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

We study the dynamics of stellar-mass black holes (BH) in star clusters with particular attention to the formation of BH-BH binaries, which are interesting as sources of gravitational waves (GW). In the present study, we examine the properties of these BH-BH binaries through direct N-body simulations of star clusters using the nbody6 code on graphical processing unit platforms. We perform simulations for star clusters with < 105 low-mass stars starting from Plummer models with an initial population of BHs, varying the cluster mass and BH-retention fraction. Additionally, we do several calculations of star clusters confined within a reflective boundary mimicking only the core of a massive star cluster which can be performed much faster than the corresponding full cluster integration. We find that stellar-mass BHs with masses similar to 10 M-circle dot segregate rapidly (similar to 100 Myr time-scale) into the cluster core and form a dense subcluster of BHs within typically 0.2-0.5 pc radius. In such a subcluster, BH-BH binaries can be formed through three-body encounters, the rate of which can become substantial in dense enough BH cores. While most BH binaries are finally ejected from the cluster by recoils received during superelastic encounters with the single BHs, few of them harden sufficiently so that they can merge via GW emission within the cluster. We find that for clusters with N greater than or similar to 5 x 104, typically 1-2 BH-BH mergers occur per cluster within the first similar to 4 Gyr of cluster evolution. Also for each of these clusters, there are a few escaping BH binaries that can merge within a Hubble time, most of the merger times being within a few Gyr. These results indicate that intermediate-age massive clusters constitute the most important class of candidates for producing dynamical BH-BH mergers. Old globular clusters cannot contribute significantly to the present-day BH-BH merger rate since most of the mergers from them would have occurred much earlier. On the other hand, young massive clusters with ages less that 50 Myr are too young to produce significant number of BH-BH mergers. We finally discuss the detection rate of BH-BH inspirals by the 'Laser Interferometer Gravitational-Wave Observatory' (LIGO) and 'Advanced LIGO' GW detectors. Our results indicate that dynamical BH-BH binaries constitute the dominant channel for BH-BH merger detection.