Hydrodynamical Simulations of Black-Hole Binary Formation in AGN Disks

We study close encounters between two single black holes (BHs) embedded in an AGN disk using a series of global 2D hydrodynamics simulations. We find that when the disk density is sufficiently high, bound BH binaries can be formed by the collision of their circum-single disks. Our analysis demonstrates that, after a BH pair passes the pericenter of their relative trajectory, post-collision gas drag may slow down the BHs, possibly forcing the two BHs to stay tightly bound. A binary formed by a close encounter can have a compact semimajor axis, large eccentricity, and retrograde orbital angular momentum. We provide a fitting formula that can accurately predict whether a close encounter can form a binary based on the gas mass and the incoming energy of the encounter. This fitting formula can be easily implemented in other long-term simulations that study the dynamical evolution of BHs in active galactic nucleus disks.