  Many galaxies are expected to harbor binary supermassive black holes (SMBHs)
in their centers. Their interaction with the surrounding gas results in
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. 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 semi-major 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 the existing simulations of the SMBH
binary-disk coupling and propose a numerical setup, which is particularly well
suited for verifying our theoretical predictions.
