Numerical integration of the Fokker-Planck equation and the evolution of star clusters

Abstract

The paper presents a numerical method for studying the evolution of spherical star clusters. The method employs direct numerical integration of the orbit-averaged Fokker-Planck equation in energy angular momentum space to advance the stellar distribution in time. Numerical results from a study of the evolution of Plummer's model are discussed and are found to be in generally good agreement with those of the Monte Carlo studies of Henon, and Spitzer and Schull, but show far less statistical noise and extend to a somewhat more advanced state of the evolution. The results tend to support the homologous core collapse conjecture of Lynden-Bell. It is found that the core collapse is observed to change in character at the time the scaled escape energy first exceeds the critical value for the onset of the gravothermal instability.