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

TL;DR

The paper investigates BH mergers occurring in AGN discs via gas-captured binaries formed through BH–BH scatterings, a channel that could contribute to LVK detections. It implements a physically grounded gas-capture formation criterion derived from hydrodynamical simulations within a semi-analytic Monte Carlo population model that spans the observed AGN SMBH mass function. The results indicate merger-rate densities of about 0.7 to 7.1 Gpc^-3 yr^-1 and observable LIGO rates of roughly 2 to 40 yr^-1, with a BH-merger mass distribution that is top-heavy and a mass-ratio distribution that is flatter than the initial BIMF. The study finds that AGN can be a non-negligible contributor to LVK events, particularly for high-mass mergers, while highlighting dependencies on BH numbers, BIMF, and disc physics, and noting caveats such as the isothermal assumption and lack of migration or repeated mergers.

Abstract

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.

Figures (11)

• Figure 1: Normalised black hole initial mass functions BIMF$_\mathrm{Tagawa}$, BIMF$_\mathrm{Bartos}$ and BIMF$_\mathrm{Baxter}$ (eqs. \ref{['eq:BIMF_tagawa']}, \ref{['eq:BIMF_bartos']} and \ref{['eq:BIMF_baxter']} respectively). BIMF$_\mathrm{Tagawa}$ is shown for $\gamma=\{1.7,1.35\}$ and BIMF$_\mathrm{Bartos}$ for $\beta=\{2,2.5\}$. The vertical lines of BIMF$_\mathrm{Tagawa}$ are a result of the $40\mathrm{M}_{\odot} \leq m_{*} < 55\mathrm{M}_{\odot}$ and $120\mathrm{M}_{\odot} \leq m_{*} \leq 140\mathrm{M}_{\odot}$ conditions of Eq. \ref{['eq:BIMF_tagawa']}. The vertical cutoff of BIMF$_\mathrm{Baxter}$, represents the lower boundary of the BH mass gap.
• Figure 2: The radial density profiles of the AGN disc generated from pAGN as a function of radial distance in the AGN disc $R$ along side the resulting modification $\mathcal{C}$ to the energy dissipation during encounter (Eqs. \ref{['eq:powerlaw_R']}-\ref{['eq:powerlaw_mod']}). Results shown for the SG$\alpha$ and SG$\beta$ disc models with parameters $M_{\rm bin}=20\mathrm{M}_{\odot}$ and $M_\bullet=\{10^{5},10^{6},10^{7},10^{8},10^{9}\}\mathrm{M}_{\odot}$.
• Figure 3: Maximum initial encounter energy $E_\mathrm{2H}$ of a binary that leads to a successfully formed binary for different impact parameters $p_{\rm 1H}$, as labelled on the curves, as a function of radial distance in the AGN disc $R$. Results shown for an SG$\alpha$ disc with parameters $M_{\rm bin}=20\mathrm{M}_{\odot}$ and $M_\bullet=[10^{5},10^{6},10^{7}]\mathrm{M}_{\odot}$. At lower $R$, the lower velocity dispersion and higher gas density allows BHs with larger initial encounter energies to dissipate enough energy to stay bound. Closer encounters at low impact parameters can extend binary formation to larger $R$.
• Figure 4: Fraction of encounters with impact parameters $p_\mathrm{1H}<r_{\rm H}$ that lead to successfully formed binaries as a function of radial distance in the SMBH disc for different $M_\bullet$, assuming an SG$\alpha$ disc. The function is shown assuming the BH mass function of BIMF$^{\gamma=2.35}_\text{Tagawa}$ and a uniform distribution of $p_\mathrm{1H}$ and $\Delta R$ is assumed. Results show AGN with higher $M_\bullet$ have a reduced formation probability for higher $R$.
• Figure 5: Fraction $f_\mathrm{align}$ of BHs with mass $M_{\rm BH}$ at radius $R$ aligning with an SG$\alpha$ AGN disc for fiducial parameters $M_\bullet=4\times10^{6}\mathrm{M}_{\odot}$, BIMF$_\text{Tagawa}^{\gamma=2.35}$ and $t_\mathrm{AGN}=10^{7}$yr. Generated by evaluating equation Eq. \ref{['eq:t_align_full']} over uniform $\cos{i}$. Figure shows higher mass BHs can align quicker, with a larger fraction aligning typically at larger radii.