Not all roads lead to merger: AGN disc properties influence the interactions of highly unequal mass black holes

ABSTRACT As the number of gravitational-wave detections of black hole binaries grows, so does the diversity of proposed formation channels. The growing sample of systems with highly unequal masses, such as GW190814 with $m_1=23.2\, {\rm M}_{\odot }$ and $m_2=2.59\, {\rm M}_{\odot }$ – corresponding to a mass ratio $q=0.112$ – cannot be readily explained by isolated binary evolution and may originate through dynamical assembly in an active galactic nucleus (AGN). We investigate AGN discs capable of producing GW190814-like mergers using pAGN to model self-consistent AGN torques, coupled with TSUNAMI, a regularised N-body code including post-Newtonian terms up to 3.5 order. Suites of N-body simulations reveal possible outcomes of binary capture and merger, mean-motion resonance interactions, and other novel dynamical pathways. We develop analytical models linking the branching ratios of captures and mergers to local disc properties, applicable to black hole populations across all mass ratios. Capture probability is primarily governed by $\mathscr {B}$, the ratio of libration time to resonance-width crossing, and is well described by a log-Gaussian, $P(\rm {capture}|\mathscr {B}) = A \exp [-(\ln \mathscr {B}-\mu)^2/2\sigma ^2]$, with $A = 0.41^{+0.04}_{-0.04}$, $\mu = 1.09^{+0.08}_{-0.07}$, $\sigma = 1.05^{+0.08}_{-0.07}$. This fit, while an upper limit, is useful for simplified population synthesis. Finally, we explore the mass ratio AGN luminosity parameter space and find that GW190814 may be formed in a low luminosity AGN of $L_{\rm AGN}\approx 10^{43.5}\ \rm erg\ s^{-1}$. A more systematic parameter space exploration and future population studies will further test our predictions.