Antonov problem and quasi-equilibrium states in an N-body system

In this paper, a quantitative characterization of the evolutionary sequence of a 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 behaviour of N-body systems in the setup of the so-called Antonov problem, i.e. a self-gravitating N-body system confined within an adiabatic wall, and try to seek a possible connection with the 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 thermal equilibrium can be characterized by a one-parameter family of stellar models. Especially, a stellar polytropic distribution satisfying the effective equation of state P∝ρ1+1/n provides an excellent approximation to the evolutionary sequence of the N-body system. Based on the numerical results, we discuss the link between the quasi-equilibrium state and the generalized thermostatistics by means of the non-extensive entropy.