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

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