Resonant recoil in extreme mass ratio binary black hole mergers

The inspiral and merger of a binary black hole system generally leads to an asymmetric distribution of emitted radiation, and hence a recoil of the remnant black hole directed opposite to the net linear momentum radiated. The recoil velocity is generally largest for comparable mass black holes and particular spin configurations, and approaches zero in the extreme mass ratio limit. It is generally believed that for extreme mass ratios eta << 1, the scaling of the recoil velocity is vertical bar V vertical bar alpha eta(2), where the proportionality coefficient depends on the spin of the larger hole and the geometry of the system (e. g. orbital inclination). The small recoil velocity is due to cancellations; while the fraction of the total binary mass radiated away in gravitational waves is O(eta), most of this energy is emitted during the inspiral phase where the momentum radiated integrates to zero over an orbit. Here, we show that for low but nonzero inclination prograde orbits and very rapidly spinning large holes (spin parameter a(star) > 0.9678) the inspiralling binary can pass through resonances where the orbit-averaged radiation-reaction force is nonzero. These resonance crossings lead to a new contribution to the kick, vertical bar V vertical bar alpha eta(3/2). For these configurations and sufficiently extreme mass ratios, this resonant recoil is dominant. While it seems doubtful that the resonant recoil will be astrophysically significant, its existence suggests caution when extrapolating the results of numerical kick results to extreme mass ratios and near-maximal spins.