Resonantly enhanced kicks from equatorial small mass-ratio inspirals

TL;DR

This paper calculates the gravitational wave recoil (kick) from eccentric black hole binary inspirals during resonant orbital configurations, revealing a faster scaling of kick velocity with mass ratio and potential for high-velocity ejections.

Contribution

It introduces a new calculation of resonantly enhanced gravitational wave kicks using black hole perturbation theory, highlighting the importance of resonance effects in small mass-ratio inspirals.

Findings

Kick velocity scales as epsilon^{3/2}

Extreme inspirals can produce kicks up to 30,000 km/s

Resonance effects significantly amplify recoil velocities

Abstract

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 calculate 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 ($e\sim 1$) inspiral around a maximally spinning black hole, we find kicks close to $30,000\;\epsilon^{3/2}$~km/s, enough to dislodge a black hole from its host cluster or even galaxy. In reality, such extreme inspirals should be very rare. Nonetheless, the astrophysical impact of kicks in less extreme inspirals could be astrophysically significant.