Impact of gas hardening on the population properties of hierarchical black hole mergers in active galactic nucleus disks

Hierarchical black hole (BH) mergers in active galactic nuclei (AGNs) are unique among formation channels of binary black holes (BBHs) because they are likely associated with electromagnetic counterparts and can efficiently lead to the mass growth of BHs. Here, we explore the impact of gas accretion and migration traps on the evolution of BBHs in AGNs. We have developed a new fast semi-analytic model, that allows us to explore the parameter space while capturing the main physical processes involved. We find that an effective exchange of energy and angular momentum between the BBH and the surrounding gas (i.e., gas hardening) during inspiral greatly enhances the efficiency of hierarchical mergers, leading to the formation of intermediate-mass BHs (up to 10⁴ M_⊙) and triggering spin alignment. Moreover, our models with efficient gas hardening show both an anticorrelation between the BBH mass ratio and the effective spin and a correlation between the primary BH mass and the effective spin. In contrast, if gas hardening is inefficient, the hierarchical merger chain is already truncated after the first two or three generations. We compare the BBH population in AGNs with other dynamical channels as well as isolated binary evolution.