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

To explain both the dynamics of a globular cluster and its production of gravitational waves from coalescing binary black holes, it is necessary to understand its population of dynamically-formed (or, `three-body') binaries. We provide a theoretical understanding of this population, benchmarked by direct $N$-body models. We find that $N$-body models of clusters on average have only 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 ($\sim 5$), especially for low-$N$ clusters ($\sim 100$), or in the case of two-mass models, low number of black holes. We argue that the presence of multiple binaries is suppressed by a high rate of binary-binary interactions, which efficiently ionise one of the binaries involved. These also lead to triple formation and potentially gravitational wave (GW) captures, which may provide an explanation for the recently reported high efficiency of in-cluster mergers in models of low-mass clusters ($\lesssim 10^5\,{\rm M}_\odot)$.