Gravitational wave mergers of accreting binary black holes in AGN discs

Binary black hole (BBH) evolution in the discs of active galactic nuclei (AGN) 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 analytic 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 ($> h_\mathrm{crit}$); whereas accreting binaries contract and eventually merge in thin discs ($< h_\mathrm{crit}$). 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 timescales in AGN discs ($\tau_\mathrm{merger} \sim 10^5 - 10^7$ yr) and estimate the associated GW merger rates ($\mathcal{R} \sim (0.2 - 5) \, \text{Gpc}^{-3} \text{yr}^{-1}$). 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.