Stellar-mass black holes in star clusters: implications for gravitational-wave radiation

We study the dynamics of stellar-mass black holes (BHs) in star clusters, with particular attention to the formation of BH-BH binaries, which are interesting as sources of gravitational waves (GWs). We examine the properties of these BH-BH binaries through direct N-body simulations of Plummer clusters of N ≤ 10⁵ low-mass stars with an initial population of stellar-mass BHs, using the nbody6 code. We find that the stellar-mass BHs segregate rapidly into the cluster core and form a dense subcluster of BHs in which BH-BH binaries form through three-body encounters. While most BH binaries are ejected from the cluster by recoils due to superelastic encounters with the single BHs, we find that for clusters with N ≳ 5 × 10⁴, typically a few of them harden sufficiently so that they can merge via GW emission within the cluster. Also, for each of such clusters there are a few escaping BH binaries that merge within a Hubble time, with most merger times being within a few Gyr. These results imply that the intermediate-age massive clusters constitute the most important class of star cluster candidates that can produce dynamical BH-BH mergers at the present epoch. The BH-BH merger rates obtained from our computations imply a significant detection rate (~30 yr^-1) for the proposed Advanced LIGO GW detector.