Fokker-Planck Models of Star Clusters with Anisotropic Velocity Distributions. II. Post-Collapse Evolution

Abstract

The evolution of spherical single-mass star clusters driven by two-body relaxation was followed beyond core collapse by numerically solving the orbit-averaged Fokker-Planck equation in energy--angular momentum space. The heating effect by three-body binaries was incorporated in the Fokker-Planck models. The development of velocity anisotropy after the core collapse is discussed in detail. The anisotropy in the outer regions continues to increase slowly after the collapse. In clusters comprising a relatively small number of stars ($N \ltsim 10000$), the post-collapse expansion is nearly self-similar and the anisotropy at each of inner Lagrangian radii is nearly constant. In clusters comprising a larger number of stars ($N \gtsim 10000$), gravothermal oscillations occur and the anisotropy at each of the inner radii oscillates with the core oscillations. There is no qualitative difference in the nature of the gravothermal oscillations between the isotropic and anisotropic Fokker-Planck models.