Massive black hole binary mergers within subparsec scale gas discs

We study the efficiency and dynamics of supermassive black hole binary mergers driven by angular momentum loss to small-scale gas discs. Such binaries form after major galaxy mergers, but their fate is unclear since hardening through stellar scattering becomes very inefficient at subparsec distances. Gas discs may dominate binary dynamics on these scales, and promote mergers. Using numerical simulations, we investigate the evolution of the semimajor axis and eccentricity of binaries embedded within geometrically thin gas discs. Our simulations directly resolve angular momentum transport within the disc, which at the radii of interest is likely dominated by disc self-gravity. We show that the binary decays at a rate which is in good agreement with analytical estimates, while the eccentricity grows. Saturation of eccentricity growth is not observed up to values e greater than or similar to 0.35. Accretion on to the black holes is variable, and is roughly modulated by the binary orbital frequency. Scaling our results, we analytically estimate the maximum rate of binary decay that is possible without fragmentation occurring within the surrounding gas disc, and compare that rate to an estimate of the stellar dynamical hardening rate. For binary masses in the range 10(5) less than or similar to M less than or similar to 10(8) M(circle dot) we find that decay due to gas discs may dominate for separations below a similar to 0.01-0.1 pc, in the regime where the disc is optically thick. The minimum merger time-scale is shorter than the Hubble time for M less than or similar to 10(7) M(circle dot). This implies that gas discs could commonly attend relatively low-mass black hole mergers, and that a significant population of binaries might exist at separations of a few hundredths of a parsec, where the combined decay rate is slowest. For more massive binaries, where this mechanism fails to act quickly enough, we suggest that scattering of stars formed within a fragmenting gas disc could act as a significant additional sink of binary angular momentum.