Local virial relation for self-gravitating system

Details Local virial relation for self-gravitating system Local virial relation for self-gravitating system

2005-12-21

arxiv.org/abs/astro-ph/0512518v1

Phys.Rev.E73:046112,2006

Astronomy and Astrophysics

Astrophysics

9 pages, 15 eps figures, RevTex, submitted to PRE

Scientific paper

10.1103/PhysRevE.73.046112

We demonstrate that the quasi-equilibrium state in self-gravitating $N$-body system after cold collapse are uniquely characterized by the local virial relation using numerical simulations. Conversely assuming the constant local virial ratio and Jeans equation for spherically steady state system, we investigate the full solution space of the problem under the constant anisotropy parameter and obtain some relevant solutions. Especially, the local virial relation always provides a solution which has a power law density profile in both the asymptotic regions $r\to 0$ and $\infty$. This type of solutions observed commonly in many numerical simulations. Only the anisotropic velocity dispersion controls this asymptotic behavior of density profile.

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