Multicomponent Models for the Dynamic Evolution of Globular Clusters

The Fokker-Planck equation has been integrated to produce a series of numerical models describing the dynamical evolution of globular clusters with a mass spectrum. Three-body binary heating is included to obtain postcollapse evolution and a steady Galactic tidal field is imposed. Since no direct interactions between stars (such as tidal captures or mergers) are considered, the models are appropriate for globular clusters with a relatively low mass (M ≤ 10⁵ M_sun). A wide range of initial mass functions is considered and the evolution of the mass function is examined. The mass function begins to change appreciably during the postcollapse expansion phase due to the selective evaporation of low-mass stars through the tidal boundary. One signature of highly evolved clusters is thus a significant flattening of the mass function. The age measured by the half-mass relaxation time increases very rapidly from a characteristic value of ∼100 at the final stage of disruption. This appears to be consistent with the sharp cutoff near 10⁸ yr in the distribution of the half-mass relaxation times for the Galactic globular clusters. We also consider the evolution of clusters containing massive dark remnants (i.e., white dwarfs or neutron stars). The efficient formation of three-body binaries among the degenerates and the relative flattening of the luminosity profile compared to the density profile, lead to postcollapse models with a sufficiently low concentration that the core may be resolvable.