Mergers of Stellar-Mass Black Holes in Nuclear Star Clusters

Mergers between stellar-mass black holes (BHs) will be key sources of gravitational radiation for ground-based detectors. However, the rates of these events are highly uncertain, given that such systems are invisible. One formation scenario involves mergers in field binaries, where our lack of complete understanding of common envelopes and the distribution of supernova kicks has led to rate estimates that range over a factor of several hundreds. A different, and highly promising, channel involves multiple encounters of binaries in globular clusters or young star clusters. However, we currently lack solid evidence of BHs in almost all such clusters, and their low escape speeds raise the possibility that most are ejected because of supernova recoil. Here, we propose that a robust environment for mergers could be the nuclear star clusters found in the centers of small galaxies. These clusters have millions of stars, BH relaxation times well under a Hubble time, and escape speeds that are several times those of globulars; hence, they retain most of their BHs. We present simulations of the three-body dynamics of BHs in this environment and estimate that, if most nuclear star clusters do not have supermassive BHs that interfere with the mergers, tens of events per year will be detectable with the advanced Laser Interferometer Gravitational-Wave Observatory.