Time-dependent stellar-mass binary black hole mergers in AGN disks: Mass distribution of hierarchical mergers

There is much debate about the channels for astrophysical origins of the stellar-mass binary black hole (BBH) mergers detected by LIGO and Virgo. Active galactic nuclei (AGNs) are promising sites for the efficient formation and rapid mergers of BBHs due to migration traps in high-density gas disks within an inner radii. In this paper, we carry out Monte Carlo simulations to explore the mass properties of mergers over time and hierarchical mergers -- with one of the black holes (BHs) being the remnant of a previous merger. We find that the predicted merger rate is $\sim 27-37~{\rm Gpc^{-3}~yr^{-1}}$ and the detection rate of LIGO/Virgo accompanying with extreme mass-ratio mergers will increase in the late stage of AGNs. The fraction of hierarchical mergers is $\sim 24\%$, and its mass-ratio peak is $\sim 0.15-0.35$. Compared with the low-generation mergers in hierarchical mergers, the mass ratio of high-generation mergers has a flatter distribution around its peak. These reveal that the BBH mergers detected by LIGO/Virgo with the extreme mass ratio or heavy component masses can be well explained in AGN channel.