Maximum Gravitational Recoil

Recent calculations of gravitational radiation recoil generated during black-hole binary mergers have reopened the possibility that a merged binary can be ejected even from the nucleus of a massive host galaxy. Here we report the first systematic study of gravitational recoil of equal-mass binaries with equal, but counteraligned, spins parallel to the orbital plane. Such an orientation of the spins is expected to maximize the recoil. We find that recoil velocity (which is perpendicular to the orbital plane) varies sinusoidally with the angle that the initial spin directions make with the initial linear momenta of each hole and scales up to a maximum of $\sim 4000\mathrm{km}{\mathrm{s}}^{-1}$ for maximally rotating holes. Our results show that the amplitude of the recoil velocity can depend sensitively on spin orientations of the black holes prior to merger.

Figure 1

The recoil velocity vs angle $\vartheta$ (including error bars) between the initial individual momenta and spins and a least-squares fit. Note that the $\vartheta =\pm \pi$ are the same SPC configuration.

Figure 2

The projection of the puncture trajectories (only 1 shown per configuration) for the 6 configurations. The orbital dynamics of the binaries are not significantly affected by the change in spin directions.

Figure 3

The $z$ component of the punctures trajectories (only 1 shown per configuration) vs time for the 6 configurations showing the dependence of the orbital plane “precession” and remnant recoil on the angle of rotation.

Figure 4

The three-dimensional trajectories of the punctures showing the orbital precession and the final recoil for the SP2 configuration. Note that the scale of the $z$ axis is $1/10$ that of the $x$ and $y$ axes.