Active galactic nucleus formation channel for stellar binary black holes

Ground-based gravitational wave detectors such as the Laser Interferometer Gravitational-Wave Observatory (LIGO) have detected hundreds of compact binary coalescences, most of which are binary black hole mergers. The astrophysical origin and formation channel of these stellar binary black hole mergers is a fundamental problem in astrophysics. Among them, the active galactic nucleus (AGN) may play an important role in forming gravitational wave sources of some binary black holes. This paper reviews the formation mechanisms of stellar binary black holes on AGN disks, gives some astrophysical characteristics of such binary black holes, and discusses how to determine whether binary black holes come from AGN disks by gravitational and electromagnetic wave observations. Compact objects, including stellar-mass black holes, can be captured and embedded into AGN disks through dynamic interactions between nuclear star clusters and the AGN disk. Once inside the disk, these black holes interact with the surrounding gas, leading to migration. Black holes may become trapped in certain specific regions due to the accretion disk's physical conditions, commonly called migration traps. On the other hand, black holes can also open a gap in the AGN disk. In this case, the black holes interact with the gas that enters the gap, causing their migration speed to slow down. In AGN disks, black holes are expected to cluster in these migration traps and gaps. Due to dynamical effects or interactions with the gas in these regions, the black holes move closer together and eventually merge. Binary black holes formed within AGN disks exhibit a range of astrophysical characteristics. Black holes merged in the inner regions of the disk typically have lower mass ratios and higher expected effective spin parameters. In contrast, binary black holes merged in the disk's outer regions tend to have larger mass ratios, with their effective spin parameters distributed around zero. Additionally, binary black hole systems in AGN disks may show high orbital eccentricities, which could leave distinct imprints on the gravitational wave signals. One key feature of mergers occurring within AGN disks, due to the gas-rich environment, is that the gravitational wave signals produced by these mergers may be accompanied by electromagnetic radiation. So far, nine candidate electromagnetic counterparts have been proposed, associated with events such as GW150914 and GW190521. Observing gravitational wave events from binary black hole mergers, alongside their potential electromagnetic counterparts, could provide critical evidences to help analyze the environments where such mergers occur. This, in turn, would enhance our understanding of the mechanisms leading to binary black hole formation and mergers.