Mass and effective spin distributions of binary black hole events: Evidence for a population of hierarchical black hole mergers in active galactic nuclei disks

The origins of the coalescing binary black holes (BBHs) detected by the advanced LIGO/Virgo are still in debate and clues may present in the mass and effective spin ($\chi_{\rm eff}$) distributions of these merger events. Here we analyze the GWTC-1 and GWTC-2.1 BBH events, and find evidence for a primary mass dependent $\chi_{\rm eff}$ distribution. Below (above) the mass of $\sim 50M_\odot$, a nearly zero (relatively high) effective spin is typical. In the joint analysis of the primary mass and $\chi_{\rm eff}$ distributions, we identify a sub-population of BBHs characterized by both a bump-like primary mass distribution extending to $\sim 100M_\odot$ and a relatively high $\chi_{\rm eff}\sim 0.3$, consistent with the expectation for the $\geq 2$g merger events in the disks of active galactic nuclei (AGNs). Our results suggest that the merger rate in AGN disks is around $1.7~{\rm Gpc}^{-3}{\rm yr}^{-1}$.