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.
