What Determines the Maximum Mass of AGN-assisted Black Hole Mergers?

TL;DR

This paper assesses the maximum mass of AGN-assisted black hole mergers using a 27-parameter semi-analytic Monte Carlo framework, linking hierarchical merger growth to AGN disk conditions. It finds that the disk lifetime $t_{ m AGN}$ is the dominant determinant of the high-mass end, with $M_{ m top}$ rising rapidly and $M_{ m top}\gtrsim 200\,M_\\odot$ requiring $t_{ m AGN}\gtrsim 40\,\

Abstract

The origin of merging binary black holes detected through gravitational waves remains a fundamental question in astrophysics. While stellar evolution imposes an upper mass limit of about 50 solar mass for black holes, some observed mergers--most notably GW190521--involve significantly more massive components, suggesting alternative formation channels. Here we investigate the maximum masses attainable by black hole mergers within active galactic nucleus (AGN) disks. Using a comprehensive semi-analytic model incorporating 27 binary and environmental parameters, we explore the role of AGN disk conditions in shaping the upper end of the black hole mass spectrum. We find that AGN disk lifetime is the dominant factor, with high-mass mergers (>200 solar mass) only possible if disks persist for ~40 Myr. The joint electromagnetic observation of an AGN-assisted merger could therefore lead to a direct measurement of the age of an AGN disk.

Figures (16)

• Figure 1: Schematic flow chart of the simulation framework. Pink blocks represent configurable models and parameters, including AGN disk properties, initial BH/stellar populations, and gas interaction models. Yellow blocks correspond to different computational processes, such as AGN disk property calculations, statistical background estimations, and Monte Carlo simulations for BH evolution. Blue blocks indicate simulation outputs, such as merger rates, mass distributions, and population evolution trends. The Monte Carlo simulations are repeated (red double arrows) to track BH status throughout the AGN lifetime, with iterations terminated when either 10,000 mergers are recorded or 10 AGNs are fully simulated.
• Figure 2: Schematic diagram illustrating the mechanisms incorporated in the program. The orange region represents the AGN disk, while the blue region denotes disk components (including both stars and BHs), which have a much smaller thickness compared to the AGN disk. All interaction types are depicted, though their positions are not drawn to scale.
• Figure 3: Interaction rate (in $\mathrm{Myr}^{-1}$) of a $10M_{\odot} +10M_{\odot}$ binary BH and single BH $10M_{\odot}$ using the fiducial model with default SMBH mass ($4\times10^6M_{\odot}$) and Gaussian ($\beta_V=0.2$) inclination distribution. The relative velocity to disk and the separation of the binary BH is labeled in the figure. Panel (a) shows how the accretion, migration and the gas dynamical friction rate of different relative velocity at different radius. Panel (b) shows how the hardening rate of a $10M_{\odot} +10M_{\odot}$ binary BH changes due to radius and separation. Panel (c) shows how the binary formation interaction rate of a $10M_{\odot}$ single BH changes at different radius. Panel (d) shows how the binary-single interaction rate with different surrounding components of a $10M_{\odot} +10M_{\odot}$ binary BH changes due to radius and separation.
• Figure 4: Merger positions and times over 100 Myr (fiducial AGN lifetime: 10 Myr) for the Gaussian model (top two rows) and the isotropic model (bottom two rows). The first column shows the spatial distribution of mergers, while the second column presents the time distribution of mergers, reflecting the shape of the instantaneous merger rate. The black lines represent all mergers, while colored lines distinguish different binary formation types or generations of merger remnants. The third column displays density heatmaps of merger position versus time for the Gaussian model (first row) and isotropic model (third row), with corresponding disk BH number density evolution shown in the second and fourth rows, respectively. The heatmaps also trace the merger history of the most massive merger before 10, 40, 70, and 100 Myr, marked by red, orange, purple, and green dots, respectively. In the number density plots, contours at $10^{13}\;\rm{pc^{-3}}$ and $10^{14}\;\rm{pc^{-3}}$ are overlaid, corresponding well to the bright, high-merger-density regions in the heatmaps.
• Figure 5: The averaged merger rate and highest 1% merger mass as a function AGN lifetime $t_{\mathrm{AGN}}$. The blue line represents the merger rate for a Gaussian distribution inclination, and the orange line is for an isotropic distribution inclination. The merger rate figure is the averaged merger rate of Fig. \ref{['fig:merger_feature']}.