Gravitational recoil in nonspinning black hole binaries: the span of test-mass results

TL;DR

This paper presents a method to accurately estimate gravitational recoil velocities in nonspinning black hole binaries by extrapolating test-mass limit waveforms across different mass ratios, aligning well with numerical relativity results.

Contribution

It introduces a novel extrapolation technique from test-mass waveforms to general mass ratios, improving recoil velocity predictions for nonspinning black hole binaries.

Findings

Derived an analytical formula for recoil velocity as a function of mass ratio.

Validated the extrapolated waveform approach against numerical relativity simulations.

Achieved accurate recoil velocity estimates across the entire mass ratio range.

Abstract

We consider binary systems of coalescing, nonspinning, black holes of masses $m_{1}$ and $m_{2}$ and show that the gravitational recoil velocity for any mass ratio can be obtained accurately by extrapolating the waveform of the test-mass limit case. The waveform obtained in the limit $m_1/m_2\ll 1$ via a perturbative approach is extrapolated in $\nu= m_{1} m_{2}/(m_{1}+m_{2})^{2} $ multipole by multipole using the corresponding, analytically known, leading-in-$\nu$ behavior. The final kick velocity computed from this $\nu$-flexed waveform is written as $v(\nu)/c = 0.04457 \nu^2\sqrt{1-4\nu}\,(1-2.07106\nu + 3.93472\nu^2 -4.78404\nu^3+2.52040\nu^{4})$ and is compatible with the outcome of numerical relativity simulations