Revealing Potential Sub-populations and Assembling Tendency of Component Black Holes for GWTC-3 events

The origins of coalescing binary black holes (BBHs) detected by the advanced LIGO/Virgo are still under debate, and clues may be present in the joint mass-spin distribution of these merger events. Here we construct phenomenological models containing two sub-populations to investigate the BBH population detected in gravitational wave observations. We find that our models can explain the GWTC-3 data rather well, and several constraints to our model are required by the data: first, the maximum mass for the component with a stellar-origin, $m_{\rm max}$, is $39.1^{+2.4}_{-2.7}M_{\odot}$ at 90\% credibility; second, about $15\%$ of the mergers happen in dynamical environments, in which $7-16\%$ of events are hierarchical mergers, and these BHs have an average spin magnitude significantly larger than the first-generation mergers, with ${\rm d}\mu_{\rm a} > 0.4 $ at $99\%$ credibility; third, the dynamical component BHs tend to pair with each other with larger total mass and higher mass ratio. An independent analysis focusing on spins is also carried out, and we find that the spin amplitude of component BHs can be divided into two groups according to a division mass $m_{\rm d} = 46.1^{+5.6}_{-5.1}M_{\odot}$. These constraints can be naturally explained by current formation channels, and our results suggest that some of the observed events were likely from AGN disks.