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 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 x 10^5 M_ødot, initial half-mass radius rh,i >= 5 pc, component mass ratio m_2/m_1 <= 2, and number ratio N_1/N_2 <= 300 when m_2=1.4 M_ødot. We derive scaling laws for \ρ_c, v_c, r_c, and r_h as functions of m_1/m_2, N, M, and time t from simple energy-balance arguments, and these agree well with the FP simulations. We have studied the conditions under which gravothermal oscillations (GTOs) occur. If Eₜₒₜ and E_c are the energies of the cluster and of the core, respectively, and tᵣₕ and t_c are their relaxation times, then \ε \≡ (Eₜₒₜ/tᵣₕ)/(E_c/trc) is a good predictor of GTOs: all models with \ε>0.01 are stable, and all but one with \ε < 0.01 oscillate. We derive a scaling law for \ε against N and m_1/m_2 and compared with our numerical results. Clusters with larger m_2/m_1 or smaller N are stabler.