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.