The tidal disruption rate in dense galactic cusps containing a supermassive binary black hole

We consider the problem of tidal disruption of stars in the centre of a galaxy containing a supermassive binary black hole with unequal masses. We assume that over the separation distance between the black holes, the gravitational potential is dominated by the more massive primary black hole. Also, we assume that the number density of stars is concentric with the primary black hole and has a power-law cusp. We show that the bulk of stars with a small angular-momentum component normal to the black hole binary orbit can reach a small value of total angular momentum through secular evolution in the gravitational field of the binary, and hence they can be tidally disrupted by the larger black hole. This effect is analogous to the so-called Kozai effect well known in celestial mechanics. We develop an analytical theory for the secular evolution of the stellar orbits and calculate the rate of tidal disruption. We compare our analytical theory with a simple numerical model and find very good agreement. Our results show that for a primary black hole mass of similar to 10(6) - 10(7)M(.), the black hole mass-ratio q > 10(-2), cusp size similar to 1 pc, the tidal disruption rate can be as large as similar to 10(-2) - 1M(.) yr(-1). This is at least 10(2) - 10(4) times larger than estimated for the case of a single supermassive black hole. The duration of the phase of enhanced tidal disruption is determined by the dynamical-friction time-scale, and it is rather short: similar to 10(5) yr. The dependence of the tidal disruption rate on the mass ratio, and on the size of the cusp, is also discussed.