Gravitational wave mergers of accreting binary black holes in AGN discs

Binary black hole (BBH) evolution in the discs of active galactic nuclei (AGNs) is a promising channel for gravitational wave (GW)-driven mergers. It is, however, unclear whether binaries interacting with the surrounding disc undergo orbital contraction or expansion. We develop a simple analytical model of accreting BBHs in AGN discs to follow the orbital evolution from the disc-dominated regime at large separations into the GW-driven regime at small separations (the coupled 'disc + GW'-driven evolution). We obtain that accreting binaries expand in thick discs with aspect ratio greater than a critical value (>h(crit)); whereas accreting binaries contract and eventually merge in thin discs (<h(crit)). Interestingly, accreting BBHs can experience faster mergers compared to non-accreting counterparts, with a non-monotonic dependence on the disc aspect ratio. The orbital contraction is usually coupled with eccentricity growth in the disc-dominated regime, which lead to accelerated inspirals in the GW-driven regime. We quantify the resulting BBH merger time-scales in AGN discs (tau(merger) similar to 10(5)-10(7) yr) and estimate the associated GW merger rates (R similar to(0.2--5)Gpc(-3)yr(-1)). Overall, accreting binaries may efficiently contract and merge in thin discs, hence this particular BBH-in-AGN channel may provide a non-negligible contribution to the observed GW merger event rate.