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

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 ${m}_{1}/{m}_{2}\ensuremath{\ll}1$ via a perturbative approach is extrapolated in $\ensuremath{\nu}={m}_{1}{m}_{2}/({m}_{1}+{m}_{2}{)}^{2}$ multipole by multipole using the corresponding, analytically known, leading-in-$\ensuremath{\nu}$ behavior. The final kick velocity computed from this $\ensuremath{\nu}$-flexed waveform is written as $v(\ensuremath{\nu})/c=0.04457{\ensuremath{\nu}}^{2}\sqrt{1\ensuremath{-}4\ensuremath{\nu}}(1\ensuremath{-}2.07106\ensuremath{\nu}+3.93472{\ensuremath{\nu}}^{2}\ensuremath{-}4.78404{\ensuremath{\nu}}^{3}+2.52040{\ensuremath{\nu}}^{4})$ and is compatible with the outcome of numerical relativity simulations