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

TL;DR

This paper addresses the origin of highly unequal mass BBH mergers, such as GW190814, by coupling self-consistent AGN-disc torques (via $p\rm{AGN}$) with an N-body integrator (TSUNAMI) that includes post-Newtonian corrections. The authors reveal that a single parameter, $\mathscr{B}=\tau_{\rm lib}/\Delta t_{\rm res}$, largely determines encounter outcomes—resonant trapping, orbit crossing, or binary capture—across diverse disc conditions, and they fit the capture probability with a lognormal model: $P(\rm{capture}|\mathscr{B})=A \exp[-(\ln\mathscr{B}-\mu)^2/(2\sigma^2)]$ with $A=0.41$, $\mu=1.10$, $\sigma=1.05$. The study connects disc luminosity to optimal mass-ratio windows for mergers, finding GW190814-like events can form in low-luminosity AGN with $L_{\rm AGN} \approx 10^{43.5}\ \rm erg\ s^{-1}$, while highlighting that many encounters do not merge due to resonant or dynamical barriers. These results provide analytic prescriptions for population synthesis and imply that AGN disc environments imprint strong, mass-dependent selection on BBH mergers and their host galaxies, informing rates, eccentricity distributions, and potential electromagnetic counterparts.

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 $m_1=23.2\,M_{\odot}$ and $m_2=2.59\,M_{\odot}$ -- 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 \texttt{pAGN} to model self-consistent AGN torques, coupled with \texttt{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, $P(\rm{capture}|\mathscr{B}) = A \exp[-(\ln \mathscr{B}-μ)^2/2σ^2]$, with $A = 0.41^{+0.04}_{-0.04}$, $μ= 1.09^{+0.08}_{-0.07}$, $σ= 1.05^{+0.08}_{-0.07}$. 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.

Figures (15)

• Figure 1: Mass gap as a function of accretion rate and SMBH mass, for a fixed viscosity parameter $\alpha=0.01$. The heat map instensity indicates the minimum gap opening mass, $m_{\rm gap}$, computed for each disc by evaluating Eqn. \ref{['eq:gap_opening_mass']} at the location between the outer migration trap and anti-trap. The contour lines shows the parameter space where $m_{\rm gap}$ matches the masses of interest, $m_{\rm gap}=2.59M_{\odot}$ or $m_{\rm gap}=23.2M_{\odot}$, giving a proxy for the discs that will produce migration traps for these masses. The stars represent the parameter values of the discs we consider in the study.
• Figure 2: The absolute value of the migration torques for $m_1$ and $m_2$ for each disc of interest. These torques include the effects of gap opening and thermal torques, shown in Eqn. \ref{['eq:torque_tot']}, with full expressions given in the appendix of gilbaum2025escape. The regions of negative torque (resulting in inward migration) are shown with solid lines, while the regions of positive torque (leading to inward migration) are shown as dashed lines.
• Figure 3: Top: orbital evolution of $m_1 = 2.59M_{\odot}$ (blue) and $m_2 = 23.2 M_{\odot}$ (red). Dashed lines are trap locations. Middle: semi-major axis and eccentricity of the inner binary from capture to merger, colour-coded with the time before merger. Bottom: The evolution of the peak gravitational wave frequency $f_{\rm GW}$ with eccentricity.
• Figure 4: An example of an orbit crossing, during an encounter at a trap in the disc $(M_{\rm SMBH}/ M_{\odot},\dot{m}, \alpha)=(10^8, 0.1, 0.01)$. In this scenario, long after an orbit crossing, a 3:4 resonance forms, synchronizing the inspiral of the two bodies.
• Figure 5: Resonance trap final locations (see Figure \ref{['fig:resonance_trap_orbit']}). We observe that the final radial locations of each BH does not coincide with any trap location, with the stability of the orbits being maintained by the resonant interaction and the opposing migrations from the gas torques.