Two‐Component Fokker‐Planck Models for the Evolution of Isolated Globular Clusters

Abstract

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 ≤ 3 × 105 M☉, initial half-mass radius rh,i ≥ 5 pc, component mass ratio m2/m1 ≥ 2, and number ratio N1/N2 ≤ 300, when m2 = 1.4 M☉. We derive scaling laws for ρc, vi, rc, and rh as functions of m1/m2, 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 Etot and Ec are the energies of the cluster and of the core, respectively, and trh and tc are their relaxation times, then ≡ (Etot/trh)/(Ec/trc) is a good predictor of GTOs: all models with > 0.01 are stable, and all but one with < 0.01 oscillate. We derive a scaling law for against N and m1/m2 and compare them with our numerical results. Clusters with larger m2/m1 or smaller N are stabler.