Fossil Gas and the Electromagnetic Precursor of Supermassive Binary
  Black Hole Mergers
  Using a one-dimensional height integrated model, we calculate the evolution
of an unequal mass binary black hole with a coplanar gas disk that contains a
gap due to the presence of the secondary black hole. Viscous evolution of the
outer circumbinary disk initially hardens the binary, while the inner disk
drains onto the primary (central) black hole. As long as the inner disk remains
cool and thin at low $\dot{M}_{\rm ext}$ (rather than becoming hot and
geometrically thick), the mass of the inner disk reaches an asymptotic mass
typically $\sim 10^{-3}-10^{-4}\Msun$. Once the semimajor axis shrinks below a
critical value, angular momentum losses from gravitational waves dominate over
viscous transport in hardening the binary. The inner disk then no longer
responds viscously to the inspiraling black holes. Instead, tidal interactions
with the secondary rapidly drive the inner disk into the primary. Tidal and
viscous dissipation in the inner disk lead to a late time brightening in
luminosity $L\propto t_{\rm minus}^{5/4}$, where $t_{\rm minus}$ is the time
prior to the final merger. This late time brightening peaks $\sim 1$ day prior
to the final merger at $\sim 0.1 L_{\rm Edd}$. This behavior is relatively
robust because of self regulation in the coupled viscous-gravitational
evolution of such binary systems. It constitutes a unique electromagnetic
signature of a binary supermassive black hole merger and may allow the host
galaxy to be identified if used in conjunction with the Laser Interferometric
Space Antenna (LISA) localization.
