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 \leq 3 \times 10 ^ { 5 } M _ { \odot } , initial half-mass radius r _ { h,i } \geq 5 { pc } , component mass ratio m _ { 2 } / m _ { 1 } \geq 2 , and number ratio N _ { 1 } / N _ { 2 } \leq 300 when m _ { 2 } = 1.4 M _ { \odot } .
We derive scaling laws for \rho _ { 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 E _ { tot } 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 \equiv ( E _ { tot } / 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 compared with our numerical results .
Clusters with larger m _ { 2 } / m _ { 1 } or smaller N are stabler .