Quasi-Equilibrium Evolution in Self-GravitatingN-Body Systems

Abstract

In this paper, a quantitative characterization of the evolutionary sequences of self-gravitating system is investigated from a thermostatistical point of view. With a particular attention to the pre-collapse stage of long-term dynamical evolution, we focus on the quasi-equilibrium behavior of the N-body systems in the setup of the so-called Antonov problem, i.e., self-gravitating N-body system confined in an adiabatic wall. After addressing the quilibrium properties of self-gravitating systems by means of the generalized entropy, a series of N-body simulation were performed starting with various initial distributions. We found that quasi-equilibrium evolution appears for certain initial conditions away from the thermal equilibrium. The quasi-equilibrium states can be approximately described by the one-parameter family of the stellar models, i.e., stellar polytropic distribution satisfying the effective equation of state P ∝ ρ 1+1/n , which might be regarded as an extremum state of the generalized non-extensive entropy.