Prompt gravitational-wave mergers aided by gas in active galactic nuclei: the hydrodynamics of binary-single black hole scatterings

ABSTRACT Black hole binary systems embedded in active galactic nucleus (AGN) discs have been proposed as a source of the observed gravitational waves (GWs) from LIGO-Virgo-KAGRA. Studies have indicated binary-single encounters could be common place within this population, yet we lack a comprehensive understanding of how the ambient gas affects the dynamics of these three-body encounters. We present the first hydrodynamical simulations of black hole binary-single encounters in an AGN disc. We find gas is a non-negligible component of binary-single interactions, leading to unique dynamics, including the formation of quasi-stable hierarchical triples. The gas efficiently and reliably dissipates the energy of the three-body system, hardening the triple provided it remains bound after the initial encounter. The hardening time-scale is shorter for higher ambient gas densities. Formed triples can be hardened reliably by $2-3$ orders of magnitude relative to the initial binary semimajor axis within less than a few AGN orbits, limited only by our resolution. The gas hardening of the triple enhances the probability for a merger by a minimum factor of $3.5-8$ depending on our assumptions. In several cases, two of the black holes can execute periapses of less than 10 Schwarzschild radii, where the dynamics were fully resolved for previous close approaches. Our results suggest that current time-scale estimates (without gas drag) for binary-single induced mergers are an upper bound. The shrinkage of the triple by gas has the prospect of increasing the chance for unique GW phenomena such as residual eccentricity, dephasing from a third object and double GW mergers.