out models of dynamical electroweak symmetry breaking . the models that _ are _ ruled out ( without fine tuning ) are those containing a large number @xmath4 of degrees of freedom , in which @xmath13 . these include large ` technicolor ' or ` walking technicolor ' theories @xcite , and randall - sundrum ( rs ) models @xcite with gauge fields in the bulk @xcite , which are related to large-@xmath4 conformal theories ( cft s ) by the ads / cft correspondence @xcite . another general problem with models of dynamical electroweak symmetry breaking is that flavor is generally not decoupled from the tev scale . in technicolor models , this is because the order parameter that breaks electroweak symmetry is a techni - fermion bilinear @xmath14 with mass dimension @xmath15 . the standard - model fermion masses therefore arise from 4-fermion operators connecting the standard model fermions with the technifermions @xcite . these operators have dimension 6 , and therefore become strong at low scales . in particular the top coupling becomes strong at a scale _ t ~_ew()^1/2 ~5 , where @xmath16 is the scale where the electroweak symmetry breaking sector becomes strongly coupled . @xmath17 is the scale where flavor must be addressed in these models . the flavor problem is less severe in models of ` walking ' technicolor , in which it is assumed that the electroweak order parameter @xmath14 has a large anomalous dimension , and scales as an operator with dimension @xmath18 @xcite . walking technicolor theories are similar to a cft with a nearly marginal ( slightly relevant ) operator that runs slowly and becomes strong and breaks electroweak symmetry . analyses based on the truncated schwinger - dyson equations show that in asymptotically free theories , @xmath19 @xcite . the scale where the top coupling becomes strong is then raised for @xmath20 to _ t _ ew ~10 . attempts to make realistic models based on strong top dynamics can be found in . in this paper , we will instead attempt to avoid strong flavor - dependent dynamics at low scales . a simple way to avoid the restriction @xmath19 is to assume that the theory is at an interacting conformal fixed point above the tev scale . this class of theories offers a solution of the hierarchy problem that is identical to asymptotically free theories such as technicolor . if the cft is coupled to a gauge theory that is asymptotically free , this gauge theory will become strong in the ir , causing the cft to flow away from its fixed point . , and we do not consider it here . ] the resulting non - perturbative dynamics can give rise to electroweak symmetry breaking . another possibility is that the cft contains a nearly marginal operator that becomes strong in the ir . these mechanisms are attractive because it generates an exponentially large hierarchy . another possible mechanism exists if the cft has a relevant operator that transforms nontrivially under a global symmetry , a discrete symmetry . the coefficient of this operator can then be naturally small , and can set the scale for the breaking of conformal and electroweak symmetry . in this mechanism , the large hierarchy is put in by hand in the form of a small coefficient , but it is technically natural . in a strong cft , flavor arises from couplings of the form @xmath21 , where @xmath22 is a standard - model fermion and @xmath23 is a cft operator with quantum numbers of the higgs . in order to decouple flavor , we would like to have the scaling dimension @xmath24 of the operator @xmath23 as small as possible . in cft s , bound on the scaling dimension of a scalar operator is @xmath25 @xcite . in the limit @xmath26 , the scalar operator behaves as a weakly - coupled scalar field , which is just the standard - model higgs . the theory is therefore fine - tuned and does not solve the hierarchy problem . however , for @xmath0 , with @xmath27 , the top quark becomes strongly coupled at the scale _ t ~_ew ( ) ^1/. this scale is _ exponentially _ large for small @xmath2 , and therefore we can plausibly have sufficiently large @xmath2 to avoid fine - tuning , while decoupling the flavor to high scales . how @xmath17 must be to avoid flavor - changing neutral currents depends on the nature of flavor violation at this scale . the most pessimistic case imaginable is that there are unsuppressed strong contributions to operators that contribute to @xmath28@xmath29 mixing at the scale @xmath17 . this requires @xmath30 , which is obtained for @xmath31 . if we assume some suppression of flavor violation for the lightest generation , we expect that the flavor scale can be significantly lower . for example , a single yukawa suppression of four - fermion operators contributing to @xmath28@xmath29 mixing lowers the flavor scale to @xmath32 , which requires @xmath33 . such values of @xmath2 are definitely plausible . for example , in f - theory constructions of ads@xmath34 duals , one finds scalar operators with dimension @xmath35 and @xmath36 @xcite . the possible application of non - supersymmetric cft s with low - dimension scalar operators to the electroweak hierarchy problem was also discussed in . the randall - sundrum model gives an explicit example of a 4d cft , and has been extensively discussed as a solution of the hierarchy problem . in this model , the higgs is usually localized in the the ir brane to obtain a large hierarchy . in this case the higgs field can be thought of as a bulk field with a large mass , and in the corresponding 4d interpretation the electroweak order parameter has a large ( @xmath37 ) scaling dimension . to obtain sufficiently large fermion masses , the fermions are put on the ir brane or in the bulk @xcite . in 4d language , this corresponds to generating fermion masses by making them mix with composite fermions so that they can feel the symmetry breaking in the strong sector . the mixing of the standard - model fermions with composite fermions was considered previously in the context of qcd - like technicolor @xcite . theories of this type are interesting alternatives to our scenario . as we discuss in the appendix , these theories generally have a potentially viable region of the parameter space where @xmath38 is just at the current experimental bound while corrections to @xmath39 require fine - tuning at the @xmath40 level @xcite . however , we will pursue scenarios where the standard - model fermions are completely elementary , just like in conventinal technicolor theories . it is a simple matter to modify the rs model to give the electroweak order parameter a smaller dimension : one simply puts a higgs scalar in the bulk , and leaves the fermions on the uv brane . electroweak symmetry is broken by a higgs potential localized on the ir brane ( ensuring that this is an ir effect ) and the bulk higgs field communicates electroweak symmetry breaking to the fermions on the uv brane . taking the higgs bulk mass parameter to be negative makes the dimension of the higgs operator in the 4d cft description smaller . however , we will show that scalar operators with @xmath5 are fine - tuned in rs . this can be traced to the fact that rs is a large-@xmath4 theory , and this fine - tuning is common to all large-@xmath4 theories . we are therefore led to a rather dark corner of theory space : non - supersymmetric 4d strongly - coupled conformal field theories with small @xmath4 . these can have a scalar operator with dimension @xmath41 with @xmath42 , and can dynamically break electroweak symmetry at the tev scale while giving large fermion masses without flavor - changing neutral currents . small-@xmath4 theories also have an acceptably small @xmath7 parameter . not much is known about the dynamics of such theories , and so our discussion of these theories is necessarily speculative . above the tev scale , the theory becomes conformally invariant , and the new strong conformal dynamics can be directly tested in direct analogy with the way qcd is tested at a high - energy @xmath43 collider . however , even the lhc will be limited to exploring the lightest ` hadrons ' of the cft , and it is not possible to make rigorous predictions for this regime . in the case where @xmath2 arises from a ( moderately ) small parameter in the fundamental theory , we argue that the theory contains a prominent scalar resonance near ( but somewhat below ) the tev scale , with couplings similar to those of a heavy standard - model higgs , but deviating from the standard - model couplings by order @xmath2 . this provides an interesting and well - motivated signal to look for at the lhc , whose observation would clearly motivate going to even higher energies in the future . this paper is organized as follows . in section 2 , we review the constraints on the operator dimension @xmath24 in various types of known models and argue that small-@xmath4 theories avoid all constraints and can have @xmath5 without fine tuning . in section 3 , we study the phenomenology of these theories , focusing mainly on the possibility of a higgs - like scalar resonance . section 4 contains our conclusions .

we point out that the flavor problem in theories with dynamical electroweak symmetry breaking can be effectively decoupled if the physics above the tev scale is strongly conformal , and the electroweak order parameter has a scaling dimension with . small- theories also have an acceptably small peskin - takeuchi parameter . a possible signal for these theories is a prominent scalar resonance below the tev scale with couplings similar to a heavy standard model higgs .

we point out that the flavor problem in theories with dynamical electroweak symmetry breaking can be effectively decoupled if the physics above the tev scale is strongly conformal , and the electroweak order parameter has a scaling dimension with . there are many restrictions on small values of : for , electroweak symmetry breaking requires a fine - tuning similar to that of the standard model ; large- conformal field theories ( including those obtained from the ads / cft correspondence ) require fine - tuning for ; ` walking technicolor ' theories can not have , according to gap equation analyses . however , strong small- conformal field theories with avoid all these constraints , and can give rise to natural dynamical electroweak symmetry breaking with a top quark flavor scale of order , large enough to decouple flavor . small- theories also have an acceptably small peskin - takeuchi parameter . this class of theories provides a new direction for dynamical electroweak symmetry breaking without problems from flavor or electroweak precision tests . a possible signal for these theories is a prominent scalar resonance below the tev scale with couplings similar to a heavy standard model higgs .

hep-ph0409274

c

we have described a new paradigm for dynamical electroweak symmetry breaking in which the electroweak symmetry breaking sector is a conformal field theory ( cft ) above the tev scale . conformal symmetry and electroweak symmetry are broken at the tev scale , triggered by an asymptotically - free gauge group or a slightly relevant operator becoming strong , or by a relevant operator with a coefficient made small naturally by symmetries . any of these mechanisms stabilizes the weak scale against quantum corrections and gives a solution of the hierarchy problem . the flavor problem of dynamical electroweak symmetry breaking is solved if the dimension of the cft operator that acts as the order parameter for electroweak symmetry breaking has a dimension @xmath24 close to 1 , the dimension of an elementary higgs scalar field . for @xmath0 , the scale where the top quark yukawa coupling becomes strong is raised to @xmath204 , where @xmath205 . for @xmath206 , this is large enough to effectively decouple flavor . finding a cft with the required properties is highly nontrivial . weakly coupled cft s can certainly have operators with dimension near 1 in the form of an elementary scalar higgs field @xmath104 , but this clearly does not solve the hierarchy problem because of the existence of the relevant operator @xmath207 with dimension near 2 . what is required is a strongly - coupled cft with a scalar operator @xmath23 with dimension @xmath0 , where strong cft dynamics renders the operator @xmath47 irrelevant by giving it a large anomalous dimension . we have shown , however , that strong cft s with large @xmath4 , including those obtained from the ads / cft correspondence , have the property that the dimension of @xmath208 is close to @xmath48 , and are therefore fine - tuned for @xmath5 . we are therefore led to consider strongly - coupled , small-@xmath4 cft s . these theories also naturally have small electroweak precision corrections , addressing another strong constraint on models of dynamical electroweak symmetry breaking . the difficulty is that there are no reliable theoretical tools for studying such theories , and in fact no explicit examples are known . in the case where the smallness of @xmath2 is due to a small parameter in the fundamental theory , we argued that there will be a prominent scalar resonance with couplings to gauge bosons and the top quark that are comparable to that of a heavy standard - model higgs , but with @xmath169 deviations that can be measured at lhc . we believe that this gives strong motivation to experimental studies of a heavy higgs - like particle , and look forward to a decisive test of these ideas .

there are many restrictions on small values of : for , electroweak symmetry breaking requires a fine - tuning similar to that of the standard model ; large- conformal field theories ( including those obtained from the ads / cft correspondence ) require fine - tuning for ; ` walking technicolor ' theories can not have , according to gap equation analyses this class of theories provides a new direction for dynamical electroweak symmetry breaking without problems from flavor or electroweak precision tests .

we point out that the flavor problem in theories with dynamical electroweak symmetry breaking can be effectively decoupled if the physics above the tev scale is strongly conformal , and the electroweak order parameter has a scaling dimension with . there are many restrictions on small values of : for , electroweak symmetry breaking requires a fine - tuning similar to that of the standard model ; large- conformal field theories ( including those obtained from the ads / cft correspondence ) require fine - tuning for ; ` walking technicolor ' theories can not have , according to gap equation analyses . however , strong small- conformal field theories with avoid all these constraints , and can give rise to natural dynamical electroweak symmetry breaking with a top quark flavor scale of order , large enough to decouple flavor . small- theories also have an acceptably small peskin - takeuchi parameter . this class of theories provides a new direction for dynamical electroweak symmetry breaking without problems from flavor or electroweak precision tests . a possible signal for these theories is a prominent scalar resonance below the tev scale with couplings similar to a heavy standard model higgs .

0907.3191

c

the main results , obtained in this work , can be summarized as follows : \i ) in qd - chain with tunneling coupling in strong electron - photon coupling regime the space propagation of rabi oscillations ( rabi waves ) takes place . for propagation of rabi waves the wave vector of the photon mode must have a nonzero component along the chain . characteristics of the rabi waves depend strongly on relations between parameter of electron - photon coupling , frequency deviation and transparency factors of tunneling barriers for both of levels . \ii ) traveling rabi waves are quantum states of the qd - chain dressed by radiation . the qualitative distinction of this states from states of single dressed atom @xcite is the space - time modulation of dressing parameter by traveling wave law . traveling rabi waves can be interpreted as entangled states of e - h pair and photons . these states are characterized by the dependence of energy on quasi - momentum and can be treated as new type of quasiparticles ( in this paper they are called rabitons ) . \iii ) there are two traveling rabi modes with different frequencies of rabi oscillations at a given value of wavenumber . the range of rabi oscillations frequencies is limited by the critical value , which is different for both modes . the qd - chain is opaque for rabi modes with frequencies lesser than critical one . the critical frequencies as well as dispersion characteristics depend on number of photons in the mode . \iv ) in general case the propagation of rabi wavepackets occurs in the form of four partial packets , which are characterized by different amplitudes and velocities of motion . rabi wavepackets transfer energy , inversion , quasimomentum , electron - electron and electron - photon quantum correlations along the chain . particularly , in the case of qd - chain interacting with quantum light in the coherent state the known collapses - revivals picture @xcite is drastically modified due to propagation effect : collapses and revivals take place in different points of space . \v ) one pair of rabi wavepackets exists due to the ground state contribution in initial state of the system , another one appears due to the contribution of excited state ( generally , initial state is arbitrary superposition of ground and excited states ) . each pair of packets moves through its own potential barrier . if one of the barriers is completely opaque , then corresponding pair of wavepackets does not move and does not spread . \vi ) rabi wavepackets propagation along the qd - chain is followed by the transformation of quantum light statistics ( for example , in initially coherent light incoherent component appears ) . if specific conditions are fulfilled then incoherent part can be decreased to zero . \vii ) in particular cases a number of rabi wavepackets can be diminished . there are two mechanisms of such diminution : tending to zero of partial wavepacket amplitude and merging of the packets due to their velocities equality . rabi waves can take place in a number of other distributed systems strongly coupled with electromagnetic field . the example are superconducting circuits based on josephson junctions , which are currently the most experimentally advanced solid - state qubits @xcite . it is evident , for example , that the chain of qubits placed inside a high - q transmission - line resonator due to the qubit - qubit capacitance coupling will support the rabi waves propagation similar to described in this article . rabi waves effect can be practically used in nanoelectronics , quantum computing , quantum informatics .

qd - chain is modeled by the set of two - level quantum systems with tunnel coupling between neighboring qds . it is shown , that traveling rabi waves are quantum states of qd - chain dressed by radiation . the effect can find practical use in quantum computing and quantum informatics .

we predict and theoretically investigate the new coherent effect of nonlinear quantum optics spatial propagation of rabi oscillations ( rabi waves ) in one - dimensional quantum dot ( qd ) chain . qd - chain is modeled by the set of two - level quantum systems with tunnel coupling between neighboring qds . the space propagation of rabi waves in the form of traveling waves and wave packets is considered . it is shown , that traveling rabi waves are quantum states of qd - chain dressed by radiation . the dispersion characteristics of traveling rabi waves are investigated and their dependence on average number of photons in wave is demonstrated . the propagation of rabi wave packets is accompanied by the transfer of the inversion and quantum correlations along the qd - chain and by the transformation of quantum light statistics . the conditions of experimental observability are analyzed . the effect can find practical use in quantum computing and quantum informatics .

astro-ph0012044

c

we have presented data which give the first high - resolution picture of the near - infrared to ultraviolet spectrum of the m87 jet , and indeed represent the first dataset of this type for any extragalactic jet . we have given a detailed discussion of the spectral morphology of the jet and the @xmath42 relationship in 3.3 and 3.4 , and discussed synchrotron spectrum model fits in 4 . these allow us to place significant constraints on the jet structure , the nature of the x - ray emission , and also the extent , need and nature of particle acceleration in the m87 jet . we discuss each of these topics in turn . our data are fully consistent with a synchrotron origin for the x - ray emission in the jet ( as proposed by bsh91 ) . the observation of variability in the x - ray emission from knot a and the nucleus ( harris et al . 1997 , 1998 ) , rules out a thermal bremsstrahlung nature for the x - ray emission . but neither our data nor the observed variability are completely sufficient to rule out an inverse - compton nature for the x - ray emission . if one assumes that the x - ray , optical and radio synchrotron emitting electrons in knots a , b and d are co - spatial , the ci model of meisenheimer et al . ( 1989 ) is ruled out because it overpredicts by large factors the observed x - ray emission . thus particle injection or acceleration can occur only in discrete sites occupying a small fraction of the jet volume . this agrees with the compactness required by the detection of x - ray variability in knot a on timescales of months ( harris et al . 1997 , 1998 ) . the ci model can be made to work for knot a if the x - ray emitting electrons in that knot occupy a region about 1/5 the projected area of knot a in the optical . similar arguments can be made for knots d ( factor 8) and b ( factor 50 ) , although their x - ray detections are less secure . measurement of the x - ray spectral index @xmath100 would allow us to discriminate between the synchrotron and inverse - compton models . inverse - compton x - ray emission would have a much flatter x - ray slope ( @xmath101 , comparable to the jet s @xmath4 and similar to the average hard x - ray slopes of low - energy peaked bl lacs ( lbl ) found by asca , see kubo et al . 1997 ) , than both the jp and kp synchrotron models , which predict @xmath102 and @xmath103 , as seen in the x - ray spectra of most high - energy peaked bl lacs ( hbl ; perlman et al . 1996 , sambruna et al . 1996 ) . unfortunately , because of the multi - component nature of the x - ray emission from the m87 region ( including cluster , galaxy and jet components ) , current x - ray data do not allow us to place good limits on the shape of the x - ray slope of m87 s jet . this could not be done from the _ einstein _ hri or rosat hri datasets due to their poor ( at most two - channel ) energy resolution . higher energy telescopes ( asca , sax and rxte ) have tried to determine the relative jet+nuclear x - ray emissions but with at best variable success due to their much poorer ( @xmath104 ) angular resolution . matsumoto et al . ( 1996 ) and allen et al . ( 2000 ) both find some evidence of a hard x - ray tail in asca data but with large error bars on the spectral shape ( @xmath105 between 2 - 10 kev ) . similar constraints ( @xmath106 ) , have recently been obtained from sax data ( guainazzi & molendi 1999 ) . however , a negative detection was obtained by rxte ( reynolds et al . 1999 ) , a non - imaging detector , which places a lower limit of @xmath107 on the spectral index of knot a , and @xmath108 on the core . comparison of the fluxes obtained in the two detections plus the upper limits , however , does reveal evidence of variability ( guainazzi & molendi 1999 , reynolds et al . thus current x - ray data can not constrain the spectral shape of any component in the m87 jet , but they do constrain the nature of the emission to nonthermal ( synchrotron or inverse - compton ) mechanisms because of the observed variability . as shown in figures 2 - 4 and 3 , the relationship between @xmath6 and @xmath4 in the m87 jet is rather complex . in the inner jet , the two appear correlated in most regions if a lag is applied to one or the other , while they are essentially anti - correlated in the outer jet . these trends are further evidence that it is impossible to model the m87 jet as an axially homogeneous jet where radio and optical synchrotron emitting electrons are completely co - spatial . instead , they support a model for the structure of the jet presented by p99 , whereby the energy spectrum of electrons in the jet , and magnetic field direction , vary significantly with distance from the jet axis . in the p99 model , higher - energy electrons are concentrated closer to the jet axis , where the magnetic field is most strongly affected by shocks and other disturbances , while lower - energy electrons occupy mainly the jet `` sheath '' at greater distances from the jet axis . at any one point , the observed spectral indices include both core and sheath contributions , with the core dominating in the optical and the sheath dominating in the radio . this model predicts that @xmath6 and @xmath4 should not vary together . it also predicts that some regions might have flatter _ observed _ values of @xmath6 than @xmath4 , since different regions can predominate in different bands . this is in fact observed at the flux maxima of hst-1 and d. the poor correlation between @xmath6 and @xmath4 in the outer jet is somewhat more surprising given the large degree of similarity between the radio and optical polarized structure in this region ( p99 ) . however , in the absence of strong shocks it is still entirely possible for energy stratification to occur without observing significant differences in polarimetry . indeed , we should point out that the mixing of previously stratified layers would not be expected to occur in a short , linear shock , and would likely produce turbulence which would be visible in the form of eddies ( not observed ) . moreover , the optical polarized structure of the outer jet , while much more similar to that seen in the radio , still does show evidence that shocks begin in the jet interior , particularly in the pre - shock regions of a and c ( refer to figures 2 , 5 and 6 of p99 ) . the details of the spectral index maps we find indicate that regions of the jet closer to the axis probably have somewhat steeper values of @xmath4 and hence @xmath81 , than the sheath . the finding that the x - ray emissions must fill a volume significantly smaller than the lower - energy emission also agrees with the stratification proposed by p99 . it should be noted that because of the observed variability , this result is independent of whether the x - ray emission mechanism is synchrotron or inverse - compton . the issue of whether _ in situ _ particle acceleration is required for the m87 jet , is complex and not well explored . as explained by bsh91 , particle acceleration is required if the magnetic field is near the equipartition value of @xmath109 g . this is underlined by our data , which yield `` synchrotron ages '' for knots d , a and b of 60 - 100 years under the jp model , and somewhat higher ( 110 - 280 years ) under the kp model , similar to values calculated by bsh91 under different assumptions . however , the radiative lifetimes of synchrotron emitting particles vary strongly with magnetic field ( @xmath110 ) , so that if the magnetic field is significantly weaker than the equipartition value ( heinz & begelman 1997 ) , it is not unfeasible to reconcile the radiative lifetimes of synchrotron emitting electrons with the length of the jet ( @xmath86 kpc ) . the local variations in optical spectral index and break frequency we find , as well as the optical , radio and x - ray variability observed in hst-1 , d and a ( biretta et al . 1999 , zhou 1998 , harris et al . 1997 , 1998 ) , represent strong evidence for particle acceleration near the flux maxima of those regions . such particle acceleration is in fact expected if knots d and hst-1 , where several variable superluminal components have been found in both hst and vla monitoring , are analogous to flaring regions in blazar jets . moreover , the details of the optical polarimetry in those and other regions ( p99 ) , where we observe magnetic field vectors to be strongly compressed transverse to the jet direction , creates all the conditions necessary for particle acceleration . if indeed the observed changes in spectral index are a product of particle acceleration , then figures 3 - 4 represent a time history of particle acceleration and synchrotron aging in the jet in regions where the implied lag @xmath111 light - crossing time of the jet . this interpretation allows us to comment on the nature of particle acceleration in the m87 jet , as well as the acceleration and cooling timescales , because it transforms the observed differences in the runs of @xmath6 and @xmath4 versus distance into time lag information . in two knot regions it appears that variations in @xmath6 lag variations in @xmath4 . in d - east , a lag of @xmath39 is observed , which translates to about 7.5 years using the observed speeds @xmath112 in this region ( bsm99 ) . the somewhat larger lag of @xmath68 seen in knot e translates to about 14 years given the speeds in bsm99 . there are also two knot regions ( hst-1 and f ) where we observe the opposite trend : @xmath6 leading @xmath4 . in the case of knot hst-1 the observed lag translates into a period of @xmath113 years given the speeds in bsm99 ( greater precision is not possible given the nearness of the point source ) , while for knot f we can not translate the lags into timescales directly since the velocity fields are not well known in those knots . if particle acceleration is present in the m87 jet , the mechanism is not well constrained . several mechanisms have been proposed , including magnetic reconnection ( lesch & birk 1999 ) and fermi acceleration in knots ( meisenheimer , yates & rser 1997 ) . the structure of the jet , which contains many shock - like , flat - spectrum knots ( see also p99 ) , argues against a major role for magnetic reconnection . in contrast , the observation of sharp changes in optical magnetic field position angle in these same flat - spectrum knots ( p99 ) , suggests compression of the magnetic field in the jet interior at these positions , more consistent with shocks . the observed spectral variations near knot maxima in the inner jet are consistent with models for flares produced by shock - induced particle acceleration . as kirk , rieger & mastichiadis ( 1998 ) have shown , the evolution of spectral index in a given band during a flare depends on the relationship of the acceleration and cooling timescales for electrons which emit in that band . where the acceleration timescale is much shorter than the cooling timescale , higher - energy emissions should lead lower - energy emissions ( georganopolous & marscher 1998 , takahashi et al . 1999 ) , so that a flare will propagate from the highest energies to lower energies . but if the cooling and acceleration timescales are close to equal near where the peak in @xmath114 is , the relationship between spectral changes is complex . in that case , at low energies , where the acceleration timescale is much faster than the cooling timescale ( note that @xmath115 for synchrotron radiation ) , their model predicts a spectral flattening in advance of the flux maximum , peaking slightly before flux maximum , followed by a decrease to values somewhat below the jet s nominal value after maximum flux , and then a return to the nominal value after the disturbance has passed . but at high energies , where @xmath116 , a spectral _ steepening _ is predicted in advance of the flux maximum , followed by a hardening as the number of newly accelerated electrons build up . under this model ( assuming no injection of fresh particles ) , flares represent the reacceleration of old particles within the jet , so they will propagate from low to high energies , _ i.e. _ observed spectral changes at higher energies will lag those at lower energies . we appear to be observing _ both _ situations at different locations in the optical emission from the m87 jet , perhaps not dissimilar from what has been seen ( on shorter timescales ) in blazars ; in particular recent observations of pks 2155@xmath117304 several examples of both types of flares were seen within a week of observation ( sambruna et al . 1999 ) . with the above data and analysis in mind we can compare our findings to those of other teams on various optical jets . unfortunately high - quality data ( either ground - based or hst ) are few and far between , and only exist on a few sources . the only other radio / optical jet to have been imaged polarimetrically with hst is 3c 273 . comparing the hst and radio polarimetry for its jet ( thomson , mackay & wright 1993 , conway et al . 1993 ) , 3c 273 seems to show more similarity between radio and optical polarized structure than does the m87 jet ( p99 ) , despite having a large number of knots . however , a deep comparison of its radio and optical polarized structure is currently impossible because of the low signal to noise of the existing , pre - costar foc polarimetry data . further , a deep analysis of its optical spectrum has not yet been done , so we need to rely on ground - based data to compare the polarized and spectral index maps . neumann , meisenheimer & rser ( 1997 ) and rser & meisenheimer ( 1991 ) have carried out a deep analysis of the near - ir to optical spectrum of the 3c273 jet ( note that the latter paper also contains ground - based polarimetry , which is also useful ) , which fortunately is largely unaffected by galaxy subtraction issues ( unlike ground - based work for m87 ) . they find considerably more variation in @xmath6 than @xmath4 for 3c 273 , as we do for m87 , and also find that 3c 273 s jet is significantly narrower in the optical than in the radio ( as we do for m87 ; see sbm96 ) . a more recent , preliminary comparison of the deep hst / wfpc2 and radio images ( rser et al . 1997 , jester et al . in prep . ) show some other differences between the jet s optical and radio structure : the optical jet appears to stop @xmath18 short of the terminal radio hotspot , and the optical and radio flux maxima of knot b are not spatially coincident . interestingly , they also find somewhat of an anti - correlation between optical polarization and spectral index structure , with low polarization and fairly flat spectral indices @xmath72 from 3c 273 s nucleus , but higher polarization and much steeper spectral indices further out . more recently , _ chandra _ has imaged the 3c273 jet , finding a rather different morphology in x - rays than either the optical or radio : one knot s flux maximum appears displaced , and the optical emission declines drastically in the knot d - h region , where the strongest radio emission is seen , analysis of the knots spectra reveal inconsistencies between the spectra of downstream knots and the predictions of ssc models ( marshall et al . further analysis and deeper comparisons of the x - ray , optical and radio structure of the 3c 273 jet will no doubt give us considerable insight into its physics . lara et al . ( 1999 ) find a steep optical spectrum for 3c264 s jet , and a broadband shape consistent with either the ci model or a significantly sub - equipartition magnetic field ( heinz & begelman 1997 ) , and that it is unlikely that the observed optical jet emissions are inverse - compton in origin . they invoke the lack of well - defined knots in the 3c264 jet as evidence against fermi acceleration in shocks . this , plus the much earlier deceleration found for the 3c264 jet ( lara et al . 1999 , baum et al . 1997 ) , are key distinctions between it and m87 , which may make 3c264 more amenable to the ci scenario than m87 , where several bright shocks are observed . high signal to noise x - ray or uv observations , as well as deeper hst imaging data in several bands ( the hst data analyzed by lara et al . were 300s snapshots ) , as well as hst polarimetry , would go a long way towards resolving the mechanism which dominates in the 3c264 jet . schwartz et al . ( 2000 ) and chartas et al . ( 2000 ) have discussed the discovery with _ chandra _ of an x - ray jet in the quasar pks @xmath118 , and the subsequent identification of optical emission from three knots in its jet in deep hst images of the field . this object is at much larger distances than 3c 273 , let alone m87 or 3c 264 , making detailed comparisons of structure difficult . however , comparisons of the structure in the radio and optical reveal large - scale correspondence but tantalizing hints of differences on scales of @xmath119 which require deeper investigation . the broadband spectra of the knots are also inconsistent with the predictions of simple ssc models , although comptonized emission from cmb photons remains a possibility ( tavecchio et al . 2000 ) one final object for which such analysis can in future be done is 3c 66b . sparks et al . ( in prep . ) are analyzing radio - optical spectral data for this object , which also shows interesting radio - optical spectral differences . by discussing the kinetic energy budget of optical jets , scarpa & urry ( 1999 ) find that their observed properties require either fairly high bulk doppler factors @xmath120 and viewing angles @xmath121 ( if equipartition is maintained ) , or magnetic fields significantly less strong than equipartition ( whereupon lower values of @xmath122 or larger viewing angles are possible ) . this is in agreement with the findings of heinz & begelman ( 1997 ) for m87 , and consistent with our results . a similar result has been found through comparison of the properties of dust disks in the 3cr sample ( sparks et al .

this is further evidence that the radio and optical emissions of the m87 jet come from substantially different physical regions . if the x - ray emissions from knots a , b and d are co - spatial with the optical and radio emission , we can strongly rule out the `` continuous injection '' model , which overpredicts the x - ray emissions by large factors . because of the short lifetimes of x - ray synchrotron emitting particles , the x - ray emission likely traces sites of particle acceleration and fills volumes much smaller than the optical emission regions .

we present 1998 hst observations of m87 which yield the first single - epoch optical and radio - optical spectral index image of the jet at 0.15 resolution . we find , comparable to previous measurements , and ( ) , slightly flatter than previous workers . reasons for this discrepancy are discussed . these observations reveal a large variety of spectral slopes . bright knots exhibit significantly flatter spectra than interknot regions . the flattest spectra ( ; comparable to or flatter than ) are found in the two inner jet knots ( d - east and hst-1 ) which contain the fastest superluminal components . the flux maximum regions of other knots have . the maps of and appear poorly correlated . in knots a , b and c , and are essentially anti - correlated with one another . near the flux maxima of two inner jet knots ( hst-1 and f ) , changes in appear to lag changes in , but in two other knots ( d and e ) , the opposite relationship is observed . this is further evidence that the radio and optical emissions of the m87 jet come from substantially different physical regions . the delays observed in the inner jet are consistent with localized particle acceleration in the knots , with for optically emitting electrons in knots hst-1 and f , and for optically emitting electrons in knots d and e. synchrotron models fit to the radio - optical data yield hz for knots d , a and b , and somewhat lower values , hz , in other regions of the jet . if the x - ray emissions from knots a , b and d are co - spatial with the optical and radio emission , we can strongly rule out the `` continuous injection '' model , which overpredicts the x - ray emissions by large factors . because of the short lifetimes of x - ray synchrotron emitting particles , the x - ray emission likely traces sites of particle acceleration and fills volumes much smaller than the optical emission regions .

0707.1907

i

the galactic center is host to a high concentration of energetic processes , driven by the interplay between the energetic output of several young star clusters , radiation and outflows powered by accretion onto the supermassive black hole , and dense molecular clouds that have large turbulent velocities . the young stellar population naturally explains the presence of the mixed - morphology supernova remnant sgr a east @xcite , a shell - like radio supernova remnant that exhibits two regions of bright , non - thermal x - ray emission @xcite , and at least two x - ray features that resemble pulsar wind nebula ( e.g. , * ? ? ? * wang , lu , & gotthelf 2006 ) . these processes also produce astronomical phenomena unique to the galactic center . for instance , fluorescent iron emission is produced where molecular clouds are bombarded by hard x - rays from transient sources ( most likely ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . finally , numerous milligauss - strength bundles of magnetic fields illuminated by energetic electrons produce radio ( * ? ? ? * ; * ? ? ? * yusef - zadeh , hewitt , & cotton 2004 ) and sometimes x - ray emission ( wang , lu , & lang 2002 ; lu , wang , & lang 2003 ) ; the origin of these non - thermal filaments is under debate . the x - ray emission from the brightest of these features has been described by various authors in the references above . however , whereas at radio wavelengths comprehensive catalogs of hii regions and non - thermal features near the galactic center are available ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , no similar catalog has been produced in the x - ray band . here , we remedy this by presenting a catalog of x - ray features identified in images produced from 1 msec of _ chandra _ observations of the central 20 pc of the galaxy . we focus on features that are clearly larger than the _ chandra _ point spread function , but that are smaller than @xmath81.5 ; i.e. , we do not include in our catalog the bulk of the emission from sgr a east @xcite , or the apparent outflow oriented perpendicular to the galactic plane and centered on the sgr a complex ( * ? ? ? * and in prep . ) . lccccc[htp ] 2000 oct 26 18:15:11 & 1561 & 35,705 & 266.41344 & @xmath929.0128 & 265 + 2001 jul 14 01:51:10 & 1561 & 13,504 & 266.41344 & @xmath929.0128 & 265 + 2001 jul 17 14:25:48 & 2284 & 10,625 & 266.40417 & 28.9409 & 284 + 2002 feb 19 14:27:32 & 2951 & 12,370 & 266.41867 & @xmath929.0033 & 91 + 2002 mar 23 12:25:04 & 2952 & 11,859 & 266.41897 & @xmath929.0034 & 88 + 2002 apr 19 10:39:01 & 2953 & 11,632 & 266.41923 & @xmath929.0034 & 85 + 2002 may 07 09:25:07 & 2954 & 12,455 & 266.41938 & @xmath929.0037 & 82 + 2002 may 22 22:59:15 & 2943 & 34,651 & 266.41991 & @xmath929.0041 & 76 + 2002 may 24 11:50:13 & 3663 & 37,959 & 266.41993 & @xmath929.0041 & 76 + 2002 may 25 15:16:03 & 3392 & 166,690 & 266.41992 & @xmath929.0041 & 76 + 2002 may 28 05:34:44 & 3393 & 158,026 & 266.41992 & @xmath929.0041 & 76 + 2002 jun 03 01:24:37 & 3665 & 89,928 & 266.41992 & @xmath929.0041 & 76 + 2003 jun 19 18:28:55 & 3549 & 24,791 & 266.42092 & 29.0105 & 347 + 2004 jul 05 22:33:11 & 4683 & 49,524 & 266.41605 & 29.0124 & 286 + 2004 jul 06 22:29:57 & 4684 & 49,527 & 266.41597 & 29.0124 & 285 + 2004 aug 28 12:03:59 & 5630 & 5,106 & 266.41477 & 29.0121 & 271 + 2005 feb 27 06:26:04 & 6113 & 4,855 & 266.41870 & 29.0035 & 91 + 2005 jul 24 19:58:27 & 5950 & 48,533 & 266.41520 & 29.0122 & 277 + 2005 jul 27 19:08:16 & 5951 & 44,586 & 266.41514 & 29.0122 & 276 + 2005 jul 29 19:51:11 & 5952 & 43,125 & 266.41509 & 29.0122 & 275 + 2005 jul 30 19:51:11 & 5953 & 45,360 & 266.41508 & 29.0122 & 275 + 2005 aug 01 19:54:13 & 5954 & 18,069 & 266.41505 & 29.0122 & 275

we present a catalog of 34 diffuse features identified in x - ray images of the galactic center taken with the _ chandra _ x - ray observatory . several of the features have been discussed in the literature previously , including 7 that are associated with a complex of molecular clouds that exhibits fluorescent line emission , 4 that are superimposed on the supernova remnant sgr a east , 2 that are coincident with radio features that are thought to be the shell of another supernova remnant , and one that is thought to be a pulsar wind nebula only a few arcseconds in projection from .

we present a catalog of 34 diffuse features identified in x - ray images of the galactic center taken with the _ chandra _ x - ray observatory . several of the features have been discussed in the literature previously , including 7 that are associated with a complex of molecular clouds that exhibits fluorescent line emission , 4 that are superimposed on the supernova remnant sgr a east , 2 that are coincident with radio features that are thought to be the shell of another supernova remnant , and one that is thought to be a pulsar wind nebula only a few arcseconds in projection from . however , this leaves 20 features that have not been reported previously . based on the weakness of iron emission in their spectra , we propose that most of them are non - thermal . one long , narrow feature points toward , and so we propose that this feature is a jet of synchrotron - emitting particles ejected from the supermassive black hole . for the others , we show that their sizes ( 0.12 pc in length for=8 kpc ) , x - ray luminosities ( between and , 28 kev ) , and spectra ( power laws with ) are consistent with those of pulsar wind nebulae . based on the star formation rate at the galactic center , we expect that pulsars have formed in the last 300 kyr , and could be producing pulsar wind nebulae . only one of the 19 candidate pulsar wind nebulae is securely detected in an archival radio image of the galactic center ; the remainder have upper limits corresponding to . these radio limits do not strongly constrain their natures , which underscores the need for further multi - wavelength studies of this unprecedented sample of galactic x - ray emitting structures .

0707.1907

c

we can roughly divide the diffuse features in the galactic center into two groups , based on their spectral properties and sizes . three of the four features with areas larger than 100 arcsec@xmath130 exhibit strong fluorescent iron emission with equivalent widths @xmath24500 ev ( the exception is g359.889 - 0.081 , which we will return to shortly ) . these features are discussed extensively in @xcite and @xcite , and are produced because hard x - rays ( @xmath247 kev ) from a transient source are being scattered by molecular gas , and causing iron to fluoresce . these features all lie in the northeast of the field . in fact , this entire quadrant of the image exhibits unusually strong diffuse fe k-@xmath131 emission ( equivalent width 570 ev ; * ? ? ? * ) . the features that we identify in this paper are simply the brightest manifestations of this pervasive scattered and fluorescent emission , and they probably trace regions of molecular gas with the highest optical depth . it is notable , however , that similar features are not seen toward other clouds with similarly high optical depth , particularly those with velocities of @xmath13220 km s@xmath133 and @xmath13240 km s@xmath133 just to the east of ( e.g. , gsten , walmsley , & pauls 1981 ; oka 1998 ) . the clouds that do not exhibit fluorescent emission are slightly in the foreground of the field , as they are seen to cast a shadow in the number of x - ray sources along their lines of sight @xcite . the clouds without associated x - ray emission must not intersect the light - front of the transient that illuminated the fluorescent features . the features with surface area @xmath41100 arcsec@xmath134 either exhibit no evidence for iron emission at 6.4 kev , or are too faint for such emission to be detected . based on their spectra , the x - ray emission from these features must either originate from a hot thermal plasma ( @xmath135 kev ; fig . [ fig : hit ] ) , or from non - thermal processes such as synchrotron or inverse - compton scattering . as we describe below , previous work on individual features suggests that they have a variety of origins . this is the first paper to provide a comprehensive compilation of their properties . for brevity , we will refer to the features without obvious fluorescent iron emission as `` streaks . '' below , we speculate about their natures . the possibility that some of the features are thermal is suggested by the detection of the 6.7 kev line from he - like iron in the combined spectra of the faint diffuse features ( fig . [ fig : ave ] ) . however , this hypothesis requires that some mechanism must be found to confine the plasma . for a characteristic temperature of @xmath87 kev , and a luminosity of @xmath136 ( 28 kev ) , the emission measure is @xmath137 @xmath127 , where @xmath138 is the electron density , @xmath139 is the hydrogen density , and @xmath140 is the volume of the emitting region . the sizes of these features are typically @xmath141 arcsec@xmath130 , which for @xmath0@xmath288 kpc corresponds to projected areas of @xmath142 pc@xmath130 . if we assume that the volume is given by @xmath143 , then the electron density of the plasma is @xmath144 @xmath127 , where @xmath145 is normalized to 50 arcsec@xmath130 , and @xmath146 to @xmath147 ( 28 kev ) . therefore , the pressure is @xmath148 erg @xmath127 . this pressure is @xmath8300 times larger than that of the diffuse , @xmath149 kev plasma in the galactic center ( @xmath150 erg @xmath127 ) , and 50 times larger than the putative 8 kev plasma there ( @xmath151 erg @xmath127 ; * ? ? ? magnetic fields would have to be strong to confine this plasma , @xmath152 mg . these fields strengths are thought to be present within radio - emitting filaments toward the galactic center @xcite , but the average field at the galactic center may be significantly lower ( e.g. , * ? ? ? thermal features could also be produced by shocks with velocities of @xmath4@xmath153=1200 km s@xmath133 ( where @xmath154 is the proton mass and @xmath155=0.5 for a plasma of electrons and protons ) . however , there are no obvious candidates for the sources of the energy powering these putative shocks ; they are not arranged as part of a shell as would be expected if they originate from a supernova ( and the lack of metal lines would be puzzling ) , and the known massive stars in the region are mostly located within 30 of sgr a * , which is several parsecs in projection from these features ( e.g. , * ? ? ? * ; * ? ? ? . given the problems with assuming that these features are thermal sources , we follow other authors and suggest that the majority of these features are non - thermal . a few of the x - ray streaks appear to be non - thermal particles accelerated in shocks where supernova remnants impact the interstellar medium . it has been noted by several authors that g359.8890.081 and g359.8990.065 ( sources 25 and 23 in table [ tab : sources ] ) lie on part of a shell - like feature seen in radio maps @xcite . these features are coincident with the brightest parts of the radio - emitting shell , which are referred to as e and f by ( * ? ? ? * and fig . [ fig : radiob ] ) . we also find four filamentary features associated with the sgr a east supernova remnant , g359.9620.062 , g359.9650.056 , g359.9640.053 , and g359.9560.052 ( sources 6 , 10 , 11 , and 13 in table [ tab : sources ] ) . of these features associated with supernova remnants , we can put strict upper limits to the equivalent width of iron emission for g359.956 - 0.052 and g359.8890.081 , @xmath4170 and @xmath4130 ev , respectively , which strongly suggests that they are non - thermal . the x - rays are probably synchrotron emission from tev electrons @xcite , which could occur in parts of remnants where the shock velocity is high and the ambient density is low , so that particles are efficiently accelerated ( e.g. , * ? ? ? supernova shocks therefore can explain 5 of the 26 streaks . at least one non - thermal radio filament has been identified with x - ray emission in the central 100 pc of the galaxy , but outside of our deep images of the central 20 pc : g 359.54 + 0.18 @xcite . this confirmed non - thermal filament produces a flux density of 150 mjy at 6 cm over the region that also emits x - rays . assuming an @xmath156 spectrum , the estimated radio luminosity of g 359.54 + 0.18 between @xmath157 hz and @xmath158 hz is @xmath159 , compared to an x - ray luminosity of @xmath160 ( 0.210 kev * ? ? ? * ) . in our image , however , only one diffuse feature that is not associated with a supernova remnant has a firm radio counterpart , g359.9590.027 ( source 14 in table [ tab : sources ] ) . its x - ray luminosity is @xmath161 ( 28 kev ) . in fig . [ fig : radiob ] @xcite , the feature has a flux density of @xmath162 mjy , which for the same assumed radio spectrum as above implies @xmath163 . a second nearby feature with a similar size , spectrum , and even orientation , g359.9700.008 ( figure [ fig : sub_small ] , panel 5 ; source 22 in table [ tab : sources ] ) , also has a marginal radio counterpart with a flux of @xmath164 mjy . for this source we find @xmath165 ( 28 kev ) and @xmath166 . therefore , a couple of the streaks could be counterparts to non - thermal radio filaments , although the relative amount of radio and x - ray flux appears highly variable . the final conventional explanation for the x - ray streaks is that they could be pulsar wind nebulae . two candidate pulsar wind nebulae in this field have been discussed in the literature . @xcite have demonstrated that the spectral and morphological properties of g359.9450.044 resemble a pulsar wind nebula , and have suggested that it is the source of the tev emission that originates near @xcite . this source is included in our catalog . @xcite have identified the point - source cxogc j174545.5285829 as another candidate pulsar based on its featureless non - thermal spectrum , its lack of long - term variability , and the detection of a faint extended tail that may represent a bow shock formed by the wind nebula . this object is not in our catalog , because the faint nebulosity was not identified by our wavelet algorithms ( see [ sec : id ] ) . from this new work , one bright feature has a morphology that makes it an especially attractive candidate to be a pulsar wind nebulae : g 0.0320.056 ( source 29 in table [ tab : sources ] ) , which has a bright head producing about half its flux , and a long tail that curves to the northwest . pulsar wind nebulae are formed when a wind of particles that is powered by the rotational energy of the neutron star encounters the ism . the resulting shock accelerates the particles further , causing them to radiate synchrotron emission ( see * ? ? ? * for a review ) . these wind nebulae have diverse morphologies , which depend upon how the pulsar wind interacts with the surrounding supernova remnant , how far the pulsar travels during the lifetime of the electrons in the wind nebula , and whether the pulsar is moving supersonically with respect to the ism . in the galactic center , few of the pulsars are likely to be moving highly supersonically . most of the region is probably suffused with hot @xmath167 kev plasma with densities of @xmath168 @xmath127 , which implies that the sound speed of the ism is @xmath8500 km s@xmath133 @xcite . in contrast , the mean three - dimensional velocities of known radio pulsars are @xmath8400 km s@xmath133 ( e.g. , * ? ? ? * ; * ? ? ? * ) , and only 2 of 169 pulsars in @xcite have measured transverse velocities @xmath24800 km s@xmath133 , which , assuming the velocities are isotropic , would translate to expected three - dimensional velocities @xmath241000 km s@xmath133 . pulsars will only be highly supersonic ( mach numbers @xmath242 ) in regions of the ism that are dense and cool , such as near molecular clouds . therefore , we would not expect bow - shock nebulae to be common ( although see * ? ? ? nonetheless , the complex morphologies we observe could be explained by interactions between wind nebulae and unseen supernova remnants ( e.g. , * ? ? ? * ) , or if the proper motion of the pulsar moves the particle acceleration region faster than the electrons can cool ( e.g. , sn g371.1 - 1.1 in * ? ? ? the characteristic sizes of known pulsar nebulae are between @xmath169 and @xmath170 cm ( cheng , taam , & wang 2004 ) , which at the galactic center ( @xmath0=8 kpc ) would have angular sizes of 0880 . this bounds the sizes of the features we observe . moreover , the x - ray luminosities of the diffuse features in the galactic center are consistent with those of known pulsar wind nebulae . galactic pulsar wind nebulae have x - ray luminosities that are as large as @xmath4@xmath171 ( 210 kev ) ; typically , @xmath4@xmath172 of the spin - down energy @xmath173 is emitted as x - rays ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? the diffuse features in our survey all have luminosities of @xmath174@xmath2 , which would imply spin - down luminosities of @xmath175 . there are @xmath886 known pulsars with @xmath173 in this range . most of these energetic pulsars have ages @xmath6@xmath176 years , although 7 of @xmath4100 known recycled millisecond pulsars have @xmath173 this high @xcite . many galactic pulsar wind nebulae are luminous at radio wavelengths , and yet we find that most of our x - ray sources do not have radio counterparts . the limits to their flux densities at 6 cm are @xmath63 mjy ( tab . [ tab : sources ] and fig . [ fig : radiob ] ) . if we assume a standard pulsar wind spectrum with logarithmic slope @xmath177 between @xmath157 and @xmath158 hz , our typical limit of 3 mjy corresponds to @xmath178 , or between @xmath179 and @xmath172 of the x - ray luminosity . this would translate to @xmath180 . for comparison , the youngest , most energetic galactic pulsars are detected with @xmath181 . however , for @xmath182 a few pulsars have @xmath183 @xcite : of @xmath830 pulsars that have been reasonably well - studied at x - ray @xcite and radio @xcite wavelengths , five stand out as having wind nebulae with @xmath184 and @xmath185 : psr b104658 @xcite , psr b182313 @xcite , psr b0355 + 54 @xcite , psr b1706 - 44 @xcite , and possibly psr j11056107 @xcite . the sources in our sample that are either bright in x - rays or that have strict limits to their radio fluxes would have to be analogous to these radio - faint pulsars . given that the lack of radio detections can be reconciled plausibly with the known properties of pulsars , we next examine whether we should expect enough energetic pulsars in the galactic center to account for the number of diffuse features that we observe . @xcite and @xcite have considered whether recycled millisecond pulsars in the galactic center could contribute to these x - ray features . based on the inferred population of galactic millisecond pulsars @xcite , they estimate that @xmath4200 could be present in our survey region . if , based on the catalog of @xcite , @xmath410% of the millisecond pulsars have @xmath186 , they also could contribute @xmath420 objects to the diffuse features at the galactic center . these pulsars will generally be traveling rather slow ( @xmath187@xmath4130 km s@xmath133 * ? ? ? * ) , relative to the sound speed of the @xmath80.8 kev plasma that takes up most of the volume of the ism at the galactic center @xcite , but they could form extended nebulae if they encounter regions of the ism with relatively low sound velocities ( @[email protected] kev ) . the filling factor of this cooler ism is unknown , but if it is @xmath3110% , a handful of millisecond pulsars could produce extended diffuse features . most of the known energetic pulsars with wind nebulas are young , and still interacting with their supernova remnants . we concentrate on these as the best candidates for the diffuse x - ray features . @xcite modeled the infrared color - magnitude diagrams of stars in several fields toward the galactic center , and , assuming an initial mass function ( imf ) of the form @xmath188 for stars with masses between 0.1 @xmath189 and 120@xmath189 , concluded that the star formation rate in the inner 30 pc of the galaxy is 0.02 @xmath189yr@xmath133 . if we assume that radio pulsars form from stars with initial masses between 8 and 30 @xmath189 ( e.g. , * ? ? ? * ; * ? ? ? * but see figer 2005 ; muno 2006 ) , then they would form at a rate of @xmath190 yr@xmath133 . however , the supernovae that produce pulsars provide them with kicks , so the loss of pulsars as they move out of the galactic center will also limit the number of pulsar wind nebulae observable there ( e.g. , * ? ? ? yr old located within 0.02 pc of . these have higher escape velocities and would be retained , but they would be faint and confused with and so would not be detected in our x - ray survey . ] there is still debate as to the three - dimensional velocity distribution of pulsars ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , so we have adopted a simplified approach to estimate the number of pulsars remaining within the 8 ( 20 pc ) radial bound of our image , based upon the observed tangential velocities for 169 radio pulsars that were tabulated by @xcite . we assume that a pulsar would remain in our image if the product of its tangential velocity @xmath187 and its lifetime @xmath191 is less than @xmath0=20 pc . using the data in @xcite , we can compute the fraction of known pulsars in that sample that have traveled a projected distance @xmath0@xmath4120 pc at a given age @xmath191 , which we call @xmath192 . if pulsars are born at a constant rate @xmath193=@xmath190 yr@xmath133 and are bright pulsar wind nebulae for a time @xmath194 , then the number of nebulae in our image is roughly @xmath195 for @xmath194=100 kyr we find that only pulsars with @xmath187@xmath24200 km s@xmath133 may have time to escape , and that out of 20 pulsars born , roughly 14 would remain within our image . if @xmath194=300 kyr , pulsars with @xmath187>70 km s@xmath133 may escape , so that 29 out of 60 pulsars would remain . in this estimate , we have not considered that some pulsars will be gravitationally bound to the galactic center . if we use the enclosed mass in @xcite , the escape velocity from a radius of 10 pc is only @xmath196 km s@xmath133 . therefore , if @xmath194 is significantly longer than 100 kyr , then the fraction of pulsars retained in the galactic center would be larger than we estimate ( 66% of pulsars have tangential velocities smaller than 200 km s@xmath133 , although many of these will have larger three - dimensional velocities ) . for comparison , if we consider candidate pulsar wind nebulae to be those features that ( 1 ) exhibit no evidence for iron emission , and ( 2 ) are not obviously associated with supernova remnants already detected in the radio , then there are also @xmath420 of them in our image . this is consistent with the numbers we expect if pulsars produce wind nebulae for 100300 kyr after their birth . finally , we note that one of the x - ray features may be a jet produced by , g359.9440.052 ( source 3 in table [ tab : sources ] ) . we highlight this source in particular in figure [ fig : jetonly ] . the object is about 15 long , and is unresolved along its short axis . our hypothesis that it is a jet is motivated by the fact that it position angle points within 2@xmath197 of . from a visual inspection of the rest of our image , we find only one candidate feature that is similarly long and thin ( located at @xmath198= 266.37688 , 29.04517 ) , but this feature is not picked up by the automated wavelet search based on the work of @xcite because it is half as bright as g359.9440.052 . the candidate jet is found by both of our wavelet algorithms , so we believe this feature is unlikely to be an artifact produced by a chance alignment of point sources , or by poisson variations in the diffuse background . the feature has a flat spectrum of slope @xmath199 and an absorption column within 1@xmath15 of the average toward the galactic center , @xmath200 @xmath18 . its luminosity is @xmath201 ( 28 kev ) . the candidate jet is not detected in the radio , with an upper limit of @xmath4145 mjy at 6 cm ( 5 ghz ) . the radio upper limit is not constraining because the feature lies along the line - of - sight toward bright , diffuse radio emission . the relative strength of the radio and x - ray emission from the synchrotron - emitting jets of quasars can be quantified using the logarithmic slope @xmath202 , where @xmath203 and @xmath204 and the x - ray and radio flux densities , and @xmath205 and @xmath206 are the frequencies at which the flux densities are computed . from the values in table [ tab : spec ] , @xmath207 njy at @xmath208 hz ( 1 kev ) . therefore , we can only constrain @xmath209 . for comparison , the quasars in the sample of @xcite have @xmath210 between 0.9 and 1.1 . therefore , one would need radio observations with a sensitivity of @xmath411 mjy to make a useful comparison between the putative jet feature near and quasar jets . further observations are warranted to determine whether g359.9440.052 is a jet of synchrotron - emitting particles that is flowing away from .

based on the weakness of iron emission in their spectra , we propose that most of them are non - thermal . one long , narrow feature points toward , and so we propose that this feature is a jet of synchrotron - emitting particles ejected from the supermassive black hole . for the others , we show that their sizes ( 0.12 pc in length for=8 kpc ) , x - ray luminosities ( between and , 28 kev ) , and spectra ( power laws with ) are consistent with those of pulsar wind nebulae . based on the star formation rate at the galactic center these radio limits do not strongly constrain their natures , which underscores the need for further multi - wavelength studies of this unprecedented sample of galactic x - ray emitting structures .

we present a catalog of 34 diffuse features identified in x - ray images of the galactic center taken with the _ chandra _ x - ray observatory . several of the features have been discussed in the literature previously , including 7 that are associated with a complex of molecular clouds that exhibits fluorescent line emission , 4 that are superimposed on the supernova remnant sgr a east , 2 that are coincident with radio features that are thought to be the shell of another supernova remnant , and one that is thought to be a pulsar wind nebula only a few arcseconds in projection from . however , this leaves 20 features that have not been reported previously . based on the weakness of iron emission in their spectra , we propose that most of them are non - thermal . one long , narrow feature points toward , and so we propose that this feature is a jet of synchrotron - emitting particles ejected from the supermassive black hole . for the others , we show that their sizes ( 0.12 pc in length for=8 kpc ) , x - ray luminosities ( between and , 28 kev ) , and spectra ( power laws with ) are consistent with those of pulsar wind nebulae . based on the star formation rate at the galactic center , we expect that pulsars have formed in the last 300 kyr , and could be producing pulsar wind nebulae . only one of the 19 candidate pulsar wind nebulae is securely detected in an archival radio image of the galactic center ; the remainder have upper limits corresponding to . these radio limits do not strongly constrain their natures , which underscores the need for further multi - wavelength studies of this unprecedented sample of galactic x - ray emitting structures .

0707.1907

c

there are several processes that appear to produce diffuse x - ray features in the galactic center : x - rays scatter off of gas in molecular clouds , and cause them to fluoresce ; supernova shocks produce x - ray emitting , tev electrons when they propagate through low - density ism ; and non - thermal radio filaments produce x - rays through a mechanism that is still not understood . however , we propose that the majority of the diffuse x - ray features are pulsar wind nebulae . a significant number of pulsars are expected at the galactic center , but because of the high dispersion measure along the line of sight , only two have so far been reported there in the radio @xcite . x - ray identifications of pulsar wind nebulae bypass the problem of the dispersion measure , and in addition are sensitive to pulsars that are not beamed toward our line of sight . therefore , the identification of @xmath820 x - ray features that are candidate pulsar wind nebulae is consistent with a basic prediction about the number of massive stars that have recently ended their lives in the galactic center . however , at the moment we lack identificaations of most of these features at other wavelengths , so further multi - wavelength studies are required to confirm our hypotheses . we are grateful to b. gaensler for informative conversations about pulsar wind nebulae . mpm was supported by the national aeronautics and space administration through chandra award number 7910613 issued by the chandra x - ray observatory center , which is operated by the smithsonian astrophysical observatory for and on behalf of the national aeronautics space administration under contract nas8 - 03060 . 0 aharonian , f. 2004 , , 425 , l13 arabadjis , j. s. , bautz , m. w. , & arabadjis , g. 2004 , , 617 , 303 arnaud , k.a . , 1996 , astronomical data analysis software and systems v , eds . jacoby g. and barnes j. , p17 , asp conf . series volume 101 arzoumanian z. , chernoff d. f. , & cordes j. m. , 2002 , apj , 568 , 289 baganoff , f. k. 2003 , , 591 , 891 becker , w. & trmper , j. 1997 , , 326 , 682 bertin , e. & arnouts , s. 1996 , , 117 , 393 brarzier , k. t. s. & johnston , s. 1999 , , 305 , 671 bykov , a. m. 2002 , , 390 , 327 cheng , k. s. , taam , r. e. , & wang , w. 2004 , , 617 , 480 cheng , k. s. , taam , r. e. , & wang , w. 2006 , , 641 , 427 cordes , j. m. & lazio , t. j. w. 1997 , , 475 , 557 faucher - 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ph/0611952 romani , r. w. , ng , c. y. , dodson , r. , & brisker , w. 2005 , , 631 , 480 rybicki , g. , & lightman , a. _ radiative processes in astrophysics _ , 1979 , john wiley & sons , inc . sakano , m. , warwick , r. s. , decourchelle , a. , & predehl , p. 2003 , , 340 , 747 sakano , m. , warwick , r. s. , decourchelle , a. , & predehl , p. 2004 , , 350 , 129 scoville , n. z. , stolovy , s. r. , reike , m. , christopher , m. , & yusef - zadeh , f. 2003 , , 594 , 294 skrutskie , m. f. 2006 , , 131 , 1163 starck , j .- l . , bijauoi , a. , valtchanov , i. , & murtagh , f. 2000 , , 147 , 139 sunyaev , r. a. , markevitch , m. , & pavlinsky , m. 1993 , , 407 , 606 valinia , a. , tatischeff , v. , arnaud , k. , ebisawa , k. , & ramaty , r. 2000 , , 543 , 733 wang , q. d. , lu , f. j. , & gotthelf , e. v. 2006 , , 367 , 937 wang , q. d. , lu , f. j. , & lang , c. c. 2002b , , 581 , 1148 wang , w. , jiang , z. j. , & cheng , k. s. 2005 , , 358 , 263 weisskopf , m. c. , brinkman , b. , canizares , c. , garmire , g. , murray , s. , & van speybroeck , l. p. 2002 , , 114 , 1 vink , j. , bleeker , j. , van der heyden , k. , bykov , a. , bamba , a. & yamazaki , r. 2006 , submitted to , astro - ph/0607307 yusef - zadeh , f. & morris , m. 1987 , , 320 , 545 yusef - zadeh , f. , wardle , m. , muno , m. , law , c. , & pound , m. 2005 , adspr , 35 , 1074 yusef - zadeh , f. , hewitt , j. w. , & cotton , w. 2004 , , 155 , 421 clccccccccccc 1 & g359.945 - 0.044 & @xmath211 & @xmath212 & 22 & 0.1 & 927 & @xmath213 & @xmath4199.0 & @xmath214 & @xmath215 & 419.6 & @xmath41100 + 2 & g359.942 - 0.045 & @xmath216 & @xmath217 & 28 & 0.1 & 927 & @xmath218 & 10.8 & @xmath219 & @xmath220 & 132.3 & @xmath4130 + 3 & g359.944 - 0.052 & @xmath221 & @xmath222 & 20 & 0.3 & 927 & @xmath223 & 11.1 & @xmath224 & @xmath225 & 29.2 & @xmath4145 + 4 & g359.950 - 0.043 & @xmath226 & @xmath227 & 55 & 0.4 & 927 & @xmath228 & 8.9 & @xmath229 & @xmath230 & 50.6 & 210@xmath12330 + 5 & g359.933 - 0.039 & @xmath231 & @xmath232 & 15 & 0.8 & 927 & @xmath233 & 3.4 & @xmath234 & @xmath235 & 8.1 & @xmath413 + 6 & g359.956 - 0.052 & @xmath236 & @xmath237 & 10 & 0.8 & 927 & @xmath238 & 3.1 & @xmath239 & @xmath240 & 12.7 & @xmath419 + 7 & g359.933 - 0.037 & @xmath241 & @xmath242 & 13 & 0.9 & 927 & @xmath243 & 17.2 & @xmath244 & @xmath245 & 22.8 & @xmath415 + 8 & g359.941 - 0.029 & @xmath246 & @xmath247 & 17 & 1.0 & 927 & @xmath248 & 11.7 & @xmath249 & @xmath250 & 18.7 & @xmath412 + 9 & g359.925 - 0.051 & @xmath251 & @xmath252 & 19 & 1.2 & 927 & @xmath253 & 7.5 & @xmath254 & @xmath255 & 18.1 & @xmath412 + 10 & g359.964 - 0.053 & @xmath256 & @xmath257 & 76 & 1.2 & 927 & @xmath258 & 41.9 & @xmath259 & @xmath260 & 151.1 & 11@xmath1233 + 11 & g359.965 - 0.056 & @xmath261 & @xmath262 & 29 & 1.4 & 927 & @xmath263 & 6.8 & @xmath264 & @xmath265 & 22.4 & @xmath412 + 12 & g359.921 - 0.052 & @xmath266 & @xmath267 & 12 & 1.4 & 927 & @xmath268 & 3.6 & @xmath269 & @xmath270 & 7.5 & @xmath411 + 13 & g359.962 - 0.062 & @xmath271 & @xmath272 & 26 & 1.4 & 927 & @xmath273 & 1.1 & @xmath274 & @xmath275 & 20.3 & 2@xmath1231 + 14 & g359.959 - 0.027 & @xmath276 & @xmath277 & 34 & 1.4 & 927 & @xmath278 & 32.7 & @xmath264 & @xmath279 & 33.6 & 20@xmath1233 + 15 & g359.971 - 0.038 & @xmath280 & @xmath281 & 148 & 1.7 & 927 & @xmath282 & 19.8 & @xmath283 & @xmath284 & 71.4 & @xmath4110 + 16 & g359.969 - 0.033 & @xmath285 & @xmath286 & 17 & 1.7 & 927 & @xmath287 & 5.6 & @xmath288 & @xmath289 & 9.0 & @xmath411 + 17 & g359.921 - 0.030 & @xmath290 & @xmath291 & 30 & 1.7 & 927 & @xmath292 & 12.7 & @xmath293 & @xmath294 & 15.7 & @xmath411 + 18 & g359.915 - 0.061 & @xmath295 & @xmath296 & 22 & 2.0 & 927 & @xmath297 & 15.2 & @xmath298 & @xmath299 & 10.0 & [email protected] + 19 & g359.983 - 0.040 & @xmath300 & @xmath301 & 35 & 2.4 & 927 & @xmath302 & 0.5 & @xmath303 & @xmath304 & 5.4 & @xmath411 + 20 & g359.904 - 0.047 & @xmath305 & @xmath306 & 32 & 2.4 & 927 & @xmath307 & 6.7 & @xmath308 & @xmath309 & 13.2 & @xmath410.2 + 21 & g359.977 - 0.076 & @xmath310 & @xmath311 & 26 & 2.7 & 927 & @xmath312 & 1.6 & @xmath313 & @xmath314 & 6.5 & @xmath414 + 22 & g359.970 - 0.008 & @xmath315 & @xmath316 & 30 & 2.7 & 927 & @xmath317 & 32.6 & @xmath318 & @xmath319 & 28.1 & [email protected] + 23 & g359.899 - 0.065 & @xmath320 & @xmath321 & 30 & 2.9 & 927 & @xmath322 & 10.7 & @xmath323 & @xmath324 & 11.0 & 6@xmath1231 + 24 & g359.897 - 0.023 & @xmath325 & @xmath326 & 42 & 3.2 & 927 & @xmath327 & 2.3 & @xmath328 & @xmath329 & 9.2 & @xmath410.4 + 25 & g359.889 - 0.081 & @xmath330 & @xmath331 & 432 & 3.9 & 927 & @xmath332 & @xmath41 - 99.0 & @xmath333 & @xmath334 & 281.9 & + 26 & g0.014 - 0.054 & @xmath335 & @xmath336 & 260 & 4.2 & 927 & @xmath337 & 28.4 & @xmath338 & @xmath339 & 78.1 & @xmath410.6 + 27 & g0.008 - 0.015 & @xmath340 & @xmath341 & 51 & 4.3 & 927 & @xmath342 & 3.1 & @xmath343 & @xmath96 & 9.2 & [email protected] + 28 & g0.021 - 0.051 & @xmath344 & @xmath345 & 190 & 4.6 & 927 & @xmath346 & 27.8 & @xmath347 & @xmath348 & 69.2 & + 29 & g0.032 - 0.056 & @xmath349 & @xmath350 & 429 & 5.3 & 927 & @xmath351 & 30.8 & @xmath352 & @xmath353 & 100.9 & + 30 & g0.029 - 0.080 & @xmath354 & @xmath355 & 838 & 5.5 & 927 & @xmath356 & 18.3 & @xmath357 & @xmath358 & 73.0 & + 31 & g0.039 - 0.077 & @xmath359 & @xmath360 & 333 & 6.0 & 927 & @xmath361 & 33.5 & @xmath362 & @xmath363 & 118.4 & + 32 & g0.062 + 0.010 & @xmath364 & @xmath365 & 1187 & 7.8 & 927 & @xmath366 & 14.7 & @xmath367 & @xmath368 & 75.9 & + 33 & g0.097 - 0.131 & @xmath369 & @xmath370 & 4181 & 10.5 & 563 & @xmath371 & @xmath41 - 99.0 & @xmath372 & @xmath373 & 529.0 & + 34 & g0.116 - 0.111 & @xmath374 & @xmath375 & 2257 & 11.0 & 574 & @xmath376 & 7.3 & @xmath377 & @xmath378 & 121.6 &

, we expect that pulsars have formed in the last 300 kyr , and could be producing pulsar wind nebulae . only one of the 19 candidate pulsar wind nebulae is securely detected in an archival radio image of the galactic center ; the remainder have upper limits corresponding to .

we present a catalog of 34 diffuse features identified in x - ray images of the galactic center taken with the _ chandra _ x - ray observatory . several of the features have been discussed in the literature previously , including 7 that are associated with a complex of molecular clouds that exhibits fluorescent line emission , 4 that are superimposed on the supernova remnant sgr a east , 2 that are coincident with radio features that are thought to be the shell of another supernova remnant , and one that is thought to be a pulsar wind nebula only a few arcseconds in projection from . however , this leaves 20 features that have not been reported previously . based on the weakness of iron emission in their spectra , we propose that most of them are non - thermal . one long , narrow feature points toward , and so we propose that this feature is a jet of synchrotron - emitting particles ejected from the supermassive black hole . for the others , we show that their sizes ( 0.12 pc in length for=8 kpc ) , x - ray luminosities ( between and , 28 kev ) , and spectra ( power laws with ) are consistent with those of pulsar wind nebulae . based on the star formation rate at the galactic center , we expect that pulsars have formed in the last 300 kyr , and could be producing pulsar wind nebulae . only one of the 19 candidate pulsar wind nebulae is securely detected in an archival radio image of the galactic center ; the remainder have upper limits corresponding to . these radio limits do not strongly constrain their natures , which underscores the need for further multi - wavelength studies of this unprecedented sample of galactic x - ray emitting structures .

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numerous spectroscopic studies of metal - poor ( [ fe / h ] @xmath9 ) candidates identified by the hk survey ( beers et al . 1985 , 1992 ) and the hamburg / eso survey ( he s ; wisotzki et al . 1996 ; christlieb et al . 2001 , 2008 ; christlieb 2003 ) have revealed that the frequency of carbon - enhanced stars increases strongly with decreasing [ fe / h ] . these stars , now known as carbon - enhanced metal - poor ( cemp ) stars , were originally defined as stars with metallicity [ fe / h ] @xmath10 and carbon - to - iron ratios [ c / fe ] @xmath11 ( beers & christlieb 2005 ) . generally , the frequency of c - rich stars increases from a few percent at higher metallicity to on the order of 20% for [ fe / h ] @xmath12 , 30% for [ fe / h ] @xmath7 , 40% for [ fe / h ] @xmath13 , and 75% for [ fe / h ] @xmath14 ( beers et al . 1992 ; norris et al . 1997 ; rossi et al . 1999 ; beers & christlieb 2005 ; cohen et al . 2005 ; marsteller et al . 2005 ; rossi et al . 2005 ; frebel et al . 2006 ; lucatello et al . 2006 ; norris et al . 2007 ; carollo et al . 2012 ; norris et al . 2013 ; spite et al . 2013 ; yong et al . this increasing trend of cemp - star frequency with declining [ fe / h ] is again confirmed from the many thousands of cemp stars found among the several hundred thousand stars with available spectra from the sloan digital sky survey ( sdss ; fukugita et al . 1996 ; gunn et al . 1998 , 2006 ; york et al . 2000 ; stoughton et al . 2002 ; abazajian et al . 2003 , 2004 , 2005 , 2009 ; pier et al . 2003 ; adelman - mccarthy et al . 2006 , 2007 , 2008 ; aihara et al . 2011 ; ahn et al . 2012 ) and the sloan extension for galactic understanding and exploration ( segue-1 ; yanny et al . 2009 ) , and segue-2 ( c. rockosi et al . , in preparation ) as described by lee et al . ( 2013 ) . there exist a number of subclasses within the cemp classification , as originally defined by beers & christlieb ( 2005 ) , which may provide direct clues to the nature of their likely progenitors . stars in the cemp-@xmath15 subclass exhibit over - abundances of @xmath15(low)-process elements such as ba and sr , the cemp-@xmath16 subclass includes stars with enhanced @xmath16(apid)-process elements such as eu , and the cemp-@xmath17 stars exhibit elemental abundance patterns associated with both the @xmath16-process and the @xmath15-process . the cemp - no subclass exhibits no over - abundances of the neutron - capture elements . the cemp-@xmath15 ( and cemp-@xmath17 ) subclasses of cemp stars are the most commonly found to date ; high - resolution spectroscopic studies show that around 80% of the cemp stars are categorized as cemp-@xmath15 ( or cemp-@xmath17 ) ( aoki et al . 2007 , 2008 ) . the favored mechanism for the production of the high [ c / fe ] ratios found for cemp-@xmath15 ( cemp-@xmath17 ) stars is mass transfer of carbon - enhanced material from the envelope of a now - defunct asymptotic giant - branch ( agb ) star to its ( presently observed ) binary companion ( suda et al . 2004 ; herwig 2005 ; komiya et al . 2007 ; sneden et al . 2008 ; masseron et al . 2010 ; bisterzo et al . 2011 , 2012 ) . observational evidence now exists to suggest that the cemp-@xmath17 stars ( and other @xmath16-process - element rich stars ) were enhanced in @xmath16-process elements in their natal gas clouds by previous generations of supernovae ( sne ) , and did not require a contribution of @xmath16-process elements from a binary companion ( see hansen et al . 2013 ) . the limited amount of long - term radial - velocity monitoring available for cemp stars indicates variations for almost all of the cemp-@xmath15 stars , confirming their binary status ( lucatello et al . 2005a ) . in addition , the cemp-@xmath15 stars are mostly , though not exclusively ( e.g. , norris et al . 2013 and references therein ) , found among metal - poor stars with [ fe / h ] @xmath18 . on the other hand , cemp - no stars are found most commonly among the extremely metal - poor ( emp ) stars , with [ fe / h ] @xmath19 ( aoki et al . 2007 ; norris et al . 2013 ) . existing radial - velocity monitoring of these objects indicates that they are found in binary systems no more frequently than other metal - poor stars ( t. hansen et al . , in preparation ) . norris et al . ( 2013 ) found no cemp-@xmath15 stars among 18 cemp stars with [ c / fe ] @xmath20 and [ fe / h ] @xmath21 , as well as no discernible variations of their radial velocities . although there is general consensus on the origin of cemp-@xmath15 stars , the likely progenitor or progenitors of the cemp - no stars are still under discussion . suggested models include massive , rapidly rotating , mega metal - poor ( mmp ; [ fe / h ] @xmath22 ) stars , which produce large amounts of c , n , and o due to distinctive internal burning and mixing episodes ( meynet et al . 2006 , 2010 ; chiappini 2013 ) , and faint ( low - energy ) sne associated with the first generations of stars , which experience extensive mixing and fallback during their explosions , and eject large amounts of c and o , but not heavier metals ( umeda & nomoto 2003 , 2005 ; tominaga et al . 2007 , 2013 ; ito et al . 2009 , 2013 ; nomoto et al . nevertheless , the origin of the cemp - no star phenomenon is yet to be fully resolved ( see norris et al . 2013 , which summarizes other possible progenitors of the c - rich stars ) . previous authors have attempted to understand the large fractions of cemp stars at low metallicity , as well as the different subclasses of the cemp stars , by invoking agb models with different masses . furthermore , there have been several efforts to constrain the form of the early initial mass function ( imf ) by reproducing the observed frequencies of cemp stars , as well as the number ratios of the different cemp subclasses . abia et al . ( 2001 ) , for example , claimed that the large number of carbon - enhanced stars found among stars of very low metallicity could be accounted for if the imf in the early history of the galaxy was dominated by higher mass stars . lucatello et al . ( 2005b ) and komiya et al . ( 2007 ) utilized population - synthesis models with an imf biased towards massive stars to compare with the fractions of observed cemp stars , and concluded that an imf comprising a larger number of intermediate- to high - mass stars could reproduce the larger fraction of the cemp stars among metal - poor stars ( [ fe / h ] @xmath23 ) better than the present - day ( salpeter ) imf . recently , suda et al . ( 2013 ) made use of the number ratios of cemp / emp , cemp - no / cemp , and nemp / cemp giant stars ( where nemp stands for nitrogen - enhanced metal - poor ) from the stellar abundances for galactic archeology ( saga ; suda et al . 2008 ) database to constrain the parameters in their binary population - synthesis model . they considered several imfs , and proposed that the imf changed from high - mass dominated in the early galaxy to low - mass ( @xmath24 @xmath0 ) dominated at present , and that this transition occurred around a metallicity of [ fe / h ] @xmath25 . the above studies carried out comparisons of the cemp fractions derived from small samples of stars comprising mostly giants . however , observational evidence indicates that the c - rich material at the surface of a giant could be easily depleted by extra mixing of cno - processed material from its interior during the so - called first dredge - up episode ( spite et al . 2005 , 2006 ; lucatello et al . 2006 ; aoki et al . it is also known that more luminous red giant - branch ( rgb ) stars are more affected by such mixing ( spite et al . 2005 , 2006 ) . therefore , if such mixing does occur , the overall cemp frequencies as estimated from giants are expected to be a lower limit . in order to avoid this complication , the best way forward would appear to be comparing model predictions with the observed cemp frequencies based on unevolved stars , such as dwarfs or main - sequence turnoff stars . the current cemp stars that have been studied with high - resolution spectroscopy are mostly giants ( for which it is simpler to obtain high s / n spectra , due to their relative brightness and moderate temperatures , which allows for lines of interest to be measured with less uncertainty ) . the numbers of observed dwarf and turnoff stars with similar observations are in any case too small to derive statistically meaningful results for different subclasses of cemp stars . in this study , we make use of stars with available carbon - to - iron ratios ( [ c / fe ] ) and [ fe / h ] , based on medium - resolution ( @xmath26 ) spectroscopy obtained during the course of the sdss , segue-1 , and segue-2 , in order to derive accurate frequencies of cemp stars among giants and turnoff stars as a function of [ fe / h ] . the derived cemp frequencies are then compared with the predictions from agb binary - synthesis models that employ the two different imfs explored by suda et al . ( the results of these comparisons should provide more stringent constraints on the imf of the milky way , and clues to the existence of progenitors _ other than agb stars _ that are capable of producing large amounts of carbon - enhanced material in the early universe . this paper is outlined as follows . in section 2 , we describe the selection criteria used to assemble the sample for this study . section 3 presents and discusses results of the comparison of the cemp frequencies for giants and main - sequence turnoff stars with the binary - synthesis model predictions , and describes a procedure for correcting the anticipated undercounts of cemp stars among warm , metal - poor turnoff stars . our conclusions are presented in section 4 .

we present a comparison of the frequencies of carbon - enhanced metal - poor ( cemp ) giant and main - sequence turnoff stars , selected from the sloan digital sky survey ( sdss ) and the sloan extension for galactic understanding and exploration ( segue ) , with predictions from asymptotic giant - branch ( agb ) mass - transfer models . thus , in order to derive more accurate estimates of cemp frequencies for stars in the milky way , it is preferable to make use of sdss / segue main - sequence turnoff stars , which are not expected to experience significant dilution .

we present a comparison of the frequencies of carbon - enhanced metal - poor ( cemp ) giant and main - sequence turnoff stars , selected from the sloan digital sky survey ( sdss ) and the sloan extension for galactic understanding and exploration ( segue ) , with predictions from asymptotic giant - branch ( agb ) mass - transfer models . we consider two initial mass functions ( imfs)a salpeter imf , and a mass function with a characteristic mass of 10 . previous observations suggest that the carbon abundances of red giants are altered during red - giant branch evolution due to mixing of their convective outer layers , resulting in a reduction of the observed carbon - abundance ratios . thus , in order to derive more accurate estimates of cemp frequencies for stars in the milky way , it is preferable to make use of sdss / segue main - sequence turnoff stars , which are not expected to experience significant dilution . however , because of the difficulty of identifying moderately carbon - enhanced stars ( [ c / fe ] ) among warm , metal - poor turnoff stars , owing to their much weaker ch-bands , we derive a correction function to compensate for the resulting undercounts of cemp stars . these comparisons indicate good agreement between the observed cemp frequencies for stars with [ fe / h ] and a salpeter imf , but not with an imf having a higher characteristic mass . thus , while the adopted agb model works well for low - mass progenitor stars , it does not do so for high - mass progenitors . our results imply that the imf shifted from high- to low - mass dominated in the early history of the milky way , which appears to have occurred at a `` chemical time '' between [ fe / h ] and [ fe / h ] . the corrected cemp frequency for the turnoff stars with [ fe / h ] is much higher than the agb model prediction from the high - mass imf , supporting the previous assertion that one or more additional mechanisms , not associated with agb stars , are required for the production of carbon - rich material below [ fe / h ] .

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figure [ fig : cfedist ] shows the distribution of [ c / fe ] for sdss / segue stars in various bins of metallicity , decreasing from the upper to lower panels . main - sequence turnoff stars are shown as solid histograms ; giants are shown as dashed histograms . inspection of this figure reveals that the overall distribution of [ c / fe ] gradually shifts ( for both turnoff stars and giants ) to higher [ c / fe ] with decreasing [ fe / h ] , with a tail extending toward higher [ c / fe ] appearing as the metallicity decreases . as the metallicity decreases below [ fe / h ] @xmath8 , this trend continues for the turnoff stars , but it is not as evident for the giants . another interesting feature seen in figure [ fig : cfedist ] is that , for [ fe / h ] @xmath7 , the turnoff stars are distributed over a wide range of [ c / fe ] , whereas the giants are mostly concentrated in the region of [ c / fe ] @xmath41 . the red vertical lines in figure [ fig : cfedist ] indicate the mean values of [ c / fe ] for the turnoff stars ( solid line ) and giants ( dashed line ) , respectively . on average , the giants appear to exhibit lower carbonicity ( by about 0.2 dex ) than the turnoff stars , down to [ fe / h ] = @xmath42 . the mean value of [ c / fe ] appears to increase with decreasing metallicity , as also found by carollo et al . ( 2012 , their figure 11 ) . they reported that the degree of carbon enhancement significantly increased from [ c / fe ] @xmath43 at [ fe / h ] = @xmath44 to [ c / fe ] @xmath45 at [ fe / h ] = @xmath46 , somewhat higher than our values ( it should be noted that a different sample of stars , as well as a different method for determination of [ c / fe ] , were employed by these authors ) . the difference in the distribution of [ c / fe ] between the turnoff stars and the giants may be explained by the different masses of the convective envelopes between the two evolutionary stages . because a giant has a much larger convective envelope , its surface material experiences more mixing , leading to reduction of the carbonicity . on the other hand , the turnoff stars have shallower convective envelopes , so that their surface abundances may not be expected to greatly change . as a result , the overall carbon abundance for the turnoff population is expected to be higher than that of the giant population , even if they were born with the same initial carbon abundance . bonifacio et al . ( 2009 ) also noted a difference in the mean [ c / fe ] between giants and turnoff stars of similar metallicities , finding a difference of about 0.2 dex ( giants being lower ) for stars with [ fe / h ] @xmath23 . they argued that this difference arises because the giants suffer from extra mixing due to first dredge - up , and have their surface carbon abundance reduced . they also suggested the stellar models employed in the analysis could contribute to this discrepancy ; they found a smaller difference between the giants and turnoff stars when deriving [ c / fe ] from a 3d , rather than a 1d model atmosphere . the black filled circles in figure [ fig : cempcom ] represent our derived differential frequencies for c - rich giants as a function of [ fe / h ] . from inspection of this figure , it appears that the cemp frequencies do not increase for [ fe / h ] @xmath47 , but rather , remain relatively constant , in contrast to the results of previous studies . as discussed by spite et al . ( 2005 , 2006 ) , lucatello et al . ( 2006 ) , and aoki et al . ( 2007 ) , this may be in part due to cn - processing , which converts carbon to nitrogen at the bottom of a star s convection zone , and in turn reduces the carbon abundance in the envelope at the time of first dredge - up . whether or not a giant experiences such mixing can be identified by measuring its @xmath48c/@xmath49c or [ c / n ] ratios , as both will be lower for an object that has gone through such an event . unfortunately , these ratios are difficult to assess from the sdss / segue spectra over the full range of metallicities we consider . in the metallicity regime of [ fe / h ] @xmath50 , our derived cemp frequencies of @xmath511% agree with the previously claimed fraction of classical ch or ba stars in the solar neighborhood ( luck & bond 1991 ) . regarding the effect of the first dredge - up , it is worth mentioning the following arguments from a theoretical point of view . according to suda et al . ( 2004 ) , first dredge - up might not play a significant role in decreasing the carbon abundance on the surface of a giant , based on an 0.8 @xmath0 model for he 0107 - 5240 ( a cemp - no star with [ fe / h ] = @xmath52 ; christlieb et al . they examined the effect of the first dredge - up following the accretion of c- and o - rich matter onto the star ( here assuming an agb mass - transfer scenario ) , and found that if its envelope is significantly c - rich ( [ c / fe ] @xmath53 ) , then after first dredge - up the surface carbon abundance changed little . this is because the surface carbon abundance is too large ( [ c / h ] @xmath54 ) prior to the dredge - up to be significantly depleted by the relatively small amount of matter in the hydrogen - burning shell , @xmath55 0.02 @xmath0 . even in cases of emp stars for which the initial carbon abundance is small , suda & fujimoto ( 2010 ) showed that the effect of the first dredge - up is also limited , due to the shallower convective envelopes in metal - poor ( as compared to metal - rich ) stars . according to their model calculation , the change of the cno abundance before and after the first dredge - up was on the order of one percent therefore , they did not notice a large impact on the surface carbon abundances after first dredge - up for stars with [ fe / h ] @xmath56 . the blue open circles in figure [ fig : cempcom ] are the predicted frequencies of cemp giants , as a function of metallicity , from agb binary - synthesis models with an imf peaked at 10 @xmath0 , while the open squares are the predicted frequencies from models using a salpeter imf , adopted from suda et al . ( 2013 ) . in their model , they included a mechanism referred to as `` pulsation - driven mass loss '' ( wood 2011 ) , which was argued to suppress the previously predicted over - production of nemp stars by izzard et al . ( 2009 ) and pols et al . it appears that the predicted cemp frequencies for the high - mass dominated imf are in relatively good agreement with the observed cemp giant frequencies for [ fe / h ] @xmath23 , but the model predicts too many c - rich stars above [ fe / h ] = @xmath42 . the predicted cemp frequencies from a salpeter imf are in good agreement with our derived frequencies for the metal - rich region ( [ fe / h ] @xmath50 ) , while the predicted cemp frequencies are far too low for stars with [ fe / h ] @xmath23 . these are similar results to those found by suda et al . ( 2013 ) , who used the giants in the saga database to compare the observed cemp frequencies with their model predictions . one of the reasons that suda et al . ( 2013 ) employed giants to derive the cemp frequency is that one can ignore effects such as atomic diffusion , which can alter the surface abundances of dwarfs and turnoff stars more significantly than in giants ( e.g. , richard et al . 2002a , b ; korn et al . 2007 ; lind et al . 2008 ) . however , our derived frequencies show a much better agreement for the salpeter imf in the metallicity region [ fe / h ] @xmath50 . in the study of suda et al . ( 2013 ) , the model - predicted frequency of the cemp stars above [ fe / h ] = @xmath57 was not well - constrained , most likely due to the selection biases associated with the assembly of their sample from previous high - resolution spectroscopic studies ( which tended to emphasize the more metal - poor and/or carbon - enhanced stars ) . in contrast , the good agreement of the frequencies calculated from our considerably less - biased sdss / segue sample with the model prediction for [ fe / h ] @xmath4 suggests that the agb binary - synthesis model with a salpeter mass function used by suda et al . ( 2013 ) works well , at least in this metallicity regime . based on the results from the comparisons of the observed cemp frequencies with model predictions from the two different imfs , we conjecture that , for very low - metallicity ( [ fe / h ] @xmath23 ) stars , the distribution of the stellar masses was dominated by rather massive stars ( @xmath5110 @xmath0 or higher ) , while for the relatively more metal - rich stars ( [ fe / h ] @xmath50 ) , it appears that the imf did not much differ from a salpeter imf , which is biased towards low - mass progenitor stars ( @xmath24 @xmath0 ) . as previously claimed by suda et al . ( 2013 ) , our results also support the idea that there must exist a shift in the imf from a high - mass dominated to low - mass dominated form in the early history of the milky way , corresponding to a `` chemical time '' between [ fe / h ] @xmath5 and [ fe / h ] @xmath6 . by way of comparison , the binary population - synthesis model of izzard et al . ( 2009 ) was able to reproduce the ratio of nemp to very metal - poor ( vmp ; [ fe / h ] @xmath12 ) stars ( that is , c and n normal stars ) _ without _ introducing an imf dominated by higher mass stars , but not the high frequency of the cemp stars . pols et al . ( 2012 ) also argued , by comparing the observed number ratio of nemp to cemp stars with their model predictions , that they could derive a similar number ratio from a salpeter imf , and ruled out an imf peaked at 10 @xmath0 claimed by komiya et al . ( 2007 ) . another interesting result emerges when one partitions the giant sample based on distance from the galactic plane . the green squares in figure [ fig : cempcom ] are the cemp frequencies for giants with distances from the galactic mid - plane ( @xmath58 ) larger than 5 kpc , whereas the red triangles represent frequencies based on those with @xmath59 kpc . the figure clearly indicates that the more distant halo giants exhibit higher frequencies of c - rich stars , while the stars closer to the galactic plane tend to have lower frequencies of c - rich stars . this same trend with vertical distance was hinted at ( due to small number statistics ) in frebel et al . ( 2006 ) , and strongly confirmed in the much larger sample of sdss / segue calibration stars by carollo et al . carollo et al . argued that this result was likely due to the fact that the outer - halo population has about twice the frequency of cemp stars , at a given low metallicity , as the inner - halo population . a few possible reasons for the observed differences in the cemp frequencies between the two spatial regions might be suggested within the context of the agb model predictions . first , the progenitors of the inner - halo population ( which dominates for @xmath60 5 kpc ) and the outer - halo population ( which , at @xmath61 5 kpc , includes more outer - halo stars ) might have formed their stars at different times , with different imfs . because the outer - halo population has more cemp stars than the model prediction for [ fe / h ] @xmath47 , it is possible that the outer - halo population might have had an imf with more intermediate - mass stars than considered by the model . on the other hand , since the cemp frequencies of the inner - halo stars are lower than the model estimate , the inner - halo population might have had an imf with less intermediate - mass stars than the proposed imf . related ideas are discussed by tumlinson et al . ( 2007 ) . another possibility is that suda et al . ( 2013 ) assumed that all cemp stars , including cemp - no objects , formed from the agb binary scenario . if there were to exist other channels of carbon production at [ fe / h ] @xmath47 , such as faint sne or rapidly rotating massive stars ( producing cemp - no stars in the subsequent generation ) , as suggested by several studies , we then might expect larger frequencies of cemp stars than the agb binary - synthesis model prediction ( as seen in figure [ fig : cempcom ] ) , even if the carbon dilution of the giants due to extra mixing is taken into account . a more detailed discussion of this is provided below . in any event , the frequency difference we find can be understood ( as argued by carollo et al . 2012 ) as the result of a change in the dominant population with distance above the plane , from the inner - halo population to the outer - halo population . carollo et al . further argued that the inner halo is dominated by stars with modest carbon enhancement ( [ c / fe ] @xmath62 ) , while the outer halo has a greater portion of stars with large carbon enhancements ( [ c / fe ] @xmath63 ) , although considerable overlap still exists . they interpreted these results , as well as the increase in the global frequency of cemp stars with distance from the galactic plane , as evidence for the possible presence of additional astrophysical sources of carbon , beyond agb production alone , associated with the progenitors of the outer - halo stars . it is difficult to separate cemp-@xmath15 and cemp - no stars from our medium - resolution sdss / segue spectra , but determination of the ratio of cemp-@xmath15/cemp - no for stars in the inner- and outer - halo populations , based on high - resolution spectroscopy , will provide not only very strong constraints on the binary - synthesis model , but clues to the origin of the different cemp frequencies between the inner- and outer - halo populations . above we have compared the derived cemp frequencies from our sample of giants with the predicted cemp frequencies from agb binary - synthesis models by suda et al . however , as previously mentioned , observations suggest that a giant can suffer from dilution of the carbon - rich material in its envelope by mixing during the first dredge - up event , resulting in a lower overall carbon abundance and ( as a population ) lower frequencies of cemp stars . absent such dilution , we would expect that the actual frequencies of cemp stars among giants would be higher than shown in figure [ fig : cempcom ] . stars near the main - sequence turnoff region do not experience dredge - up episodes ; rather , they preserve unpolluted material on their surfaces . it might be possible that their surface abundances could be affected by atomic diffusion , but because the impact on the carbon abundance is not well known , we do not take this concern into consideration in this study . thus , we expect that one could obtain a more valid estimate of the frequencies of cemp stars in a given population by making this evaluation using main - sequence turnoff stars . since turnoff stars evolve quickly into giants during their evolution , we might expect that the frequencies of cemp stars inferred from stars near the main - sequence turnoff should be the same as for giants that have not yet mixed carbon - depleted material into their envelopes . therefore , it is desirable to compare the predictions from the models to the frequencies of cemp stars derived from the turnoff stars . however , additional complications exist . the stars located near the main - sequence turnoff are relatively warmer than the red giants , and as a result , for a given carbon abundance , the molecular ch @xmath3-band feature becomes significantly weaker . to make matters more difficult , at low metallicity ( assuming carbon is not enriched ) a star s ch @xmath3-band will also become lower in strength . even with high - resolution spectroscopy aoki et al . ( 2013 ) noted that , although they were able to detect the ch @xmath3-band for a star with [ c / fe ] @xmath64 and [ fe / h ] @xmath65 at @xmath30 @xmath66 k , they failed to measure the ch @xmath3-band for [ c / fe ] @xmath2 in their sample of very metal - poor stars . these effects become even more prevalent for medium - resolution spectra , hence the calculated cemp frequencies obtained from the turnoff stars may also be lower than the actual values . in order to address this difficulty , and to provide a check on just how many c - rich halo stars may have been misclassified as c - normal objects ( [ c / fe ] @xmath67 ) for stars around the turnoff region , we have performed the following experiment . following the prescription by lee et al . ( 2013 ) , we inject artificial noise ( with characteristics similar to that for a typical sdss / segue spectrum ) into the grid of synthetic spectra that are used to estimate [ c / fe ] . the noise - added synthetic spectra have s / n = 40 , 45 , and 50 , which are typical of the quality of the sdss / segue spectra in our study with @xmath59 kpc ( justification for this choice is provided below ) . at each s / n there are 25 different realizations . these spectra are processed through the sspp to determine estimates of [ c / fe ] . with the measured [ c / fe ] in hand , we then derive the cemp frequencies of the spectra , as a function of [ fe / h ] , which have an _ estimated _ [ c / fe ] less than @xmath68 among the spectra with @xmath69 [ c / fe ] @xmath70 for giants , turnoff stars , and dwarf stars ( note that we employ discrete [ c / fe ] values , @xmath71 , and @xmath72 for the synthetic spectra ) . for the purpose of this exercise , we define giants as models with parameters in the ranges 4500 k @xmath33 @xmath30 @xmath33 5500 k and 1.0 @xmath33 @xmath31 @xmath73 , turnoff stars for 5750 k @xmath33 @xmath30 @xmath33 6500 k and 3.5 @xmath33 @xmath31 @xmath74 , and dwarfs for 4500 k @xmath33 @xmath30 @xmath33 5500 k and 4.5 @xmath33 @xmath31 @xmath75 . figure [ fig : corfun ] shows the results of this experiment . the plus signs represent the actual frequencies of cemp stars , which are set to 1.0 . the green squares indicate giants , the red circles the turnoff stars , and the blue triangles the dwarfs . the bottom plot exhibits the residuals in the derived fractions ( simply 1 the fractions ) in each category . inspection of this figure reveals that some of the c - rich dwarfs and giants start to be classified as c - normal ( [ c / fe ] @xmath76 ) from around [ fe / h ] @xmath12 ; the number of the misclassified stars slowly increases with decreasing metallicity . by way of comparison , the c - rich turnoff stars begin to be misclassified as c - normal stars as metallicity drops below [ fe / h ] = @xmath77 ; this misclassification rapidly increases with declining metallicity , as expected . we now derive a correction function for capturing the `` true '' cemp frequency , as a function of [ fe / h ] , for the sdss / segue turnoff stars , based on the results of the test carried out above . we then use this correction function to adjust the frequency calculation , among the stars with @xmath78 [ c / fe ] @xmath2 , taking the `` missing '' c - rich stars into account . since the giants are more luminous than the turnoff stars , they can probe to greater distances in the galaxy . this increases the likelihood of introducing a greater number of giants than turnoff stars into a magnitude - limited sample ( the frequency of giants can also be influenced by the luminosity function of the halo field stars , as well as by shifts in the mix of stellar populations between the nearby and more distant halo stars ) . this possible population transition has already been noted in figure [ fig : cempcom ] , and discussed in detail in the previous section . thus , in order to make sure we are sampling the giants and turnoff stars in similar regions of the galaxy , we restrict our considerations to the stars with @xmath59 kpc for the calculation of the cemp frequencies . figure [ fig : cempcor ] shows the differential frequencies of c - rich stars for main - sequence turnoff stars , as a function of [ fe / h ] , as red open triangles ; the corrected frequencies are indicated as green filled triangles . the blue open circles represent the predicted turnoff cemp frequencies from an agb binary - synthesis model with an imf peaked at 10 @xmath0 , while the magenta open squares indicates the prediction obtained using a salpeter imf . for comparison , the filled black circles are the frequencies from the giants with @xmath60 5 kpc given in figure [ fig : cempcom ] . the behavior seen in this figure is consistent with our expectations , in that the cemp frequencies for the giants are lower than that for the turnoff sample , at least at the lowest metallicities . note that the corrected cemp frequencies for the turnoff stars are , on average , higher than the uncorrected frequencies , by about 5% . the figure also shows that the models produce higher cemp frequencies for the turnoff stars than for the giants for both imfs ( compare with figure [ fig : cempcom ] ) , which at least qualitatively agrees with the observations . the small difference in the model - predicted cemp frequencies between the giants and turnoff stars ( figures [ fig : cempcom ] and [ fig : cempcor ] ) may arise from the difference in the mass of the convective envelope ; a star that evolves to the giant stage has a much deeper convective zone , and hence more effective dilution , resulting in lower cemp frequencies derived for the giants . our derived cemp frequencies from the distance - restricted turnoff sample appears to be in good agreement with the model prediction based on a salpeter imf ( magenta open squares ) , down to [ fe / h ] = @xmath42 . this reaffirms that the agb model for progenitor stars in the low - mass range works well . however , the model estimate of the cemp frequency does not reproduce the observed frequencies for [ fe / h ] @xmath23 . unlike the case for the giants ( figure [ fig : cempcom ] ) , the observed cemp frequencies from our turnoff sample do not agree with the model estimation from the top - heavy imf for [ fe / h ] @xmath23 at all , as these remain roughly flat instead of growing dramatically with decreasing metallicity . one reason for the large discrepancy between the model estimates and the observed frequencies of cemp stars may be uncertainties of the model parameters adopted for producing carbon in the agb star , and subsequent processes that enrich ( or deplete ) the envelope with carbon . below we discuss known sources of uncertainty associated with the agb binary - synthesis model , which may result in changes of the predicted carbon abundance of the secondary star . most agb stars in the mass range of @xmath5118 @xmath0 can produce carbon , but whether or not they develop carbon - enriched envelopes depends on the efficiency of the third dredge - up ( tdu ) and helium - flash driven deep mixing ( he - fddm ; fujimoto et al . 1990 , 2000 ) events for [ fe / h ] @xmath23 . at present , it is not fully understand how such episodes depend on the mass and metallicity of an agb star . for example , lau et al . ( 2009 ) claimed , in a study of the evolution of agb stars with metallicity between z = 10@xmath79 and 10@xmath80 , that the he - fddm did not take place for z @xmath81 independent of the mass of a star , and that this event did not occur for a star with @xmath82 @xmath0 , regardless of its metallicity . however , suda & fujimoto ( 2010 ) found , from an extensive set of stellar evolution models , that the he - fddm event occurred for a star with @xmath83 @xmath0 for zero metallicity , while it occurred for a star with @xmath84 @xmath0 for @xmath85 [ fe / h ] @xmath86 . they also found that the tdu episode was restricted to a mass range of @xmath87 1.55 @xmath0 for [ fe / h ] = @xmath88 , and that this mass range becomes smaller as the metallicity decreases . in the adopted models from suda et al . ( 2013 ) , the increasing fractions of cemp stars comes from the he - fddm , which can enhance the surface carbon abundance by a factor of 10 , from [ c / h ] @xmath54 to @xmath89 , regardless of the initial metallicity of the models , for stars with masses of 0.83 @xmath0 . in this view , the value of [ c / fe ] for the secondary component ( the presently observed cemp star ) of a given binary increases with decreasing [ fe / h ] , so that a larger fraction of cemp stars can be achieved at lower metallicity . it is also assumed that the efficiency of the binary mass transfer and the mass - loss rates do not depend on metallicity . in addition , among these agb stars , the intermediate - mass ( @xmath5138 @xmath0 ) objects can be enriched with nitrogen by operation of the hot - bottom burning ( hbb ) process , which converts carbon into nitrogen by cn processing , and predicts the production of nemp stars ( johnson et al . however , the dependency of the hbb on the mass and metallicity of an agb star is yet not well - established . even taking into account the uncertainties in the parameters of the agb models , a more plausible interpretation of our results may be the existence of additional ( non - agb ) carbon - production mechanisms , as discussed in the introduction , which result in large frequencies of cemp stars in the metallicity regime [ fe / h ] @xmath7 . the current observations certainly favor this interpretation , since most cemp - no stars in the galaxy appear at [ fe / h ] @xmath40 , and these stars do not commonly exhibit the radial velocity variations that would be expected if membership in a binary system were required ( as in the agb mass - transfer scenario ) . the adopted models , however , assume that all cemp - no stars form from the agb binary mass - transfer scenario , rather than including additional sources that have been argued are likely to be present in the early universe . according to the agb models , low - mass ( @xmath90 @xmath0 ) agb stars efficiently create @xmath15-process elements by generating extra neutrons via the @xmath49c(@xmath91,n)@xmath92o reaction , while a weak @xmath15-process ( for light @xmath15-process elements ) operates by @xmath93ne(@xmath91,n)@xmath94 mg for the intermediate - mass stars . cemp - no stars could form in the agb mass - transfer scenario by suppressing the formation of the @xmath49c pocket for intermediate mass stars ( @xmath95 @xmath0 ; suda et al . thus , in order to preferentially produce cemp - no stars at low metallicity and maintain the observed ratio of cemp - no/(cemp-@xmath15 @xmath96 cemp - no ) , which is close to 0.5 at [ fe / h ] @xmath65 ( from table 1 of suda et al . 2013 ) , the models have to assume that the @xmath49c pocket does not form in stars with metallicity significantly below [ fe / h ] = @xmath42 . it has also been suggested ( komiya et al . 2007 ) that a secondary star with an agb primary having 0.8 @xmath0 @xmath97 @xmath0 could become a cemp-@xmath15 star following mass transfer , while systems that include an agb primary with @xmath95 @xmath0 could produce c without the enhancement of neutron - capture elements , leading to a cemp - no star following mass transfer . however , current agb models do not satisfactorily explain the absence of the @xmath49c pocket at low metallicities , even though this assumption has been invoked to explain the observed decreasing trend of [ pb / ba ] for cemp stars with [ fe / h ] @xmath23 ( aoki et al . 2002 ; suda et al . 2004 ; barbuy et al . 2005 ; cohen et al . 2006 ; aoki et al . it is also significant that ito et al . ( 2013 ) obtained a rather low upper limit on the abundance of lead ( log @xmath98(pb ) @xmath99 ) for the [ fe / h ] @xmath100 cemp - no star bd@xmath9644@xmath101493 , while previous predictions called for log @xmath98(pb ) @xmath102 at these low metallicities if the lead were produced by the @xmath15-process ( cohen et al . 2006 ) . chemical abundances of cemp - no stars observed with high - resolution spectroscopy ( e.g. , ito et al . 2009 , 2013 ; norris et al . 2013 ) support other scenarios for significant carbon production . their abundance patterns are similar to the predictions from massive , rapidly rotating , mmp stars ( meynet et al . 2006 , 2010 ) or faint sne that experience mixing and fallback ( umeda & nomoto 2003 , 2005 ; tominaga et al.2007 , 2013 ; kobayashi et al . 2011 ; ito et al . 2013 ; nomoto et al . if such mechanisms are the dominant sources of the large amounts of carbon produced at low metallicity , these scenarios also favor an imf that preferentially produces massive stars . in fact , one might also expect a rather abrupt `` break '' in the cemp frequencies when the primary carbon sources change in nature such a sudden change can be seen for the turnoff stars in figure [ fig : cempcor ] below [ fe / h ] @xmath8 . although we are not able to distinguish cemp - no stars from cemp-@xmath15 stars in our sample , given that the majority of the cemp - no stars are found with [ fe / h ] @xmath40 , our derived frequencies imply that non - agb related phenomenon may be the dominant mechanisms for producing large carbon abundances at extremely low [ fe / h ] . finally , we see that a similar behavior in the cemp frequencies with [ fe / h ] applies to the turnoff stars with @xmath103 [ fe / h ] @xmath104 as for the giants , suggesting that the proposed shift in an imf occurred over this chemical interval .

previous observations suggest that the carbon abundances of red giants are altered during red - giant branch evolution due to mixing of their convective outer layers , resulting in a reduction of the observed carbon - abundance ratios . these comparisons indicate good agreement between the observed cemp frequencies for stars with [ fe / h ] and a salpeter imf , but not with an imf having a higher characteristic mass . our results imply that the imf shifted from high- to low - mass dominated in the early history of the milky way , which appears to have occurred at a `` chemical time '' between [ fe / h ] and [ fe / h ] . the corrected cemp frequency for the turnoff stars with [ fe / h ] is much higher than the agb model prediction from the high - mass imf , supporting the previous assertion that one or more additional mechanisms , not associated with agb stars , are required for the production of carbon - rich material below [ fe / h ] .

we present a comparison of the frequencies of carbon - enhanced metal - poor ( cemp ) giant and main - sequence turnoff stars , selected from the sloan digital sky survey ( sdss ) and the sloan extension for galactic understanding and exploration ( segue ) , with predictions from asymptotic giant - branch ( agb ) mass - transfer models . we consider two initial mass functions ( imfs)a salpeter imf , and a mass function with a characteristic mass of 10 . previous observations suggest that the carbon abundances of red giants are altered during red - giant branch evolution due to mixing of their convective outer layers , resulting in a reduction of the observed carbon - abundance ratios . thus , in order to derive more accurate estimates of cemp frequencies for stars in the milky way , it is preferable to make use of sdss / segue main - sequence turnoff stars , which are not expected to experience significant dilution . however , because of the difficulty of identifying moderately carbon - enhanced stars ( [ c / fe ] ) among warm , metal - poor turnoff stars , owing to their much weaker ch-bands , we derive a correction function to compensate for the resulting undercounts of cemp stars . these comparisons indicate good agreement between the observed cemp frequencies for stars with [ fe / h ] and a salpeter imf , but not with an imf having a higher characteristic mass . thus , while the adopted agb model works well for low - mass progenitor stars , it does not do so for high - mass progenitors . our results imply that the imf shifted from high- to low - mass dominated in the early history of the milky way , which appears to have occurred at a `` chemical time '' between [ fe / h ] and [ fe / h ] . the corrected cemp frequency for the turnoff stars with [ fe / h ] is much higher than the agb model prediction from the high - mass imf , supporting the previous assertion that one or more additional mechanisms , not associated with agb stars , are required for the production of carbon - rich material below [ fe / h ] .

1310.3277

c

we have compared our derived cemp frequencies from the sdss / segue giant sample with that predicted by agb binary - synthesis models with two different imfs a salpeter imf , and an imf with a characteristic mass of 10 @xmath0 . good agreement of the cemp frequencies for [ fe / h ] @xmath50 with the salpeter imf indicates that the adopted agb model works well for low - mass progenitor stars . qualitatively , better agreement with an imf biased to higher - mass progenitors is found for [ fe / h ] @xmath47 , suggesting that the nature of the imf shifted from one that is high - mass dominated in the early history of the milky way galaxy , to one that is now low - mass dominated . this transition appears to have occurred , in `` chemical time '' , between [ fe / h ] @xmath5 and [ fe / h ] @xmath6 , as other recent studies have argued ( e.g. , suda et al . 2011 , 2013 ; yamada et al . 2013 ) . as noted by other recent work , the more distant halo giants ( those with @xmath58 @xmath105 kpc ) exhibit higher frequencies of cemp stars compared to those closer to the galactic plane . a plausible explanation for this difference is the expected change of the dominant stellar populations from the inner - halo to the outer - halo population , coupled with the assumption that the outer - halo stars are associated with progenitors capable of producing large amounts of carbon without the accompanying production of heavy metals . thus , one might expect that the inner - halo population harbors a higher ratio of cemp-@xmath15/cemp - no stars , while the opposite may apply to the outer - halo population . tests of this hypothesis are underway ( d. carollo et al . , in preparation ) . the weak ch @xmath3-bands for moderately carbon - enhanced stars ( @xmath1 [ c / fe ] @xmath2 ) among warm , metal - poor main - sequence turnoff stars results in their likely having been undercounted by previous assessments of cemp frequencies . we have derived a correction function to compensate for this , making use of noise - added synthetic spectra . the corrected cemp frequencies for turnoff stars are , on average , higher by @xmath106% than with the uncorrected frequencies . both the corrected and uncorrected cemp frequencies derived from the turnoff sample exceed those of the giants for [ fe / h ] @xmath7 . we have made use of main - sequence turnoff stars with @xmath59 kpc to compute more realistic cemp frequencies than obtained by using giants ( or the combination of giants with other classes ) , corrected as mentioned above . for [ fe / h ] @xmath107 , our corrected cemp frequencies agree with the model predictions based on a salpeter imf , indicating that the agb model used in this study is probably not far from reality , at least as applied to low - mass stellar progenitors . however , unlike the case for the giant sample , the top - heavy imf model does not reproduce the observed trend of the cemp frequencies for the turnoff stars at all . the combination of these results from the giant and turnoff samples suggests that the current agb binary - synthesis model may not be suitable for creating carbon - enhanced envelopes for intermediate- to high - mass stars ( 38 @xmath0 ) . as the agb binary - synthesis model ( using a salpeter imf or a top - heavy imf ) predict far too low frequencies of cemp stars for our turnoff sample , there likely exists one or more additional mechanisms capable of producing carbon - rich stars below [ fe / h ] = @xmath88 , the metallicity regime where the cemp - no stars dominate over the subclass of cemp-@xmath15 stars . funding for sdss - iii has been provided by the alfred p. sloan foundation , the participating institutions , the national science foundation , and the u.s . department of energy office of science . the sdss - iii web site is http://www.sdss3.org/. sdss - iii is managed by the astrophysical research consortium for the participating institutions of the sdss - iii collaboration including the university of arizona , the brazilian participation group , brookhaven national laboratory , university of cambridge , carnegie mellon university , university of florida , the french participation group , the german participation group , harvard university , the instituto de astrofisica de canarias , the michigan state / notre dame / jina participation group , johns hopkins university , lawrence berkeley national laboratory , max planck institute for astrophysics , max planck institute for extraterrestrial physics , new mexico state university , new york university , ohio state university , pennsylvania state university , university of portsmouth , princeton university , the spanish participation group , university of tokyo , university of utah , vanderbilt university , university of virginia , university of washington , and yale university . y.s.l . is a tombaugh fellow . t.s . was supported by the jsps grants - in - aid for scientific research ( 23224004 ) . this work was supported in part by grant phy 08 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we consider two initial mass functions ( imfs)a salpeter imf , and a mass function with a characteristic mass of 10 . however , because of the difficulty of identifying moderately carbon - enhanced stars ( [ c / fe ] ) among warm , metal - poor turnoff stars , owing to their much weaker ch-bands , we derive a correction function to compensate for the resulting undercounts of cemp stars . thus , while the adopted agb model works well for low - mass progenitor stars , it does not do so for high - mass progenitors .

we present a comparison of the frequencies of carbon - enhanced metal - poor ( cemp ) giant and main - sequence turnoff stars , selected from the sloan digital sky survey ( sdss ) and the sloan extension for galactic understanding and exploration ( segue ) , with predictions from asymptotic giant - branch ( agb ) mass - transfer models . we consider two initial mass functions ( imfs)a salpeter imf , and a mass function with a characteristic mass of 10 . previous observations suggest that the carbon abundances of red giants are altered during red - giant branch evolution due to mixing of their convective outer layers , resulting in a reduction of the observed carbon - abundance ratios . thus , in order to derive more accurate estimates of cemp frequencies for stars in the milky way , it is preferable to make use of sdss / segue main - sequence turnoff stars , which are not expected to experience significant dilution . however , because of the difficulty of identifying moderately carbon - enhanced stars ( [ c / fe ] ) among warm , metal - poor turnoff stars , owing to their much weaker ch-bands , we derive a correction function to compensate for the resulting undercounts of cemp stars . these comparisons indicate good agreement between the observed cemp frequencies for stars with [ fe / h ] and a salpeter imf , but not with an imf having a higher characteristic mass . thus , while the adopted agb model works well for low - mass progenitor stars , it does not do so for high - mass progenitors . our results imply that the imf shifted from high- to low - mass dominated in the early history of the milky way , which appears to have occurred at a `` chemical time '' between [ fe / h ] and [ fe / h ] . the corrected cemp frequency for the turnoff stars with [ fe / h ] is much higher than the agb model prediction from the high - mass imf , supporting the previous assertion that one or more additional mechanisms , not associated with agb stars , are required for the production of carbon - rich material below [ fe / h ] .

1505.04495

m

variability features can be divided into two broad categories : periodic and non - periodic feature . the former is easier to detect and model using statistical and model - specific fitting procedures as a form of fourier series ( e.g. , @xcite ) . but the latter is rather ambiguous , since it is not always possible to characterize flux variation and to define a reliable range for some parameters . to overcome this difficulty , @xcite calculated many basic statistics that can describe the distribution of fluxes even in the limit of few data points . one interesting approach is to select stochastically varying features in quasar - like sources . the correlated variability of quasars is well parameterized by a damped random walk model , providing a simple statistical description of their characteristic timescales and amplitudes ( e.g. , @xcite ) . in this work we use a modified version of the fast @xmath0 periodogram algorithm ( f@xmath0 ) and the change - point analysis ( cpa ) method for detecting and assessing the significance of periodic and non - periodic signals , respectively . we first searched a periodic feature by f@xmath0 technique that calculates the minimized @xmath0 as a function of frequency at the desired number of harmonics @xcite . with the best - fit frequency , we compared the ratio between the variance of the data after subtracting the best - fit model and full - amplitude of model function . this algorithm use a fourier series truncated at harmonic @xmath23 as a model function : @xmath24 the fitting coefficients ( @xmath25 , @xmath26 , and @xmath27 ) obtained in each harmonic model provide a reasonable description of a generic periodic feature , irrespective of the feature shape , as discussed by @xcite . figure [ fig2 ] shows example light curves of both periodic ( new variable star ; v1983 ) and long - term ( v1092 ) variable stars in our sample , respectively . because the optimal choice of @xmath23 depends on the true shape of the signal , the fit quality is evaluated for each model with standard @xmath0 statistics , and then checked the residual ( phase - folded ) light curves after the subtraction of the best - fit model . to test the significance of a signal , we use the ratio between the full - amplitude of the model function ( @xmath28 = @xmath29 ) and the rms scatter ( @xmath30 ) of the data after model subtraction : @xmath31 the lower limit for the ratio is empirically set to @xmath32 = 0.95 based on light curve inspections . @xmath32-values less than 0.95 indicate that we do not expect any significant ( semi- ) periodic signals for a given light curve . even when the source is poorly described by the harmonic fit , this indicator provides a hint of a generic periodic signal ( see right panel of figure [ fig2 ] ) . most variability detection methods require conventional models that are mainly focused on the periodic signals , and are not suitable for the study of arbitrary - shaped , non - periodic , and sporadic variations . also , in many cases , signal estimation is equated with smoothing of data for de - noising . this sometimes discards vital information in time series data . we introduce a non - parametric method to extract all significant features based on the cpa using local statistics . change - point analysis is a method to identify abrupt variations in sequential data . it is widely used in the statistics and data mining communities as well as in the field of time domain astronomy ( see e.g. , @xcite and reference therein ) . using a combination of cumulative sum scheme ( cusum ) and bootstrap rank statistics @xcite , we produce a series of estimated change - points which correspond to the moments of apparent systematic changes . for a given dataset \{@xmath33 , @xmath34 , @xmath35 , @xmath36 } of size @xmath37 , the cusum values are given by @xmath38 for @xmath39 = @xmath40 , where @xmath41 = 0 and the mean value @xmath42 for the sample of @xmath37 values of @xmath43 . an inflection point at which the sign of the cusum slope changes is used to determine whether a given interval of data should be kept as one ( @xmath44=@xmath45=@xmath35=@xmath46=@xmath42 ) or subdivided into two subintervals ( @xmath44=@xmath35=@xmath47@xmath48@xmath49=@xmath46 ) . based on @xmath50 bootstrap samples that are randomly re - ordered original values , we estimate the confidence level ( c.l . ) to reduce the false positives by random noise . here are the main procedure of each bootstrap process : * we generate a bootstrap sample of @xmath37 dataset , denoted \{@xmath51 , @xmath52 , @xmath35 , @xmath53 } , by randomly re - ordering the original @xmath37 values without replacement . * based on the bootstrap dataset , we calculate the bootstrap cusum @xmath54 by using equation ( 4 ) , and then obtain the maximum , minimum , and difference of the bootstrap cusum . @xmath55 where @xmath56 @xmath57 * we check whether the bootstrap difference @xmath58 is less than the original difference @xmath59 . it is straightforward to derive estimates of confidence level as follows : @xmath60 where @xmath61 typically more than 90% confidence level is suitable for most cases . when a sudden change is detected , the location of change - point is initially determined as follow : @xmath62 } \left|s_{t}\right|,\ ] ] where @xmath63 denotes the last point before the change occurred . the time - series data is split into two segments on each side of the change point , and the analysis is repeated for each segment until no more significant change point is detected . once this set is generated , all the change - point locations and their confidence levels are re - estimated in a backward elimination manner . using only the sample in the segment bounded by adjacent change - points , we re - calculate these parameters detected by the forward procedure to obtain more accurate estimations . when any initial change - point fails the criteria in the backward procedure , we eliminate this change - point estimate . this process repeats until no further improvement is possible . the final change points thus define the segments ( i.e. , piecewise constant level sets ) , characterized by the start and end time of a given interval with its mean and variance . after this procedure , signal detection process is performed for each segment separately . to detect significant outlying features occurring at specific levels in light curve , we adopt a simple criteria similar to micro - lensing alert system @xcite in the presence of hetero - scedastic measurement errors ( @xmath64 ) : @xmath65 @xmath66 @xmath67 @xmath68 where the mean @xmath69 and deviation @xmath70 are the local statistics for a given segment , @xmath64 is the photometric error at epoch @xmath71 , and @xmath72 is the number of consecutive points which satisfy the equations ( 8a8c ) . the different combination of @xmath73 values are used for maximize the detection efficiency of significant outlying features . the values of @xmath73 were taken to be at least larger than 3 , 1 , and 3 , respectively . as a result , statistically significant events were flagged as candidate flare sources if at least three contiguous points satisfy the above criteria . example of flare - like feature detection is shown in the left panel of figure [ fig3 ] . by applying the cpa method to the entire light curves , we efficiently identified several hundred instances of abrupt brightness changes without any smoothing or interpolation of the raw data . we use the same limits of cpa thresholds to find eclipsing - like event detection , except the first term of equation ( 8) , i.e. , @xmath74 . the cpa method is useful to detect the moments of eclipse ingress , center , or egress in cases where the eclipsing pattern is not repeated or the coverage is not sufficient for the detection through conventional period analysis ( e.g. , box - fitting least - squares method ) . example of eclipsing - like feature detection is shown in the right panel of figure [ fig3 ] . we will discuss this issue further in section 5.1 . for periodicity , we first used the vartools light curve analysis program to determine likely periods of variable stars . this code computes three different periodograms for the light curves;(i ) lomb - scargle ( ls : @xcite ) , ( ii ) analysis of variance ( aov : @xcite ) , and ( iii ) box - fitting least - squares ( bls : @xcite ) algorithms . because each method is sensitive to different types of periodic variables , it is often useful to combine results from many different analysis of periodicity . basically we adopt the similar treatment as in @xcite . we limited the search range of these algorithms to periods between 0.01 and 30 days with relatively fine frequency resolution of less than 0.01/@xmath75 ( @xmath75 is the time - span of the light curve ) . we also obtained period estimates from the statistical technique sigspec @xcite . it calculates the spectral significance ( sig ) levels based on the analytical solution for discrete fourier transform amplitude spectrum , including dependencies on frequency and phase . in recent years , this package is mainly used in the study of stellar pulsation ( i.e. , asteroseismology ) , which shows up as small , periodic variations in the brightness of the stars ( e.g. , @xcite ) . in order to further crosscheck results of periodicity analysis , we also performed a multi - step period search algorithm msperiod @xcite . figure [ fig4 ] shows examples of three selected light curves ; power spectrum and phased diagram corresponding to the highest peak . the differences in the various algorithms depend strongly on the shape of variation . one case ( v2256 ) shows that all periods are essentially identical ( @xmath76 0.0784 days ) , while in the other cases the derived period differ a lot . visual inspections are necessary for v2173 and v1482 to choose the most plausible periods ; @xmath77 and 2.595 respectively .

the intent of this work is to examine the entire sample of over 30,000 objects for periodic , aperiodic , and sporadic behaviors in their light curves . we show a modified version of the fast periodogram algorithm ( f ) and change - point analysis ( cpa ) as tools for detecting and assessing the significance of periodic and non - periodic variations . moreover , 30 of the previously identified variables are found to be false positives resulting from time - dependent systematic effects .

we present a comprehensive re - analysis of stellar photometric variability in the field of the open cluster m37 following the application of a new photometry and de - trending method to mmt / megacam image archive . this new analysis allows a rare opportunity to explore photometric variability over a broad range of time - scales , from minutes to a month . the intent of this work is to examine the entire sample of over 30,000 objects for periodic , aperiodic , and sporadic behaviors in their light curves . we show a modified version of the fast periodogram algorithm ( f ) and change - point analysis ( cpa ) as tools for detecting and assessing the significance of periodic and non - periodic variations . the benefits of our new photometry and analysis methods are evident . a total of 2306 stars exhibit convincing variations that are induced by flares , pulsations , eclipses , starspots , and unknown causes in some cases . this represents a 60% increase in the number of variables known in this field . moreover , 30 of the previously identified variables are found to be false positives resulting from time - dependent systematic effects . new catalog includes 61 eclipsing binary systems , 92 multiperiodic variable stars , 132 aperiodic variables , and 436 flare stars , as well as several hundreds of rotating variables . based on extended and improved catalog of variables , we investigate the basic properties ( e.g. , period , amplitude , type ) of all variables . the catalog can be accessed through the web interface ( http://stardb.yonsei.ac.kr/ ) .

1505.04495

c

we cataloged and investigated a variety of photometric variables in the field of m37 using our new light curves , which were obtained from archival imaging data of one - month long exo - planet transit survey with the 6.5-m mmt telescope . this new dataset allows a rare opportunity to explore different types of variability of short ( @xmath12minutes ) and long ( @xmath12one - month ) time - scales simultaneously . we find 61 eclipsing binary systems ( eb ) , 92 multiperiodic variable stars ( mp ) , 132 aperiodic variables ( a ) , and 436 flare stars ( f ) , as well as several hundreds of rotating variables ( r ) . our work has increased the number of known variable stars in this field by 60% . the new variable catalog has been made available on the web ( http://stardb.yonsei.ac.kr/ ) . we would like to thank the anonymous referee for helpful suggestion . this research was supported by basic science research program of the national research foundation of korea ( 2011 - 0030875 ) . i.b . acknowledges the support from kasi - yonsei drc program of korea research council of fundamental science and technology ( drc-12 - 2-kasi ) . benk , j. m. , kolenberg , k. , szab , r. , et al . 2010 , , 409 , 1585 benzm , a. o. & gdel , m. 2010 , , 48 , 241 breger , m. , stich , j. , garrido , r. , et al . 1993 , , 271 , 482 butler , n. r. & bloom , j. s. 2011 , , 141 , 93 chang , s .- w . , byun , y .- i . , & hartman , j. d. 2015 , , 149 , 135 ( paper i ) ciardi , d. r. , braun , k. v. , bryden , g. , et al . 2011 , , 141 , 108 covey , k. r. , ivezi , . , schlegel , d. , et al . 2007 , , 134 , 2398 cutri , r. m. , skrutskie , m. f. , van dyk , s. , et al . 2003 , the irsa 2mass all - sky point source catalog , nasa / ipac infrared science archive , http://irsa.ipac.caltech.edu/applications/gator/ debosscher , j. , sarro , l. m. , aert , c. , et al . 2007 , , 475 , 1159 debosscher , j. , sarro , l. m. , lpez , m. , et al . 2009 , , 506 , 519 devor , j. 2005 , , 628 , 411 eyer , l. & mowlavi , n. 2008 , j. phys . ser . , 118 , 012010 girardi , l. , grebel , e. k. , odenkirchen , m. , & chiosi , c. 2004 , , 422 , 205 girardi , l. , groenewegen , m. a. t. , hatziminaoglou , e. , & da costa , l. 2005 , , 436 , 895 glicenstein , j. -f . 2001 , in asp conf . 239 , microlensing 2000 : a new era of microlensing astrophysics , ed . j. w. menzies & penny d. sackett . 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( new york : cambridge university press ) reegen , p. 2007 , , 467 , 1353 samus , n. n. , durlevich , o. v. , kazarovets , e. v. , et al . 2009 , vizier online data catalog : b / gcvs , 1 , 2025 scargle , j. d. 1982 , , 263 , 835 schtz , n. & holschneider , m. 2011 , , 84 , 021120 schwarzenberg - czerny , a. 1989 , , 241 , 153 shin , m .- s . & byun , y .- 2004 , jkas , 37 , 79 taylor , w. 2000 , in change - point analyzer 2.0 shareware program , taylor enterprises , libertyville , illinois . , http://www.variation.com/cpa ccrrrrrrrrrrrrc & 055220.39 + 323319.65 & & & & 13.677 & 0.285 & 0.191 & & 13.406 & 0.609 & 12.447 & 0.270 & 0.063 & eb + & 055216.58 + 322815.32 & & & 16.792 & 14.840 & 0.564 & 0.290 & 14.471 & 14.653 & 0.688 & 13.539 & 0.287 & 0.134 & eb + & 055233.01 + 323241.91 & 0.4225 & 0.320 & 17.982 & 15.789 & 0.560 & 0.329 & 15.284 & 16.051 & 0.728 & 14.267 & 0.355 & 0.012 & eb + & 055253.26 + 323301.47 & 0.5582 & 0.235 & 18.079 & 15.634 & 0.762 & 0.477 & 15.093 & 15.948 & 0.938 & 13.951 & 0.497 & 0.101 & eb + & 055300.63 + 322450.81 & 0.2788 & 0.310 & 18.036 & 15.915 & 0.459 & 0.481 & 15.235 & 16.184 & 0.585 & 14.421 & 0.359 & 0.084 & mp + & 055150.53 + 323234.70 & 0.1098 & 0.343 & 18.218 & 15.973 & 0.591 & 0.173 & 15.622 & & & 14.739 & 0.342 & -0.009 & mp + & 055239.09 + 323631.27 & 0.3577 & 0.433 & 19.858 & 17.252 & 1.039 & 0.056 & 17.065 & 17.890 & 0.815 & 15.779 & 0.446 & 0.196 & eb + & 055234.32 + 323218.70 & 0.1195 & & & & & & & & & & & & u + & 055214.91 + 322441.35 & 0.0909 & & 14.873 & 13.233 & 0.137 & 0.128 & 13.114 & 13.298 & 0.370 & 12.348 & 0.171 & 0.042 & p + & 055200.49 + 323648.19 & 0.9432 & 0.075 & 16.844 & 14.151 & 0.928 & 0.436 & 13.493 & 14.762 & 0.531 & 12.356 & 0.567 & 0.131 & p + rccrrcrrrl 1 & & 055616.79 + 322514.20 & 15.915 & 3.5872 & f@xmath121 & 310.1 & 0.3331 & 68.9 & + & & & & 7.1768 & f@xmath122(=2f@xmath121 ) & 35.4 & 0.2906 & 11.3 & + & & & & 10.7619 & f@xmath123(=3f@xmath121 ) & 22.8 & 0.0418 & 10.3 & + & & & & 5.6768 & f@xmath124 & 19.5 & 0.2369 & 5.7 & + & & & & 14.3473 & f@xmath125 & 13.8 & 0.9990 & 7.1 & + 2 & & 055506.89 + 323303.20 & 15.973 & 9.1040 & f@xmath121(=f@xmath123-f@xmath122 ) & 343.4 & 0.5433 & 172.7 & + & & & & 18.2081 & f@xmath122(=f@xmath123-f@xmath121 ) & 89.9 & 0.2201 & 53.6 & + & & & & 27.3122 & f@xmath123(=f@xmath121+f@xmath122 ) & 27.6 & 0.9237 & 19.7 & + & & & & 8.7545 & f@xmath124 & 15.4 & 0.5801 & 8.1 & + & & & & 11.9319 & f@xmath125 & 14.5 & 0.5557 & 6.3 & + & & & & 36.4178 & f@xmath126(=2f@xmath122 ) & 10.1 & 0.0527 & 10.4 & + & & & & 14.9868 & f@xmath127 & 8.8 & 0.9887 & 4.5 & + & & & & 16.8695 & f@xmath128 & 7.9 & 0.7280 & 4.5 & + 3 & & 055519.81 + 323541.23 & 15.245 & 8.4261 & f@xmath121 & 79.0 & 0.9052 & 84.8 & + & & & & 16.8561 & f@xmath122(=2f@xmath121 ) & 7.6 & 0.6488 & 8.3 & + & & & & 17.7044 & f@xmath123 & 8.0 & 0.5895 & 9.1 & + & & & & 16.4751 & f@xmath124 & 6.9 & 0.5617 & 7.3 & + & & & & 8.8787 & f@xmath125 & 4.9 & 0.4440 & 5.2 & + & & & & 12.0801 & f@xmath126 & 4.8 & 0.8357 & 5.0 & + & & & & 9.2640 & f@xmath127 & 5.9 & 0.6453 & 6.4 & + & & & & 10.6455 & f@xmath128 & 5.4 & 0.0597 & 6.0 & + & & & & 13.5604 & f@xmath129 & 4.8 & 0.8005 & 4.9 & + & & & & 16.2578 & f@xmath130 & 5.1 & 0.6379 & 5.3 & + & & & & 8.0470 & f@xmath131 & 4.5 & 0.8268 & 4.7 & + & & & & 2.3825 & f@xmath132 & 5.2 & 0.7274 & 3.6 & + & & & & 4.3812 & f@xmath133 & 4.3 & 0.3942 & 4.2 & + & & & & 14.9483 & f@xmath134 & 3.9 & 0.8404 & 4.0 & + 4 & & 055600.99 + 323041.25 & 15.873 & 12.7176 & f@xmath121 & 14.4 & 0.0994 & 8.1 & + & & & & 7.8896 & f@xmath122 & 13.8 & 0.4901 & 6.0 & + & & & & 12.7698 & f@xmath123 & 10.5 & 0.0175 & 6.0 & close to f@xmath121 + & & & & 14.4564 & f@xmath124 & 9.6 & 0.0884 & 6.5 & + 5 & & 055527.32 + 322543.01 & 16.511 & 10.0341 & f@xmath121(=f@xmath132-f@xmath122 ) & 23.0 & 0.4259 & 137.9 & + & & & & 10.4706 & f@xmath122(=f@xmath132-f@xmath121 ) & 13.0 & 0.8171 & 77.9 & + & & & & 17.1389 & f@xmath123 & 8.7 & 0.9050 & 51.9 & + & & & & 14.0376 & f@xmath124 & 6.1 & 0.6801 & 33.6 & + & & & & 13.0968 & f@xmath125 & 3.7 & 0.1837 & 20.9 & + & & & & 12.8019 & f@xmath126 & 3.1 & 0.2056 & 17.4 & + & & & & 15.0841 & f@xmath127 & 2.1 & 0.7887 & 11.6 & + & & & & 13.6263 & f@xmath128 & 1.3 & 0.1260 & 7.1 & + & & & & 11.1091 & f@xmath129 & 1.4 & 0.2454 & 8.7 & + & & & & 27.1718 & f@xmath130 & 1.0 & 0.7296 & 6.7 & + rccrrrrrrc 1 & & 055122.14 + 322942.40 & 16.742 & 0.009 & 0.096 & 443.5 & 4730 & + 2 & & 055123.93 + 324357.22 & 15.837 & 0.003 & 0.017 & 14.0 & 4706 & + 3 & & 055124.73 + 324312.36 & 18.360 & 0.004 & 0.028 & 1.8 & 4730 & 13.260 + 4 & & 055125.42 + 323600.45 & 17.564 & 0.002 & 0.017 & 1.6 & 4730 & 21.199 + 5 & & 055127.04 + 323225.57 & 15.458 & 0.002 & 0.010 & 7.7 & 4592 & + 6 & & 055128.19 + 322931.14 & 17.854 & 0.004 & 0.029 & 3.4 & 4730 & + 7 & & 055129.26 + 323235.44 & 18.515 & 0.005 & 0.029 & 1.4 & 4730 & + 8 & & 055130.48 + 324053.05 & 18.348 & 0.005 & 0.033 & 1.9 & 4730 & 7.709 + 9 & & 055131.24 + 323059.61 & 17.688 & 0.008 & 0.046 & 12.9 & 4730 & + 10 & & 055131.87 + 324233.83 & 17.482 & 0.004 & 0.026 & 5.1 & 4730 & + rccrcrrrc 1 & & 055120.47 + 322200.75 & 20.690 & 1 & 53742.40307 & 0.093 & 0.17 & + & & & & 2 & 53742.46247 & 0.135 & 0.08 & + 2 & & 055121.46 + 322856.90 & 19.990 & 1 & 53730.34740 & 0.221 & 0.55 & + & & & & 2 & 53733.19093 & 0.176 & 0.21 & + & & & & 3 & 53735.19767 & 0.039 & 0.49 & + & & & & 4 & 53737.33376 & 0.188 & 0.30 & + 3 & & 055123.45 + 322948.83 & 20.809 & 1 & 53732.22482 & 0.061 & 0.32 & + & & & & 2 & 53732.35513 & 0.133 & 1.11 & + & & & & 3 & 53742.35427 & 0.281 & 0.23 & + 4 & & 055124.44 + 324407.71 & 15.143 & 1 & 53730.32306 & 0.010 & 1.47 & + 5 & & 055124.78 + 323440.56 & 18.368 & 1 & 53728.24480 & 0.026 & 0.17 & + & & & & 2 & 53742.44376 & 0.117 & 0.24 & + & & & & 3 & 53753.25302 & 0.139 & 0.16 & + 6 & & 055124.82 + 322937.32 & 20.017 & 1 & 53726.39533 & 0.046 & 0.10 & var + 7 & & 055125.41 + 323800.03 & 18.086 & 1 & 53726.27563 & 0.041 & 0.58 & var + & & & & 2 & 53727.30272 & 0.025 & 0.46 & + 8 & & 055125.71 + 323106.38 & 20.553 & 1 & 53734.23990 & 0.072 & 0.20 & var + & & & & 2 & 53756.08268 & 0.079 & 0.60 & + 9 & & 055126.78 + 324024.73 & 17.971 & 1 & 53726.43908 & 0.030 & 0.29 & + 10 & & 055127.86 + 322854.79 & 22.181 & 1 & 53727.19210 & 0.360 & 0.58 & var +

we present a comprehensive re - analysis of stellar photometric variability in the field of the open cluster m37 following the application of a new photometry and de - trending method to mmt / megacam image archive . this new analysis allows a rare opportunity to explore photometric variability over a broad range of time - scales , from minutes to a month . this represents a 60% increase in the number of variables known in this field . new catalog includes 61 eclipsing binary systems , 92 multiperiodic variable stars , 132 aperiodic variables , and 436 flare stars , as well as several hundreds of rotating variables . the catalog can be accessed through the web interface ( http://stardb.yonsei.ac.kr/ ) .

we present a comprehensive re - analysis of stellar photometric variability in the field of the open cluster m37 following the application of a new photometry and de - trending method to mmt / megacam image archive . this new analysis allows a rare opportunity to explore photometric variability over a broad range of time - scales , from minutes to a month . the intent of this work is to examine the entire sample of over 30,000 objects for periodic , aperiodic , and sporadic behaviors in their light curves . we show a modified version of the fast periodogram algorithm ( f ) and change - point analysis ( cpa ) as tools for detecting and assessing the significance of periodic and non - periodic variations . the benefits of our new photometry and analysis methods are evident . a total of 2306 stars exhibit convincing variations that are induced by flares , pulsations , eclipses , starspots , and unknown causes in some cases . this represents a 60% increase in the number of variables known in this field . moreover , 30 of the previously identified variables are found to be false positives resulting from time - dependent systematic effects . new catalog includes 61 eclipsing binary systems , 92 multiperiodic variable stars , 132 aperiodic variables , and 436 flare stars , as well as several hundreds of rotating variables . based on extended and improved catalog of variables , we investigate the basic properties ( e.g. , period , amplitude , type ) of all variables . the catalog can be accessed through the web interface ( http://stardb.yonsei.ac.kr/ ) .

1305.2793

r

figure [ mermom]a shows the merlin integrated intensity of the two oh ( 1720 mhz ) masers spots detected toward w51b . the locations of the maser spots with respect to the w51 region is shown in fig . the positions and central velocities are in good agreement with those reported by @xcite from vla observations ( see table [ lines ] ) . the results from fitting a gaussian profile to the maser spectra at the emission peaks are given in table [ lines ] , along with the results from earlier vla observations for reference @xcite . at the resolution of the merlin data ( @xmath50 mas , p.a.=@xmath51 ) the two maser spots remain unresolved . however , maps of the velocity field of the two masers ( see figs . [ mermom]b , and c ) are notably different , with the w51_1 spot showing a moire pattern indicative of no resolved velocity structure ( note the very small width of the displayed velocities ) , while the w51_2 spot shows a clear se - nw velocity gradient with higher velocities to the nw . the fitted merlin peak velocity and fwhm line width is @xmath52 km s@xmath4 and @xmath53 km s@xmath4 for w51_1 , while for w51_2 the fitted values are @xmath54 and @xmath55 km s@xmath4 ( also see table [ lines ] ) . for comparison , at assumed kinetic temperatures of 50 to 125 k , the thermal line width of oh ranges from 0.3 to 0.6 km s@xmath4 . thus , roughly 1/2 to 1/3 of the observed line width can be attributed to thermal motion , with the remaining line width is due to bulk or non - thermal motions . the integrated intensities and velocities ( moment 1 ) of this region as observed with the vlba with a resolution of @xmath56 mas ( @xmath57 ) are shown in figures [ vlbamom ] a , b , c , and d. these results are in excellent agreement with the merlin results w51_1 remains a single , though elongated maser feature with little velocity structure while w51_2 is composed of two distinct maser spots w51_2a , and w51_2b with velocities differing by only @xmath58 km s@xmath4 but with considerable velocity structure . the fitted line parameters from the vlba data are given in table [ lines ] . the fitted fwhm line width for w51_1 is in excellent agreement with that observed with merlin . the combined line width of the two components of w51_2 resolved by the vlba is consistent with the merlin line width of this maser , although the individual vlba line widths of w51_2a and w51_2b are slightly narrower . we also fitted 2-d gaussian components to the merlin and vlba integrated intensity images in order to measure the maser locations , angular sizes , and flux densities . the results are given in table 2 . the masers were unresolved by the vla and so the peak intensity @xmath59 is equivalent to the integrated flux density @xmath60 . interestingly , only about half of the vla a - configuration integrated flux density is recovered by the merlin observations , while the vlba and merlin recover a similar integrated flux density . if these masers are non - time variable , this suggests that merlin and the vlba resolved out about half the total flux density . this suggests that these masers have a `` core - halo '' morphology as seen previously for oh ( 1720 mhz ) , ch@xmath61oh , and h@xmath62o masers ( see for example * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . from the vlba integrated intensity images , the devonvolved fitted sizes of the maser spots are w51_1 : @xmath63 mas ( p.a.@xmath64 ) , w51_2a : @xmath65 mas ( p.a.@xmath66 ) , and w51_2b : @xmath67 mas ( p.a.@xmath68 ) ; with statistical uncertainties of about @xmath69 . for reference , at 6 kpc , 10 mas@xmath70 cm or @xmath71 au using the peak intensities given in table [ lines ] these sizes correspond to peak brightness temperatures of @xmath72 , @xmath73 , and @xmath74 k for w51_1 , w51_2a , and w51_2b , respectively . from the merlin full stokes polarization data , the maser spot w51_1 has a polarized intensity ( @xmath75=sqrt(@xmath76 ) of @xmath77 and a position angle of @xmath78 , while the polarized intensity of w51_2 is @xmath79 at @xmath80 . the uncertainty in the position angles ( @xmath81 ) are dominated by the position angle calibration uncertainty which we estimate to be about @xmath34 . the merlin linear polarization position angles are shown in fig . @xcite reported a polarized intensity of @xmath82 and @xmath83 for w51_2 , but the polarization position angle calibration available for those data were very uncertain . following @xcite , we fit the zeeman magnetic field strength using the thermal zeeman equation @xmath84 @xmath85@xmath86 where @xmath87 is stokes @xmath88 , @xmath89=0.6536 hz @xmath19g@xmath4 , and @xmath86 is the derivative of stokes @xmath90 . the parameter @xmath85@xmath91@xmath92 , is the magnitude of the magnetic field strength times a constant @xmath93 that may depend on the angle @xmath94 between the magnetic field @xmath95 and the line - of - sight . for example , for thermal lines @xmath96 ; the meaning of @xmath93 for the oh ( 1720 mhz ) maser case will be discussed further in 4.3 . figures [ b_mer ] and [ b_vlba ] show the zeeman fits for the merlin and vlba data , respectively . the fitted values of @xmath85 are also listed in table 2 . the signal - to - noise of these fits are outstanding with s / n up to 30 ( merlin for w51_1 ) and s / n=7 ( vlba for w51_1 ) . the observed values of @xmath85 from 1.5 to 2.2 mg are in good agreement with the vla observations of @xcite . for the maser with the simplest velocity structure , w51_1 , the merlin and vlba magnetic field results are in excellent agreement . for w51_2 , which the vlba data reveal is composed of two spots , the merlin value is essentially an intensity weighted average of the two individual vlba results . these data are of sufficient quality that by following @xcite we also independently derived @xmath85 by fitting gaussian components to the left and right circularly polarized profiles independently and determining the line splitting directly , i.e. @xmath85=@xmath97 . for example , for w51_2a the line splitting is @xmath98 km s@xmath4 . this method yielded consistent results with the thermal zeeman equation values listed in table 2 . the 90 cm ( 330 mhz ) images presented in this work ( for example fig [ fig1]a ) are qualitatively similar to the @xmath99 resolution 90 cm image presented by @xcite , but the resolution and sensitivity are significantly improved . figure [ fig1]a shows the vla b+c+d configuration 90 cm image of the w51 region ( resolution @xmath100 , see table 1 ) with the three major components w51a ( hii region complex ) , w51b ( hii region complex ) , and w51c ( snr ) identified . the oh ( 1720 mhz ) masers lie about @xmath101 west of the w51b hii region [email protected] , and are coincident with an unresolved 90 cm source with an angular size of @xmath103 at a position of ( j2000 ) @xmath104 ( see fig . [ fig1]a ) . the w51 region is shown for the first time at a wavelength longer than 2 m in figure [ fig1]b . the vla 400 cm b+c configuration image with a resolution of @xmath105 ( see table 1 ) reveals diffuse , extended non - thermal emission concentrated mostly to the eastern side of the w51c snr , with some diffuse emission also appearing toward the northwestern boundary of the w51c snr . most interesting for the purpose of the current study is the non - thermal 400 cm emission that appears to partially encircle the [email protected] hii region and the discovery of an unresolved 400 cm source coincident with 90 cm emission and the oh ( 1720 mhz ) masers . hereafter , we will call this source of non - thermal emission w51b_nt . it is notable that the area toward the southern portion of the w51b string of hii regions is invisible at 400 cm , consistent with these regions being in the foreground of the w51c snr , and free - free absorbing the 400 cm emission from w51c along this line - of - sight ( see for example * ? ? ? * ; * ? ? ? to aid comparison of the thermal vs non - thermal gas , figures [ big]a , b , shows three - color images constructed from the spitzer glimpse 4.5 and 8 @xmath19 m bands and the vla 90 cm and 400 cm data , respectively . the mid - infrared emission traces thermal ionized gas , as well as emission from dust and pahs @xcite . its morphology matches closely that of the molecular cloud associated with w51b ( see for example * ? ? ? * ; * ? ? ? * ) . the 90 cm emission ( fig . [ big]a ) traces both bright synchrotron ( snr ) emission _ and _ optically thick free - free emission from hii regions . in contrast , the 400 cm emission ( fig . [ big]b ) traces _ only _ synchrotron emission except where it is absorbed by foreground free - free emission . [ big]c and d show the large scale _ rosat _ soft and _ asca _ hard x - ray emission , respectively , first presented by @xcite . soft x - rays trace hot ( @xmath106 kev ) thermal gas from the snr , except where it is absorbed by the intervening total column of atomic and molecular gas . in contrast , the hard x - rays are mostly unaffected by the column of gas along the line of sight and originates from even hotter thermal gas , including a pulsar wind nebula candidate and young stars with fast winds . we detect diffuse 90 cm emission at the location of the pulsar wind nebula candidate cxo j192318.5 + 1403035 from ( * ? ? ? * the location is indicated on figs . [ big]a - d ) , but it is not clear if it arises from a distinct source compared to the overall diffuse snr emission . similar to the 400 cm emission , there is a lack of strong soft x - ray emission toward the southern portions of the w51b hii region complex . in fig . [ big]d we also indicate the region in which strong tev emission was detected by the magic telescope @xcite . a zoomed in view of the 21 cm continuum emission in the vicinity of [email protected] and w51b_nt is shown in figure [ zoom]a at @xmath100 resolution . for comparison , the 400 cm emission and archival soft and hard x - ray emission from _ chandra _ ( see * ? ? ? * ) of the same field are shown in figures [ zoom]b , c , and d. these images show the coincidence of 21 , 90 , and 400 cm emission toward w51b_nt , as well as the presence of a faint hard x - ray source at this position . unfortunately , this emission is too weak to extract a useful spectrum . the nature of the stronger hard x - ray source to the nw of w51b_nt is unknown . after accounting for the background contribution we estimate integrated flux densities for w51b_nt ( defined by the 90 cm 0.15 jy beam@xmath4 contour shown in fig . [ big]a , though it is partially obscured by the maser symbol ) of @xmath6 0.5 , 1.3 , and 0.6 jy at 400 cm , 90 cm , and 21 cm , respectively . the uncertainty of these flux densities are dominated by the background estimate , and are not accurate to better than @xmath107 jy . the low 400 cm flux density is almost certainly a result of free - free absorption along this complex line - of - sight ( see for example * ? ? ? the 21 and 90 cm flux densities imply a non - thermal radio spectral index of @xmath108 ( @xmath109 ) . other groups have searched for possible non - thermal sources in the w51 complex . in particular , @xcite used the bonn 11 cm galactic plane survey ( resolution @xmath110 ) along with iras 60 @xmath19 m images to disentangle the thermal and non - thermal components of w51 . though uncertain with respect to absolute flux densities , their resulting images show the well - known thermal sources in w51a and w51b as well as the non - thermal w51c snr . interestingly , they also see evidence for a non - thermal source west of the g49.2 - 0.3 hii region . more qualitative evidence for the existence of non - thermal emission in the vicinity of w51b_nt was presented by @xcite at 151 mhz with a resolution of @xmath111 with a double source detected near g49.2 - 0.3 with a separation of a few arcminutes ( note that the published declination scale of the 151 mhz image must be displaced to the south by 5 arc min * ? ? ? though suggestive , these early data have too poor an angular resolution to be useful in the current analysis . the jcmt co(32 ) integrated intensity from 40 to 95 km s@xmath4 with a resolution of @xmath112 is shown in figure [ co]a . representative spectra are shown in figs . [ co]b - g ) , and where observed , the @xmath17co(21 ) spectra are also shown ( figs . [ co]d - f ) . from these data we find that co emission partially encircles w51b_nt with the strongest emission along the eastern and southern boundaries . this enhanced co(32 ) emission is coincident with the locations of the oh ( 1720 mhz ) masers which are located towards the se corner of the w51b_nt source ( fig . [ co]e , profile `` nt_oh '' is taken from the maser location ) . the spectra in the w51b_nt region ( figs . [ co]d , e , f ) show at least three components : ( i ) a narrow ( @xmath113 km s@xmath4 ) , but strong feature @xmath114 k at @xmath115 km s@xmath4 ; ( ii ) a broad ( @xmath116 km s@xmath4 wide ) feature with a strength of @xmath117 k also centered around 70 km s@xmath4 ; and ( iii ) a narrow ( @xmath118 km s@xmath4 ) , weak blue - shifted feature at 60 km s@xmath4 . the appearance of the dramatically broadened component ( ii ) in the vicinity of w51b_nt is strongly indicative of a shock . the co throughout the mapped region has an average peak velocity of about 70 km s@xmath4 ( @xmath119 km s@xmath4 ) , in agreement with components ( i ) and ( ii ) toward the masers . thus , while the broad velocity width observed toward the w51b_nt region is exceptional , it does not appear that the w51b_nt region arises from a distinct cloud along the line of site , but is co - distant with the nearby hii regions like [email protected] . additionally , the velocities of the narrow and broad co components at 70 and 71 km s@xmath4 , respectively , are in excellent agreement with the range of oh ( 1720 mhz ) maser velocities ( 69 - 72 km s@xmath4 ; see table [ lines ] ) . other features of note in the full co(32 ) raster ( see fig . [ co]b - g ) : ( i ) the emission associated with the [email protected] hii region is comparatively weak and is composed of two main components that bracket the radio recombination line velocity from @xcite of 67.2 km s@xmath4 . ( ii ) along the sw rim of the hii region is a compact `` clump '' with the strongest co(32 ) emission in the mapped region ( 40 k ) , but with narrow ( 4 km s@xmath4 ) line widths . ( iii ) the southernmost co(32 ) clump labelled `` yso '' shows evidence of bipolar outflow emission predominantly in an east - west direction , but with a third component to the north . the `` yso '' source is also associated with weak 90 cm and 20 cm emission , though its appearance is unremarkable in the mid - ir . from these clues , it seems likely this source is an intermediate to massive protostar with the radio continuum arising from optically thick free - free emission . the appearance of the co(32 ) and @xmath17co(21 ) spectra toward w51b_nt , with a broad ( @xmath116 km s@xmath4 ) component superposed on a narrow ( @xmath113 km s@xmath4 ) feature at the lsr velocity is in good agreement with other co(32 ) studies of snr oh ( 1720 mhz ) maser regions ( see for example * ? ? ? * ; * ? ? ? * ) . to facilitate comparison of all four observed thermal molecular line species , we convolved the jcmt co(32 ) and @xmath17co(21 ) cubes to @xmath120 resolution to match the cso hcn(32 ) and hco@xmath18(32 ) data . spectra of all four species at this resolution toward the centroid of the oh maser location are shown in figure [ densitytemperature]a , and the parameters from gaussian fits using the casa task specfit are given in table [ cofits ] .

the 400 cm image shows non - thermal emission surrounding the g49.2 - 0.3 hii region , and a compact source of non - thermal emission ( w51b_nt ) coincident with the previously - identified oh ( 1720 mhz ) maser spots , non - thermal 21 and 90 cm emission , and a hard x - ray source . this interaction also appears in the thermal molecular gas which partially encircles w51b_nt and exhibits narrow pre - shock ( km s ) and broad post - shock ( km s ) velocity components . confirmation of the w51b / w51c interaction provides additional evidence in favor of this region being one of the best candidates for hadronic particle acceleration known thus far .

we present a comprehensive view of the w51b hii region complex and the w51c supernova remnant using new radio observations from the vla , vlba , merlin , jcmt , and cso along with archival data from _ spitzer _ , _ rosat _ , _ asca _ , and _ chandra_. our vla data include the first cm ( 74 mhz ) continuum image of w51 at high resolution ( ) . the 400 cm image shows non - thermal emission surrounding the g49.2 - 0.3 hii region , and a compact source of non - thermal emission ( w51b_nt ) coincident with the previously - identified oh ( 1720 mhz ) maser spots , non - thermal 21 and 90 cm emission , and a hard x - ray source . w51b_nt falls within the region of high likelihood for the position of tev-ray emission . using the vlba three oh ( 1720 mhz ) maser spots are detected in the vicinity of w51b_nt with sizes of 60 to 300 au and zeeman effect magnetic field strengths of 1.5 to 2.2 mg . the multiwavelength data demonstrate that the northern end of the w51b hii region complex has been partly enveloped by the advancing w51c snr and this interaction explains the presence of w51b_nt and the oh masers . this interaction also appears in the thermal molecular gas which partially encircles w51b_nt and exhibits narrow pre - shock ( km s ) and broad post - shock ( km s ) velocity components . radex radiative transfer modeling of these two components yield physical conditions consistent with the passage of a non - dissociative c - type shock . confirmation of the w51b / w51c interaction provides additional evidence in favor of this region being one of the best candidates for hadronic particle acceleration known thus far .

1305.2793

i

we have presented a wide range of new data toward the w51c snr and the w51b hii region complex . using merlin and the vlba we have spatially resolved the oh ( 1720 mhz ) masers in this region and explored their magnetic field properties , establishing that ( 1 ) the magnetic field strengths range from 1.5 to 2.2 mg ( using the thermal zeeman equation ) ; ( 2 ) the field strengths do not increase with angular resolution ( except where features were spatially unresolved and spectrally blended by previous , lower - resolution observations ) suggesting the field is relatively smooth on these scales ; ( 3 ) the maser spots sizes are relatively large compared to hii region masers , with linear dimensions of @xmath186 cm or @xmath187 au at 6 kpc and brightness temperatures of @xmath188 k ; ( 4 ) the linear polarized intensities are a few percent and the position angle of the linear polarization is nearly zero ; and ( 5 ) the linear polarization properties suggest that the angle between the magnetic field vector and the line - of - sight is @xmath189 , and that the difference between the magnetic field strengths measured using the thermal equation and the total field strength is likely to be small . more quantitative analysis requires a detailed polarization model for the j=3/2 case . we have presented the most sensitive , highest angular resolution long wavelength images of this region to date at 90 cm and 400 cm observed with the vla showing the non - thermal radio continuum emission from the w51c snr with unprecedented detail . these data reveal ( 1 ) the presence of non - thermal radio continuum emission in the vicinity of the oh ( 1720 mhz ) masers , which we denote w51b_nt ; ( 2 ) that the w51b hii region complex must lie in front of the w51c snr in agreement with previous soft x - ray observations ; and ( 3 ) that the nearby hii region [email protected] ( @xmath190 east of the masers ) has been at least partially enveloped by the w51c snr by comparing the expected versus observed 400 cm absorption . through comparison with previous x - ray data , we also find that a source of hard x - rays is coincident with w51b_nt , though the signal is too faint to model the spectrum . using observations of co(32 ) , @xmath17co(21 ) , hco@xmath18(32 ) , and hcn(32 ) in the vicinity around the oh ( 1720 mhz ) masers , we have discovered a ring of shocked gas partially encircling the non - thermal emission of w51b_nt , coincident spatially and kinematically with the oh ( 1720 mhz ) masers . radiative transfer modeling of the physical conditions in the narrow velocity , unshocked gas yields a column density of @xmath191 @xmath125 , a density of @xmath192 @xmath10 , and a temperature of 26 - 32 k. the broad velocity , shocked gas is significantly smaller than the beam leading to a range of possible column densities ( @xmath193 @xmath125 ) and hence physical conditions , but the most likely density and temperatures are @xmath194 @xmath10 and 50 - 100 k , consistent with the passage of a c - shock . clb thanks the jcmt and the university of hawaii for fellowship support during the course of this research . imh thanks nrao for pre - doctoral fellowship support during the course of this project . we would also like to thank professors william ( bill ) watson and moshe eliztur for helpful discussions about maser polarization properties . we are also grateful for the help provided by darek lis and simon radford in obtaining the cso spectra . this research has made use of nasa s astrophysics data system . we acknowledge the use of nasa s _ skyview _ facility ( http://skyview.gsfc.nasa.gov ) located at nasa goddard space flight center . ll date & 2002 jan 14 , 15 , 18 ( mmo1b06 ) + bandwidth & 0.25 mhz + spectral channels & 256 + channel separation & 0.17 km s@xmath4 + velocity resolution & 0.24 km s@xmath4 + spectral line rms noise@xmath195 & 5 mjy beam@xmath4 + synthesized beam & 221 mas @xmath196 125 mas p.a.@xmath197 + dates & 2000 dec 02,03 , & 04 ( bb129 ) + bandwidth & 0.25 mhz + spectral channels & 256 + channel separation & 0.17 km s@xmath4 + velocity resolution & 0.24 km s@xmath4 + spectral line rms noise@xmath195 & 9 mjy beam@xmath4 + synthesized beam & 12.5 mas@xmath198 mas p.a.@xmath199 + dates b - array & 2002 jun 06 & 22 ( ab1031 ) + date c - array & 2006 oct 24 ( ab1219 ) + bandwidth & 1.5 mhz + spectral channels & 64 + continuum rms noise & 100 mjy beam@xmath4 + synthesized beam ( b+c ) & @xmath200 p.a . @xmath201 + date a - array & 2003 aug 23 ( ab1089 ) + dates b - array & 2002 jun 06 & 22(ab1031 ) + dates c - array & 2002 nov 02 ; 2002 dec 13 & 30(ab1031 ) + date d - array & 2003 feb 08 ( ab1077 ) + bandwidth & 3.0 mhz + spectral channels & 32 + continuum rms noise & 12 mjy beam@xmath4 + synthesized beam ( b+c+d ) & @xmath202 p.a.@xmath203 + synthesized beam ( a+b+c+d ) & @xmath204 p.a.@xmath205 + date c - array & 2006 nov 13 ( ab1219 ) + date d - array ( used for continuum only ) & 1992 jul ( ak301 ) + bandwidth ( c ) & 3.0 mhz + spectral channels ( c ) & 32 + continuum rms noise ( c+d ) & 5 mjy beam@xmath4 + spectral line rms noise@xmath195 ( c ) & 3 mjy beam@xmath4 + synthesized beam ( c+d continuum ) & @xmath202 p.a.@xmath203 + synthesized beam ( c hi line ) & @xmath206 p.a.@xmath207 + dates & 2004 mar 29 ; apr 20 - 25 ; jun 11 & 12 ( m04ah45a2 ) + rest frequency & 345.79599 ghz + observing mode & single sideband + velocity resolution & 1.08 km s@xmath4 + primary beam & @xmath208 + spectral line rms noise@xmath195 & 0.1 k + dates & 2005 sep 22 ( m05bh49c ) + rest frequency & 220.39868 ghz + observing mode & double sideband + velocity resolution & 1.1 km s@xmath4 + primary beam & @xmath43 + spectral line rms noise@xmath195 & 0.15 k + dates & 2012 nov 08 + rest frequencies & 265.886 & 267.558 ghz + observing mode & double sideband + velocity resolution & 0.6 & 1.2 km s@xmath4 + primary beam & @xmath143 + spectral line rms noise@xmath195 & 0.02 & 0.014 k + [ observing ] lcccccccc w51_1 & vla & & & 72.0 ( 0.02 ) & 0.9 ( 0.05 ) & 2.6 ( 0.05 ) & 2.6 ( 0.05 ) & @xmath209 + & merlin & & & 72.018 ( 0.002 ) & 0.902 ( 0.004 ) & 1.234 ( 0.004 ) & 1.38 ( 0.02 ) & @xmath209 + & vlba & 19 22 53.8210 & + 14 15 43.462 & 72.06 ( 0.01 ) & 0.901 ( 0.03 ) & 0.211 ( 0.007 ) & 1.05 ( 0.05 ) & @xmath210 + w51_2 & vla & & & 69.1 ( 0.02 ) & 1.2 ( 0.05 ) & 6.1 ( 0.05 ) & 6.1 ( 0.05 ) & @xmath211 + & merlin & & & 69.031 ( 0.001 ) & 1.183 ( 0.002 ) & 2.939 ( 0.004 ) & 3.12 ( 0.02 ) & @xmath212 + & vlba_a & 19 22 54.3632 & + 14 15 40.219 & 68.965 ( 0.002 ) & 1.064 ( 0.004 ) & 1.029 ( 0.004 ) & 2.07 ( 0.02 ) & @xmath213 + & vlba_b & 19 22 54.3608 & + 14 15 40.247 & 69.050 ( 0.004 ) & 0.957 ( 0.009 ) & 0.700 ( 0.005 ) & 1.20 ( 0.04 ) & @xmath214 + [ lines ] lcccc @xmath122co 32 & narrow & 70.65 @xmath215 0.03 & 18.57 @xmath215 0.28 & 4.99 @xmath215 0.09 + & broad & 70.12 @xmath215 0.18 & 6.72 @xmath215 0.26 & 18.64 @xmath215 0.52 + & blueshifted & 59.40 @xmath215 0.15 & 2.30 @xmath215 0.26 & 3.00 @xmath215 0.43 + @xmath17co 21 & narrow & 71.05 @xmath215 0.07 & 4.31 @xmath215 0.22 & 3.20 @xmath215 0.20 + & broad & 70.1 & 0.49 @xmath215 0.16 & 15.47 @xmath215 4.43 + & blueshifted & 59.4 & 0.43 @xmath215 0.18 & 3.0 + hco+ 32 & narrow & 71.03 @xmath215 0.16 & 0.20 @xmath215 0.02 & 4.4 @xmath215 0.5 + & broad & 69.6 @xmath215 0.3 & 0.21 @xmath215 0.02 & 18.0 @xmath215 1.0 + & blueshifted & 59.3 @xmath215 0.3 & 0.07 @xmath215 0.01 & 3.0 + hcn 32 & narrow & 69.6 @xmath215 0.2 & 0.07 @xmath215 0.01 & 1.7 @xmath215 0.4 + & broad & 69.7 @xmath215 0.3 & 0.16 @xmath215 0.02 & 14.9 @xmath215 1.0 + & blueshifted & 57.4 @xmath215 0.4 & 0.06 @xmath215 0.01 & 3.0

we present a comprehensive view of the w51b hii region complex and the w51c supernova remnant using new radio observations from the vla , vlba , merlin , jcmt , and cso along with archival data from _ spitzer _ , are detected in the vicinity of w51b_nt with sizes of 60 to 300 au and zeeman effect magnetic field strengths of 1.5 to 2.2 mg . the multiwavelength data demonstrate that the northern end of the w51b hii region complex has been partly enveloped by the advancing w51c snr and this interaction explains the presence of w51b_nt and the oh masers . radex radiative transfer modeling of these two components yield physical conditions consistent with the passage of a non - dissociative c - type shock .

we present a comprehensive view of the w51b hii region complex and the w51c supernova remnant using new radio observations from the vla , vlba , merlin , jcmt , and cso along with archival data from _ spitzer _ , _ rosat _ , _ asca _ , and _ chandra_. our vla data include the first cm ( 74 mhz ) continuum image of w51 at high resolution ( ) . the 400 cm image shows non - thermal emission surrounding the g49.2 - 0.3 hii region , and a compact source of non - thermal emission ( w51b_nt ) coincident with the previously - identified oh ( 1720 mhz ) maser spots , non - thermal 21 and 90 cm emission , and a hard x - ray source . w51b_nt falls within the region of high likelihood for the position of tev-ray emission . using the vlba three oh ( 1720 mhz ) maser spots are detected in the vicinity of w51b_nt with sizes of 60 to 300 au and zeeman effect magnetic field strengths of 1.5 to 2.2 mg . the multiwavelength data demonstrate that the northern end of the w51b hii region complex has been partly enveloped by the advancing w51c snr and this interaction explains the presence of w51b_nt and the oh masers . this interaction also appears in the thermal molecular gas which partially encircles w51b_nt and exhibits narrow pre - shock ( km s ) and broad post - shock ( km s ) velocity components . radex radiative transfer modeling of these two components yield physical conditions consistent with the passage of a non - dissociative c - type shock . confirmation of the w51b / w51c interaction provides additional evidence in favor of this region being one of the best candidates for hadronic particle acceleration known thus far .

astro-ph0606079

i

the x - ray luminosities of solar - type stars , when they are very young , are prodigious . indeed , it is now well established that low - mass pre main - sequence ( pms ) stars can emit x - rays at levels up to @xmath1 times that of the present - day sun ( e.g. * ? ? ? but after two decades of research since t tauri stars ( ttss ) were first identified as strong x - ray sources ( e.g. * ? ? ? * ) , we still do not know the origins of x - ray production in young stars . while flares observed in the x - ray light curves suggest that the x - rays are produced mainly in solar - analog magnetic reconnection flares , the absence of an obvious rotation - activity relation in these stars prevents a clear association of the x - rays to dynamo - generated fields @xcite . the flares can be so powerful that non - solar geometries of the magnetic fields must be considered , including field lines linking the star with the protoplanetary disk @xcite . in addition , the role of accretion is unclear , and may affect the production of x - rays either directly or indirectly . for example , energetic shocks associated with accretion flows at or near the stellar surface may enhance x - ray production , as has been suggested in the detailed spectroscopic analyses of tw hya @xcite and bp tau @xcite . at the same time , the mass - loading of magnetic field lines may actually inhibit x - ray production in accreting systems , as suggested by @xcite . these issues are reviewed more fully in @xcite . we have undertaken a synoptic study of the orion nebula cluster ( onc ) combining a nearly continuous , 13-d _ chandra _ observation with simultaneous , multi - wavelength , time - series photometry in the optical . a specific motivation is to establish the incidence of time - correlated x - ray and optical variability in order to begin disentangling the roles of magnetic and accretion activity in the production of x - rays . for example , accretion shocks on the surfaces of classical ttss ( cttss ; ttss that still possess accretion disks ) produce strong variability at optical wavelengths , caused by time - variable accretion , rotational modulation of accretion hot spots , " or both @xcite . if x - rays are produced near the sites of accretion shocks , then one might expect that changes in the strength of these shocks will induce changes in the strength of the x - ray emission , and that x - ray and optical variability might therefore be correlated in time . alternatively , x - rays may originate in coronal structures associated with magnetically active regions on these stars , in which case we might expect that x - ray emission will be more pronounced when the magnetically active regions ( which appear as dark photospheric spots in the optical ) face toward us , and least pronounced when these regions face away from us ; that is , optical and x - ray variability will be anti - correlated in time . more complex behavior may result from the superposition of these effects , emphasizing the need for time - resolved measurements . more generally , by establishing the frequency with which x - ray and optical variations are co - temporal , we seek to constrain the extent to which the sources of the x - ray and optical variability may be co - spatial or otherwise causally linked . detailed analyses of simultaneous , time - resolved x - ray and optical variability have previously been reported for three pms stars : the cttss v773 tau @xcite and bp tau @xcite , and the weak - lined tts ( wtts ) v410 tau @xcite . in none of these were the optical and x - ray variability found to be time - correlated . unfortunately , in all three cases the statistical significance of the results were limited by the short duration of the x - ray observations : v773 tau was observed by rosat for 6.7 hr , bp tau was observed by rosat for 8 hr , and v410 tau was observed by _ chandra _ for 7.2 hr . the combined x - ray / optical dataset reported here includes some 800 members of the onc and thus represents , by a factor of hundreds , the largest attempt to date to study the relationship between x - ray and optical variability in pms stars . we will report results from this database in stages , focusing first on statistical properties of the study sample as a whole . in this first paper , we establish the incidence of _ time - correlated _ optical and x - ray variability . a companion paper ( * ? ? ? * hereafter paper ii ) focuses on _ time - averaged _ measures of optical and x - ray variability , and on the relationship between these variability indicators and basic stellar properties . this database will then form the basis for follow - up studies focusing on fine - grained analyses of individual objects . in [ data ] , we present the x - ray and optical time - series database that forms the basis for these studies and describe the methods that we employ in this paper to search for time - correlated x - ray / optical variability . in [ corr - time ] , we identify 40 candidate stars with possible time - correlated optical and x - ray variability , and classify them according to common light - curve characteristics to guide follow - up study of these interesting objects . importantly , these candidates represent at most @xmath2% of our study sample ; @xmath3% of the stars in our sample exhibit no evidence for time - correlated optical and x - ray variability . as we discuss in [ discussion ] , these results imply that the sites of optical and x - ray variability in pms stars are not in the vast majority of cases instantaneously one and the same . a direct causal link between the sources of optical and x - ray variability in pms stars is not supported by our study . we summarize our findings in [ conclusions ] .

we present a database of time - series photometry of the orion nebula cluster obtained with two ground - based telescopes at different longitudes to provide simultaneous coverage with the 13-d _ chandra _ observation of the cluster . main - sequence ( pms ) stars represents , by a factor of hundreds , the largest synoptic , multi wavelength - regime , time - series study of young stars to date . this database will permit detailed analyses of the relationship between optical and x - ray variability among a statistically significant ensemble of pms stars , with the goal of elucidating the origins of pms x - ray production . in this first paper , we present the optical observations , describe the combined x - ray / optical database , and perform an analysis of time - correlated variability in the optical and x - ray light curves . we identify 40 stars ( representing 5% of our study sample ) with possible time - correlated optical and x - ray variability . more generally , we find very little evidence to suggest a direct causal link between the sources of optical and x - ray variability in pms stars . the conclusion that accretion is a primary driver of x - ray production in pms stars is not supported by our findings .

we present a database of time - series photometry of the orion nebula cluster obtained with two ground - based telescopes at different longitudes to provide simultaneous coverage with the 13-d _ chandra _ observation of the cluster . the resulting database of simultaneous optical and x - ray light curves for some 800 pre main - sequence ( pms ) stars represents , by a factor of hundreds , the largest synoptic , multi wavelength - regime , time - series study of young stars to date . this database will permit detailed analyses of the relationship between optical and x - ray variability among a statistically significant ensemble of pms stars , with the goal of elucidating the origins of pms x - ray production . in this first paper , we present the optical observations , describe the combined x - ray / optical database , and perform an analysis of time - correlated variability in the optical and x - ray light curves . we identify 40 stars ( representing 5% of our study sample ) with possible time - correlated optical and x - ray variability . examples of both positive and negative time - correlations are found , possibly representing x - ray flares and persistent coronal features associated with both cool and hot surface spots ( i.e. magnetically active regions and accretion shocks ) . we also find two possible examples of white - light " flares coincident with x - ray flares ; these may correspond to the impulsive heating phase in solar - analog flares . however , though interesting , these represent unusual cases . more generally , we find very little evidence to suggest a direct causal link between the sources of optical and x - ray variability in pms stars . the conclusion that accretion is a primary driver of x - ray production in pms stars is not supported by our findings .

astro-ph0606079

r

in this section we present the results of our analysis of time - correlated optical and x - ray variability in our database of 814 coup sources with simultaneous optical and x - ray light curves . we identify 40 candidate stars whose optical and x - ray light curves appear to be correlated or anti - correlated in time . these represent the first such cases yet reported for pms stars , and we classify these objects according to possible physical origins for the observed variability . more generally , however , time - correlated variability evidently occurs very rarely in our study sample . following the procedure described in [ corr ] , we have searched for time - correlated variability in the optical and x - ray light curves of the 814 stars in our database . forty stars show evidence for the x - ray light curve being time - correlated with at least one optical light curve on the basis of a non - parametric kendall s @xmath33 test ( [ corr ] ) . these 40 stars are listed in table [ correlated - table ] , and their x - ray and optical light curves shown in figs . [ coup28][coup1608 ] . relative to our entire study sample of 814 stars , the fractional incidence of time - correlated variability represented by these 40 stars is @xmath38 . in our study sample , 178 stars are neither optically nor x - ray variable according to the bb and @xmath27 statistical measures discussed in [ methods ] ( see also paper ii for a thorough analysis and discussion of these time - averaged variability indicators ) . if we exclude these 178 stars from the comparison sample ( leaving 636 stars ) , the 40 stars exhibiting time - correlated variability then represent a fractional incidence of @xmath39% . in any case , time - correlated optical and x - ray variability is evidently an uncommon phenomenon in our sample . from statistical arguments , it is probable that a number of these candidates will be spurious . estimating the number of expected false positives accurately is complicated by the fact that a given star may possess multiple optical light curves that are not statistically independent . we may , however , estimate an upper limit to the expected number of false positives , given that we adopted a kendall s @xmath33 null - hypothesis probability of 0.01 as our criterion for identifying these candidates , and that our search for time - correlated variability in our sample of 814 stars involves 1944 different @xmath0 optical light curves ( [ corr ] ) . this implies 1920 false positives . as a reality check on the kendall s @xmath33 statistic , we have additionally performed a monte carlo simulation in which we applied the kendall s @xmath33 test to one million random pairings of our optical and x - ray light curves , and we find that kendall s @xmath33 probabilities of less than 0.01 occur with a frequency of 1.4% , very close to the expected value of 1.0% . the candidates listed in table [ correlated - table ] include a total of 63 @xmath0 light curves that are found to be time - correlated with their associated x - ray light curves according to kendall s @xmath33 , and thus represent a @xmath40 detection of time - correlated variability over the expected number of false positives . it is not possible on the basis of these statistical arguments alone to determine which of these candidates are the false positives and which are the true time - correlated variables . in many cases , the appearance of the x - ray and optical variations are quite dissimilar , so the statistical correlation may often not arise from a physical correlation . some candidates might nonetheless be regarded as more credible than others based on the number of their optical light curves that pass the kendall s @xmath33 test . for example , coup 122 ( fig . [ coup122 ] ) has four optical light curves ( @xmath0 ) and all four of them are identified as time - correlated with the x - ray light curve ( see table [ correlated - table ] ) . in contrast , coup 1309 ( fig . [ coup1309 ] ) also has four optical light curves , none of which appear to be convincingly correlated with the x - ray light curve , and indeed only one of them is identified as time - correlated by the kendall s @xmath33 statistic . in other cases , only one optical light curve is identified as being time - correlated with the x - ray light curve even though the other optical light curves share a similar morphology . for example , in coup 152 ( fig.[coup152 ] ) the @xmath8- and @xmath10-band light curves are not identified as time - correlated , despite a very similar morphology to the @xmath9-band light curve . common sense suggests that this is not a physically meaningful result ; instead , it is likely that small , random noise differences among the optical light curves allow just one of them to pass the 0.01 kendall s @xmath33 probability threshold . such a precarious correlation is less credible than , e.g. , the case of coup 122 ( fig . [ coup122 ] ) noted above . the reader may wish to apply other subjective criteria to the light curves shown in figs . [ coup28][coup1608 ] . we thus do not attempt to identify specific candidates in table [ correlated - table ] as definitive . rather , we emphasize that these 40 candidates have been identified on an objective , statistical basis and that an estimated upper limit on the number of false positives suggests that @xmath41 of these candidates may represent _ bona fide _ cases of time - correlated optical and x - ray variability . this implies an overall incidence of time - correlated variability in our sample of @xmath42% . time - correlated optical and x - ray variability is evidently an uncommon phenomenon in our sample . if x - ray production in pms stars is connected to accretion related processes , we might expect time - correlated optical / x - ray variability to be more common among actively accreting stars , as these stars may be more likely to have their optical variability dominated by accretion . following previous studies ( e.g. * ? ? ? * ; * ? ? ? * ) , we take the accretors " to be those stars with strongly in emission , i.e. , ew [ ] @xmath43 , and non - accretors " to be those with clearly in absorption , i.e. , ew [ ] @xmath44 . ew [ ] measurements have been reported for 493 stars in our study sample . of these , 151 stars are accretors and 145 stars are non - accretors , as defined here ( the remainder show indeterminate values close to 0 ) is an imperfect indicator of accretion . as shown by @xcite , some pms stars with clear accretion signatures in h@xmath45 do not manifest this accretion activity in . it is therefore possible or even likely that some low - level accretors will go undetected in . the criterion that we adopt for identifying the presence of accretion is thus in practice a conservative one ; stars with ew [ ] @xmath43 and ew [ ] @xmath44 are securely identified as accretors and non - accretors , while some stars with indeterminate values close to 0 may be weakly accreting objects that will go unidentified as such . ] . eighteen of the 40 stars in table [ correlated - table ] have ew [ ] measurements allowing them to be clearly classified as accretors or non - accretors ( table [ correlated - table ] ) . these 18 stars are roughly evenly divided in terms of their accretion properties ( 10 accretors , 8 non - accretors ) . thus there is no indication that accretors are more likely than non - accretors to exhibit time - correlated optical and x - ray variability . in this section , we discuss the 40 stars that we have identified as candidates for time - correlated x - ray / optical variability ( table [ correlated - table ] ) . classifying them according to common light curve characteristics , we suggest physical interpretations for the origins of the observed variability . note that , due to the often complex nature of the observed variability , some stars are not classified while others may be included in more than one category ( see table [ correlated - table ] for an overview ) . this discussion is presented to highlight what may represent the first examples in the literature of time - correlated optical and x - ray variability among pms stars , and to guide follow - up investigation of these specific objects . we remind the reader that in fact the overwhelming majority of the stars in our study sample do not exhibit evidence for time - correlated optical and x - ray variability . several stars show periodic or quasi - periodic modulations in their optical light curve(s ) on time scales that appear to be consistent with optical variability periods ( @xmath46 ) reported for them in the literature . the persistence of the periodicity suggests that it is related to the stars rotation periods and that we are seeing either dark spots in regions of magnetic activity , or accretion hot spots , rotating in and out of view . at the same time , these stars x - ray light curves exhibit typical coronal flare - like morphologies that are coincident in time with extrema in the optical light curves . this type of behavior is found both in cases for which the x - ray / optical correlations are positive and negative , and among both accretors and non - accretors . sources for which an x - ray flare coincides with optical maximum ( positive correlations ) include , , , , and . sources for which an x - ray flare coincides with optical minimum ( anti - correlations ) include , , and . additional stars that can be included in this category are those with no previously reported @xmath46 but which still show gradual ( and possibly periodic ) modulations in at least one optical light curve . sources for which an x - ray flare coincides with optical maximum ( positive correlations ) include , , and . sources for which an x - ray flare coincides with optical minimum ( anti - correlations ) include , , and . finally , there are some stars whose time - correlations are dominated by other behavior ( see groups b / c below ) but which in addition exhibit x - ray flares near optical maximum or minimum . sources for which an x - ray flare coincides with optical maximum include and . sources for which an x - ray flare coincides with optical minimum include and . it is possible that these stars represent examples of physical associations between regions of x - ray flaring and stellar spots either hot accretion spots ( positive correlations ) or dark magnetic spots ( anti - correlations ) . however , it is also possible that these stars represent a more general class of objects that show periodic rotational modulation and x - ray flares with no preferred correlation with rotational phase . for example , if we assume a typical @xmath46 of 6 d , and that x - ray flares occur randomly in time with a typical duration of 0.3 d , then the probability of finding either a correlation or anti - correlation is @xmath47% . moreover , among the ten cases of positive correlations included above , only three show clear evidence of active accretion . in any case , detailed follow - up of these stars in comparison to the full sample of coup sources showing x - ray flares should help resolve these interpretations . we have found several stars that show gradual and periodic or quasi - periodic variations in both their optical and x - ray light curves ; in particular , the x - ray light curves do not exhibit the flare - like features that characterize the objects in group a. assuming that modulation in the x - ray light curve indicates the presence of a stable structure ( within the time span of the _ chandra _ observation ) that moves in and out of view as the star rotates , its origin could be a bright accretion spot or a magnetically active region on the stellar surface . in the first case , a positive correlation with the optical light curves might be expected . in the second , an x - ray bright coronal feature accompanied by a photospheric dark spot would give rise to anti - correlated behavior . there are nine cases for which the x - ray and optical light curves produce a net anti - correlation : , , , , , , , and . with the exception of the last object , which showed weak signatures of active accretion in the observations of @xcite , the available ew [ ] measurements are consistent with these stars all being non - accretors , and therefore implying that the photometric and x - ray variations are not related to accretion . all but one star ( coup 1521 ) have previously published optical periods , and the variability observed in our optical light curves is fully consistent with those periods . in addition , the x - ray light curves of three of these stars ( coup 161 , 1355 , and 1521 ) have been independently found by @xcite to be periodic , with x - ray periods @xmath48 that are equal to the optical periods ( i.e. @xmath49 ; see table [ correlated - table ] ) , corroborating the interpretation that the x - ray variability arises from rotational modulation . as discussed by @xcite , this rotational modulation implies that the x - ray emission is produced in close proximity to the stellar surface , such that the x - ray emitting region is occulted as it rotates to the back side of the star . these objects thus represent compelling cases of stars having stable coronal structures that are in close spatial proximity to and likely to be physically linked with dark , magnetically active regions on their surfaces . interestingly , for and , @xcite find @xmath50 ( see table [ correlated - table ] ) . that is , the light curves exhibit two x - ray modulations for each optical modulation . this is particularly evident in ( fig . [ coup139 ] ) . of course , this behavior may simply be the result of randomly repeating flares and/or randomly elevated x - ray emission levels , as discussed for the group a stars . another interpretation is that the stellar coronae in these cases have two x - ray bright regions , separated by @xmath51 in longitude , but that we only see a dark , magnetically active region on the stellar surface associated with one of them . [ coup1590 ] ) , which exhibits an x - ray light curve that appears to oscillate between two different amplitudes , may be a case in point . in addition to these stars with anti - correlated light curves , there are 14 stars that exhibit positive correlations in their x - ray / optical light curves . they are : , , , , , , , , and . @xcite have searched for periodicity in the x - ray light curves of eight of these 14 stars , and have identified two of them ( and ) as having definitive periodic x - ray light curves , with periods equal to ( or half of ) the published @xmath46 . they also identified another three of these stars ( , , and ) as having likely " periodic x - ray light curves . thus , the incidence of periodic x - ray modulation among objects with positively correlated optical / x - ray light curves appears to be high . the positive correlation between the x - ray and optical light curves suggests that these cases represent stable x - ray bright structures physically associated with photospheric hot spots , rotating in and out of view . these hot spots may be the footpoints of mass accretion streams on the stellar surface . alternatively , the observed positively correlated x - ray / optical light curves may represent examples of x - ray faint coronal structures i.e . coronal holes that are co - spatial with dark , magnetically active regions on the stellar surface . however , an interpretation of accretion hot spots is more strongly supported by the ew [ ] properties of these 14 stars , which include some of the strongest accretion signatures found in the entire study sample ( table [ correlated - table ] ) . among these , ( fig . [ coup250 ] ) is particularly interesting , having been identified by @xcite as having a periodic x - ray light curve . this star may thus be a good example of a star having stable structures that are physically associated with accretion hot spots on their surfaces . follow - up modeling and analysis of the color information contained in our multi - band optical light curves should help to clarify whether we are in fact observing hot spots in this object . many of the x - ray flares seen in the coup dataset resemble solar long - duration flares seen with the _ goes _ and _ yohkoh _ satellites which cover the _ chandra _ spectral band . the peak luminosities and durations , and hence total energies , of the coup flare plasma emission are orders of magnitude higher than seen in solar flares . but it is reasonable to suggest that , as in solar flares , the long - duration soft ( _ chandra _ band ) x - ray flares are preceeded by brief impulsive phases when particle acceleration , radio gyrosynchrotron , hard ( @xmath52 kev ) x - ray emission , and optical white - light " continuum increases occur ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? the impulsive phase has , on rare occasions , been seen in magnetically active stars , notably the rs cvn systems @xmath53 gem @xcite and hr 1099 @xcite and dme stars prox cen @xcite and ev lac @xcite . two stars in our study sample and exhibit rather irregular optical light curves that show punctuated increases in brightness that are positively correlated with short - duration flares in the x - ray light curves . while these correlations may be coincidences , we think it is worthwhile to highlight these objects since they may represent the best candidates for the occurrence of white - light magnetic flares . we note that has also been identified as a candidate in groups a and b above due to the particularly complex nature of the observed variability . in particular , we caution that the optical brightening event " near day 10.5 may simply be related to the longer - term , quasi - periodic optical variability of this object . on the other hand , while we have very little data for , what we do have is tantalizing . a single optical measurement , brighter than the mean brightness level by @xmath54 , occurs precisely in the time bin of a very brief x - ray flare that at its peak is @xmath55 times brighter than the mean x - ray flux level for this object . we have carefully scrutinized the optical data for this star and believe the observed optical brightening event to be credible .

the resulting database of simultaneous optical and x - ray light curves for some 800 pre examples of both positive and negative time - correlations are found , possibly representing x - ray flares and persistent coronal features associated with both cool and hot surface spots ( i.e. magnetically active regions and accretion shocks ) . however , though interesting , these represent unusual cases .

we present a database of time - series photometry of the orion nebula cluster obtained with two ground - based telescopes at different longitudes to provide simultaneous coverage with the 13-d _ chandra _ observation of the cluster . the resulting database of simultaneous optical and x - ray light curves for some 800 pre main - sequence ( pms ) stars represents , by a factor of hundreds , the largest synoptic , multi wavelength - regime , time - series study of young stars to date . this database will permit detailed analyses of the relationship between optical and x - ray variability among a statistically significant ensemble of pms stars , with the goal of elucidating the origins of pms x - ray production . in this first paper , we present the optical observations , describe the combined x - ray / optical database , and perform an analysis of time - correlated variability in the optical and x - ray light curves . we identify 40 stars ( representing 5% of our study sample ) with possible time - correlated optical and x - ray variability . examples of both positive and negative time - correlations are found , possibly representing x - ray flares and persistent coronal features associated with both cool and hot surface spots ( i.e. magnetically active regions and accretion shocks ) . we also find two possible examples of white - light " flares coincident with x - ray flares ; these may correspond to the impulsive heating phase in solar - analog flares . however , though interesting , these represent unusual cases . more generally , we find very little evidence to suggest a direct causal link between the sources of optical and x - ray variability in pms stars . the conclusion that accretion is a primary driver of x - ray production in pms stars is not supported by our findings .

0902.2867

c

we have introduced a straightforward and physically intuitive procedure that we call ` mode reduction ' to simplify the multimode description of squeezed light to the bare essentials . for photon - subtraction experiments , this means that the homodyne signal is reduced to an effective two - mode description and the detector signal requires one extra orthogonal effective mode . we derived the wigner function of the homodyne signal conditional upon the detection of a single photon , and we also showed how to average over possible measurement outcomes . the general mode - reduction formalism was then applied to a detailed model describing photon subtraction of gaussian spatiotemporal pulses of squeezed light . this model features many experimental parameters such as beam waists and duration of the pulses that can be independently measured . indeed , our model does not have free fitting parameters . this allows one to study in detail what are the crucial experimental parameters to produce optimally negative wigner functions with pulses of squeezed light . we compared our new model to the empirical model that was used before to analyze photon - subtraction experiments in @xcite . in fact , the formulae for the output wigner functions look similar . one crucial difference is that the empirical model does have a free parameter , namely the quantity called the modal purity . in our model modal purities also occur , be it with a slightly different meaning , but they are fixed quantities . a good agreement between our model and experiments therefore gives more understanding than an accurate fit with the empirical model . we found that in the range of parameters of the measurements in @xcite , both our model and the empirical model are accurate . we reasoned that modal purities in our model would be systematically higher , and in our numerical example we found this to be the case . the accuracy of the empirical model strongly depends on the availability of the free parameter . it was nevertheless a surprise in the theoretical analysis that the mixing angles @xmath194 and @xmath346 , describing the relative probability of measuring a photon in either one of two effective modes , differ at most @xmath365 in a whole range of squeezing parameters . our mode - reduction procedure is closely related to the analysis of photon - subtraction experiments of refs . one could express our mode - reduction parameters in terms of elements of the covariance matrix of refs . . our output wigner function in eq . ( [ wj ] ) then reduces to the one in ref . @xcite , but only in the special case that all our mode reduction parameters are real - valued so that @xmath366 in eq . ( [ dj ] ) vanishes . this we assumed for simplicity in sec . [ sec : concretemultimode ] . our mode - reduction procedure is carried out in the heisenberg picture . we think that our approach has some advantages . in our approach it becomes quite intuitive in what sense it goes beyond the empirical model of ref . @xcite . in our concrete multimode analysis , we include effects not considered in ref . @xcite , such as the transverse beam profile , for which we found that wider pump beams lead to more negative wigner functions . in conclusion , we presented a very concise model that can account for the multimode nature of projective photon - counting measurements . it gives an intuitive picture of photon - subtraction experiments , close to the empirical model previously published . this multimode model therefore gives consistent results , in agreement with previously published experiments where pulses of light with negative wigner functions were produced conditionally . our model can be used to predict the changes in the output upon variation of experimentally relevant parameters , and to optimize the setup design . we thank k. mlmer for useful discussions . this work has been supported by the danish research council through quantop , by compas , and by the niels bohr international academy .

we present a general model to account for the multimode nature of the quantum electromagnetic field in projective photon - counting measurements . we apply this method to a multimode model describing broadband parametric downconversion , thereby improving the analysis of existing experimental results . we find excellent agreement with previously published experimental results , using fewer free parameters than before , and discuss the implications of our analysis for the optimized production of states with negative wigner functions .

we present a general model to account for the multimode nature of the quantum electromagnetic field in projective photon - counting measurements . we focus on photon - subtraction experiments , where non - gaussian states are produced conditionally . these are useful states for continuous - variable quantum information processing . we present a general method called mode reduction that reduces the multimode model to an effective two - mode problem . we apply this method to a multimode model describing broadband parametric downconversion , thereby improving the analysis of existing experimental results . the main improvement is that spatial and frequency filters before the photon detector are taken into account explicitly . we find excellent agreement with previously published experimental results , using fewer free parameters than before , and discuss the implications of our analysis for the optimized production of states with negative wigner functions .

cond-mat9510025

c

in this paper , we have presented a general theory of tubules and helical ribbons based on the concept of chiral molecular packing . this theory shows that tubules can have both uniform and modulated states . in the uniform state , tubules have a constant orientation of the molecular tilt with respect to the equator of the cylinder . in the modulated state , tubules have a periodic , helical modulation in the direction of the molecular tilt , and corresponding ripples in the curvature of the cylinders . in this section , we discuss the experimental evidence for these theoretical predictions . there are two types of experimental evidence supporting the concept that the formation of tubules and helical ribbons is due to chiral molecular packing . first , many experiments have seen helical markings that wind around tubules , giving tubules a chiral substructure . clearly , helical ribbons always have a chiral structure . it is reasonable that the observed chirality of these microstructures results from a chiral packing of the molecules . second , recent experiments have found that diacetylenic lipid tubules have a very strong circular dichroism , which indicates a local chiral packing of the molecules , regardless of whether a chiral pattern is visible on the surface of the cylinder @xcite . the same diacetylenic lipid molecules in solution or in large spherical vesicles have very low circular dichroism . these results show that the molecular packing in tubules is chiral , while the molecular packing in spherical vesicles is not chiral . so far , there has not been any direct test of our prediction of tilt modulation no experiments have been sensitive to the local direction of molecular tilt in tubules . however , the helical markings on tubules provide indirect evidence for this prediction . in some cases , these helical markings are boundaries between sections of tubules with different numbers of bilayers in the walls . however , in other cases , helical markings appear even when there is no detectable discontinuity in the number of bilayers , as in fig . [ tubulephoto ] . these helical markings are apparently stable , because they do not anneal away in time , and hence seem to be a characteristic of the equilibrium state of tubules . our interpretation is that these helical markings are the orientational domain walls predicted by our theory . in this interpretation , the domain walls are visible in electron micrographs because impurities accumulate there and colloidal particles from the solution preferentially adsorb there . such preferential diffusion of impurities to orientational domain walls has been observed directly in langmuir monolayers @xcite . of course , this interpretation of the observed helical markings provides only indirect support for our theory . for a more direct test of our theory , one would need an experiment that can directly probe the local direction of molecular tilt . one possible experimental technique is fluourescence microscopy with polarized laser excitation . this technique has been used to observe variations in the local tilt direction in langmuir monolayers @xcite . to apply this technique to tubules , one would either ( a ) use the intrinsic fluorescence of the constituent amphiphilic molecules , ( b ) attach a fluorescent group to the molecules , or ( c ) put a fluorescent probe into the membrane that forms tubules . one would then illuminate the tubules with polarized light from a laser source . variations in the direction of molecular tilt would then lead to variations in the intensity of fluorescence , which could be detected using confocal microscopy or near - field scanning optical microscopy . through this approach , optical techniques could detect the predicted helical modulation in the tilt direction in the modulated state . the ripples in tubule curvature predicted by our theory may be the modulations seen by yager _ et al . _ @xcite and by thomas _ et al . _ electron micrographs taken in those experiments show very clear helical variations in the tubule curvature . however , other experiments have not observed any ripples on tubules , within the resolution of the electron micrographs . the preliminary data are not yet sufficient to explain why ripples are seen in some experiments but not in others . our prediction of a first - order transition between the uniform and modulated states of tubules also has some experimental support . et al . _ have measured the magnetic birefringence and specific heat of both single - bilayer and multi - bilayer tubules , as functions of temperature through the melting transition @xcite . they find that single - bilayer tubules undergo a second - order melting transition , with strong pretransitional effects , while multi - bilayer tubules undergo a first - order melting transition . furthermore , single - bilayer tubules show an anomalous peak in the specific heat about 3 degrees _ below _ the main peak associated with melting into the untilted phase . this anomalous peak is consistent with our predicted transition between the modulated and the uniform states of tubules . the modulated state should occur in the 3 degree window between the anomalous peak and the main melting peak , where the membrane elastic constants are low , and the uniform state should occur at lower temperatures , below the anomalous peak . thus , our theory may explain this heat - capacity anomaly . as a final point , we note that our theory for the modulated state of tubules leads to an interesting scenario for the kinetic evolution of flat membranes or large spherical vesicles into tubules . this scenario , first proposed in ref . @xcite , is illustrated in fig . [ kinetics ] . when a flat membrane or large spherical vesicle is cooled from an untilted into a tilted phase , it develops tilt order . because of the molecular chirality , the tilt order forms a series of stripes separated by domain walls , as shown in fig . [ kinetics]a . each stripe forms a ripple in the membrane curvature , and each domain wall forms a ridge in the membrane . thus , the domain walls are narrow regions where different parts of the amphiphilic molecules come into contact with neighboring molecules and with the solvent . as a result , the domain walls become weak lines in the membrane , and the membrane tends to fall apart along those lines . the membrane thereby forms a series of narrow ribbons . these ribbons are free to twist in solution to form helices , as shown in fig . [ kinetics]b . those helices may remain as stable helical ribbons , or alternatively they may grow wider to form tubules , as shown in fig . [ kinetics]c . note that this proposed mechanism for tubule formation can only operate if the initial vesicle size is larger than the favored ribbon width . if the initial vesicle is too small , it can not transform into a tubule . this prediction is consistent with the experimental observation that large spherical vesicles ( with diameter greater than 1 @xmath0 m ) form tubules upon cooling , while small spherical vesicles ( diameter less than 0.05 @xmath0 m ) do not @xcite . thus , the theoretical prediction of stripes in the tilt direction gives some insight into the kinetics of the tubule - formation process . in conclusion , in this paper we have shown the range of possible states that can occur in tubules . tubules can have a uniform state , as was considered by earlier investigators , but they can also have a modulated state , with a periodic helical variation in direction of molecular tilt and in the curvature of the membrane . there is at least indirect evidence that the modulated state occurs in actual experimental systems . a more definitive test of this theoretical prediction requires direct experimental probes of variations in the molecular tilt direction . jvs and jms acknowledge support from the office of naval research , as well as the helpful comments of g. b. benedek , d. s. chung , and l. sloter . fcm acknowledges partial support from the national science foundation under grant no . dmr-9257544 , and from the petroleum research fund , administered by the american chemical society . p. yager and p. schoen , mol . . cryst . * 106 * , 371 ( 1984 ) . j. m. schnur , science * 262 * , 1669 ( 1993 ) . r. shashidhar and j. m. schnur , in _ self - assembling structures and materials _ ( american chemical society books , washington , 1994 ) , p. 455 . t. gulik - krzywicki and j. m. schnur ( unpublished ) . m. markowitz and a. singh , langmuir * 7 * , 16 ( 1991 ) . d. s. chung , g. b. benedek , f. m. konikoff , and j. m. donovan , proc . usa * 90 * , 11341 ( 1993 ) . t. tachibana , s. kitazawa , and h. takeno , bull . 43 * , 2418 ( 1970 ) . n. nakashima , s. asakuma , and t. kunitake , j. am . soc . * 107 * , 509 ( 1985 ) . a. singh _ et al . lipids * 47 * , 135 ( 1988 ) . g . de gennes , c. r. acad . paris * 304 * , 259 ( 1987 ) . j. s. chappell and p. yager , biophys . j. * 60 * , 952 ( 1991 ) . m. a. markowitz , j. m. schnur , and a. singh , chem . lipids * 62 * , 193 ( 1992 ) . t. c. lubensky and j. prost , j. phys . ii ( france ) * 2 * , 371 ( 1992 ) . j. h. georger _ et al . , _ j. am . 109 * , 6169 ( 1987 ) . w. helfrich and j. prost , phys . a * 38 * , 3065 ( 1988 ) . ou - yang zhong - can and liu ji - xing , phys . lett . * 65 * , 1679 ( 1990 ) ; phys . a * 43 * , 6826 ( 1991 ) . j. s. chappell and p. yager , chem . lipids * 58 * , 253 ( 1991 ) ; p. yager , j. chappell , and d. d. archibald , in _ biomembrane structure and function the state of the art , _ edited by b. p. gaber and k. r. k. easwaran ( adenine press , schenectady , ny , 1992 ) . p. nelson and t. powers , phys . 69 * , 3409 ( 1992 ) ; j. phys . ii ( france ) * 3 * , 1535 ( 1993 ) . j. v. selinger and j. m. schnur , phys . lett . * 71 * , 4091 ( 1993 ) . s. a. langer and j. p. sethna , phys . a * 34 * , 5035 ( 1986 ) . g. a. hinshaw , r. g. petschek , and r. a. pelcovits , phys . lett . * 60 * , 1864 ( 1988 ) ; g. a. hinshaw and r. g. petschek , phys . rev . a * 39 * , 5914 ( 1989 ) . a. e. jacobs , g. goldner , and d. mukamel , phys . a * 45 * , 5783 ( 1992 ) . t. c. lubensky and f. c. mackintosh , phys . rev . lett . * 71 * , 1565 ( 1993 ) . chen , t. c. lubensky , and f. c. mackintosh , phys . e * 51 * , 504 ( 1995 ) . a. tardieu , v. luzzati , and f. c. reman , j. mol . biol . * 75 * , 711 ( 1973 ) . j. a. n. zasadzinski , j. schneir , j. gurley , v. elings , and p. k. hansma , science * 239 * , 1013 ( 1988 ) . d. r. nelson and l. peliti , j. phys . ( paris ) * 48 * , 1085 ( 1987 ) ; see also h. s. seung and d. r. nelson , phys . a * 38 * , 1005 ( 1988 ) . r. treanor and m. d. pace , biochim . acta * 1046 * , 1 ( 1990 ) . s. l. brandow , d. c. turner , b. r. ratna , and b. p. gaber , biophys . j. * 64 * , 898 ( 1993 ) . see also e. sackmann , h .- duwe , and w. pfeiffer , physica scripta * t25 * , 107 ( 1989 ) . b. n. thomas , c. r. safinya , r. j. plano , and n. a. clark , science * 267 * , 1635 ( 1995 ) . w. helfrich , z. naturforsch . * 28c * , 693 ( 1973 ) . chen and f. c. mackintosh , europhys . lett . * 30 * , 215 ( 1995 ) . p. yager , p. e. schoen , c. davies , r. price , and a. singh , biophys . j. * 48 * , 899 ( 1985 ) . b. n. thomas , personal communication . f. c. mackintosh and t. c. lubensky , phys . 67 * , 1169 ( 1991 ) . j. m. schnur _ et al . , _ science * 264 * , 945 ( 1994 ) . x. qiu , j. ruiz - garcia , k. j. stine , c. m. knobler , and j. v. selinger , phys . lett . * 67 * , 703 ( 1991 ) . g. nounesis _ et al . , _ preprint . a. s. rudolph and t. g. burke , biochim . acta * 902 * , 349 ( 1987 ) . b. m. peek , j. h. callahan , k. namboodiri , a. singh , and b. p. gaber , macromolecules * 27 * , 292 ( 1994 ) .

we present a general theory for the equilibrium structure of cylindrical tubules and helical ribbons of chiral lipid membranes . this theory is based on a continuum elastic free energy that permits variations in the direction of molecular tilt and in the curvature of the membrane . the theory shows that the formation of tubules and helical ribbons is driven by the chirality of the membrane .

we present a general theory for the equilibrium structure of cylindrical tubules and helical ribbons of chiral lipid membranes . this theory is based on a continuum elastic free energy that permits variations in the direction of molecular tilt and in the curvature of the membrane . the theory shows that the formation of tubules and helical ribbons is driven by the chirality of the membrane . tubules have a first - order transition from a uniform state to a helically modulated state , with periodic stripes in the tilt direction and ripples in the curvature . helical ribbons can be stable structures , or they can be unstable intermediate states in the formation of tubules .

1004.1199

i

optical microvariability ( om ; variations with small amplitude in time scales from minutes to hours ) in quasars can be a powerful tool to constrain the energy emission models of active galactic nuclei . some studies indicate that om does not depend on the radio properties of quasars ( see @xcite , hereafter pi ; @xcite ; @xcite ; @xcite , hereafter pii ) . however , the mechanism responsible for om has not been characterized . concerning this topic , variability studies in the optical bands acquired a particular relevance , because the optical / uv excess is identified with the emission from the accretion disk ( e.g. , @xcite ; @xcite ; @xcite ; @xcite ; @xcite ) . unfortunately , all the proposed scenarios are very complex when the emission from additional spectral components is considered . in photometric studies , the properties of the spectral energy distribution ( sed ) of quasars era characterized by the spectral index , which is defined as the slope of a curve in a plane @xmath0 , and calculated as magnitude differences at different bands ( e.g. , @xcite ; @xcite ) . during variability events , changes in the shape of this sed can give us important information about the emission processes . for instance , evidence from variability studies strongly indicates that om has non - thermal nature in both bl lac objects and flat spectrum radio quasars ( fsrqs ; e.g. , @xcite ; @xcite ; @xcite ; @xcite ; @xcite , @xcite , @xcite ) , but in the case of fsrqs the contribution of a thermal component must be considered in the spectrum of these objects ( e.g. , @xcite ; @xcite ; @xcite ) . concerning quasars , short - term variability ( variations with amplitudes of tenths of a magnitude and time scales of weeks to months ) might have thermal origin ( e.g. , @xcite ) . nevertheless , all these studies usually employ two bands , or only the average of color values is used , losing thus information about _ texture _ of shortest variations ( see @xcite ; @xcite ; @xcite ; @xcite ) . in order to discern where the om in quasars originates , we assume that emission from the accretion disk must be related to thermal processes , while the emission from the jet must be related to non - thermal processes . during om events , the spectral component responsible for the variation may display characteristic color changes . then , we developed a method with quasi - simultaneous observations at three optical bands to analyze these color changes that accompanied microvariability events . this paper is organized as follows : in section [ datos ] , we shortly comment on the data treatment ; in section [ sed ] , we define a spectral variability index and how to determine the om origin ; in section [ results ] , we analyze the data ; finally , we discuss the results in section [ discusion ] ; while a summary and conclusions are given in section [ summary ] .

we present a method that we developed to discern where the optical microvariability ( om ) in quasars originates : in the accretion disk ( related to thermal processes ) or in the jet ( related to non - thermal processes ) . analyzing nearly simultaneous observations in three different optical bands of continuum emission , we are able to determine the origin of several isolated om events .

we present a method that we developed to discern where the optical microvariability ( om ) in quasars originates : in the accretion disk ( related to thermal processes ) or in the jet ( related to non - thermal processes ) . analyzing nearly simultaneous observations in three different optical bands of continuum emission , we are able to determine the origin of several isolated om events . in particular , our method indicates that from nine events reported by , three of them are consistent with a thermal origin , three to non - thermal , and three can not be discerned . the implications for the emission models of om are briefly discussed .

1309.7127

i

@xcite ( also known as ) is an optically visible h ii region @xcite in the serpens - aquila rift region . located at @xmath6 , @xmath7 , it is visible as a bipolar nebula at mid and far ir wavelengths ; harbouring complex features such as filamentary structures and an embedded arc - shaped nebula ( figure [ fig_colourcompositepacs160100irac8 ] ) . early co observations of this region showed the w40 h ii region to be located at the edge of the molecular cloud @xcite , resulting in the well - known blister morphology . even so , the full extent of the molecular gas in this region is not mapped so far . only the central few arcminutes of this cloud are mapped , using isotopologues of co , finding the mass of central cloud core to be @xmath2 100@xmath8 @xcite . w40 also has an associated dense molecular clump of @xmath2 20 diameter (; @xcite ) . a large scale , weak molecular outflow is also found , through co observations , to originate in the molecular cloud @xcite . located at a galactic latitude of @xmath2 3.5@xmath9 , this region is above the main galactic plane , and the distance estimates to it vary from 300 to 900 pc ( * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * and references therein ) . in the present work , we have adopted a distance of 500 pc from @xcite . the central region of the w40 molecular cloud and h ii region is known to host an embedded cluster of young stars , with a significant population of early - type sources @xcite , with the earliest spectral type of about o9.5 @xcite . this cluster of early - type sources also partially reveals itself as a cluster of compact radio sources , coexisting with other compact radio sources which are classified as candidate ultra - compact h ii regions and radio variable sources @xcite . together , these observations show that the w40 molecular cloud / h ii region is one of the few nearby regions with active star formation away from the galactic plane , hosting an embedded cluster including high - mass stars , and thus representing a template laboratory to investigate the process of star formation . recent observations of the larger serpens - aquila rift in the ( sub)millimeter wavelengths include this region , and have produced a systematic , unbiased sample of starless as well as protostellar dense cores within this cloud @xcite . also , high resolution x - ray observation using _ chandra _ has revealed the near - complete census of young stellar population within the embedded cluster @xcite . low frequency radio observations show newer compact sources in this region @xcite . despite the multitude of individual studies of the w40 molecular cloud , embedded cluster and h ii region , at wavelengths ranging from x - rays to radio , an analysis of the overall star formation scenario in w40 is pending . in this paper , the aim is to fill this lacuna by using the vast archival dataset together with new nir and radio observations . in section [ section_observations - and - analysis ] , we present the observations ( archival or otherwise ) and data reduction procedures . we discuss the results pertaining to stellar sources ( classification and their analysis ) , the morphology , and the physical parameters of the region from various datasets in sections [ section_ysos ] , [ section_morphology ] , and [ section_physicalparameters ] , respectively ; followed by a discussion on the possible star formation scenario in section [ section_star - formation - scenario ] . the main conclusions are presented in section [ section_conclusions ] . + + + + +

archival _ spitzer _ free - free emission spectral energy distribution ( sed ) analysis is used to obtain physical parameters of the overall photoionized region and the irs5 sub - region . this multiwavelength scenario is suggestive of star formation having resulted from merging of multiple filaments to form a hub .

we present a multiwavelength study of the star - forming region using infrared ( ir ) observations in ukirt _ jhk _ bands , _ spitzer _ irac bands , and _ herschel _ pacs bands ; 2.12 m h narrow - band imaging ; and radio continuum observations from gmrt ( 610 and 1280 mhz ) , in a field of view ( fov ) of 34 40 . archival _ spitzer _ observations in conjunction with near - ir ( nir ) observations are used to identify 1162 classii / iii and 40 class i sources in the fov . the nearest - neighbour stellar surface density analysis shows that majority of these young stellar objects ( ysos ) constitute the embedded cluster centered on the high - mass source irs1a south . some ysos , predominantly younger population , are distributed along and trace the filamentary structures at lower stellar surface density . the cluster radius is obtained as 0.44pc - matching well with the extent of radio emission - with a peak density of 650pc . the _ jhk _ data is used to map the extinction in the region which is subsequently used to compute the cloud mass . it has resulted in 126m and 71m for the central cluster and the northern irs5 region , respectively . narrow - band imaging displays significant emission , which prominently resembles fluorescent emission arising at the borders of dense regions . radio continuum analysis shows this region as having blister morphology , with the radio peak coinciding with a protostellar source . free - free emission spectral energy distribution ( sed ) analysis is used to obtain physical parameters of the overall photoionized region and the irs5 sub - region . this multiwavelength scenario is suggestive of star formation having resulted from merging of multiple filaments to form a hub . star formation seems to have taken place in two successive epochs , with the first epoch traced by the central cluster and the high - mass star(s ) - followed by a second epoch which is spreading into the filaments as uncovered by the class i sources and even younger protostellar sources along the filaments . the irs5 h ii region displays indications of swept - up material which has possibly led to the formation of protostars .

1309.7127

c

in this paper , we carried out a multiwavelength study of the galactic star - forming w40 h ii region . our main conclusions are as follows : 1 . using the mir data from _ spitzer _ in conjunction with nir data from ukirt , 1202 ysos were identified in the region , out of which 40 are class i sources and 1162 are class ii / iii sources . analysis of the yso distribution and nearest - neighbour surface density yields the cluster radius as @xmath2 0.44 pc and peak surface density as 650 pc@xmath4 . mass calculation using extinction map yields a value of @xmath2 126 m@xmath5 within this radius . 2 . the filamentary structures were examined to reveal 3 parsec scale filaments emanating from the midriff . two of them ( filaments 1 and 3 in our labelling ) contain most of the youngest ysos aligned along their lengths . filament 2 was found to be relatively diffuse with hardly any of the youngest ysos . 3 . sed fitting using the radio continuum emission at 610 mhz and 1280 mhz for the total emission region yielded the value of electron density to be @xmath2 1265 @xmath37 218 @xmath63 and the total lyman continuum luminosity to be @xmath2 1.67 @xmath3 10@xmath71 photons s@xmath21 . the dynamical age , for the ambient density ranging from 1000 to 15000 @xmath63 , ranges from @xmath2 0.19 to 0.78 myr . the irs5 arc - shaped nebular region was found to be distinct from the rest of the emission region , and was thus examined in radio separately . the electron density was obtained to be 288 @xmath37 55 @xmath63 and a lower limit on the dynamical age to be @xmath2 0.11 myr . a comparison of radio continuum photon luminosity with the tabulated values from @xcite shows irs5 to be of b1v spectral type , reaffirming previous estimate from @xcite . extinction map gives a value of @xmath2 71 m@xmath5 as the mass for this arc - shaped nebula . 5 . the star formation seems to have taken place in two successive epochs , with the formation of relatively - older class ii / iii and the central high - mass sources - resulting in a cluster which is centered around the high - mass star irs 1a south - followed by that of the youngest sources ( class 0/i , and starless cores ) . a distinct case is of the irs5 nebular region , where material seems to have been swept - up to the edge of this arc - shaped nebula by the expanding h ii region of the irs5 source . we thank the anonymous referee for a thorough and critical reading of the manuscript , and for the suggestions which helped in improving this paper . k.k.m . , m.s.n.k . , d.k.o . , and m.r.s . acknowledge support from marie curie irses grant ( 230843 ) under the auspices of which this work was carried out . k.k.m . would like to thank hendrik linz , mpia ( heidelberg ) for his invaluable help in obtaining the _ herschel _ data . this research made use of data products from the _ spitzer _ space telescope archive . these data products are provided by the services of the infrared science archive operated by the infrared processing and analysis centre / california institute of technology , funded by the national aeronautics and space administration and the national science foundation .

observations in conjunction with near - ir ( nir ) observations are used to identify 1162 classii / iii and 40 class i sources in the fov . the nearest - neighbour stellar surface density analysis shows that majority of these young stellar objects ( ysos ) constitute the embedded cluster centered on the high - mass source irs1a south . star formation seems to have taken place in two successive epochs , with the first epoch traced by the central cluster and the high - mass star(s ) - followed by a second epoch which is spreading into the filaments as uncovered by the class i sources and even younger protostellar sources along the filaments .

we present a multiwavelength study of the star - forming region using infrared ( ir ) observations in ukirt _ jhk _ bands , _ spitzer _ irac bands , and _ herschel _ pacs bands ; 2.12 m h narrow - band imaging ; and radio continuum observations from gmrt ( 610 and 1280 mhz ) , in a field of view ( fov ) of 34 40 . archival _ spitzer _ observations in conjunction with near - ir ( nir ) observations are used to identify 1162 classii / iii and 40 class i sources in the fov . the nearest - neighbour stellar surface density analysis shows that majority of these young stellar objects ( ysos ) constitute the embedded cluster centered on the high - mass source irs1a south . some ysos , predominantly younger population , are distributed along and trace the filamentary structures at lower stellar surface density . the cluster radius is obtained as 0.44pc - matching well with the extent of radio emission - with a peak density of 650pc . the _ jhk _ data is used to map the extinction in the region which is subsequently used to compute the cloud mass . it has resulted in 126m and 71m for the central cluster and the northern irs5 region , respectively . narrow - band imaging displays significant emission , which prominently resembles fluorescent emission arising at the borders of dense regions . radio continuum analysis shows this region as having blister morphology , with the radio peak coinciding with a protostellar source . free - free emission spectral energy distribution ( sed ) analysis is used to obtain physical parameters of the overall photoionized region and the irs5 sub - region . this multiwavelength scenario is suggestive of star formation having resulted from merging of multiple filaments to form a hub . star formation seems to have taken place in two successive epochs , with the first epoch traced by the central cluster and the high - mass star(s ) - followed by a second epoch which is spreading into the filaments as uncovered by the class i sources and even younger protostellar sources along the filaments . the irs5 h ii region displays indications of swept - up material which has possibly led to the formation of protostars .

quant-ph0210174

i

an important prediction of quantum theory is the existence of irreducible fluctuations of electromagnetic fields in vacuum . besides their numerous observable consequences in microscopic physics , vacuum fluctuations also have observable effects in macroscopic physics , for example the casimir force they exert on mirrors @xcite . casimir calculated this force in a geometrical configuration where two plane mirrors are placed a distance @xmath0 apart and parallel to each other , the area @xmath1 of the mirrors being much larger than the squared distance @xmath2 . he considered the ideal case of perfectly reflecting mirrors and obtained an expression which , remarkably , depends only on the geometrical quantities @xmath1 and @xmath0 and on the fundamental constants @xmath3 and @xmath4 @xmath5 this attractive force has been observed in a number of ` historical ' experiments @xcite which confirmed its existence and main properties @xcite . several recent experiments reached an accuracy in the % range by measuring the force between a plane and a sphere @xcite or two cylinders @xcite . similar experiments were also performed with mems @xcite ( see also @xcite ) . an experiment studied the plane - plane configuration considered by casimir @xcite but , as a consequence of the difficulties associated with this geometry , reached only a 15% accuracy ( see reviews of recent experiments in @xcite ) . the casimir force is the most accessible experimental consequence of vacuum fluctuations in the macroscopic world while vacuum energy is known to raise a serious problem with respect to gravity and cosmology ( see references in @xcite ) . this is a reason for testing the predictions of quantum field theory concerning the casimir effect with the greatest care and accuracy . the theory of the casimir force is also a key point for the experiments searching for the new weak forces predicted by theoretical unification models to arise at distances between nanometer and millimeter @xcite . the casimir force is indeed the dominant effect between two neutral objects at @xmath6 m or sub@xmath6 m distances so that an accurate knowledge of its theoretical expectation is as crucial as the precision of measurements in such experiments @xcite . in this context , it is essential to account for the differences between the ideal case considered by casimir and the real experimental situation . recent experiments use metallic mirrors which show perfect reflection only at frequencies below their plasma frequency . they are performed at room temperature , with the effect of thermal fluctuations superimposed to that of vacuum fluctuations . in the most accurate experiments , the force is measured between a plane and a sphere , and not between two parallel planes . the surface state of the plates , in particular their roughness , should also affect the force . a large number of works have been devoted to the study of these effects and we refer the reader to @xcite for a bibliography . the evaluation of the casimir force between imperfect lossy mirrors at non zero temperature has given rise to a burst of controversial results @xcite which constitutes a part of the motivations for the present work . for the sake of comparing experimental measurements and theoretical expectations , it is necessary to have at one s disposal a reliable expression of the casimir force in the experimental situation . in the present paper , we focus our attention on the effect of imperfect reflection of the mirrors . other effects , in particular the effect of temperature , will be addressed in follow - on papers . we consider the original casimir geometry with two perfectly plane and parallel mirrors . except for these assumptions , we consider arbitrary frequency dependences for the mirrors which , in particular , may be lossy . we evaluate the casimir force as the effect of vacuum radiation pressure on the fabry - perot cavity formed by the two mirrors . the net force results from the balance between the repulsive and attractive contributions associated respectively with resonant or antiresonant frequencies . it is obtained as an integral over the axis of real frequencies , including the contribution of evanescent waves besides that of ordinary waves . it is then transformed into an integral over imaginary frequencies by using physical properties fulfilled by all real mirrors . the formula obtained here for the casimir force turns out to be identical to the expression already published in @xcite but the new derivation has a wider scope of validity than the previous one since it remains valid for lossy mirrors . the fact that the formula keeps the same form despite the widening of the assumptions is intimately related to a theorem which relates the spectral density of the fields inside the cavity to the reflection amplitudes seen by the same fields . this theorem was demonstrated in @xcite and @xcite in specific cases and we prove it in the present paper without any restriction . to this aim , we introduce a systematic treatment of lossy mirrors and cavities as dissipative networks @xcite . we define scattering and transfer matrices for elementary networks like the interface between two media or the propagation over a given length in a medium . we then deduce the matrices associated with composed networks , like the optical slab or the multilayer mirror . the results obtained in this manner are therefore applicable to a large variety of mirrors , still with the assumption of perfect plane geometry . in the particular case of a slab with a large width , the lifshitz expression @xcite is recovered . at the limit of perfectly reflectors , the ideal casimir formula ( [ eqcasimir ] ) is obtained . more generally , the expression gives the casimir force as an integral written in terms of the reflection amplitudes characterizing the two mirrors . this integral is finite as soon as the amplitudes obey the general properties of scattering theory already alluded to . in other words , the difficulties usually associated with the infiniteness of vacuum energy are solved by using the properties of real mirrors themselves rather than through an additional formal regularization technique . we finally show that the same physical properties constrain the variation of the casimir force . in particular , they invalidate proposals which has been done for ` tayloring ' the force at will by using mirrors with specially designed scattering amplitudes @xcite . in these proposals , the balance between attractive and repulsive contributions to the force is change , leading to the hope that the casimir force could reach large or have its sign changed from an attractive force to a repulsive one @xcite . using the simple model of a one - dimensional space , it has already been shown @xcite that these hopes can not be met for arbitrary mirrors built up with dielectric layers . here , the argument is generalized to the casimir geometry in three - dimensional space with the following conclusions : the casimir force can not exceed the value obtained for perfect mirrors , it remains attractive for any cavity length and its value is a decreasing function of the cavity length . this is true for any mirror obtained by piling up layers of media described by dielectric functions . this definition of multilayer dielectric mirrors includes the case of metallic layers , provided that magnetic effects play a negligible role in the optical response .

the additional fluctuations accompanying losses are deduced from expressions of the optical theorem . a general proof is given for the theorem relating the spectral density inside the cavity to the reflection amplitudes seen by the inner fields . the force is obtained as an integral over the real frequencies , including the contribution of evanescent waves besides that of ordinary waves , and , then , as an integral over imaginary frequencies .

we present a new derivation of the casimir force between two parallel plane mirrors at zero temperature . the two mirrors and the cavity they enclose are treated as quantum optical networks . they are in general lossy and characterized by frequency dependent reflection amplitudes . the additional fluctuations accompanying losses are deduced from expressions of the optical theorem . a general proof is given for the theorem relating the spectral density inside the cavity to the reflection amplitudes seen by the inner fields . this density determines the vacuum radiation pressure and , therefore , the casimir force . the force is obtained as an integral over the real frequencies , including the contribution of evanescent waves besides that of ordinary waves , and , then , as an integral over imaginary frequencies . the demonstration relies only on general properties obeyed by real mirrors which also enforce general constraints for the variation of the casimir force .

astro-ph0603254

i

for over twenty years the evolution , and eventual dispersal , of discs around young stars has been an important area of study , for theories of both star and planet formation . it is now well - established that at an age of @xmath1yr most stars are surrounded by discs that are optically thick at optical and infrared wavelengths @xcite . observations at millimetre wavelengths show that these discs have masses that are typically a few percent of a solar mass @xcite , and so discs are widely believed to be potential sites for planet formation . however at an age of @xmath2yr most stars are not seen to have discs , suggesting that disc lifetimes are typically a few myr ( e.g. * ? ? ? how stars lose their discs remains an unsolved question . the distribution of t tauri stars ( tts ) at infrared wavelengths provides some insight into this problem . these objects tend to fall into two distinct groups : those whose emission is consistent with a stellar photosphere plus an optically thick disc , and those which are compatible with purely photospheric emission . [ note that these two classes usually coincide with the spectroscopic classifications of classical and weak - lined t tauri stars ( ctts and wtts ) respectively . ] a number of authors have noted that very few transition objects are observed between the ctt and wtt loci @xcite . observations at longer wavelengths show a similar behaviour , both in the mid - infrared @xcite and at millimetre wavelengths @xcite . these observations suggest that discs are dispersed very rapidly , with the dispersal time estimated to be @xmath3yr @xcite . moreover the simultaneous decline is disc emission across such a wide range in wavelength suggests that the dispersal is essentially simultaneous across the entire radial extent of the disc ( see also discussion in @xcite ) . this `` two - time - scale '' behaviour is inconsistent with conventional models of disc evolution , such as viscous evolution models @xcite or models of magnetospheric clearing @xcite . such models predict power - law declines in disc properties , and therefore predict dispersal times which are always of the same order as the disc lifetime . however ( * ? ? ? * hereafter cgs01 ) showed that models which combine photoevaporation of the disc with viscous evolution can reproduce this two - time - scale behaviour . in this model , known as the `` uv - switch '' model ( cgs01 ) , ionizing radiation from the central star produces a photoevaporative wind at large radii . detailed models of photoevaporative winds were constructed by ( * ? ? ? * see also @xcite ) for the cases of both weak and strong stellar winds . in the case of tts we consider only the weak stellar wind case . in this case ionizing radiation from the star creates an ionized layer on the surface of the disc , with conditions akin to an hii region . beyond some critical radius , known as the gravitational radius , the local thermal energy of the ionized is greater than its gravitational energy and the gas escapes as a wind . the gravitational radius is therefore given by @xmath4 where @xmath5 is the sound speed of the ionized gas , typically 10kms@xmath6 . @xcite show that the wind rate is determined by the the density at the ionization front , and find an integrated mass - loss rate of @xmath7 where @xmath8 is the ionizing flux produced by the star . more recent studies have extended the study of the details in a number of ways @xcite , and recent hydrodynamic modelling has resulted in slight modification of the quantitative results . when hydrodynamic effects are considered the `` effective @xmath9 '' is reduced by a factor of 5 @xcite , and the mass - loss rate is reduced by a factor of around 3 @xcite . however the qualitative behaviour is unchanged from that of @xcite . the so - called `` uv - switch '' model of cgs01 couples a photoevaporative wind to a simple disc evolution model . at early times in the evolution the accretion rate through the disc is much larger than the wind rate , and the wind has a negligible effect . however at late times photoevaporation becomes important , depriving the disc of resupply inside @xmath9 . at this point the inner disc drains on its own , short , viscous time - scale , giving a dispersal time much shorter than the disc lifetime . a number of similar studies have now been conducted @xcite , and this class of models show a number of attractive properties . however cgs01 highlighted two key problems with the model . firstly , the model requires that tts produce a rather large ionizing flux , of order @xmath10 ionizing photons per second . they also found that the outer disc , beyond @xmath9 was dispersed much too slowly to satisfy millimetre observations of wtts , a finding re - affirmed by recent sub - millimetre observations @xcite . we have previously shown that it is reasonable to treat tt chromospheres as having a constant ionizing flux in the range @xmath11@xmath12s@xmath6 @xcite , and we now seek to address the `` outer disc problem '' . in a companion paper ( * hereafter paper i ) , we highlighted an important flaw in the uv - switch model . the uv - switch model relies on the wind parametrization of @xcite , which assumes that the disc is extremely optically thick to lyman continuum photons at all radii . @xcite find that the diffuse ( recombination ) field dominates the photoevaporation at all radii of interest , as the direct field suffers extremely strong attenuation by the disc atmosphere . however we note that at late times in the uv - switch model the inner disc is drained , and is therefore optically thin to ionizing radiation . consequently the direct field is important after the inner disc has drained . in paper i we constructed detailed hydrodynamic models of the wind driven by the direct field , and derived a functional form for the mass - loss rate : @xmath13 \ , \mathrm m_{\odot}\mathrm{yr}^{-1 } \ , .\end{aligned}\ ] ] here @xmath14 and @xmath15 are order - of - unity scaling constants , @xmath16 is the mean molecular weight of the gas , @xmath17 is a power - law index , @xmath18 is the ratio of the disc scale - height to radius , and @xmath19 and @xmath20 are the inner and outer disc radii respectively . our numerical analysis fixed the values of the scaling constants to be @xmath21 and @xmath22 ( for @xmath23 ) . as noted in paper i , both the geometry of the radiative transfer problem and the form of the wind are qualitatively similar to the strong wind case of @xcite . however the effect of the direct radiation field is to increase the efficiency of the wind . consequently the mass - loss rate due to direct photoevaporation is around an order of magnitude larger than that from the diffuse field , and is significant at late stages of the evolution . the diffusion equation for the evolution of disc surface density @xmath24 is @xcite @xmath25 - \dot{\sigma}_{\mathrm { wind}}(r , t ) \ , , \ ] ] where @xmath26 is the kinematic viscosity and the term @xmath27 represents the mass - loss due to photoevaporation . cgs01 solved this equation using the `` weak - wind '' profile of @xcite . at some point in the evolution the mass - loss rate from the wind falls to a level comparable to the accretion rate through the disc , and at this point the disc is rapidly drained inside @xmath9 . however , as mentioned above , cgs01 neglect the influence of the direct radiation field after this inner draining occurs . consequently they find that the time - scale for dispersal of the outer disc is limited by the time material takes to diffuse inward to @xmath9 ( as the most of the mass - loss occurs close to @xmath9 ) . further , the @xmath28 dependence of the wind profile at large radii means that the mass - loss rate due to photoevaporation decreases significantly with time as the inner edge of the disc moves outward . consequently the dispersal of the outer disc occurs on the viscous time - scale of the _ outer _ disc , and thus the outer disc is dispersed in a time comparable to the disc lifetime , much too slowly to satisfy observational constraints . we suggest that photoevaporation by the direct radiation field results in a dispersal time significantly shorter than that predicted by cgs01 , and now seek to model the effects of this process on the evolution of the outer disc . in this paper we seek to incorporate the result of paper i into models of disc evolution . we do this by solving the equation for the evolution of the surface density of a geometrically thin disc , including the photoevaporative wind as a sink term . in section [ sec : timescales ] we present a simple time - scale analysis , which demonstrates the significance of the direct radiation field . in section [ sec : disc_model ] we construct a numerical model of disc evolution in the presence of a photoevaporative wind . we the use a simple prescription to model the observed spectral energy distribution ( sed ) of the evolving disc , and construct a set of models which cover a broad range in parameter space ( section [ sec : sed_model ] ) . in section [ sec : results ] we present our results , comparing the predicted seds to recent observational data . in section [ sec : dis ] we discuss the implications and limitations of our results , and in section [ sec : summary ] we summarize our conclusions .

this model combines viscous evolution with photoevaporation of the disc , in a manner similar to . however in a companion paper we have shown that at late times such models must consider the effect of stellar radiation directly incident on the inner disc edge , and here we model the observational implications of this process . we use a simple prescription to model the spectral energy distribution of the evolving disc , and demonstrate that the model is consistent with observational data across a wide range of wavelengths . [ firstpage ] accretion , accretion discs circumstellar matter planetary systems : protoplanetary discs stars : pre - main - sequence

we present a new model for protoplanetary disc evolution . this model combines viscous evolution with photoevaporation of the disc , in a manner similar to . however in a companion paper we have shown that at late times such models must consider the effect of stellar radiation directly incident on the inner disc edge , and here we model the observational implications of this process . we find that the entire disc is dispersed on a time - scale of orderyr after a disc lifetime of a few myr , consistent with observations of t tauri ( tt ) stars . we use a simple prescription to model the spectral energy distribution of the evolving disc , and demonstrate that the model is consistent with observational data across a wide range of wavelengths . we note also that the model predicts a short `` inner hole '' phase in the evolution of all tt discs , and make predictions for future observations at mid - infrared and millimetre wavelengths . [ firstpage ] accretion , accretion discs circumstellar matter planetary systems : protoplanetary discs stars : pre - main - sequence

astro-ph0603254

i

we have presented a new model for the evolution of protoplanetary discs . our model combines viscous evolution with photoevaporation of the disc by stellar radiation , and includes the effects of the direct radiation field at late stages of the evolution ( using the wind prescription derived in paper i ) . we have constructed a numerical model for the evolving disc , and used a simple prescription to model the behaviour of the spectral energy distribution as the disc evolves . our fiducial model predicts that the disc is completely dispersed on a time - scale of order @xmath0yr after a lifetime of a few myr , consistent with observationally derived time - scales . our results are consistent with observational data across a broad range in wavelengths , and allow us to place weak constraints on some model parameters : we derive ionizing fluxes in the range @xmath11@xmath168s@xmath6 and viscosity parameters ( @xmath52 ) in the range @xmath1750.4 . we also make predictions as to what will be seen in future observations in the mid - infrared and at millimetre wavelengths . to date this is the only model of disc evolution which can reproduce the rapid disc dispersal seen in observations of t tauri discs . we note also that the model suggests that all evolving discs pass through a short `` inner hole '' phase . during this phase the outer disc mass is of order 0.001m@xmath63 , and we predict that inner hole sources should represent around 110% of the observed population of tts . we compare the predictions of the model with the handful of inner hole sources observed to date and show that some , but not all , of these objects are consistent with the predictions of our model .

we present a new model for protoplanetary disc evolution . we find that the entire disc is dispersed on a time - scale of orderyr after a disc lifetime of a few myr , consistent with observations of t tauri ( tt ) stars . we note also that the model predicts a short `` inner hole '' phase in the evolution of all tt discs , and make predictions for future observations at mid - infrared and millimetre wavelengths .

we present a new model for protoplanetary disc evolution . this model combines viscous evolution with photoevaporation of the disc , in a manner similar to . however in a companion paper we have shown that at late times such models must consider the effect of stellar radiation directly incident on the inner disc edge , and here we model the observational implications of this process . we find that the entire disc is dispersed on a time - scale of orderyr after a disc lifetime of a few myr , consistent with observations of t tauri ( tt ) stars . we use a simple prescription to model the spectral energy distribution of the evolving disc , and demonstrate that the model is consistent with observational data across a wide range of wavelengths . we note also that the model predicts a short `` inner hole '' phase in the evolution of all tt discs , and make predictions for future observations at mid - infrared and millimetre wavelengths . [ firstpage ] accretion , accretion discs circumstellar matter planetary systems : protoplanetary discs stars : pre - main - sequence

astro-ph9909115

i

the dynamical evolution of dense star clusters is a problem of fundamental importance in theoretical astrophysics , but many aspects of the problem have remained unresolved in spite of years of numerical work and improved observational data . on the theoretical side , some key unresolved issues include the role played by primordial binaries and their dynamical interactions in the overall cluster dynamics and in the production of exotic sources ( hut 1992 ) , and the importance of tidal shocking for the long - term evolution and survival of globular clusters in the galaxy ( gnedin , lee & ostriker 1999 ) . on the observational side , we now have many large data sets providing a wealth of information on blue stragglers , x - ray sources and millisecond pulsars , all found in large numbers in dense clusters ( e.g. , bailyn 1995 ; camilo 2000 ; piotto 1999 ) . although it is clear that these objects are produced at high rates through dynamical interactions in the dense cluster cores , the details of the formation mechanisms , and in particular the interplay between binary stellar evolution and dynamical interactions , are far from understood . following the pioneering work of hnon ( 1971a , b ) , many numerical simulations of globular cluster evolution were undertaken in the early 1970 s , by two groups , at princeton and cornell , using different monte - carlo methods , now known as the `` princeton method '' and the `` cornell method '' ( see spitzer 1987 for an overview of the methods ) . in the princeton method , the orbit of each star is integrated numerically , while the diffusion coefficients for the change in velocity @xmath4 and @xmath5 ( which are calculated analytically ) are selected to represent the average perturbation over an entire orbit . energy conservation is enforced by requiring that the total energy be conserved in each radial region of the cluster . the princeton method assumes an isotropic , maxwellian velocity distribution of stars to compute the diffusion coefficients , and hence does not take in to account the anisotropy in the orbits of the field stars . one advantage of this method is that , since it follows the evolution of the cluster on a dynamical timescale , it is possible to follow the initial `` violent relaxation '' phase more easily . unfortunately , for the same reason , it also requires considerably more computing time compared to other versions of the monte - carlo method . in the cornell method , also known as the `` orbit - averaged monte - carlo method '' , the changes in energy @xmath6 and angular momentum @xmath7 per unit time ( averaged over an orbit ) are computed analytically for each star . hence , the time consuming dynamical integration of the orbits is not required . in addition , since the diffusion coefficients are computed for both @xmath8 _ and _ @xmath9 , the cornell method does take in to account the anisotropy in the orbits of the stars . the `` hnon method '' is a variation of the cornell method , in which the velocity perturbations are computed by considering an encounter between pairs of neighboring stars . this also allows the local 2-d phase space distribution @xmath10 to be sampled correctly . our code is based on a modified version of hnon s method . we have modified hnon s algorithm for determining the timestep and computing the representative encounter between neighboring stars . our method allows the timestep to be made much smaller in order to resolve the dynamics in the core more accurately . we describe the basic method and our modifications in more detail below in 2 . the monte - carlo methods were first used to study the development of the gravothermal instability ( spitzer & hart 1971a , b ; hnon 1971a , b ) and to explore the effects of a massive black hole at the center of a globular cluster ( lightman & shapiro 1977 ) . in those early studies , the available computational resources limited the number of particles used in the monte - carlo simulations to @xmath11 . since this is much smaller than the real number of stars in a globular cluster ( @xmath12 ) , each particle in the simulation represents effectively a whole spherical shell containing many stars , and the method provides no information about individual objects and their dynamical interactions . more recent implementations have used up to @xmath13 particles and have established the method as a promising alternative to direct @xmath2-body integrations ( stodlkiewicz 1986 ; giersz 1998 ) . monte - carlo simulations have also been used to study specific interaction processes in globular clusters , such as tidal capture ( di stefano & rappaport 1994 ) , interactions involving primordial binaries ( hut , mcmillan , & romani 1992 ) and stellar evolution ( portegies zwart 1997 ) . however , in all these studies the background cluster was assumed to have a _ fixed structure _ , which is clearly not realistic . the main goal of our study is to perform monte - carlo simulations of cluster dynamics treating both the cluster itself and all relevant interactions self - consistently , including all dynamical interactions involving primordial binaries . this idea is particularly timely because the latest generation of parallel supercomputers now makes it possible to do such simulations for a number of objects equal to the actual number of stars in a globular cluster . using the correct number of stars in a cluster simulation ensures that the relative rates of different dynamical processes ( which all scale differently with the number of stars ) are correct . this is crucial if many different dynamical processes are to be incorporated , as we plan to do in this study . in addition to monte - carlo and @xmath2-body simulations , a new method was developed , mainly by cohn and collaborators , based on the direct numerical integration of the orbit - averaged fokker - planck equation ( cohn 1979 , 1980 ; statler , ostriker & cohn 1987 ; murphy & cohn 1988 ) . unlike the monte - carlo methods , the direct fokker - planck method constructs the ( smooth ) distribution function of the system on a grid in phase space , effectively providing the @xmath14 limit of the dynamical behavior . the original formulation of the method used a 2-d phase space distribution function @xmath10 ( cohn 1979 ) . however , the method was later reduced to a 1-d form using an isotropized distribution function @xmath15 ( cohn 1980 ) . the reduction of the method to one dimension speeded up the calculations significantly . in addition , the use of the chang & cooper ( 1970 ) differencing scheme provided much better energy conservation compared to the original 2-d method . the 1-d method provided very good results for isolated clusters , in which the effects of velocity anisotropy are small . the theoretically predicted emergence of a power - law density profile in the late stages of evolution for isolated single - component systems has been clearly verified using this method ( cohn 1980 ) . calculations that include the effects of binary interactions , including primordial binaries , have also allowed the evolution to be followed beyond core collapse ( gao 1991 ) . however , results obtained using the 1-d method showed substantial disagreement with @xmath2-body results for tidally truncated clusters , in which the evaporation rate is dramatically affected by the velocity anisotropy . ignoring the velocity anisotropy led to a significant overestimate of the evaporation rate from the cluster , resulting in shorter core - collapse times for tidally truncated clusters ( portegies zwart 1998 ) . a recent implementation of the fokker - planck method by drukier ( 1999 ) has extended the algorithm to allow a 2-d distribution function , while also improving the energy conservation . a similar 2-d method has also been developed by takahashi ( 1995 , 1996 , 1997 ) . the new implementations produce much better agreement with @xmath2-body results ( takahashi & portegies zwart 1998 ) , and can also model the effects of mass loss due to stellar evolution ( takahashi & portegies zwart 1999 ) , as well as binary interactions ( drukier 1999 ) . for many years direct @xmath2-body simulations were limited to systems with @xmath16 stars . new , special - purpose computing hardware such as the grape ( makino 1997 ) now make it possible to perform direct @xmath2-body simulations with up to @xmath17 single stars ( hut & makino 1999 ) , but the inclusion of a significant fraction of primordial binaries in these simulations remains prohibitively expensive . the large dynamic range of the orbital timescales of the stars in the cluster presents a serious difficulty for @xmath2-body simulations . the orbital timescales can be as small as the periods of the tightest binaries . the direct integration of stellar orbits is especially plagued by this effect . these difficulties are overcome using techniques such as individual integration timesteps , and various schemes for regularizing binaries ( see , e.g. , aarseth 1998 for a review ) . these short - cuts introduce specific selection effects , and complicate code development considerably . instead , in the monte - carlo methods , individual stellar orbits are represented by their constants of the motion ( energy @xmath6 and angular momentum @xmath7 for a spherical system ) and perturbations to these orbits are computed periodically on a timestep that is a fraction of the relaxation time . thus the numerical integration proceeds on the natural timescale for the overall dynamical evolution of the cluster . note also that , because of exponentially growing errors in the direct integration of orbits , @xmath2-body simulations , just like monte - carlo simulations , can only provide a statistically correct representation of cluster dynamics ( goodman 1993 ; hernquist , hut , & makino 1993 ) . a great advantage of the monte - carlo method is that it makes it particularly easy to add more complexity and realism to the simulations one layer at a time . the most important processes that we will focus on initially will be stellar evolution and mass loss through a tidal boundary . interactions of single stars with primordial binaries , binary - binary interactions , stellar evolution in binaries , and a detailed treatment of the influence of the galaxy , including tidal shocking of the cluster when it passes through the galactic disk , will be incorporated subsequently . recent improvements in algorithms and available computational resources have allowed meaningful comparisons between the results obtained using different numerical methods ( see for example the `` collaborative experiment '' by heggie 1999 ) . however , there still remain substantial unresolved differences between the results obtained using various methods . for example , the lifetimes of clusters computed recently using different methods have been found to vary significantly . lifetimes of some clusters computed using direct fokker - planck simulations by chernoff & weinberg ( 1990 ) are up to an order of magnitude shorter than those computed using @xmath2-body simulations and a more recent version of the fokker - planck method ( takahashi & portegies zwart 1998 ) . it has been found that , in many cases , the differences between the two methods can be attributed to the lack of an appropriate discrete representation of the cluster in the fokker - planck simulations . this can lead to an over - estimate of the mass - loss rate from the cluster , causing it to disrupt sooner . recently , new calibrations of the mass loss in the fokker - planck method ( takahashi & portegies zwart 1999 ) that account for the slower mass loss in discrete systems , has led to better agreement between the methods . the limitation of @xmath2-body simulations to small @xmath2 ( especially for clusters containing a large fraction of primordial binaries ) makes it particularly difficult to compare the results with fokker - planck calculations , which are effectively done for very large @xmath2 ( portegies zwart 1998 , heggie 1999 ) . this gap can be filled very naturally with monte - carlo simulations , which can be used to cover the entire range of @xmath2 s not accessible by other methods . the realization over the last 10 years that primordial binaries are present in globular clusters in dynamically significant numbers has completely changed our theoretical perspective on these systems ( see . e.g. , the review by hut 1992 ) . most importantly , dynamical interactions between hard primordial binaries and other single stars or binaries are now thought to be the primary mechanism for supporting a globular cluster against core collapse ( mcmillan , hut , & makino 1990 , 1991 ; gao 1991 ) . in addition , exchange interactions between primordial binaries and compact objects can explain very naturally the formation of large numbers of x - ray binaries and recycled pulsars in globular cluster cores ( sigurdsson & phinney 1995 ; davies & hansen 1998 ; portegies zwart 1997 ) . previously , it was thought that primordial binaries were essentially nonexistent in globular clusters , and so other mechanisms such as tidal capture and three - body encounters had to be invoked in order to form binaries dynamically during core collapse . however , these other mechanisms have some serious problems , and are much more likely to result in mergers than in the formation of long - lived binaries ( chernoff 1996 ; kochanek 1992 ; kumar & goodman 1996 ) . hubble space telescope ( hst ) observations have provided direct constraints on primordial binary fractions in clusters . the binary fraction is a key input parameter for any realistic study of cluster dynamics . for example , the recent observation of a broadened main sequence in ngc 6752 , based on hst pc images of its core , suggest that the binary fraction is probably in the range 15%38% in the inner core ( rubenstein & bailyn 1997 ) . despite the fact that binaries play a crucial role in the late phases of evolution of a cluster , the overall evolution of a binary population within a cluster , and its direct implications for the formation rate of observable binaries and blue stragglers remains poorly understood . in addition , the relative importance of binaries in a cluster , like many other physical processes , may depend on the actual size ( @xmath2 ) of the cluster . this makes it difficult to extend results obtained from smaller @xmath2-body simulations to realistic globular cluster models . when the initial primordial binary fraction is below a certain critical value , a globular cluster core can run out of binaries before the end of its lifetime , i.e. , before being evaporated in the tidal field of the galaxy ( mcmillan & hut 1994 ) . without the support of binaries , the cluster will undergo a much deeper core collapse and so - called gravothermal oscillations ( sugimoto & bettwieser 1983 ; breeden 1994 ; makino 1996 ) . at maximum contraction , the core density may increase by many orders of magnitude , leading to greatly enhanced interaction rates . our new monte - carlo code will allow us to follow the evolution of a cluster through this phase , including in detail the dynamical interactions between the @xmath18 objects in the core . of particular interest is the possibility that successive collisions and mergers of ms stars might lead to a _ runaway process_. the recent hst observations of stellar cusps in the cores of m15 ( guhathakurta 1996 , sosin & king 1997 ) and ngc 6624 ( sosin & king 1995 ) have generated renewed interest in the possibility of massive black holes in globular clusters . the most significant unresolved theoretical issue concerns the manner in which such a black hole could form in a dense cluster . one of the likely routes , which we plan to examine with our simulations , is via the collisions and mergers of main - sequence stars , leading to the runaway build - up of a massive object and its eventual gravitational collapse ( portegies zwart 1999 ) . a very significant effect of the galactic environment on a cluster is the gravitational shock heating of the cluster due to passages close to the bulge and through the disk . when a cluster passes through the galactic disk , it experiences a time - varying gravitational force that pulls the cluster toward the equatorial plane . the net effect of the shock is to induce an increase in the average energy of the stars , causing the binding energy of the cluster to decrease , and the rate of escape of stars through evaporation to increase ( chernoff , kochanek , & shapiro 1986 ) . in addition , in some cases , `` shock - induced relaxation '' can be almost as important as two - body relaxation in the overall evolution of the cluster ( gnedin , lee & ostriker 1999 ; gnedin & ostriker 1997 ) . both the energy shift and the relaxation induced by tidal shocking can be incorporated in our monte - carlo method by assuming an orbit for the cluster around the galactic center and introducing an appropriate perturbation to the energy of the stars each time the cluster passes through the disk . this can be done without adding much computational overhead to the problem , since tidal shocking only occurs twice during the orbital period of the cluster . the ability of the monte - carlo method to model such effects simultaneously with a realistic treatment of the internal dynamical evolution of the cluster makes it a very useful tool in verifying and extending previous results obtained using other methods . the star - by - star representation of the system in monte - carlo simulations makes it easy to study of the evolution of a particular population of stars within a cluster . for example , the evolution of a population of neutron stars could be followed closely , to help predict their properties and expected distributions within clusters . of particular interest are m15 and 47 tuc , which have both been the targets of several highly successful searches for pulsars ( anderson 1992 ; robinson 1995 ; camilo 2000 ) . the observed properties of pulsars in these clusters are found to be very different . the pulsars in 47 tuc are all millisecond pulsars , and most are in short - period binaries , while those in m15 are mostly single recycled pulsars with longer pulse periods . this suggests that these two clusters may provide very different dynamical environments for the formation of recycled pulsars .

our method is based on a modified version of hnon s monte - carlo algorithm for solving the fokker - planck equation . our code allows us to follow the evolution of a cluster containing up to stars to core collapse in hours of computing time . in this paper we find excellent agreement with other methods , establishing our new code as a robust tool for the numerical study of globular cluster dynamics using a realistic number of stars . = cmb10 scaled 2

we present a new parallel supercomputer implementation of the monte - carlo method for simulating the dynamical evolution of globular star clusters . our method is based on a modified version of hnon s monte - carlo algorithm for solving the fokker - planck equation . our code allows us to follow the evolution of a cluster containing up to stars to core collapse in hours of computing time . in this paper we present the results of test calculations for clusters with equal - mass stars , starting from both plummer and king model initial conditions . we consider isolated as well as tidally truncated clusters . our results are compared to those obtained from approximate , self - similar analytic solutions , from direct numerical integrations of the fokker - planck equation , and from direct-body integrations performed on a grape-4 special - purpose computer with . in all cases we find excellent agreement with other methods , establishing our new code as a robust tool for the numerical study of globular cluster dynamics using a realistic number of stars . = cmb10 scaled 2

astro-ph9909115

r

in this section , we describe our first results using the new monte - carlo code to compute the evolution of the plummer and king models . we explore the evolution of the plummer model in detail , and compare our results with those obtained using fokker - planck and @xmath2-body methods . we also compare core - collapse times and mass - loss rates for the series of king models ( @xmath160 ) , including a tidal radius , with similar results obtained by quinlan ( 1996 ) using a 1-d fokker - planck method . we first consider the evolution of a cluster with the plummer model ( which is a polytropic model , with index @xmath161 ; see , e.g. , binney & tremaine 1987 ) as the initial condition . perhaps the best known result for single component systems , is the expected homologous evolution of the halo , leading to the eventual development of a power - law density profile between the core and the outer halo , during the late phases of evolution . at late times the cluster evolves through a sequence of nearly self - similar configurations , with the core contracting and a power - law halo with density @xmath162 expanding out . the development of this power law has been predicted theoretically ( lynden - bell & eggleton 1980 ; heggie & stevenson 1988 ) , and verified using direct fokker - planck integrations ( cohn 1980 ) . the exponent @xmath41 is theoretically and numerically estimated to be about @xmath163 ( spitzer 1987 ) . however , since the theoretical derivations are based on an analysis of the fokker - planck equation , it is not surprising that the numerical fokker - planck integrations ( which solve the same fokker - planck equation numerically ) reproduce the theoretical exponent exactly . due to limitations in computing accurate density profiles using a small number of stars , this result has not been confirmed independently using an @xmath2-body simulation . here , we explore numerically for the first time the development of this power law using an independent method . some early results were obtained using previous versions of the monte - carlo method , but with a small number of stars @xmath19 ( duncan & shapiro 1982 ) . although the monte - carlo method can be thought of as just another way of solving the fokker - planck equation , there are significant differences between solving the equation in the continuous limit ( @xmath164 ) , as in direct fokker - planck integrations , and by using a discrete system with a finite @xmath2 as in our method . there are also many subtle differences in the assumptions and approximations made in the two methods , and even in different implementations of the same method . in figures 2a c we show the density profile of the cluster at three different times during its evolution , up to core collapse . we start with an @xmath127 isolated plummer model , and follow the evolution up to core - collapse , which occurs at @xmath165 . this simulation , performed with @xmath127 stars , took about 18 cpu hours on the sgi / cray origin2000 . in our calculations , the core - collapse time is taken as the time when the the innermost lagrange radius ( radius containing 0.3% of the total mass of the cluster ) becomes smaller than 0.001 ( in our units described in 2.8 ) , at which point the simulation is terminated . given the very rapid evolution of the core near core collapse , we find that we can determine the core - collapse time to within @xmath166 . the accuracy is limited mainly by noise in the core . the value we obtain for @xmath167 is in very good agreement with other core - collapse times between @xmath168 for the plummer model , reported using other methods . for example quinlan ( 1996 ) obtains a core collapse time of @xmath169 for the plummer model using a 1-d fokker - planck method , and takahashi ( 1993 ) finds a value of @xmath170 , using a variational method to solve the 1-d fokker - planck equation . figure 2a shows the density profile at an intermediate time @xmath171 during the evolution . the dotted line indicates the initial plummer profile . at this point in the evolution , we still see a well defined core , with the core density increased by a factor of @xmath172 compared to the initial core density . we see the power - law density profile developing , with the best - fit index @xmath173 . in figure 2b , we show the density profile just before core collapse , at @xmath174 . we see that the core density has now increased by a factor of @xmath175 over the initial core density . the power law is now clearly visible , with the best - fit index @xmath176 . finally , in figure 2c , we show the density profile at core - collapse , @xmath177 . the dashed line now indicates the _ theoretical _ power law with @xmath178 . we see that the actual density profile seems to approach the theoretical profile asymptotically as the system approaches core collapse . at this point in the evolution , the core density as measured in our simulation is about @xmath179 times greater than the initial density . in a globular cluster with @xmath180 , an average stellar mass @xmath181 , and a mean velocity dispersion @xmath182 , this would correspond to a number density of @xmath183 . note that a real globular cluster is not expected to reach such high core densities , since the formation of binaries and the subsequent heating of the core due to binary interactions become significant at much lower densities . numerical noise due to the extremely small size of the core makes it difficult to determine the core radius and density accurately at this stage . this also causes the numerical accuracy of the monte - carlo method to deteriorate , forcing us to stop the computation . thus , we find that the power - law structure of the density profile as the cluster approaches core collapse is consistent with theoretical predictions , and the power - law index approaches its theoretical value asymptotically during the late stages of core collapse . next , we look at the evolution of the lagrange radii ( radii containing constant fractions of the total mass ) , and we compare our results with those of an equivalent @xmath2-body simulation . in figure 3 , we show the evolution of the lagrange radii for an @xmath3 direct @xmath2-body integration by makino ( 1996 ) and for our monte - carlo integration with @xmath184 stars . time in the direct @xmath2-body integration is scaled to the initial relaxation time ( the standard time unit in our monte carlo method ) using equation ( 27 ) with @xmath185 ( see heggie & mathieu 1986 ; giersz & heggie 1994 ; makino 1996 ) . the agreement between the @xmath2-body and monte carlo results is excellent over the entire range of lagrange radii and time . the small discrepancy in the outer lagrange radii is caused in part by a different treatment of escaping stars in the two models . in the monte carlo model , escaping stars are removed from the simulation and therefore not included in the determination of the lagrange radii , whereas in the @xmath2-body model escaping stars are not removed . the difference is further explained by the effect of strong encounters , which is greater in the @xmath2-body simulation by a factor @xmath186 , or about 20% . in an isolated cluster , the overall evaporation rate is very low ( less than 1% of stars escape up to core collapse ) . in this regime , the escape of stars is dominated by strong interactions in the core . since the orbit - averaged fokker - planck equation is only valid when the fractional energy change per orbit is small , it does not account for strong interactions . hence , our monte - carlo simulations can not accurately predict the rate of evaporation from an isolated cluster ( see , e.g. , binney & tremaine 1987 , 8.4 ) . this problem does not occur in tidally truncated clusters , where the escape rate is much higher , and is dominated by the diffusion of stars across the tidal boundary , and not by strong interactions . in figure 4 we show the evolution of various global quantities for the system during the same simulation as in figure 3 . the virial ratio ( @xmath187 , where @xmath188 and @xmath189 are the total kinetic and potential energies of the cluster ) remains very close to 0.5 ( within 1% ) , indicating that dynamical equilibrium is maintained very well during the entire simulation . the virial ratio provides a very good measure of the quality of our numerical results , since it is not controlled in our calculations ( except for the initial model , which is constructed to be in equilibrium ) . we see that in the absence of a tidal radius , there is very little mass loss ( less than 1% ) , and hence very little energy is carried away by escaping stars . king models ( king 1966 ) have long been used to fit observed profiles of globular clusters . they usually provide a very good fit for most clusters , except for those which have reached core collapse . a king model has a well - defined , nearly constant - density core , and a `` lowered maxwellian '' velocity distribution , which represents the presence of a finite tidal radius . a king model is usually specified in terms of the dimensionless central potential @xmath190 or , equivalently , the central concentration @xmath191 , where @xmath192 is the tidal radius , and @xmath71 is the core radius . we study the evolution of the entire family of king models from @xmath193 to @xmath194 , in two different configurations . we first consider the evolution of an isolated cluster i.e. , even though the initial king model is truncated at its finite tidal radius , we do not enforce that tidal boundary during the evolution , allowing the cluster to expand indefinitely . we compute the core - collapse times for the entire sequence of king models . we then redo the calculations with a tidal boundary in place , to determine the enhanced rate of mass loss from the cluster and the final remaining mass at the time of core collapse . we compare our results for the sequence of king models with equivalent results obtained by quinlan ( 1996 ) using direct fokker - planck integrations in 1-d . in table 1 , we show the core collapse times for the various models , along with the equivalent results from quinlan ( 1996 ) . all our monte - carlo calculations were performed using @xmath127 stars . we see that the agreement in the core collapse times for isolated clusters is excellent ( within a few percent for the low-@xmath190 models , and within 10% up to @xmath195 ) . for @xmath196 , the agreement is still good , considering that the models start off in a highly collapsed state and therefore have very short core - collapse times , which leads to larger fractional errors . in figure 5 , we show the evolution of the lagrange radii for a tidally truncated king model with @xmath197 . the initial tidal radius is @xmath198 times the virial radius . in this case , the mass loss through the tidal boundary is very significant , as is seen from the evolution of the outer lagrange radii . the mass loss causes the tidal radius to constantly move inward , which further accelerates the process . figure 6 shows the evolution of the total mass and energy of the tidally truncated cluster . only 44% of the initial mass is retained in the cluster at core - collapse . also , the binding energy of the cluster is significantly lower at core - collapse , since the escaping stars carry away mass as well as kinetic energy from the cluster . in contrast , the evolution of an isolated @xmath197 king model is very much like that of the isolated plummer model described earlier , with a very low mass loss rate , and a longer core - collapse time of @xmath199 ( in excellent agreement with the value of @xmath200 computed by quinlan 1996 ) . our results for clusters with a tidal boundary show systematic differences from the 1-d fokker - planck results of quinlan ( 1996 ) . we find that the mass loss through the tidal boundary is significantly higher for the low - concentration models ( @xmath201 ) in the fokker - planck models . for the high - concentration ( @xmath202 ) models , the difference between isolated models and tidally truncated models is small , and the agreement between the methods remains very good . hence , for low @xmath190 , our models undergo core collapse at a much later time compared to the fokker - planck models , and retain more mass at core collapse . this discrepancy is caused by the 1-d nature of the fokker - planck models . in 1-d fokker - planck calculations , stars are considered lost from the cluster when their energy is greater than the energy at the tidal radius . this clearly provides an overestimate of the escape rate , since it assumes the most extended radial orbits for stars , and ignores stars on more circular orbits with high angular momentum , which would have much smaller orbits at the same energy . in contrast , in the monte - carlo method , the orbit of each star is computed using its energy _ and _ angular momentum , which allows the apocenter distance to be determined correctly . stars are considered lost only if their apocenter distances from the cluster center are greater than the tidal radius . as stars on radial orbits are removed preferentially , this creates an anisotropy within the cluster , which affects the overall evolution . the artificially high rate of mass loss in 1-d fokker - planck simulations has also been pointed out recently in comparisons with @xmath2-body results ( portegies zwart 1998 ; takahashi & portegies zwart 1999 ) . these authors show that , with appropriate modifications , the results of 2-d fokker - planck calculations can be made to agree much better with those from @xmath2-body simulations . indeed , we find that our result for the @xmath197 model with a tidal boundary ( @xmath203 , and @xmath204 ) agrees much better with that obtained using the improved 2-d fokker - planck method , which gives @xmath205 , and @xmath206 ( takahashi 1999 , private communication ) . for further comparison , and to better understand the cause of the higher mass loss in the 1-d fokker - planck calculation , we have performed a monte - carlo simulation using the same energy - based escape criterion that is used in the 1-d fokker - planck integrations . we find that using the energy - based escape criterion for @xmath197 gives @xmath207 , and @xmath208 , which agrees better with the 1-d fokker - planck result , but a significant discrepancy still remains . this is not surprising , since , even when using a 1-d escape criterion , our underlying method still remains 2-d . again , our result agrees better with the corresponding result obtained by takahashi ( 1999 , private communication ) using the energy - based escape criterion in his 2-d fokker - planck method , @xmath209 , and @xmath210 . it is reassuring to note that the differences between our 2-d results and 1-d fokker - planck results are also mirrored in the 2-d fokker - planck calculations of takahashi . since our monte - carlo method is intrinsically 2-d , it is not possible for us to do a true 1-d ( isotropic ) calculation to compare results directly with 1-d fokker - planck calculations .

we present the results of test calculations for clusters with equal - mass stars , starting from both plummer and king model initial conditions . our results are compared to those obtained from approximate , self - similar analytic solutions , from direct numerical integrations of the fokker - planck equation , and from direct-body integrations performed on a grape-4 special - purpose computer with . in all cases

we present a new parallel supercomputer implementation of the monte - carlo method for simulating the dynamical evolution of globular star clusters . our method is based on a modified version of hnon s monte - carlo algorithm for solving the fokker - planck equation . our code allows us to follow the evolution of a cluster containing up to stars to core collapse in hours of computing time . in this paper we present the results of test calculations for clusters with equal - mass stars , starting from both plummer and king model initial conditions . we consider isolated as well as tidally truncated clusters . our results are compared to those obtained from approximate , self - similar analytic solutions , from direct numerical integrations of the fokker - planck equation , and from direct-body integrations performed on a grape-4 special - purpose computer with . in all cases we find excellent agreement with other methods , establishing our new code as a robust tool for the numerical study of globular cluster dynamics using a realistic number of stars . = cmb10 scaled 2

0910.2097

i

renormalization group ( rg ) , which is a powerful instrument for analyzing different strongly coupled systems @xcite(see also @xcite for more recent reviews ) , is usually based upon an appropriate division of the whole set of variables into two subsets : so called `` fast '' and `` slow '' variables with subsequent elimination of the fast ones . the resulting slow system is usually expected to behave essentially in the same way as the initial one but with coupling constants changed . successive application of this transformation results in a flow in the space of couplings . after each step of the rg transformation the information about exact values of fast variables is lost for the observer to whom only slow variables are available . it seems natural then to expect , that this information loss should lead to the irreversible character of the corresponding rg flow . this irreversibility is a subject of an intensive study for several decades now , starting from the famous work of zamolodchikov @xcite , who showed under certain assumptions that in two dimensions ( 2d ) there exists a function on a space of coupling constants ( a kind of lyapunov function ) which always decreases along the rg flow and at fixed points coincides with the central charge @xmath0 of corresponding conformal theories . `` irreversibility '' here means that the flow in the space of couplings resembles that of a simple dissipative system with a given trajectory never returning back to its starting point , thus excluding limit cycles or more complex strange attractors . in 2d theories the @xmath0-theorem of ref . @xcite states that the rg evolution is exactly of this type and looks like a simple monotonic flow downhill in the couplings space from fixed points with large @xmath0 to those with smaller values of the central charge . much work have been done in this direction and the @xmath0-theorem was studied in detail with its possible generalizations to higher dimensions ( see e.g. @xcite and references therein and also @xcite for quite recent development ) . still the interesting possibility that in general the flow may be more complicated , and may even exhibit chaotic behavior , like in case of many other nonlinear mappings , attracts some attention @xcite ( probably the first example of a chaotic rg flow was found for spin systems on hierarchical lattices @xcite , see also @xcite ) . the models where such peculiarities are observed are however rather artificial , so that the question whether they could take place in more realistic cases remains somewhat unclear . though this problem is rather complicated mathematically it looks much simpler from the physical point of view . the wilsonian rg transformation is designed in such a way that all finite dimensionless correlation lengths in a translationally invariant system always decrease @xcite . to say this another way , all masses ( measured in units of an ultra - violet cut - off ) grow and it seems quite natural that the effective number of massless modes , ( in 2d measured by the central charge @xmath0 ) can not increase . the argument based on the growth of masses , though not completely rigorous , is quite general , hence something unusual , like limit cycles in the flow , may be expected only in some special systems with only infinite correlation lengths or with infinite number of correlation lengths which can be arbitrarily large ( when we have e.g. a self - similar spectrum of masses converging to zero @xcite ) . but in systems with finite number of well defined correlation lengths the rg flow should probably always be irreversible . this argument however seems to be unrelated to the aforementioned information loss and information aspects probably play no role in the irreversibility , which may seem somewhat strange . probably the most known attempt to study rg irreversibility using information theory tools is the approach of ref . @xcite where the relative entropy was introduced in quantum field theory and some monotonicity theorems for it , as a function of relevant couplings , were proved and its relation to @xmath0-theorem was discussed . in this paper we present a somewhat different , entirely information theory based approach to the problem of the rg flow , oriented more on discrete real space rg transformations in different lattice spin systems . clearly , information - theoretic considerations are too general to lead to some non - trivial concrete results , but still , as we shall see below they may impose some restrictions on the possible character of the flow . first , in section 2 we evaluate an exact amount of information loss for a single step of the renormalization as a kind of conditional entropy of fast variables ( compare with @xcite ) . as one might expect , this information loss is equal to the decrease of entropy under the rg transformation . thus it is possible to establish a general theorem about the monotonic decrease of the total entropy ( and relative entropy as well ) under general coarse graining as a result of information loss . the monotonic decrease of entropy along the rg flow is neither something unusual ( see e.g. @xcite ) nor very interesting , because the entropy is proportional to the total number of degrees of freedom and should certainly decrease when some of them are integrated out . hence this monotonic behavior does not directly lead to the irreversibility of the flow . an interesting thing may happen however , if the entropy of a finite system possesses an additive size - independent part . if this part of the entropy also decreases , as the total entropy does , then it may provide the proper lyapunov function , because it does not explicitly depend on the number of variables and its change is entirely due to the flow of coupling constants . we will show that this takes place in 1d ising model , where this subextensive part of the entropy is known as the `` excess entropy '' and was studied in detail as a measure of statistical complexity of spatial structures @xcite . this excess entropy equals to the mutual entropy of two halves of the system which is actually the reason why it decreases under coarse graining . unfortunately we are unable to present a general theorem concerning the monotonicity of such excess entropy in higher dimensions . it appears possible though to prove quite a different monotonicity theorem , but only for a certain class of real space lattice rg transformations , namely for decimations , when exactly half of variables are eliminated on each step . the proof is based on the analysis of a new quantity introduced in section 3,mutual information of slow and fast variables . contrary to the information loss this mutual information shows how much information about eliminated fast variables is still present after a single step of the wilsonian renormalization . the nonnegativity of the mutual information may alone impose some restrictions on the character of the flow leading to its irreversibility . for the decimations of the aforementioned type in lattice models we will show that the entropy per lattice site monotonically grows as a result of the positivity of the mutual information of spins on two identical sublattices , one of which is eliminated in the course of the rg transformation . therefore such decimation transformations , though they results in highly non - linear mappings , always lead to irreversible flows in the space of couplings . simple examples of such a behavior are discussed in section 4 , where one- and two - dimensional classical spin models and also the continuum limit gaussian model are considered . note , however , that the theorem holds true only for systems with real actions , when information theory can be applied , while e.g. it is not valid for the ising model with complex external magnetic field where the decimation rg flow is known to be chaotic @xcite . the theorem is also invalid for spin models on hierarchical lattices @xcite , because decimations are not associated there with decomposition of these finite and inhomogeneous lattices into two identical sublattices . the entropy per site growth may seem somewhat unexpected , because it takes place not only in the trivial case , when the flow goes to the high - temperature fixed point , but even when we start from points located in the ordered phase . rg trajectories that start from points below the phase transition can never end in the fully disordered trivial fixed point , since for decimation the mean magnetization is conserved along the flow , but nevertheless the entropy per site ( and hence the amount of disorder ) will always grow . this is a peculiar feature of the decimation and does not take place for other possible renormalization schemes , like e.g. the majority rule block spin transformation also discussed in section 4 .

we present a possible approach to the study of the renormalization group ( rg ) flow based entirely on the information theory . its positivity results in the monotonic decrease of the informational entropy under renormalization . this , however , does not necessarily imply the irreversibility of the rg flow , because entropy is an extensive quantity and explicitly depends on the total number of degrees of freedom , which is reduced . it is shown that for certain real space decimation transformations the positivity of the mutual information directly leads to the monotonic growth of the entropy per lattice site along the rg flow and hence to its irreversibility .

we present a possible approach to the study of the renormalization group ( rg ) flow based entirely on the information theory . the average information loss under a single step of wilsonian rg transformation is evaluated as a conditional entropy of the fast variables , which are integrated out , when the slow ones are held fixed . its positivity results in the monotonic decrease of the informational entropy under renormalization . this , however , does not necessarily imply the irreversibility of the rg flow , because entropy is an extensive quantity and explicitly depends on the total number of degrees of freedom , which is reduced . only some size - independent additive part of the entropy could possibly provide the required lyapunov function . we also introduce a mutual information of fast and slow variables as probably a more adequate quantity to represent the changes in the system under renormalization and evaluate it for some simple systems . it is shown that for certain real space decimation transformations the positivity of the mutual information directly leads to the monotonic growth of the entropy per lattice site along the rg flow and hence to its irreversibility .

0910.2097

c

in this paper we have tried to understand what limitations on the rg flow may follow from the information theory , because wilsonian rg transformation , when some fast variables are integrated out , is obviously related to the information loss . this transformation is similar in a sense to a signal transmission through a noisy channel , the fast variables being the input , while the slow ones play the role of the output available to a receiver . the information loss is defined here as an average conditional entropy of the eliminated fast variables when the remaining slow variables are fixed . from the nonnegativity of this quantity ( which holds at least for systems with discrete variables , like e.g. classical spins ) it follows immediately that the informational entropy @xmath19 of the system can not increase under renormalization . unfortunately this result is not very interesting , and does not lead to the irreversibility of the rg flow , because it applies to the total extensive entropy , proportional to the size of the system , which effectively shrinks after renormalization . this shrinking is evident for real space rg schemes , where some lattice sites are eliminated and the system size is smaller if measured in new lattice constant , but equally applies to momentum space wilsonian renormalization due to final rescaling of momenta . only if @xmath19 possesses some volume independent additive part @xmath150 , then this part , if it also decreases under renormalization , may provide the required lyapunov function , that depends only on couplings . physically its decrease may be attributed to a loss of information about massless modes , but this does not follow directly from that of @xmath19 and should be deduced independently . then , to be monotonous @xmath150 must have also some independent definition . for 1d ising model this quantity is just the subextensive excess entropy and we explicitly check its monotonicity under rg transformation . this behavior for a finite block of spins in an infinite chain follows directly from information theory , because excess entropy in this case is just the mutual information of two halves of the system @xcite , which decreases under coarse graining . note also that for 1d systems with periodic boundary conditions the excess entropy is @xmath151 where @xmath152 is the degeneracy of the largest eigenvalue of the transfer matrix which always decreases along the rg flow . this is somewhat similar to what is known for critical 2d systems defined on a long cylinder of size @xmath335 with , say , @xmath336 and periodic boundary condition in the @xmath295 direction . in this case the first finite size correction in the expansion of entropy in @xmath337 is @xmath338 ) @xcite , where @xmath0 is the central charge . therefore the subextensive part @xmath150 in entropy in 2d should decrease as a consequence of the @xmath0-theorem . however in both these examples the subleading term in entropy is discontinuous and does not directly lead to a proper lyapunov function . this means that the extraction of the required part from the entropy of finite size system is somewhat ambiguous and depends on the boundary condition . one may suggest , however , that in general there might exist some size - independent information - based quantity defined on the whole space of couplings ( maybe some kind of relative entropy or higher order mutual information @xcite ) that is monotonic along the flow and at fixed points coincides with some kind of excess entropy , but this point is not clear . the main aim of the present paper was , however , apart from demonstrating some examples of informational approach , to introduce a different quantity , namely the mutual information of fast and slow variables @xmath88 , which shows how much information about the eliminated variables is still stored in the renormalized effective action . this quantity does not suffer from the `` shrinking size '' trouble and is less sensitive to the overall decrease in the number of degrees of freedom , though it is generally more difficult to evaluate . there exist however some real space decimation transformations for which this mutual information can be easily calculated . this happens e.g. if the original lattice may be decomposed in two identical sublattices and rg transformation eliminates spins on one sublattice . then the nonnegativity of @xmath88 results in the increase of entropy per lattice cite and rg flow resembles a relaxation to equilibrium . this result does not depend on interactions and may be true also for a larger set of models . what is actually needed is that the rg transformation must be represented as a product of such decimations . the approach to irreversibility based on the mutual information is different from those trying to generalize zamolodchikov s @xmath0-theorem and possibly may provide some additional information about the rg flows . it may appear interesting also to apply the present approach to the momentum space renormalization in field theory or to study more complicated correlations along the flow and some higher - order mutual information . i am very grateful to a.c.d . van enter , j. gaite , v. losyakov , a. marshakov , a. morozov for valuable discussions and comments , and to l. shchur for some useful advices . the work was supported in part by rfbr grants 09 - 02 - 00886 , 10 - 02 - 00509 , rfbr - ukraine 09 - 01 - 90493 and by federal agency for science and innovations of russian federation under contract 14.740.11.0081 . wilson and j. kogut , phys . rep . * 12 * 75 ( 1974 ) ; k.g . wilson , rev . phys . * 47 * 773 ( 1975 ) c. bagnuls and c bervillier , phys . rep . * 348 * 91 ( 2001 ) ; b. delamotte , arxiv : cond - mat/0702365 a.b . zamolodchikov , pisma zh . teor . fiz . * 43 * 565 ( 1986 ) [ jetp lett . * 43 * 730 ( 1986 ) ] j.l . cardy , phys . lett . * b215 * 749 ( 1988 ) ; i. jack and h. osborn , nucl . phys . * b343 * 647 ( 1990 ) ; a. cappelli , d. friedan and j.i . latorre , nucl . * b352 * 616 ( 1991 ) ; a.h . castro neto and e. fradkin , nucl . * b400 * 525 ( 1993 ) ; s. forte and j.i . latorre , nucl . * b535 * 709 ( 1998 ) ; t. appelquist , a.g . cohen and m. schmaltz , phys . d * 60 * 045003 ( 1999 ) ; a. cappelli , g. dappollonio , r. guida and n. magnoli , arxiv : hep - th/0009119 ; d. anselmi , acta phys . * 52 * 573 ( 2002 ) ; e. barnes , k.a . intriligator , b. wecht and j. wright , nucl . phys . * b702 * , 131 ( 2004 ) d.l . jafferis , i.r . klebanov , s.s . pufu and b.r . safdi , arxiv:1103.1181 ; a. amariti and m. siani , arxiv:1105.3979 ; i.r . klebanov , s.s . pufu and b.r . safdi , arxiv:1105.4598 . a. morozov and a.j . niemi , nucl . phys . * b666 * 311 ( 2003 ) s.r . mckay , a.n . berker and s. kirkpatrick , phys . rev , lett . * 48 * 767 ( 1982 ) ; n.m . vraki , j. kertsz and w. selke , j. phys . a * 15 * l427 ( 1982 ) ; b. derrida , j .- eckmann and a. erzan , j. phys . a * 16 * 893 ( 1983 ) p.h . damgaard and g. thorleifsson , phys . a * 44 * 2738 ( 1991 ) ; p.h . damgaard , int . j. of mod . a * 7 * 6933 ( 1992 ) b.p . dolan , phys . e * 52 * 4512 ( 1995 ) s.d . gazek and k.g . wilson , phys . lett . * 89 * 230401 ( 2002 ) ; e. braaten and h .- w . hammer , phys . lett . * 91 * 102002 ( 2003 ) ; s. d. gazek and k.g . wilson , arxiv : cond - 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( wiley , hoboken , ny ) 2006 s. krinsky and d. furman , phys . lett . * 32 * 731 ( 1974 ) ; phys . b * 11 * 2602 ( 1975 ) l.p . kadanoff and a. houghton , phys . b * 11 * 377 ( 1975 ) l. sneddon and m.n . barber , j. phys . c : solid state phys . * 10 * 2563 ( 1977 ) i. affleck and a.w.w . ludwig , phys . lett . * 67 * 161 ( 1991 ) ; d. friedan and a. konechny , phys . lett . * 93 * 030402 ( 2004 ) a.c.d . van enter , r. fernndez and a.d . sokal , j. stat . * 72 * 879 ( 1993 ) ; a.c.d . van enter , f. redig and e. verbitskiy , arxiv:0804.4060 l.p . kadanoff , rev . * 49 * 267 ( 1977 ) th . niemeijer and j.m.j . van leeuwen , in phase transition and critical phenomena , vol . 6 , eds . c. domb and m.s . green ( academic press , new york , 1976 ) t.h . berlin and m. kac , phys . 86 * 821 ( 1952 ) r.p . feynman and a.r . hibbs , quantum mechanics and path integrals ( mcgraw hill inc . , new york , 1965 ) kadanoff , statistical physics . statics , dynamics and renormalization ( world scientific , singapore , 2000 ) h. matsuda , phys . e * 62 * 3096 ( 2000 ) h.w.j . blte , j.l . cardy and m.p . nightingale , phys . lett . * 56 * 742 ( 1986 ) ; i affleck , phys . rev . lett . * 56 * 746 ( 1986 )

the average information loss under a single step of wilsonian rg transformation is evaluated as a conditional entropy of the fast variables , which are integrated out , when the slow ones are held fixed . only some size - independent additive part of the entropy could possibly provide the required lyapunov function . we also introduce a mutual information of fast and slow variables as probably a more adequate quantity to represent the changes in the system under renormalization and evaluate it for some simple systems .

we present a possible approach to the study of the renormalization group ( rg ) flow based entirely on the information theory . the average information loss under a single step of wilsonian rg transformation is evaluated as a conditional entropy of the fast variables , which are integrated out , when the slow ones are held fixed . its positivity results in the monotonic decrease of the informational entropy under renormalization . this , however , does not necessarily imply the irreversibility of the rg flow , because entropy is an extensive quantity and explicitly depends on the total number of degrees of freedom , which is reduced . only some size - independent additive part of the entropy could possibly provide the required lyapunov function . we also introduce a mutual information of fast and slow variables as probably a more adequate quantity to represent the changes in the system under renormalization and evaluate it for some simple systems . it is shown that for certain real space decimation transformations the positivity of the mutual information directly leads to the monotonic growth of the entropy per lattice site along the rg flow and hence to its irreversibility .

1506.06503

m

the computations presented in this paper were performed using a modified version of the publicly available smoothed particle hydrodynamics ( sph ) code gadget-2 @xcite . a major modification to the original gadget-2 is the inclusion of time - dependent chemistry . the version we use here follows the formation and destruction of h@xmath20 as introduced by @xcite in addition to the simplified treatment of the co chemistry that was proposed by @xcite . in @xcite , it was shown that this co network has a similar accuracy to the more exhaustive treatment of @xcite , but incurs around one third of the computational cost . we do not include freeze - out of co onto dust grains in this model , but as this generally occurs only in regions where the @xmath1co emission is already optically thick @xcite , we do not expect this omission to significantly affect our results . as well as following the chemical evolution of the gas , we also model its thermal evolution . we account for dynamical heating due to shocks and adiabatic compression and cooling due to adiabatic rarefaction in the same fashion as in the unmodified version of gadget-2 . in addition , we also account for the main radiative and chemical heating and cooling processes occurring in the ism . these include fine structure cooling from c@xmath21 , c and o , molecular line cooling from h@xmath6 and co , photoelectric heating and cosmic ray heating . at high gas densities , collisions between gas particles and dust grains also play an important role in regulating the thermal energy balance , cooling the gas if @xmath22 and heating it if @xmath23 . full details of how we treat these processes and a number of other , less important , contributors to the overall thermal energy balance can be found in our previous papers @xcite , and a summary of the most important processes included can be found in figure 4 in @xcite . the attenuation of the interstellar radiation field ( isrf ) is treated using the treecol algorithm , introduced by @xcite . in this paper , the spectral shape of the isrf is based on the prescription of @xcite in the ultraviolet and @xcite at longer wavelengths . the strength of the isrf is varied in the different simulations as described in section [ sec : sfr - proxy ] below . the clouds are assumed to be bathed in a uniform isrf , and treecol is used to compute the attenuated spectrum that reaches each sph particle in the computational volume . since the above - mentioned papers , we have made two significant changes to the chemical model . the first was to update our treatment of the photodissociation of co from the prescription given in @xcite , to that described in the recent paper of @xcite . the second change that we have made to the chemical model is the inclusion of the effects of cosmic - ray ionisation of atomic carbon @xmath24 and cosmic - ray induced photodissociation of c and co @xmath25 these processes were not included in the chemical model described in @xcite . we assume that the rates of all three processes are proportional to @xmath26 , the cosmic ray ionisation rate of atomic hydrogen . for processes [ react1 ] and [ react2 ] , we use the rates given in @xcite as a basis , but rescale them by a factor @xmath27 , where @xmath28 is the value of the cosmic ray ionisation rate adopted by @xcite . similarly , to compute the rate of process [ react3 ] , we use the value given in @xcite as a basis , but rescale it to make it consistent with our choice of @xmath26 . the @xmath1co ( 1 - 0 ) emission maps that form the basis of the analysis in this paper were created using the radmc-3d radiative transfer codedullemond / software / radmc-3d/ ] . the level populations in the non - lte limit are computed using the the large velocity gradient approximation @xcite , as implemented in radmc-3d by @xcite . we assume that collisions with h@xmath6 dominate the excitation of the co rotational levels and adopt the values for the collisional excitation rate coefficients given in the leiden atomic and molecular database @xcite . all of the clouds in this study start as uniform spheres of gas , onto which a three - dimensional turbulent velocity field has been superimposed . two cloud masses are examined in this paper : a `` low - mass '' cloud , with a mass of @xmath29 , and a `` high - mass '' cloud of mass @xmath30 . in most of the runs , we take the initial hydrogen nuclei number density of the gas to be @xmath31 , yielding initial radii for the low- and high - mass clouds of 8.8 pc and 19 pc , respectively . in addition , we performed two simulations of high - mass clouds with a much higher initial density , @xmath32 ; these denser clouds had an initial radius of around 4 pc . the mass resolution in this study is kept fixed , with the mass of an sph particle being set at 0.005@xmath33 . the low - mass clouds therefore have @xmath34 sph particles , while the high - mass clouds have @xmath35 sph particles . the minimum resolvable self - gravitating mass - element in this calculation is therefore 0.5@xmath33 in both cases @xcite . in practice , this means that we can follow the collapse of the cloud until the gas number density reaches a value of around @xmath36 . at this point , we halt the collapse and perform the analysis that is presented in this paper . we note that we would not expect the results presented here to change if we were to follow the collapse to higher densities , as at these densities , the co ( 1 - 0 ) line will be highly optically thick ( see e.g. * ? ? ? * ) , and in any case much of the co will be frozen out onto dust grains . the velocity fields are generated with a ` natural ' mix of solenoidal and compressive modes ( i.e. a ratio of 2:1 ) . this is generated on a 128@xmath37 grid . this velocity field is left to freely decay in shocks , rather than being continuously driven during the course of the simulation . in most of the simulations , the initial energy in the velocity field , @xmath38 , was set to be half the initial gravitational potential energy of the cloud , @xmath39 , so that the clouds are initially in virial equilibrium . this means that the initial rms turbulent velocity @xmath40 is 2.4 kms@xmath41 for the low - mass clouds and 5.2 kms@xmath41 for the high - mass clouds . in terms of the virial parameter @xmath42 these clouds have @xmath43 . in addition , we also examine one high density cloud for which we set @xmath44 , so that the cloud is initially unbound ( see section [ sect : sfr ] ) . note that most of the simulations presented here adopt the same random seed for the turbulent velocity field . however we also run one of the simulations with a different seed , to gauge the sensitivity of our results to the underlying cloud structure that is created by the turbulent motions . from previous modelling , it has been found that in cold gas with densities of around @xmath45 , most of the hydrogen is in the form of h@xmath20 . in contrast , the carbon in this gas is still predominantly in the form of c@xmath46 ( see e.g. * ? ? ? * ; * ? ? ? * ) . the initial chemical state of the gas in the majority of the runs presented in this study is motivated by this previous work . we start most of our runs with all of the hydrogen already in the form of h@xmath6 , but assume that the carbon and oxygen are present in the form of c@xmath21 and o , respectively . we adopt total abundances ( relative to the number density of hydrogen nuclei ) for the carbon and oxygen nuclei of @xmath47 and @xmath48 respectively , consistent with the values measured in the local ism @xcite . similarly , we adopt a dust - to - gas mass ratio of 0.01 , consistent with the value in the local ism . in our runs with very high uv fields , it is unclear whether starting with all of the hydrogen in molecular form is a good approximation , as in this case , one would expect the equilibrium h@xmath6 fraction in low density gas to be much smaller than in the models of @xcite and @xcite . to address this uncertainty , we ran two additional high - mass models with the hydrogen initially in atomic form . the post - processing of the simulation data in radmc-3d first requires that the sph particle data is interpolated onto a regular cartesian grid . this is done using the standard sph smoothing formalism . to ensure that we catch small , high density pockets of gas , we employ a radmc-3d cell - size of 0.068pc , such that the high - mass cloud calculations have @xmath49 cells and the low - mass cloud calculations have @xmath50 cells . we find that such a resolution is sufficient to get converged values for the probability density function of co ( 1 - 0 ) emission , from which it follows that the various mean values that we examine later are also converged . once the position - position - velocity maps are obtained , we then integrate the emission along the z - axis to create maps of the integrated intensity , @xmath51 . in this study , we vary two of the environmental conditions that can affect the chemical balance of clouds : the strength of the isrf and the cosmic - ray ionisation rate . both of these are thought to vary with the local star formation rate , and so we assume here that the strength of these processes can be used as a proxy for the star formation rate . as mentioned above , the isrf used here is taken to have a shape described by a combination of the @xcite and @xcite radiation fields . in one set of runs those representing clouds in an environment with a star formation rate similar to that in the local ism , which we denote as sfr@xmath52 we adopt the same normalization for the isrf as in the papers of @xcite and @xcite . our fiducial isrf therefore has a strength @xmath53 in @xcite units . for this study , we are mainly interested in how the isrf heats the gas and affects its chemical state . photons with energies above 6 ev are responsible for the photoelectric heating ( the dominant heat source in low extinction regions of these clouds ) , and photons with energies above 11.2 ev and 11.5 ev are responsible for dissociating h@xmath20 and co respectively . since most of the photons in this part of the isrf come from massive , young stars , it is reasonable to assume that , to a first approximation , the strength of the relevant portion of the isrf scales linearly with the local star formation rate . at longer wavelengths , the isrf is dominated by older stellar populations and this assumption is less well - founded . however , the strength of the isrf at these wavelengths has little effect on the temperature or chemistry of the gas , and so for simplicity , we assume that in regions with higher star formation rates , we can simply scale the entire isrf upwards , rather than changing its spectral shape . we also assume that the cosmic ray ionisation rate scales linearly with the star formation rate . this assumption is reasonable : supernova remnants are the main source of cosmic rays in the galactic ism , and the lifetime of a typical cosmic ray within the galaxy is around 15 myr @xcite , so the cosmic ray energy density , and hence the cosmic ray ionisation rate , should track the star formation rate fairly closely . in this study , in addition to the runs representing the behaviour of clouds in the local ism , with @xmath54 , we also perform simulations where we increase the strength of the isrf and the cosmic ray ionisation rate by factors of 10 or 100 , corresponding to star formation rates of @xmath55 or @xmath56 , respectively . [ cols="^,^,^,^,^,^",options="header " , ]

varies with the environmental conditions in which a molecular cloud is placed . our investigation is centred around two environmental conditions in particular : the cosmic ray ionisation rate ( crir ) and the strength of the interstellar radiation field ( isrf ) . since both these properties of the interstellar medium have their origins in massive stars , we make the assumption in this paper that both the strength of the isrf and the crir scale linearly with the local star formation rate ( sfr ) . the cloud modelling in this study first involves running numerical simulations that capture the cloud dynamics , as well as the time - dependent chemistry , and ism heating and cooling . these simulations are then post - processed with a line radiative transfer code to create syntheticco ( 1 - 0 ) emission maps from which can be calculated .

we present a series of numerical simulations that explore how the ` x - factor ' , the conversion factor between the observed integrated co emission and the column density of molecular hydrogen varies with the environmental conditions in which a molecular cloud is placed . our investigation is centred around two environmental conditions in particular : the cosmic ray ionisation rate ( crir ) and the strength of the interstellar radiation field ( isrf ) . since both these properties of the interstellar medium have their origins in massive stars , we make the assumption in this paper that both the strength of the isrf and the crir scale linearly with the local star formation rate ( sfr ) . the cloud modelling in this study first involves running numerical simulations that capture the cloud dynamics , as well as the time - dependent chemistry , and ism heating and cooling . these simulations are then post - processed with a line radiative transfer code to create syntheticco ( 1 - 0 ) emission maps from which can be calculated . we find that for virialised clouds with mean density 100 , is only weakly dependent on the local sfr , varying by a factor of a few over two orders of magnitude in sfr . in contrast , we find that for similar clouds but with masses of , the x - factor will vary by an order of magnitude over the same range in sfr , implying that extra - galactic star formation laws should be viewed with caution . however , for denser ( ) , super - virial clouds such as those found at the centre of the milky way , the x - factor is once again independent of the local sfr . galaxies : ism ism : clouds ism : molecules molecular processes

1609.02684

i

the calculation of electronic and vibronic transition matrix elements between electronic states of the same or different spin and/or spatial symmetry is a ubiquitous task in the modeling of photochemical and photophysical processes . prime examples include the modeling of non - adiabatic dynamics processes @xcite as well as light - induced excited spin - state trapping phenomena @xcite . the theoretical description of these processes builds upon the calculation of intersystem crossing rates @xcite which , besides electronic and vibronic coupling elements , requires the evaluation of spin - orbit ( so ) coupling ( soc ) matrix elements . similarly , calculating magnetic properties @xcite such as molecular g - factors and electron - nucleus hyperfine coupling , which are central parameters in electron paramagnetic resonance ( epr ) spectroscopy , requires spin - orbit coupled wave functions @xcite . to this end , correlated two- and four - component _ ab initio _ wave function @xcite , and density functional theory approaches @xcite . in the present study we focus on epr g - tensors for testing purposes , but it should be noted that the underlying novel method of gaining access to wave functions that include the effects from soc has a vast range of applications . while it is possible to treat soc variationally , a considerable number of two - step correlated wave function approaches for the calculation of molecular g - factors were developed over the past decades ( see , for example , refs . and literature citations in these works and in refs . ) . in these schemes , the calculation of a number of non- or scalar - relativistic many - particle spin - free states that are eigenfunctions of the spin - squared operator @xmath0 , is decoupled from a subsequent perturbative or variational mixing of the latter through the so coupling operator to obtain so coupled many - electron wave functions ( e.g. by diagonalization `` state - interaction '' ) . it is straightforward to calculate properties such as g - factors in the basis of the eigenstates of the so operator subsequently . appealing features of the two - step approaches are that valuable insight into contributions of each ( ground or excited ) spin - state to the g - tensor is gained , and that the underlying wave function basis is spin - adapted . the price to pay is the need to calculate a sufficient number of spin - free states to interact , which can amount up to several hundred states to achieve convergence for ( heavy - element containing ) molecules where electron correlation and spin - orbit coupling contributions can be of similar order of magnitude . open shell electronic structures are often governed by strong electron correlation effects . in this context , multiconfigurational methods are the preferred methods of choice @xcite which typically split electron correlation into a static and a dynamic contribution . however , such a separation requires careful attention @xcite . a well - established approach to handle static correlation is the complete active space self - consistent field ( casscf ) ansatz @xcite which requires to select a tailored number of ( partially occupied ) active orbitals . the selection of active orbitals is a tedious procedure but can be automatized @xcite . since the computational cost of traditional casscf scales exponentially with the number of active orbitals and electrons , tractable active orbital spaces are presently limited to about 18 electrons in 18 orbitals @xcite . these limitations can be overcome by resorting to the density matrix renormalization group ( dmrg ) approach @xcite in quantum chemistry @xcite which , in combination with a self - consistent - field orbital optimization ansatz ( dmrg - scf ) @xcite , is capable of approximating casscf wave functions to chemical accuracy with merely a polynomial scaling . dmrg - scf therefore allows to handle much larger active orbital spaces that can boldly surpass the casscf limit . to account in addition for spin - orbit coupling in a dmrg framework , variational so approaches @xcite as well as two - step approaches @xcite based on spin - free dmrg wave functions have been reported recently . in this work , we present a generalized state - interaction approach for _ nonorthogonal _ spin - free matrix product state ( mps ) wave functions which enables the evaluation of arbitrary one- and two - particle transition matrix elements as well as so coupling matrix elements . diagonalization of the so hamiltonian matrix , for instance , yields spin - orbit coupled wave functions as linear combinations of the uncoupled , spin - pure mps states . the latter can ( but do not have to ) be obtained as results from one or several dmrg - scf orbital optimization calculations . this allows for utmost flexibility in the individual dmrg - scf steps as each state - specific or spin - specific state - averaged orbital optimization is given the possibility to reflect potential relative differences in open - shell occupancies . for example , transition metal as well as lanthanide and actinide complexes often exhibit different @xmath1- and @xmath2-occupations ( transition metals ) and @xmath1- , @xmath2- and @xmath3-occupations ( lanthanides / actinides ) in ground- and electronically excited electronic states of various spin symmetries . however , a set of wave functions that were optimized individually generally implies mutual nonorthogonality of the respective mo bases . moreover , the mo bases may neither be orthogonal to each other nor non - interacting which can , e.g. , strongly affect the calculation of transition moments between such electronic states @xcite . as first shown in a landmark paper by malmqvist @xcite , an elegant approach for the calculation of matrix elements and transition density matrices is the transformation to a biorthonormal basis for the bra and ket orbital basis of the respective wave functions . a change of the mo basis to a biorthonormal orbital basis necessitates , however , not only to transform all one- and two - electron integrals but to also `` counter - rotate '' the configuration basis of the wave function . for configuration - interaction ( ci)-type expansions , the rotations and counter - rotations can be achieved by a sequence of single - orbital transformations @xcite that require only one - electron operations . subsequently , standard second - quantization algebra can be exploited for the evaluation of overlap matrix elements as well as arbitray one- and two - particle matrix elements between the states in the biorthonormal basis . in a recent work , olsen @xcite exploited the potential of the biorthonormal approach further to devise an efficient algorithm for ci and orbital optimization schemes based on nonorthogonal orbitals . in contrast to previous nonorthogonal ci approaches ( cf . ref . ) , this newly proposed algorithm @xcite requires only the calculation of one- and two - particle reduced density matrices . in this paper , we derive the working equations to calculate one- and two - particle matrix elements between mps wave functions that may be originally expressed in different , mutually nonorthogonal molecular orbital bases . following the work of malmqvist @xcite , the central element of our algorithm is the transformation of the bra and ket mps wave functions to a biorthonormal basis representation . it is important to stress that the latter transformation is not needed if the mps wave functions that are considered for state interaction share a common mo basis ( cf . refs . and ) . after solving a generalized eigenvalue equation of the form @xmath4 with the hamiltonian matrix * h * expressed in the basis of the dmrg - scf wave functions and the overlap matrix * s * we obtain a set of fully orthogonal and non - interacting states as linear combinations of the dmrg - scf wave functions with the expansion coefficients given by * c*. since malmqvist s approach @xcite assumes either a full ci expansion or , in general terms , a wave function expansion that is closed under de - excitation @xcite we probe the closedness of our mps wave function transformation by systematically increasing its numerical accuracy for a given active orbital space . in section [ sec : secqnoo ] we briefly discuss the theoretical framework for a second quantization formalism based on nonorthogonal orbitals . in section [ sec : mps - mpo ] we introduce an algorithm to calculate expectation values for nonorthogonal wave functions in an mps and matrix - product operator ( mpo ) representation of the wave function and operators @xcite , respectively , based on a nonunitary orbital transformation and demonstrate in section [ sec : si - mps ] how the latter can be exploited for a nonorthogonal mps state - interaction ( mps - si ) _ ansatz_. numerical examples for the calculation of g - factors for @xmath5- and @xmath6-type actinide complexes are presented in section [ sec : secnumex ] .

we present a state - interaction approach for matrix product state ( mps ) wave functions in a nonorthogonal molecular orbital basis . the key element is the transformation of the mps wave functions of different states from a nonorthogonal to a biorthonormal molecular orbital basis representation exploiting a sequence of non - unitary transformations following a proposal by malmqvist ( _ int . j. quantum chem . _ * 30 * , 479 ( 1986 ) ) .

we present a state - interaction approach for matrix product state ( mps ) wave functions in a nonorthogonal molecular orbital basis . our approach allows us to calculate for example transition and spin - orbit coupling matrix elements between arbitrary electronic states provided that they share the same one - electron basis functions and active orbital space , respectively . the key element is the transformation of the mps wave functions of different states from a nonorthogonal to a biorthonormal molecular orbital basis representation exploiting a sequence of non - unitary transformations following a proposal by malmqvist ( _ int . j. quantum chem . _ * 30 * , 479 ( 1986 ) ) . this is well - known for traditional wave - function parametrizations but has not yet been exploited for mps wave functions .

gr-qc0501029

i

we give in this paper a summary of our research program ( commenced in @xcite ) on the quantum statistical dynamics of relativistic particles moving in a quantum field . the relativistic particles are not coupled to each other explicitly but only through their interactions with a quantum field . because of this we need to take into consideration both the effect of each particle on the quantum field and the backreaction of the quantum field on each particle . a self - consistent treatment of the particle - field system dynamics is thus necessary . the backreaction from the field engenders _ nonlinear _ coupling amongst the particles , and _ non - markovian _ dynamics . we present a new approach to this problem which highlights the stochastic effects of noise , decoherence , dissipation , fluctuations , and correlations , and their interconnections . in @xcite we presented the basic framework built on the concepts of quantum open systems @xcite , the model of quantum brownian motion ( qbm ) @xcite , and the methodologies of the influence functional @xcite , closed - time - path ( in - in ) @xcite coarse - grained effective action @xcite , and world line quantization @xcite . in @xcite we applied this framework to spinless relativistic moving particles in a quantum scalar field , and derived the stochastic equations of motion , known as the abraham - lorentz - dirac - langevin ( aldl ) equations , for their trajectories with self - consistent backreaction . the quantum fluctuations of the field are partially encoded as a stochastic noise in the aldl equations . the mean trajectory obtained from taking the stochastic average is governed by abraham - lorentz - dirac ( ald ) equations with modified coefficients whose time - dependence enforce causality . here we use the approach developed in @xcite to analyze a uniformly accelerated particle where the trajectory is self - consistently determined by its interaction with a quantum field ( this includes the effects of radiation reaction and vacuum fluctuations ) . this important example illustrates the interconnections between radiation , radiation reaction , dissipation , quantum fluctuations , and the unruh effect . specifically , the uniform acceleration alters the quantum vacuum which in turn induces thermal - like fluctuations in the trajectory of a particle . this manifestation of the unruh effect in terms of fluctuating trajectories is in contrast to the original formulation and more common derivations @xcite , where a particle with internal degrees of freedom ( called a detector in the literature @xcite ) moving on a uniformly accelerating prescribed trajectory feels hot at the unruh temperature @xmath0 . before delving into the technical details , in the remainder of this section we discuss the outstanding physical issues touched on in this work . in sec . 2 we describe the relation of classical radiation , radiation reaction , vacuum fluctuations and quantum radiation , correcting the misconception of directly linking vacuum fluctuations with radiation reaction . in sec . 3 we present the main structure of our approach based on the open system concept and the coarse - grained effective action techniques . we show the steps leading to a derivation of the ald - langevin equation for charges moving in a quantum field . in sec . 4 we specialize to the case of a particle moving in a background field which imparts to it uniform acceleration on the average , and derive the unruh effect . we discuss how this example can serve as an analog for studying the stochastic dynamics of black hole event horizons . in sec . 5 we step back for a broader perspective and give some discussions of a ) the special features of this new approach and its potential in overcoming the stumbling blocks present in existing approaches ; and b ) applications of these results and directions for further development . in this program of investigation we take a microscopic approach and an open - systems perspective , using quantum field theory as the tool to provide a first - principles derivation of moving particles interacting with a quantum field . we begin with the closed system of quantum particles and fields . a _ closed system _ can be meaningfully partitioned into subsystems if there exists discrepancies in the scales describing each subsystem , or in accordance to the physical scales present in their interaction strengths ( energy or time scales ) in relation to the probing scale or resolution accuracy . if we are interested in the details of one such subsystem ( e.g. , particle dynamics ) and decide to ignore certain details of the other subsystems ( e.g. , details in the quantum field configurations , such as correlations and phase information ) comprising the _ environment _ , the distinguished subsystem is rendered an _ open system_. the overall effect of the coarse - grained environment on the open - system can be captured by the influence functional technique of feynman and vernon @xcite , or the closely related closed - time - path ( ctp ) effective action method of schwinger and keldysh @xcite . these are the initial value , or in - in , formulations suitable for following the time evolution of a system , in contradistinction to the usual in - out ( schwinger - dewitt ) effective action formulation useful for s - matrix calculations . for the model of particle - field interactions under study , coarse - graining the quantum field yields a nonlocal _ coarse - grained effective action _ ( cgea ) for the particle motion @xcite . an exact expression may be found in the special case that the particle and field are initially uncorrelated , and the field state is gaussian . the cgea may be used to treat the fully nonequilibrium quantum dynamics of interacting particles . however , when higher - order quantum corrections are suppressed by decoherence , the influence of the quantum fluctuations of the field may be encoded as stochastic noise , and the cgea can be transcribed into a _ stochastic effective action _ @xcite describing the stochastic particle motion . upon further coarse - graining , taking the stochastic average gives the semiclassical particle trajectory . let us analyze the physics of nonequilibrium processes for such particle - field systems at separate levels . * classical * level : from the complete quantum microscopic description of the system ( particle ) and the environment ( field ) , a classical description is reached when the system and environment are coarse - grained to an extent that both the particle and field histories are fully decohered @xcite . the fully coarse - grained trajectory for the particle with backreaction from the fully coarse - grained field then obeys classical equations of motion , such as the ald equation . the coarse - graining length scale necessary to achieve full classicality typically far exceeds the length scale for backreaction pathologies like preacceleration and runaway solutions . * semiclassical * level : this is often defined as a classical system ( particles or detectors ) interacting with a quantum environment ( quantum field ) . it can be obtained from the complete quantum microscopic description by fully coarse - graining the environment ( the quantum field ) and finding the quantum average of the particle trajectory . in the special but important class when the field enters linearly in the particle - field interaction term , and without field self - interactions , coarse graining over the quantum field gives an exact cgea . the cgea yields the equations of motion for the system which in the leading order approximation is the semiclassical limit , followed by higher - order quantum corrections . in this particular situation , if decoherence can sufficiently suppress the nonlinear quantum corrections to the semiclassical equations of motion from the particle , then the semiclassical limit from the cgea agrees with the classical limit . * stochastic * level : going beyond a mean - trajectory ( or fully coarse - grained ) description of the particle , a stochastic component in the particle trajectory appears , as induced by the quantum field fluctuations manifesting as a classical stochastic noise counterbalancing the quantum dissipation in the system dynamics . the cgea may be transcribed into a stochastic effective action , encoding much of the quantum statistical information of the field and the state of motion of the system in a noise correlator for the particle . the stochastic effective action yields classical stochastic equations of motion for the system which embodies a quantum dissipation effect ( _ over and above _ the classical radiation reaction ) that balances the quantum fluctuations via a fluctuation - dissipation relation ( fdr ) . the classical theory of moving charges interacting with a classical electromagnetic ( em ) field , when the backreaction of the em field is included , has many controversial difficulties @xcite . the generally accepted classical equation of motion for a charged , spinless point particle including radiation - reaction is the abraham - lorentz - dirac ( ald ) equation @xcite : @xmath1 ( see sec . ii for notations and definitions . ) the timescale @xmath2 determines the relative importance of the radiation - reaction term . for electrons , @xmath3 secs , which is the time it takes light to cross the electron classical radius @xmath4 m . the ald equation is pathological . because it is a third order differential equation , it requires the specification of the initial acceleration in addition to the usual position and velocity required by second order differential equations . this leads to the existence of runaway solutions . physical ( e.g. non - runaway ) solutions may be enforced by transforming eq . ( [ classical lorentz - dirac equation ] ) to a second order integral equation with boundary condition such that the final energy of the particle is finite and consistent with the total work done on it by external forces . but the removal of runaway solutions yields acausal solutions that pre - accelerate on timescales @xmath5 this is a source of lingering questions on whether the classical theory of point particles and fields is causal . there have been many efforts to understand charged particle radiation - reaction in the classical and quantum theory . to satisfy the self - consistency and causality requirements different measures are introduced to the underlying model . examples include imposing a high - energy cutoff for the field , an extended charge distribution , special boundary conditions , particle spin , and the use of perturbation theory or order reduction techniques @xcite . previous work closely related to ours include those on quantum langevin equations @xcite , and the application of the feynman - vernon influence functional to non - relativistic particle coherence @xcite and stochastic gravity @xcite . a major distinction of our work is the focus on relativistic systems , non - equilibrium processes , and nonlinear particle - field interaction . consider the situation where a localized particle at rest has some quantum fluctuations in its position just before an external force is applied at time @xmath6 , and where , by chance , the fluctuation is one that seems to anticipate the force creating the _ _ appearance _ _ of preacceleration . or , consider a situation where a quantum fluctuation produces the _ appearance _ of runaway acceleration for some period of time . while such specific fluctuations may be highly improbable to realize , they are among the set of fine - grained solutions in a sum - over - histories formulation of quantum mechanics . these examples illustrate the observational challenges to distinguishing cause and effect on a fine - grained quantum scale . why is there such a difficulty ? the underlying microscopic theory may be consistent ( though for field theory this may not be obvious ) and causal , in the sense that the operator equations of motion are causal , but the quantum state ( for particle or field ) is inherently nonlocal . observables ( expectation values ) of the particle motion involve both the operator equations of motion and the nonlocal quantum state , and thus the question of causality for trajectories requires more careful treatment . operationally , we do not observe fine - grained histories ; instead we observe coarse - grained histories where the coarse - graining scale is set by the measurement resolution in both time and space . with coarse graining , the quantum fluctuations giving highly nonclassical trajectories are suppressed , and we therefore expect that a causal and consistent quantum theory should yield , upon suitable coarse graining , a classical or semiclassical limit that is pathology free . this is an oversimplified sketch of a more elaborate theory @xcite based on the decoherent history approach to quantum mechanics @xcite . a particularly interesting class of dynamics from the solutions to the ald equation is that of a uniformly accelerated particle , defined by @xmath7 . this class of dynamics exemplifies many of the important issues under discussion . first , it follows from the ald equations that the classical radiation reaction force vanishes despite the existence of classical ( lamor ) radiation registered as an energy flux at infinity . hence , there is no direct balance between radiation and radiation reaction . there is one existing belief that since radiation is associated with radiation reaction , the extra work done on the particle against the radiation reaction force must directly provide the energy that goes into radiation , but this is a static viewpoint that neglects the full interplay of particle , near field ( the so - called acceleration or shott field ) , and far field ( the radiation field ) dynamics . fields are dynamical entities with unusual properties ( such as nonlocality and field correlations ) much more complex than just radiation , which is a far - field definition , and energy can be attributed to a variety of sources other than radiation . for example , the acceleration field is known to contain energy and do work . one can not simply equate work done against radiation reaction forces with the energy ( instantaneously ) radiated into infinity . it would require a ` freezing out ' of the near - field s ability to exchange or adjust the form of its energy consistently in time to be commensurate with the far field behavior known as radiation . during periods of uniform acceleration , the energy transfer into radiation comes from acceleration fields , leaving zero radiation reaction . this is a special situation . during periods of nonuniform acceleration , there is radiation reaction , and one finds a mixture of field components ; but even then , the energy apportioned to radiation can not be instantaneously ascribed to work done against radiation reaction . on matters related to fields one should look carefully at the energy content locally and guard against making global statements . it has long been known that a uniformly accelerated detector ( uad ) ( a detector is defined as a particle with some internal degree of freedom ) coupled to a quantum field following a prescribed trajectory registers its quantum field vacuum as a thermal state with temperature @xmath8 this is the unruh effect @xcite , often cited as an analog of hawking effect @xcite . but there are important differences : in the case of a black hole , real radiation of thermal nature is emitted at the hawking temperature . for a uniformly accelerated detector ( uad ) there is no emitted radiation associated with the unruh effect ( see , e.g. , @xcite and references therein ) except for a transient period when the charge is coming into equilibrium with its environment @xcite . for a uniformly accelerated _ charge _ ( uac ) there is of course classical radiation , but it is different from the unruh radiation , which is a distinctly quantum effect . we demonstrate below that for a uniformly accelerated charge interacting with a quantum field , the vacuum fluctuations induce stochastic fluctuations in the particle _ trajectory _ with a thermal character . we can refer to this as the unruh effect for charges , the role of the detector is played by the particle motion itself rather than an internal degree of freedom . in the semiclassical limit ( neglecting quantum corrections from the particle ) the _ average _ emitted radiation is the usual classical radiation : there is no additional net quantum radiation from the particle . what is new and interesting in our finding is that there could be radiation associated with the stochastic component of the particle trajectory . for instance , these could conceivably generate fluctuations in the emitted radiation , perhaps with a thermal character , or they could produce other non - classical correlations in the radiation . this requires further investigation . it has been shown that for a uniformly accelerated detector on a fixed trajectory the field correlation is altered around the detector , but as these altered correlations fall off faster than radiation they can be considered as a vacuum polarization effect @xcite . similar vacuum polarization effects are also expected for a moving charge ( contrast this prediction with @xcite ) . finally , the radiation emitted by an evaporating ( shrinking ) black hole under non - equilibrium conditions is expected to have a non - thermal component @xcite over and above the usual thermal ( hawking ) part . we are using the analog with non - uniformly accelerated detectors or charges to investigate this issue @xcite .

we present a stochastic theory for the nonequilibrium dynamics of charges moving in a quantum scalar field based on the worldline influence functional and the close - time - path ( ctp or in - in ) coarse - grained effective action method . we summarize ( 1 ) the steps leading to a derivation of a modified abraham - lorentz - dirac equation whose solutions describe a causal semiclassical theory free of runaway solutions and without pre - acceleration patholigies , and ( 2 ) the transformation to a stochastic effective action which generates abraham - lorentz - dirac - langevin equations depicting the fluctuations of a particle s worldline around its semiclassical trajectory . we point out the misconceptions in trying to directly relate radiation reaction to vacuum fluctuations , and discuss how , in the framework that we have developed , an array of phenomena , from classical radiation and radiation reaction to the unruh effect , are interrelated to each other as manifestations at the classical , stochastic and quantum levels . using this method we give a derivation of the unruh effect for the spacetime worldline coordinates of an accelerating charge . our stochastic particle - field model , which was inspired by earlier work in cosmological backreaction , can be used as an analog to the black hole backreaction problem describing the stochastic dynamics of a black hole event horizon . .5 cm _ - invited talk given by blh at the international assembly on relativistic dynamics ( iard ) , june 2004 , saas fee , switzerland . to appear in a special issue of foundations of physics ( 2005 ) .

we present a stochastic theory for the nonequilibrium dynamics of charges moving in a quantum scalar field based on the worldline influence functional and the close - time - path ( ctp or in - in ) coarse - grained effective action method . we summarize ( 1 ) the steps leading to a derivation of a modified abraham - lorentz - dirac equation whose solutions describe a causal semiclassical theory free of runaway solutions and without pre - acceleration patholigies , and ( 2 ) the transformation to a stochastic effective action which generates abraham - lorentz - dirac - langevin equations depicting the fluctuations of a particle s worldline around its semiclassical trajectory . we point out the misconceptions in trying to directly relate radiation reaction to vacuum fluctuations , and discuss how , in the framework that we have developed , an array of phenomena , from classical radiation and radiation reaction to the unruh effect , are interrelated to each other as manifestations at the classical , stochastic and quantum levels . using this method we give a derivation of the unruh effect for the spacetime worldline coordinates of an accelerating charge . our stochastic particle - field model , which was inspired by earlier work in cosmological backreaction , can be used as an analog to the black hole backreaction problem describing the stochastic dynamics of a black hole event horizon . .5 cm _ - invited talk given by blh at the international assembly on relativistic dynamics ( iard ) , june 2004 , saas fee , switzerland . to appear in a special issue of foundations of physics ( 2005 ) .

astro-ph0508611

i

deuterium , which is produced during primordial nucleosynthesis and then destroyed by astration , is a key element in cosmology . whereas measurements in low - metallicity qso absorption systems probe d / h at look - back times of @xmath6 gyrs , the present epoch deuterium abundance can be measured in the interstellar medium ( ism ) . the ( _ far ultraviolet spectroscopic explorer _ ) mission has brought significant progress on the measurement . d / h likely has a single value in the local bubble pc - size low - density cavity in which the solar system is embedded ( see , i.e. , sfeir et al . @xcite ) ] , in the range @xmath7 ( moos et al . @xcite ; hbrard & moos @xcite ) . however , it now appears that this local abundance should not be considered as a canonical value characteristic of the milky way at the present epoch , as it was usually believed before studies . indeed , numerous distant sight lines , i.e. sight lines probing the interstellar medium beyond the local bubble , have shown deuterium abundances in disagreement with the local bubble one ( see , e.g , laurent et al . @xcite , jenkins et al . @xcite , lemoine et al . @xcite , sonneborn et al . @xcite , hoopes et al . @xcite ) . hbrard & moos ( @xcite ) reported a trend in the deuterium abundance based on d / o , d / n , and previously reported d / h measurements : the deuterium abundance is lower than in the local bubble for the most distant sight lines exhibiting the highest hydrogen column densities . more recent work by wood et al . ( @xcite ) confirms this low value . these results suggest that the deuterium abundance might be locally abnormally higher than the present epoch value . while hbrard & moos ( @xcite ) suggested that the present epoch ratio would be significantly lower than @xmath8 , linsky et al . ( @xcite ) recently proposed a ratio higher than @xmath9 assuming that deuterium could be significantly depleted onto dust grains ( see jura @xcite ; wood et al . @xcite ; draine @xcite ) . both values may challenge deuterium evolution models , the baryonic density of the universe inferred from primordial d / h measurements , and our understanding of the physics of the interstellar medium . regardless of the actual scenario , it is now clear that local measurements are not enough to assess , and that deuterium studies in the distant interstellar medium are mandatory . only a few are available now . here we report the measurement of the deuterium abundance in the interstellar medium toward 9 ( [ hd90087 ] ) . this sight line is studied thanks to new observations of this target . _ iue _ ( _ international ultraviolet explorer _ ) archival spectra are also used to constrain the neutral hydrogen column density from the fits of the line wings . both in terms of distance and column densities , 9 provides the farthest galactic line of sight for which deuterium abundance has been measured from far ultraviolet absorption lines to date . hence , many interstellar clouds are probed along this sight line . this will tend to average out the peculiarities of individual galactic regions , such as the local bubble , in order to reach measurements that are characteristic of the interstellar medium on large scales . we supplement our study with a reconsideration of the column density measurement toward from spectra , allowing an updated interstellar d / o measurement on this sight line ( [ feige ] ) .

both in terms of distance and column densities , 9 has the longest and densest sight line observed in the galactic disk for which a deuterium abundance has been measured from ultraviolet absorption lines so far . because many interstellar clouds are probed along this sight line , possible variations in the properties of individual clouds should be averaged out . we have measured interstellar column densities of neutral atoms , ions , and molecules by simultaneously fitting the interstellar absorption lines detected in the different channels . as far as possible , saturated lines were excluded from the fits in order to minimize possible systematic errors . _ iue _ ( _ international ultraviolet explorer _ ) archival data are also used to measure neutral hydrogen . we report d / o and d / h ( s ) . we supplement our study with a revision of the oxygen abundance toward , a moderately distant ( pc ) sdob star , located pc below the galactic plane . excluding saturated lines from the fits of

we present a study of the deuterium abundance along the extended sight line toward 9 with the _ far ultraviolet spectroscopic explorer _ ( _ fuse _ ) . 9 is a o9.5iii star located in the galactic disk at a distance of kpc away from the sun . both in terms of distance and column densities , 9 has the longest and densest sight line observed in the galactic disk for which a deuterium abundance has been measured from ultraviolet absorption lines so far . because many interstellar clouds are probed along this sight line , possible variations in the properties of individual clouds should be averaged out . this would yield a deuterium abundance which is characteristic of the interstellar medium on scales larger than the local bubble . the spectra of 9 show numerous blended interstellar and stellar features . we have measured interstellar column densities of neutral atoms , ions , and molecules by simultaneously fitting the interstellar absorption lines detected in the different channels . as far as possible , saturated lines were excluded from the fits in order to minimize possible systematic errors . _ iue _ ( _ international ultraviolet explorer _ ) archival data are also used to measure neutral hydrogen . we report d / o and d / h ( s ) . our new results confirm that the gas - phase deuterium abundance in the distant interstellar medium is significantly lower than the one measured within the local bubble . we supplement our study with a revision of the oxygen abundance toward , a moderately distant ( pc ) sdob star , located pc below the galactic plane . excluding saturated lines from the fits of the spectra is critical ; this led us to derive an column density about two times larger than the one previously reported for . the corresponding updated d / o ratio on this sight line is d / o ( s ) , which is lower than the one measured within the local bubble . the dataset available now outside the local bubble , which is based primarily on measurements , shows a contrast between the constancy of d / o and the variability of d / h . as oxygen is considered to be a good proxy for hydrogen within the interstellar medium , this discrepancy is puzzling .