Linear TemperatureMass relation and Local virial relation: Two hypotheses for selfgravitating systems
Abstract
We propose two hypotheses which characterize the quasiequilibrium state that realizes after a cold collapse of selfgravitating system. The first hypothesis is the linear temperaturemass (TM) relation, which yields a characteristic nonGaussian velocity distribution. The second is the local virial (LV) relation, which, combining the linear TM relation, determines a unique mass density profile as $\rho(r)={\rho}%_{0}r^{4}e^{r_0/r}$. Although this density profile is unphysical in the central region, the region is just inner a few percent around the center of a bound region in cumulative mass, which is beyond the resolution of our numerical simulations. Hence posing two hypotheses is compatible to the numerical simulations for almost the whole region of the virialized bound state. Actually, except for this inner part, this density profile fits well to the data of cold collapse simulations. Two families of spherical and isotropic models, polytropes and King models, are examined from a view point of these two hypotheses. We found that the LV relation imposes a strong constraint on these models: only polytropes with index $n \sim 5$ such as Plummer's model are compatible with the numerical results characterized by the two hypotheses among these models. King models with the concentration parameter $% c \sim 2$ violate the LV relation while they are consistent with the $R^{1/4} $ law for the surface brightness. Hence the above characteristics can serve as a guideline to build up the models for the bound state after a cold collapse, besides the conventional criteria concerning the asymptotic behavior.
 Publication:

arXiv eprints
 Pub Date:
 March 2004
 arXiv:
 arXiv:astroph/0403411
 Bibcode:
 2004astro.ph..3411S
 Keywords:

 Astrophysics;
 Condensed Matter  Statistical Mechanics;
 Physics  Computational Physics
 EPrint:
 11 pages, 14 figures, submitted to PRE. The comments and the analyses for the density profile are replaced. The figures for the case with a large number of particles are added