Recoil Velocities from Equal-Mass Binary-Black-Hole Mergers

TL;DR

Using two independent methods it is shown that the merger of such binaries yields velocities as large as approximately 440 km/s for black holes having unequal spins that are antialigned and parallel to the orbital angular momentum.

Abstract

The final evolution of a binary black-hole system gives rise to a recoil velocity if an asymmetry is present in the emitted gravitational radiation. Measurements of this effect for non-spinning binaries with unequal masses have pointed out that kick velocities $\sim~175$ km/s can be reached for a mass ratio $\simeq 0.36$. However, a larger recoil can be obtained for equal-mass binaries if the asymmetry is provided by the spins. Using two independent methods we show that the merger of such binaries yields velocities as large as $\sim 440$ km/s for black holes having unequal spins that are antialigned and parallel to the orbital angular momentum.

Figures (3)

• Figure 1: Recoil velocity as function of time for a binary system of nonspinning black holes with a mass ratio of $2/3$ at an initial separation $4.1\,M$. The set of curves (a) and (b) differ in the choice of the integration constant, while the solid and dashed lines show the two independent computations of the momentum flux [eqs. \ref{['eq:Pdot']} and \ref{['eq:gi']}].
• Figure 2: Recoil velocity as function of time for the sequence of runs i.e., from $r0$ with $-a_1 = a_2 = 0.586$, to r4 with $a_1 = 0, a_2=0.586$). Note that the merger is delayed for smaller values of $|a_1|$.
• Figure 3: Kick velocities and error bars for different spin ratios; the dashed lines show a linear fit of all the data when the point at $a_1/a_2=1$ is given an infinite weight since $|v|_{\rm kick} = 0$ for $a_1=a_2$.