The Hydrodynamic Evolution of Binary Black Holes Embedded within the Vertically Stratified Disks of Active Galactic Nuclei

Stellar-mass black holes can become embedded within the disks of active galactic nuclei (AGNs). Afterwards, their interactions are mediated by their gaseous surroundings. Here, we study the evolution of stellar-mass binary black holes (BBHs) embedded within AGN disks using three-dimensional hydrodynamic simulations and analytic methods, focusing on environments where the AGN disk scale height H is greater than or similar to the BBH sphere of influence. We model the local surroundings of the embedded BBHs using a wind tunnel formalism and characterize different accretion regimes based on the local properties of the disk. We develop prescriptions for accretion and drag for embedded BBHs. Using these prescriptions with AGN disk models that can represent the Toomre-unstable outer regions of AGN disks, we study the long-term evolution of BBHs as they migrate through the disk. We find that BBHs typically merge within less than or similar to 1-30 Myr, increasing their mass significantly in the process, allowing BBHs to enter (or cross) the pair-instability supernova mass gap. The BBH accretion rate often exceeds the Eddington limit, sometimes by several orders of magnitude. Many embedded BBHs will merge before migrating significantly in the disk. We also discuss possible electromagnetic signatures during and following the inspiral, finding that it is generally unlikely for the bolometric luminosity of the BBH to exceed the AGN luminosity.