Two-component Fokker-Planck models for the evolution of isolated globular clusters

Two-component (normal and degenerate stars) models are the simplest realization of clusters with a mass spectrum because high-mass stars evolve quickly into degenerates, while low-mass stars remain on the main sequence for the age of the universe. Here we examine the evolution of isolated globular clusters by using two-component Fokker-Planck (FP) models that include heating by binaries formed in tidal capture and in three-body encounters. Three-body binary heating dominates, and the postcollapse expansion is self-similar, at least in models with total mass M less than or equal to 3 x 10(5) M., initial half-mass radius r(h,i) greater than or equal to 5 pc, component mass ratio m(2)/m(1) greater than or equal to 2, and number ratio N-1/N-2 less than or equal to 300, when m(2) = 1.4 M.. We derive scaling laws for rho(c), v(i), r(c), and r(h) as functions of m(1)/m(2), N, M, and time t from simple energy-balance arguments; these agree well with the FP simulations. We have studied the conditions under which gravothermal oscillations (GTOs) occur. If E-lot and E-c are the energies of the cluster and of the core, respectively, and t(rh) and t(c) are their relaxation times, then epsilon = (E-lot/t(rh))/(E-c/t(rc)) is a good predictor of GTOs: all models with epsilon > 0.01 are stable, and all but one with epsilon < 0.01 oscillate. We derive a scaling law for epsilon against N and m(1)/m(2) and compare them with our numerical results. Clusters with larger m(2)/m(1) or smaller N are stabler.