Black Hole Merger Rates in AGN: contribution from gas-captured binaries

It has been suggested that merging black hole (BH) binaries in active galactic nucleus (AGN) discs formed through two-body scatterings via the gas-capture process may explain a significant fraction of BH mergers in AGN and a non-negligible contribution to the observed rate from LIGO-VIRGO-KAGRA. We perform Monte Carlo simulations of BH and binary BH formation, evolution and mergers across the observed AGN mass function using a novel physically motivated treatment for the gas-capture process derived from hydrodynamical simulations of BH-BH encounters in AGN and varying assumptions on the AGN disc physics. The results suggest that gas-captured binaries could result in merger rates of 0.73 - 7.1Gpc$^{-3}$yr$^{-1}$. Most mergers take place near the outer boundary of the accretion disk, but this may be subject to change when migration is considered. The BH merger rate in the AGN channel in the Universe is dominated by AGN with supermassive BH masses on the order of 10$^{7} M_\odot$ , with 90% of mergers occurring in the range 10$^{6} M_\odot$ - 10$^{8} M_\odot$ . The merging mass distribution is flatter than the initial BH mass power law by a factor $Δξ$ = 1.1 to 1.2, as larger BHs can align with the disc and successfully form binaries more efficiently. Similarly, the merging mass ratio distribution is flatter, therefore the AGN channel could easily explain the high mass and unequal mass ratio detections such as GW190521 and GW190814. When modelling the BH binary formation process using a simpler dynamical friction treatment, we observe very similar results, where the primary bottleneck is the alignment time with the disk. We find the most influential parameters on the rates are the anticipated number of BHs and their mass function. We conclude that AGN remain an important channel for consideration, particularly for gravitational wave detections involving one or two high mass BHs.

💡 Research Summary

This paper presents a comprehensive study estimating the merger rate of binary black holes (BBHs) formed via the “gas-capture” process in the accretion discs of active galactic nuclei (AGN). The core advancement is the application of a physically motivated binary formation criterion, derived from high-resolution hydrodynamical simulations of BH-BH encounters in gaseous media, to a population synthesis model spanning the observed AGN mass function.

The research employs Monte Carlo simulations that integrate several key components:

1. AGN Disc Model: The disc structure is based on the Siwek & Goodman (2003) model, considering both α-disc and β-disc viscosity prescriptions. Disc properties (density, sound speed) are calculated self-consistently, with the outer boundary set by the Toomre Q gravitational instability condition.
2. Black Hole Population: Stellar-mass BHs are assumed to form from stars following a Kroupa (2001) initial mass function. These BHs are distributed in a spherical, mass-segregated cusp around the supermassive black hole (SMBH). Only a fraction of these, on orbits that intersect the AGN disc, are considered for binary formation. The study tests three different Black Hole Initial Mass Functions (BIMFs): one from solar-metallicity stellar evolution (Tagawa et al.), a simple power-law (Bartos et al.), and one constrained by gravitational wave observations and theory (Baxter et al.).
3. Gas-Capture Formation Criterion: Instead of using a simplistic dynamical friction formula, the model adopts a prescription from hydrodynamical simulations (Rowan et al. 2024; Whitehead et al. 2024a). This criterion defines the energy dissipated during the first close encounter of two BHs as a function of their closest approach distance (relative to their Hill radius) and the local gas density in the disc. A successful binary formation is determined based on this energy loss.
4. Merger Calculation: The simulation tracks the formation and subsequent evolution of these gas-captured binaries across a range of SMBH masses (10^5 to 10^9 M⊙), accounting for AGN lifetime. The merger rate is then integrated over the cosmological AGN mass function.

The key findings are:

• Merger Rate: The predicted volumetric merger rate from the gas-capture channel in AGN discs is in the range of 0.73 – 7.1 Gpc⁻³ yr⁻¹. This constitutes a potentially significant contribution to the overall BBH merger rate observed by LIGO-Virgo-KAGRA.
• Mass Distribution Shift: The mass distribution of merging BHs is flatter (i.e., has a less steep slope) than the initial BIMF by Δξ = 1.1–1.2. This is because more massive BHs align with the disc plane faster, enhancing their efficiency in forming binaries. Similarly, the mass ratio distribution of merging binaries is also flatter, making this channel a natural explanation for detections like GW190814 (with an unequal mass ratio) and GW190521 (with high component masses).
• Dominant AGN Hosts: The AGN channel’s contribution to the cosmic merger rate is dominated by AGN with SMBH masses around 10^7 M⊙, with 90% of mergers occurring in hosts with SMBH masses between 10^6 and 10^8 M⊙.
• Robustness of the Channel: Perhaps surprisingly, using the detailed hydro-based capture model versus a simpler dynamical friction treatment yielded very similar overall merger rates. This indicates that the primary bottleneck in the process is not the detailed gas dynamics during the encounter, but rather the time it takes for a BH to align its orbit with the AGN disc. The most influential parameters on the final rate are the assumed total number of BHs in the disc and their mass function.

The study concludes that the AGN disc environment, particularly through the gas-capture formation mechanism, remains a crucial and robust channel for producing BBH mergers. It is especially promising for explaining gravitational-wave events involving high-mass and asymmetric black holes, solidifying its importance in the landscape of astrophysical merger scenarios.