Evolution of tidally truncated globular clusters with anisotropy

Abstract

The evolution of tidally truncated globular clusters is investigated by integrating a two-dimensional Fokker-Planck equation that allows the development of velocity anisotropy. We start from the isotropic Plummer model with tidal cut-off and follow the evolution through the core collapse. The heating by a three-body binary is included to obtain the evolution past the core collapse. The radial anisotropy in the velocity dispersion develops during the pre-collapse evolution in the outer parts of the cluster. However, the anisotropy becomes highly depressed during the post-collapse evolution because of rapid loss of radial orbits. Maximum radial anisotropy appears just after the beginning of the expansion, and the degree of anisotropy decreases slowly as the total mass of the cluster decreases. The density profiles of pre-collapse and early-phase post-collapse clusters require King-Michie models, while the late phases of clusters can be well represented by isotropic King models. However, the detailed radial behaviour of the degree of anisotropy of our Fokker-Planck model is somewhat different from that of the best-fitting King-Michie models.