  We study the evolution of disk accretion during the merger of supermassive
black hole binaries in galactic nuclei. In hierarchical galaxy formation
models, the most common binaries are likely to arise from minor galactic
mergers, and have unequal mass black holes. Once such a binary becomes embedded
in an accretion disk at a separation of the order of 0.1 pc, the merger
proceeds in two distinct phases. During the first phase, the loss of orbital
angular momentum to the gaseous disk shrinks the binary on a timescale of ~10
Myr. The accretion rate onto the primary black hole is not increased, and can
be substantially reduced, during this disk-driven migration. At smaller
separations, gravitational radiation becomes the dominant angular momentum loss
process, and any gas trapped inside the orbit of the secondary is driven
inwards by the inspiralling black hole. The implied accretion rate just prior
to coalescence exceeds the Eddington limit, so the final merger is likely to
occur within a common envelope formed from the disrupted inner disk, and be
accompanied by high velocity (~10,000 km/s) outflows.
