Demographics of three-body binary black holes in star clusters: Implications for gravitational waves

Abstract

To explain both the dynamics of a globular cluster and its production of gravitational waves from coalescing binary blackholes, it is necessary to understand its population of dynamically formed (or, ‘three-body’) binaries. We provide a theoreticalunderstanding of this population, benchmarked by direct N-body models. We find that N-body models of clusters on average haveonly one three-body binary at any given time. This is different from theoretical expectations and models of binary populations,which predict a larger number of binaries (∼5), especially for low-N clusters (∼100), or in the case of two-mass models, lownumber of black holes. We argue that the presence of multiple binaries is suppressed by a high rate of binary–binary interactions,which efficiently ionize one of the binaries involved. These also lead to triple formation and potentially gravitational wavecaptures, which may provide an explanation for the recently reported high efficiency of in-cluster mergers in models of low-massclusters ( 105 M).