Filling the disk hollow following binary black hole merger: The
  transient accretion afterglow
  Tidal torques from a binary black hole (BHBH) empty out the central regions
in any circumbinary gaseous accretion disk. The balance between tidal torques
and viscosity maintain the inner edge of the disk at a radius r ~ 1.5a -- 2a,
where a is the binary semimajor axis. Eventually, the inspiraling binary
decouples from disk and merges, leaving behind a central hollow ("donut hole")
in the disk orbiting the remnant black hole. We present a simple,
time-dependent, Newtonian calculation that follows the secular (viscous)
evolution of the disk as it fills up the hollow down to the black hole
innermost stable circular orbit and then relaxes to stationary equilibrium. We
use our model to calculate the electromagnetic radiation ("afterglow") spectrum
emitted during this transient accretion epoch. Observing the temporal increase
in the total electromagnetic flux and the hardening of the spectrum as the
donut hole fills may help confirm a BHBH merger detected by a gravitational
wave interferometer. We show how the very existence of the initial hollow can
lead to super-Eddington accretion during this secular phase if the rate is not
very far below Eddington prior to decoupling. Our model, though highly
idealized, may be useful in establishing some of the key parameters, thermal
emission features and scalings that characterize this transient. It can serve
as a guide in the design and calibration of future
radiation-magnetohydrodynamic simulations in general relativity.
