  Supermassive black hole binaries (SMBHBs) in galactic nuclei are thought to
be a common by-product of major galaxy mergers. We use simple disk models for
the circumbinary gas and for the binary-disk interaction to follow the orbital
decay of SMBHBs with a range of total masses (M) and mass ratios (q), through
physically distinct regions of the disk, until gravitational waves (GWs) take
over their evolution. Prior to the GW-driven phase, the viscous decay is in the
stalled "secondary-dominated" regime. SMBHBs spend a non-negligible fraction of
10^7 years at orbital periods t_var between a day and a year. A dedicated
optical or X-ray survey could identify coalescing SMBHBs statistically, as a
population of periodically variable quasars, whose abundance N_var is
proportional to t_var^alpha, in a range of periods t_var around tens of weeks.
SMBHBs with M < 10^7 M_sun, with 0.5 < alpha < 1.5, would probe the physics of
viscous orbital decay, whereas the detection of a population of higher-mass
binaries, with alpha=8/3, would confirm that their decay is driven by GWs. The
lowest mass SMBHBs (M < 10^{5-6} M_sun) enter the GW-driven regime at short
orbital periods, in the frequency band of the Laser Interferometric Space
Antenna (LISA). While viscous processes are strongly sub-dominant in the last
few years of coalescence, they could reduce the amplitude of any unresolved
background of near-stationary LISA sources. We discuss constraints on the SMBHB
population available from existing data, and the sensitivity and sky coverage
requirements for a detection in future surveys. SMBHBs may also be identified
from velocity shifts in their spectra; we discuss the expected abundance of
SMBHBs as a function of their orbital velocity.
