Tidal stellar disruptions by massive black hole pairs: II. Decaying
  binaries
  Tidal stellar disruptions have traditionally been discussed as a probe of the
single, massive black holes (MBHs) that are dormant in the nuclei of galaxies.
In Chen et al. (2009), we used numerical scattering experiments to show that
three-body interactions between bound stars in a stellar cusp and a
non-evolving "hard" MBH binary will also produce a burst of tidal disruptions,
caused by a combination of the secular "Kozai effect" and by close resonant
encounters with the secondary hole. Here we derive basic analytical scalings of
the stellar disruption rates with the system parameters, assess the relative
importance of the Kozai and resonant encounter mechanisms as a function of
time, discuss the impact of general relativistic (GR) and extended stellar cusp
effects, and develop a hybrid model to self-consistently follow the shrinking
of an MBH binary in a stellar background, including slingshot ejections and
tidal disruptions. In the case of a fiducial binary with primary hole mass
M_1=10^7\msun and mass ratio q=M_2/M_1=1/81, embedded in an isothermal cusp, we
derive a stellar disruption rate \dot{N_*} ~ 0.2/yr lasting ~ 3X10^5 yr. This
rate is 3 orders of magnitude larger than the corresponding value for a single
MBH fed by two-body relaxation, confirming our previous findings. For q<<0.01,
the Kozai/chaotic effect could be quenched due to GR/cusp effects by an order
of magnitude, but even in this case the stellar-disruption rate is still two
orders of magnitude larger than that given by standard relaxation processes
around a single MBH. Our results suggest that >~10% of the tidal-disruption
events may originate in MBH binaries.
