Binary mergers and growth of black holes in dense star clusters

We model the dynamical evolution of primordial black holes ( BHs) in dense star clusters using a simplified treatment of stellar dynamics in which the BHs are assumed to remain concentrated in an inner core, completely decoupled from the background stars. Dynamical interactions involving BH binaries are computed exactly and are generated according to a Monte Carlo prescription. Recoil and ejections lead to complete evaporation of the BH core on a timescale similar to 10(9) yr for typical globular cluster parameters. Orbital decay driven by gravitational radiation can make binaries merge, and, in some cases, successive mergers can lead to significant BH growth. Our highly simplified treatment of the cluster dynamics allows us to study a large number of models and to compute statistical distributions of outcomes, such as the probability of massive BH growth and retention in a cluster. We find that, in most models, there is a significant probability ( similar to 20% - 80%) of BH growth with final masses >= 100 M (circle dot). In one case, a BH formed with mass approximate to 620 M (circle dot). However, if the typical merger recoil speed ( due to asymmetric emission of gravitational radiation) significantly exceeds the cluster escape speed, no growth ever occurs. Independent of the recoil speed, we find that BH- BH mergers enhanced by dynamical interactions in cluster cores present an important source of gravitational waves for ground- based laser interferometers. Under optimistic conditions, the total rate of detections by Advanced LIGO could be as high as a few tens of events per year from inspiraling BHs from clusters.