Modeling the retention probability of black holes in globular clusters: Kicks and rates

We simulate black hole binary interactions to examine the probability of mergers, black hole growth, and gravitational radiation signals using a specific initial distribution of masses for black holes in globular clusters and a simple semianalytic formalism for dynamical interactions. We include three-body recoil and the latest results in numerical relativity for gravitational radiation recoil. It is found that while 99% of binaries are ejected from low-metallicity, low-mass clusters, metal-rich massive clusters retain 5% of their binaries. An interesting fraction of the ejected binaries, especially those from high-mass, high-metallicity systems, merge on timescales short enough to be gravitational radiation sources during their mergers with rates approaching those expected for galactic field black hole binaries. While the merger rates are comparable, the much larger mass of these binaries and their localization will make them appealing targets for advanced study at the Laser Interferometer Gravitational-Wave Observatory. We single out two possible Milky Way clusters (NGC 6441 and NGC 6388) as having the properties for a good probability of retention.