Black hole binary formation in AGN discs: from isolation to merger

Motivated by the increasing number of detections of merging black holes by LIGO-VIRGO-KAGRA, black hole (BH) binary mergers in the discs of active galactic nuclei (AGNs) is investigated as a possible merger channel. In this pathway, BH encounters in the gas disc form mutually bound BH binary systems through interaction with the gas in the disc and subsequently inspiral through gravitational torques induced by the local gas. To determine the feasibility of this merger pathway, we present the first three-dimensional global hydrodynamic simulations of the formation and evolution of a stellar-mass BH binaries AGN discs with three different AGN disc masses and five different initial radial separations. These 15 simulations show binary capture of prograde and retrograde binaries can be successful in a range of disc densities including cases well below that of a standard radiatively efficient alpha disc, identifying that the majority of these captured binaries are then subsequently hardened by the surrounding gas. The eccentricity evolution depends strongly on the orbital rotation where prograde binaries are governed by gravitational torques form their circumbinary mini disc, with eccentricities being damped, while for retrograde binaries the eccentricities are excited to >~ 0.9 by accretion torques. In two cases, retrograde binaries ultimately undergo a close periapsis passage which results in a merger via gravitational waves after only a few thousand binary orbits. Thus, the merger time-scale can be far shorter than the AGN disc lifetime. These simulations support an efficient AGN disc merger pathway for BHs.