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 65,536 stars, performed on the GRAPE family of special-purpose computers. We find that star clusters with initial half-mass relaxation times ≲25 Myr are dominated by stellar collisions, the first collisions occurring at or near the point of core collapse, which is driven by the segregation of the most massive stars to the cluster center, where they end up in hard binaries. 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 5 Myr and with present-day half-mass relaxation times ≲100 Myr are expected to contain an IMBH.