Accretion and orbital inspiral in gas-assisted supermassive black hole binary mergers

Many galaxies are expected to harbor binary supermassive black holes (SMBHs) in their centers. Their interaction with the surrounding gas results in the accretion and exchange of angular momentum via tidal torques, facilitating binary inspiral. Here, we explore the non-trivial coupling between these two processes and analyze how the global properties of externally supplied circumbinary disks depend on the binary accretion rate. By formulating our results in terms of the angular momentum flux driven by internal stresses, we come up with a very simple classification of the possible global disk structures, which differ from the standard constant $\dot{M}$ accretion disk solution. The suppression of accretion by the binary tides, leading to a significant mass accumulation in the inner disk, accelerates binary inspiral. We show that once the disk region strongly perturbed by the viscously transmitted tidal torque exceeds the binary semimajor axis, the binary can merge in less than its mass-doubling time due to accretion. Thus, unlike the inspirals driven by stellar scattering, the gas-assisted merger can occur even if the binary is embedded in a relatively low-mass disk (lower than its own mass). This is important for resolving the "last parsec" problem for SMBH binaries and understanding powerful gravitational wave sources in the universe. We argue that the enhancement of accretion by the binary found in some recent simulations cannot persist for a long time and should not affect the long-term orbital inspiral. We also review existing simulations of SMBH binary–disk coupling and propose a numerical setup which is particularly well suited to verifying our theoretical predictions.