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

TL;DR

This paper investigates the dynamics of binary black holes in star clusters, revealing that three-body interactions are common and significantly influence gravitational wave events, including captures and triple formations.

Contribution

It demonstrates that three-body BBH interactions are prevalent and crucial for understanding GW capture rates and triple formation, resolving previous discrepancies in cluster simulations.

Findings

Almost all BBHs in interactions are three-body binaries

GW capture rates are independent of initial binary properties

Triple formation via ZLK oscillations contributes to BBH mergers

Abstract

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 ZLK 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 $R=1Gpc^{-3}yr^{-1}$ 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 ZLK oscillations, although their merger rate is lower than GW captures. Our results will help with the interpretation of future GW signals from eccentric BBHs