Accretion Disks Around Binary Black Holes: A Quasistationary Model
  Tidal torques acting on a gaseous accretion disk around a binary black hole
can create a gap in the disk near the orbital radius. At late times, when the
binary inspiral timescale due to gravitational wave emission becomes shorter
than the viscous timescale in the disk, the binary decouples from the disk and
eventually merges. Prior to decoupling the balance between tidal and viscous
torques drives the disk to a quasistationary equilibrium state, perturbed
slightly by small amplitude, spiral density waves emanating from the edges of
the gap. We consider a black hole binary with a companion of smaller mass and
construct a simple Newtonian model for a geometrically thin, Keplerian disk in
the orbital plane of the binary. We solve the disk evolution equations in
steady state to determine the quasistationary, (orbit-averaged) surface density
profile prior to decoupling. We use our solution, which is analytic up to
simple quadratures, to compute the electromagnetic flux and approximate
radiation spectrum during this epoch. A single nondimensional parameter
Td/Tvis, equal to the ratio of the tidal to viscous torque at the orbital
radius, determines the disk structure, including the surface density profile,
the extent of the gap, the existence of an inner disk, and the accretion rate.
The solution reduces to the Shakura-Sunyaev profile for a stationary accretion
disk around a single black hole in the limit of small Td/Tvis. Our solution may
be useful for choosing physical parameters and setting up quasistationary disk
initial data for detailed numerical simulations that begin prior to decoupling
and track the subsequent evolution of a black hole binary-disk system.
