The role of gas in the merging of massive black holes in galactic nuclei. I. Black hole merging in a spherical gas cloud

Using high-resolution smoothed particle hydrodynamics 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 both observational and theoretical work that indicate the presence of large amounts of gas in the central regions of merging galaxies. N-body simulations have shown that the coalescence of a massive black hole binary eventually stalls in a stellar background. However, our simulations suggest that the massive black hole binary will finally merge if it is embedded in a gaseous background. Here we present results in which the gas is assumed to be initially spherical with a relatively smooth distribution. In the early evolution of the binary, the separation decreases as a result of the gravitational drag exerted by the background gas. In the later stages, when the binary dominates the gravitational potential in its vicinity, the medium responds by forming an ellipsoidal density enhancement whose axis lags behind the binary axis, and this offset produces a torque on the binary that causes continuing loss of angular momentum and is able to reduce the binary separation to distances where gravitational radiation is efficient. Assuming typical parameters from observations of ultraluminous infrared galaxies, we predict that a black hole binary will merge within 10(7) yr; therefore, these results imply that in a merger of gas-rich galaxies, any massive central black holes will coalesce soon after the galaxies merge. Our work thus supports scenarios of massive black hole evolution and growth in which hierarchical merging plays an important role. The final coalescence of the black holes leads to gravitational radiation emission that would be detectable out to high redshift by LISA. We show that similar physical effects, which we simulate with higher resolution than in previous work, can also be important for the formation of close binary stars.