The Evolution of Globular Clusters in the Galaxy

We investigate the evolution of globular clusters using N -body calculations and anisotropic Fokker-Planck calculations. The models include a mass spectrum, mass loss due to stellar evolution, and the tidal field of the parent galaxy. Recent N -body calculations have revealed a serious discrepancy between the results of N -body calculations and isotropic Fokker-Planck calculations. The main reason for the discrepancy is an oversimplified treatment of the tidal field employed in the isotropic Fokker-Planck models. In this paper we perform a series of calculations with anisotropic Fokker-Planck models with a better treatment of the tidal boundary and compare these with N -body calculations. The new tidal boundary condition in our Fokker-Planck model includes one free parameter. We find that a single value of this parameter gives satisfactory agreement between the N -body and Fokker-Planck models over a wide range of initial conditions. Using the improved Fokker-Planck model, we carry out an extensive survey of the evolution of globular clusters over a wide range of initial conditions varying the slope of the mass function, the central concentration, and the relaxation time. The evolution of clusters is followed up to the moment of core collapse or the disruption of the clusters in the tidal field of the parent galaxy. In general, our model clusters, calculated with the anisotropic Fokker-Planck model with the improved treatment for the tidal boundary, live longer than isotropic models. The difference in the lifetime between the isotropic and anisotropic models is particularly large when the effect of mass loss via stellar evolution is rather significant. On the other hand the difference is small for relaxation-dominated clusters which initially have steep mass functions and high central concentrations. Subject headings: Galaxy: kinematics and dynamics — galaxies: kinematics and dynamics — galaxies: star clusters — globular clusters: general — open clusters and associations: general — methods: numerical Present address: Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Hubble Fellow