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Phys. Rev. E 73, 046112 (2006) [8 pages]

Local virial relation for self-gravitating system

Osamu Iguchi,1 Yasuhide Sota,2,3 Akika Nakamichi,4 and Masahiro Morikawa1
1Department of Physics, Ochanomizu University, 2-1-1 Ohtuka, Bunkyo-ku, Tokyo 112-8610, Japan
2Department of Physics, Ochanomizu University, 2-1-1 Ohtuka, Bunkyo, Tokyo 112-8610, Japan
3Advanced Research Institute for Science and Engineering, Waseda University, Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan
4Gunma Astronomical Observatory, 6860-86, Nakayama, Takayama, Agatsuma, Gunma 377-0702, Japan
Received 21 December 2005; published 10 April 2006

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

©2006 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevE.73.046112
DOI: 10.1103/PhysRevE.73.046112
PACS: 98.10.+z; 05.10.-a
  • 98.10.+z
    Stellar dynamics and kinematics
  • 05.10.-a
    Computational methods in statistical physics and nonlinear dynamics
  • YEAR: 2006
KEYWORDS: clusters of galaxies, N-body problems, cosmology, numerical analysis

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