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Evolution of binary black holes in AGN accretion discs: Disc-binary interaction and gravitational wave emission

Binary black hole (BBH) mergers are the primary sources of gravitational wave (GW) events detected by LIGO/Virgo. Binary black holes embedded in the accretion discs of active galactic nuclei (AGN) are possible candidates for such GW events. We develop an idealised analytic model for the orbital evolution of BBHs in AGN accretion discs by combining the evolution equations of disc-binary interaction and GW inspiral. We investigate the coupled `disc+GW'-driven evolution of BBHs transitioning from the disc-driven regime at large orbital separations into the GW-driven regime at small separations. In this evolution channel, BBH mergers are accelerated by a combination of orbital decay and orbital eccentricity growth in the disc-dominated regime. We provide a quantification of the resulting merger timescale $τ_\text{merger}$, and analyse its dependence on both the accretion disc and binary orbital parameters. By computing the evolution of the orbital eccentricity as a function of the GW frequency, we predict that most binaries in AGN discs should have significant residual eccentricities ($e \sim 0.01-0.1$), potentially detectable by LISA. We further discuss the potentials and caveats of this particular BBH-in-AGN channel in the framework of binary evolutionary paths.