Hiromichi Tagawa, Zoltán Haiman, Bence Kocsis

Ground-based gravitational wave (GW) observatories have detected approximately 200 binary black hole (BH) mergers. The astrophysical origin of these events are debated, with evidence suggesting that at least a subset originated from dynamic environments characterized by frequent close encounters. Accretion disks in active galactic nuclei (AGNs) are of particular interest, as certain observed features could be more readily produced within such environments. In this paper, we investigate the expected properties of mergers in these environments, and their dependence on various parameters, using one-dimensional $N$-body simulations combined with a comprehensive semi-analytical model. In our fiducial model, the distributions of masses and mass ratios ($q$) are similar to those observed. However, they depend strongly on the lifetime and density of the AGN disk and on the number and accretion efficiency of BHs, with higher masses predicted as these quantities increase. The most massive mergers, such as GW231123, can be produced either by efficient gas accretion or by hierarchical mergers among $\geq 3$ generations of BHs. The observed negative correlation between $q$ and the average effective spin ($χ_{\rm eff}$), along with the positive correlation between $χ_{\rm eff}$ and the chirp mass ($M_{\rm chirp}$), can be explained by a combination of efficient gas accretion, which promotes spin alignment, and hierarchical mergers, which produce high-$|χ_{\rm eff}|$ and low-$q$ binaries. Hierarchical mergers can also explain the negative correlation between $q$ and the dispersion of $χ_{\rm eff}$, as well as the positive correlation between $|χ_{\rm eff}|$ and $M_{\rm chirp}$. We present a comprehensive study on how the expected distribution of each of these quantities depends on model parameters and assumptions, which will aid the interpretation of observed GW population properties.