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

Using SPH numerical simulations, we investigate the effects of gas on the inspiral 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 (Escala, Larson, Coppi & Mardones 2004; henceforth Paper I), by studying more realistic models. 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 Paper I, in the early evolution of the system the binary separation diminishes due to gravitational drag, and in the later stages the medium responds by forming an ellipsoidal density enhancement whose axis lags behind the binary axis; this offset produces a torque on the binary that causes continuing loss of angular momentum and is able to reduce the separation to distances where gravitational radiation is efficient. In the simulations that we perform, we find that the coalescence timescale for the MBH binary varies between 5 10^6 yr and 2.5 10^7 yr. For MBHs that satisfy the observed `m-sigma_c' relation, we predict 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. We also predict that if the MBHs depart from the `m-sigma_c' relation, the MBH binary can create a circumbinary gap in the disk that stalls the coalescence, but this gap formation can act as a self-regulatory mechanism on MBH growth that can help to explain the existence of the `m-sigma_c' relation.