Resonantly enhanced kicks from equatorial small mass-ratio inspirals

We calculate the kick generated by an eccentric black hole binary inspiral as it evolves through a resonant orbital configuration where the precession of the system temporarily halts. As a result, the effects of the asymmetric emission of gravitational waves build up coherently over a large number of orbits. Our results are calculated using black hole perturbation theory in the limit where the ratio of the masses of the orbiting objects epsilon = m/M is small. The resulting kick velocity scales as epsilon(3/2), much faster than the epsilon(2) scaling of the kick generated by the final merger. For the most extreme case of a very eccentric (e similar to 1) inspiral around a maximally spinning black hole, we find kicks close to 30 000 epsilon(3/2) km/s, enough to dislodge an intermediate-mass black hole from its host globular cluster. In reality, such extreme inspirals should be very rare. Nonetheless, the astrophysical impact of kicks in less extreme inspirals could be astrophysically significant.