Interactions among binary black holes in star clusters: Eccentric gravitational wave captures and triple formation

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Numerical simulations of star clusters with black holes find that there is only a single dynamically active binary black hole (BBH), at odds with the theoretical expectation of ∼5 dynamically formed -- or, commonly referred to as `three-body' -- BBHs in clusters with a few hundred BHs. We test the recent suggestion that this tension is because interactions among three-body BBHs were neglected in the theory. We use the public catalogue of Cluster Monte Carlo models to obtain a sample of strong BBH-BBH interactions, which we integrate using post-Newtonian equations of motion up to 3.5PN. We explore the nature of the BBHs involved in BBH-BBH interactions in star clusters, as well as the various outcomes: gravitational wave (GW) captures and the associated eccentricities at the frequencies of ground-based GW detectors, as well as BH triple formation and their contribution to BBH mergers via the Lidov-Kozai mechanism. We find that almost all BBHs involved in BBH-BBH interactions are indeed three-body binaries and that BBH formation and disruption in BBH-BBH interactions occur at approximately the same rate, providing an explanation for the finding of a single dynamically active BBH in N-body models. An important implication is that the resulting rates of GW capture and triple formation are independent of uncertain initial binary properties. With the use of a population synthesis model for BBH-BBH interactions in globular clusters, we obtain a local rate of GW captures of mathcal R (z≃ 0) ≃ 1 Gpc^ yr^ as well as their eccentricity distribution and redshift dependence. We find that a BBH-BBH interaction is more likely to trigger a GW merger than a BH-BBH interaction. We also confirm that stable triples that are assembled in BBH-BBH interactions can merge via von Zeipel-Lidov-Kozai oscillations, although their merger rate is lower than GW captures. Our results will help with the interpretation of future GW signals from eccentric BBHs.