Massive Black Holes in Star Clusters. I. Equal‐Mass Clusters

Abstract

In this paper we report results of collisional N-body simulations of the dynamical evolution of equal-mass star clusters containing a massive central black hole. Each cluster is composed of between 5000 and 180,000 stars together with a central black hole that contains between 0.2% and 10% of the total cluster mass. We find that for large enough black hole masses, the central density follows a power-law distribution with slope ρ ∼ r -1.75 inside the radius of influence of the black hole, in agreement with predictions from earlier Fokker-Planck and Monte Carlo models. The tidal disruption rate of stars is within a factor of 2 of that derived in previous studies. It seems impossible to grow an intermediate-mass black hole (IMBH) from an M ≤ 100 M ⊙ progenitor in a globular cluster by the tidal disruption of stars, although M = 10 3 M ⊙ IMBHs can double their mass within a Hubble time in dense globular clusters. The same is true for the supermassive black hole at the center of the Milky Way. Black holes in star clusters will feed mainly on stars tightly bound to them, and the repopulation of these stars causes the clusters to expand, reversing core collapse without the need for dynamically active binaries. Close encounters of stars in the central cusp also lead to an increased mass-loss rate in the form of high-velocity stars escaping from the cluster. A companion paper will extend these results to the multimass case.