Statistical Mechanics of a Collisionless Self-Gravitating System

Abstract

Recently Lynden-Bell proposed a theory of the mixing phase during which a stellar system approaches a quasi-equilibrium state. By using a new type of statistics related to Fermi-Dirac statistics he derived a final or quasi-equilibrium distribution. In the present paper computer experiments with a one-dimensional model are performed to determine whether a self-gravitating system will approach the Lynden-Bell distribution. A number of initial distributions with various degrees of departure from a minimum energy or stationary state are investigated. Depending on the initial conditions, it is found that from 80 to 96% of the stars in the system approach the Lynden-Bell distribution.