Binary black hole mergers in AGN accretion discs: gravitational wave rate density estimates

The majority of gravitational wave (GW) events detected so far by LIGO/Virgo originate from binary black hole (BBH) mergers. Among the different binary evolution paths, the merger of BBHs in accretion discs of active galactic nuclei (AGNs) is a possible source of GW detections. We consider an idealised analytical model of the orbital evolution of BBHs embedded in an AGN accretion disc. In this framework, the disc-binary interaction increases the orbital eccentricity and decreases the orbital separation, driving the BBH into a regime where GW emission eventually leads to coalescence. We compute the resulting GW merger rate density from this channel based on a weighted average of the merger timescales of a population of BBHs radially distributed within the AGN accretion disc. The predicted merger rates broadly lie in the range $\mathcal{R} \sim (0.002 - 18) \, \mathrm{Gpc^{-3} yr^{-1}}$. We analyse the dependence of the merger rate density on both the accretion disc and binary orbital parameters, emphasising the important role of the orbital eccentricity. We discuss the astrophysical implications of this particular BBH-in-AGN formation channel in the broader context of binary evolution scenarios.