Evolution of Multi-mass Globular Clusters in Galactic Tidal Field with the Effects of Velocity Anisotropy

We study the evolution of globular clusters with mass spectra under the influence of the steady Galactic tidal field, including the effects of velocity anisotropy. Similar to single-mass models, velocity anisotropy develops as the cluster evolves, but the degree of anisotropy is much smaller than isolated clusters. Except for very early epochs of the cluster evolution, nearly all mass components become tangentially anisotropic at the outer parts. We have compared our results with multi-mass, King-Michie models. The isotropic King model better fits to the Fokker-Planck results because of tangential anisotropy. However, it is almost impossible to fit the computed density profiles to the multi-mass King models for all mass components. Thus if one attempts to derive global mass function based on the observed mass function in limited radial range using multimass King models, one may get somewhat erratic results, especially for low mass stars. We have examined how the mass function changes in time. Specifically, we find that the power-law index of the mass function decreases monotonically with the total mass of the cluster. This appears to be consistent with the behaviour of the observed slopes of mass functions for a limited number of clusters, although it is premature to compare quantitatively because there are other mechanisms in contributing the evaporation of stars from the clusters. The projected velocity profiles for anisotropic models with the apocenter criterion for evaporation show significant flattening toward the tidal radius compared to isotropic model or anisotropic model with the energy criterion. Such a behaviour of velocity profile appears to be consistent with the observed profiles of collapsed cluster M15.