title: Local virial relation for self-gravitating system.
abstract: 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.
authors.affiliation: Department of Physics, Ochanomizu University, 2-1-1 Ohtuka, Tokyo 112-8610, Japan. osamu@phys.ocha.ac.jp
authors.forename: Osamu
authors.initials: O
authors.lastname: Iguchi
authors.forename: Yasuhide
authors.initials: Y
authors.lastname: Sota
authors.forename: Akika
authors.initials: A
authors.lastname: Nakamichi
authors.forename: Masahiro
authors.initials: M
authors.lastname: Morikawa