Orbital Migration of Interacting Stellar Mass Black Holes in Disks around Supermassive Black Holes. III. Mass Distribution of Hierarchical Mergers

Abstract

Active galactic nucleus (AGN) disks are a promising location for the formation of binary black holes (BBHs) that will merge on relatively short timescales and be detected by LIGO-Virgo-KAGRA (LVK). To compare the mass function (MF) of black holes (BHs) undergoing hierarchical mergers in AGN disks to the inferred MFs from LVK observations, we perform 360 simulations with an N-body code augmented to include an analytic model for migration torques and other gas forces. We focus on the region surrounding migration traps in AGN disks where migration torques cancel out and BHs converge. We find that regardless of changes in the initial MF and BBH merger criteria, frequent mergers deplete the number of BHs with masses $\lesssim 10$~$M_\odot$ and fill the upper mass gap with a roughly uniform distribution from 40--100~$M_\odot$, with a slight overabundance around ${\approx}70~M_\odot$ from resonant orbiters. We also find an average merger rate of $\sim 6$~Gpc$^{-3}$~yr$^{-1}$ for migration-trap-aided BBH mergers in our AGN disk model. $\sim 40\%$ of these mergers have uneven mass ratios and 16\% have a primary mass $\in[50-100]~M_\odot$. Therefore, AGN disks could easily be the source of BBH mergers observed by LVK that are difficult to produce through traditional stellar evolution channels. Our simulations also form a separate higher-mass intermediate mass black hole (IMBH) population $>200~M_\odot$ after $\sim 2$~Myr. Future gravitational wave detectors can use observations of this IMBH population to constrain models of AGN accretion disks.