Assisted inspirals of stellar mass black holes embedded in AGN discs: Solving the ‘final au problem’

We explore the evolution of stellar mass black hole binaries (BHBs) which are formed in the self-gravitating discs of active galactic nuclei (AGN). Hardening due to three-body scattering and gaseous drag are effective mechanisms that reduce the semimajor axis of a BHB to radii where gravitational waves take over, on time-scales shorter than the typical lifetime of the AGN disc. Taking observationally motivated assumptions for the rate of star formation in AGN discs, we find a rate of disc-induced BHB mergers (⁠| $\mathcal {R} \sim 3\ {\rm yr}^{-1}\ {\rm Gpc}^{-3}$ |⁠, but with large uncertainties) that is comparable with existing estimates of the field rate of BHB mergers, and the approximate BHB merger rate implied by the recent Advanced LIGO detection of GW150914. BHBs formed thorough this channel will frequently be associated with luminous AGN, which are relatively rare within the sky error regions of future gravitational wave detector arrays. This channel could also possess a (potentially transient) electromagnetic counterpart due to super-Eddington accretion on to the stellar mass black hole following the merger.