The runaway growth of intermediate-mass black holes in dense star clusters

We study the growth rate of stars via stellar collisions in dense star clusters, calibrating our analytic calculations with direct N-body simulations of up to 65536 stars, performed on the GRAPE family of computers. We find that star clusters with initial half-mass relaxation times < ∼ 20Myr are dominated by stellar collisions, the first collisions occurring at or near the point of core collapse. The majority of collisions occur with the same star, resulting in the runaway growth of a supermassive object. This object can grow up to ∼ 0.1% of the mass of the entire star cluster and could manifest itself as an intermediate-mass black hole (IMBH). The phase of runaway growth lasts until mass loss by stellar evolution arrests core collapse. Star clusters older than about 4Myr and with present-day half-mass relaxation times < ∼ 80Myr are expected to contain an IMBH. The star cluster may sink to the Galactic center by dynamical friction before stellar evolution starts to dominate the evolution of the cluster core. If the cluster reaches the center it deposits its IMBH there. If stellar evolution dominates first, the cluster dissolves and the runaway growth of the IMBH is terminated. Without the mediation of the star cluster the black hole cannot sink much farther toward the Galactic center, and it remains in orbit at roughly the galactocentric radius where disruption occurred. The mass ratio between the star cluster and the compact object is comparable to the ratio of the masses of Galactic bulges to their central black holes, suggesting that this process may be able to account for the supermassive black holes observed in many galaxies.