Modeling the Retention Probability of Black Holes in Globular Clusters: Kicks and Rates

Abstract

We simulate black hole binary interactions to examine the probability of mergers and black hole growth and gravitational radiation signals using a specific initial distribution of masses for black holes in globular clusters and a simple semi-analytic formalism for dynamical interactions. We include 3-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 LIGO. We single out two possible Milky Way clusters (NGC 6441 and NGC 6388) as having the properties for a good probability of retention.