Further insight into gravitational recoil

TL;DR

The paper tests an empirical recoil formula for merging spinning, unequal-mass black-hole binaries using full numerical relativity with mass ratio $q=3/8$ across four configuration families. By aligning late-inspiral trajectories and analyzing both in-plane and out-of-plane recoil contributions, the authors find a robust average angle between spin- and mass-induced recoils of $\igl\langle\xi\bigr\rangle\approx 145^\circ$, with the predicted recoil magnitudes agreeing closely for several families and moderately for others. A reanalysis of the SP6 configuration supports the model, and the results indicate that most of the recoil is generated near merger, with post-Newtonian theory providing correct functional dependence but not absolute amplitudes. Overall, the work supports using a simplified two-component recoil model with a nearly constant $\xi$ for astrophysical recoil predictions, while highlighting the need for higher-accuracy simulations and careful extrapolations to the $\,\eta\to0$ limit.

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.

Figures (6)

• Figure 1: The value of $H$ calculated by inverting Eq. (\ref{['eq:vperp']}) as determined from simulations by the AEI, PSU, and NASA/GSFC groups. The thick line is the weighted average and the thin lines are the expected uncertainty in the average.
• Figure 2: The trajectory differences $\vec{r} = \vec{r}_1 - \vec{r}_2$ for the 'F' and 'S' series rotated so that the late-inspiral matches the $\rm Q_{38}$ trajectory. The plots show the rotation angle $\Phi_{\rm track}$
• Figure 3: The trajectory differences $\vec{r} = \vec{r}_1 - \vec{r}_2$ for the 'A' series, as well as $\rm Q_{38}$. Note that there is no angle $\Phi_{\rm track}$ that will make the late-time trajectories overlap. Here the spin-orbit hang-up effect changes the orbital trajectory significantly.
• Figure 4: $\xi$ versus $\Delta/m = S_2/m_2 - S_1/m_1$ as calculated in this work for a mass ratio $q=3/8$ and from the data published by the NASA/GSFC group for a mass ratio $q=2/3$ provided in Ref. Baker:2007gi. We plot $\xi_{\rm track}$, $\xi_{\psi_4}$, and $\xi_{\rm Formula}$ for the 'F' and 'S' configurations and $\xi_{\rm Formula}$ for 'A' configurations. The thick horizontal line and the two thin horizontal line show the average value $\langle \xi \rangle$ and its uncertainty (as calculated in this work from our simulations). The data displays significant scatter, but appears to be consistent with $\xi = {\rm const}$.
• Figure 5: The normalized orbital angular momentum vector $\vec{\ell} = \vec{L} / |\vec{L}|$ versus time for the SP6 configuration up to merger. Note the rapid change in the direction at late times.