Further insight into gravitational recoil

TL;DR

This paper evaluates the accuracy of an empirical formula for predicting recoil velocities in spinning, unequal-mass black-hole mergers across different configurations, confirming its reliability in most cases.

Contribution

The study tests and validates an empirical recoil velocity formula for black-hole mergers with various spin configurations, expanding its applicability.

Findings

Good agreement for configurations with minimized spin effects

Reasonable agreement for configurations with significant spin-orbit coupling

Reaffirmation of the empirical formula's predictive power for large recoil velocities

Abstract

We test the accuracy of our recently proposed empirical formula to model the recoil velocity imparted to the merger remnant of spinning, unequal-mass black-hole binaries. We study three families of black-hole binary configurations, all with mass ratio q=3/8 (to maximize the unequal-mass contribution to the kick) and spins aligned (or counter aligned) with the orbital angular momentum, two with spin configurations chosen to minimize the spin-induced tangential and radial accelerations of the trajectories respectively, and a third family where the trajectories are significantly altered by spin-orbit coupling. We find good agreement between the measured and predicted recoil velocities for the first two families, and reasonable agreement for the third. We also re-examine our original generic binary configuration that led to the discovery of extremely large spin-driven recoil velocities and inspired our empirical formula, and find reasonable agreement between the predicted and measured recoil speeds.