Gravitational wave mergers of accreting binary black holes in AGN discs

TL;DR

This paper develops an analytic model for binary black hole evolution in AGN discs, showing how disc thickness influences orbital contraction or expansion, and estimating merger timescales and rates relevant for gravitational wave observations.

Contribution

It introduces a simple analytic model for accreting BBHs in AGN discs, revealing the impact of disc aspect ratio on orbital evolution and merger rates, a novel insight into this formation channel.

Findings

Accreting binaries expand in thick discs and contract in thin discs.

Faster mergers occur in accreting binaries compared to non-accreting ones.

Estimated merger timescales range from 10^5 to 10^7 years, with rates up to 5 Gpc^-3 yr^-1.

Abstract

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.