Antonov Problem and Quasi-Equilibrium States in N-body System

In this paper, a quantitative characterization for the evolutionary sequence of stellar self-gravitating system is investigated, focusing on the pre-collapse stage of the long-term dynamical evolution. In particular, we consider the quasi-equilibrium behaviors 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 and try to seek a possible connection with thermostatistics of self-gravitating systems. For this purpose, a series of long-term N -body simulations with various initial conditions are performed. We found that a quasi-equilibrium sequence away from the thermal equilibrium can be characterized by the one-parameter family of the stellar models. Especially, the stellar polytropic distribution satisfying the effective equation of state P ∝ ρ provides an excellent approximation to the evolutionary sequence of the N -body system. Based on the numerical results, we discuss a link between the quasi-equilibrium state and the generalized thermostatistics by means of the non-extensive entropy.