The Role of Gas in the Merging of Massive Black Holes in Galactic Nuclei. II. Black Hole Merging in a Nuclear Gas Disk

Using high-resolution SPH numerical simulations, we investigate the effects of gas on the in-spiral and merger of a massive black hole binary. This study is motivated by the very massive nuclear gas disks observed in the central regions of merging galaxies. Here we present results that expand on the treatment in a previous work by studying models in which the gas is in a disk. We run a variety of models, ranging from simulations with a relatively smooth gas disk to cases in which the gas has a more clumpy spatial distribution. We also vary the inclination angle between the plane of the binary and the plane of the disk, and the mass ratio between the MBHs and the gaseous disk. We find that, as in our previous work, in the early evolution of the system the binary separation diminishes mainly due to dynamical friction exerted by the background gas, and in the later stages the gaseous medium responds by forming an ellipsoidal density enhancement whose axis lags behind the binary axis. This offset produces a gravitational torque on the binary that causes continuing loss of angular momentum and is able to reduce the separation to distances at which gravitational radiation is efficient. The main difference is that between these two regimes we now find a new transition regime that was not apparent in our previous paper, in which the evolution is temporarily slowed down when neither of these mechanisms is fully effective. In the variety of simulations that we perform, we find that the coalescence timescale for the MBH binary varies between 5 × 10⁶ and 2.5 × 10⁷ yr for typical ULIRGs. For MBHs that satisfy the observed "m-σ_c" relation, our simulations suggest that in a merger of galaxies that have at least 1% of their total mass in gas, the MBHs will coalesce soon after the galaxies merge.