Hierarchical Black Hole Mergers in Active Galactic Nuclei

This work explores the active galactic nucleus (AGN) disk scenario for hierarchical black hole (BH) mergers. In AGNs, a central super-massive BH (SMBH) is surrounded by an extremely dense gaseous accretion disk. The stellar-sized BHs orbiting the SMBH are thus subject to strong gas torques and experience damping: their orbital eccentricity and inclination with respect to the disk plane are suppressed. Some of the stellar BHs eventually end up orbiting inside the disk, and suffer Type I migration, similar to what happens to planets in protoplanetary disks. The disk may develop migration traps, where migration stalls and BHs accumulate. This enhances interactions among BHs, with consequent efficient binary formation and, thanks to gas hardening, rapid merger. Because of the deep gravitational potential of the SMBH, the merger remnants are usually retained in the system and they can often go through multiple episodes of pair-up and merger. Hence, AGNs are promising environments for the formation of BHs in the upper mass gap with masses between 50 and 130 solar masses and intermediate-mass black holes (IMBHs) with masses between one hundred and one hundred thousand solar masses. In this Thesis work, we have developed a semi-analytical code which allows to easily explore BBH production in such environments, without the need of extensive N-body hydrodynamical simulations. Our model includes a formalism for BBH formation in migration traps and BBH evolution, as well as prescriptions for BH spin orientations. The physical parameters of the system, such as the mass of the SMBH and the density and thickness of the disk, strongly influence BH dynamics. Thanks to the computational efficiency of our code, we are able to explore the properties of BBH mergers in a variety of disk models. We find that, in disks with medium to high gas density or with low thickness, there is a large production of remnant BHs with masses up to a few thousands solar masses. On the other hand, disks that are thick and diluted are not able to prompt efficient migration, thus they produce no BBH mergers. Finally, we qualitatively compare our simulation outputs with gravitational-wave data from the LIGO–Virgo–KAGRA collaboration and we deduce that high-mass BBH merger detections could have been produced in AGN disks.