Massive black hole binary mergers within sub-pc scale gas discs

TL;DR

This study uses numerical simulations to show that small-scale gas discs can effectively drive supermassive black hole binary mergers at sub-parsec scales, especially for lower mass binaries, potentially resolving the final parsec problem.

Contribution

It provides the first detailed numerical analysis of binary evolution within self-gravitating gas discs, highlighting the role of gas in facilitating mergers at small separations.

Findings

Gas discs can dominate binary decay below 0.01-0.1 pc for M < 10^7 Msun.

Binary eccentricity grows up to e > 0.35 without saturation.

Merger timescales are shorter than the Hubble time for lower mass binaries.

Abstract

[ABRIDGED] We study 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 sub-parsec distances. Gas discs may dominate binary dynamics on these scales, and promote mergers. Using numerical simulations, we investigate the evolution of the orbits 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 > 0.35. Accretion onto 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 occuring 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 < M/Msun < 10^8 we find that decay due to gas discs may dominate for separations below a ~ 0.01--0.1 pc, where the disc is optically thick. The minimum merger time scale is shorter than the Hubble time for M < 10^7 Msun. 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 pc, where the combined decay rate is slowest. For more massive binaries, we suggest that scattering of stars formed within a fragmenting gas disc could act as a significant additional sink of binary angular momentum.