Gravitational recoil from spinning binary black hole mergers

TL;DR

The paper demonstrates that equal-mass binary black hole mergers with opposite spins can produce substantial gravitational recoil, with a linear scaling $V\approx 475\ \mathrm{km\,s^{-1}}\,a$ and kicks up to about $\sim$400 km s$^{-1}$ for high spins. Using the Moving Puncture method within the BSSN framework, the authors compute kicks from both energy-momentum flux and mode decompositions of the Weyl scalar $\Psi_4$, finding that a few dominant mode overlaps largely control the recoil and that the radiated energy is about $3.3\%$ with angular momentum around $27\%$. These results imply that spin-induced kicks could eject supermassive black holes from dwarf galaxies, influencing SMBH demographics, while highlighting convergence limitations tied to weaker higher-order modes. The study provides a quantitative assessment of spin effects on kicks and identifies the key modes driving the recoil in equal-mass, anti-aligned-spin binaries.

Abstract

The inspiral and merger of binary black holes will likely involve black holes with both unequal masses and arbitrary spins. The gravitational radiation emitted by these binaries will carry angular as well as linear momentum. A net flux of emitted linear momentum implies that the black hole produced by the merger will experience a recoil or kick. Previous studies have focused on the recoil velocity from unequal mass, non-spinning binaries. We present results from simulations of equal mass but spinning black hole binaries and show how a significant gravitational recoil can also be obtained in these situations. We consider the case of black holes with opposite spins of magnitude $a$ aligned/anti-aligned with the orbital angular momentum, with $a$ the dimensionless spin parameters of the individual holes. For the initial setups under consideration, we find a recoil velocity of $V = 475 \KMS a$. Supermassive black hole mergers producing kicks of this magnitude could result in the ejection from the cores of dwarf galaxies of the final hole produced by the collision.

Figures (8)

• Figure 1: Fluxes of energy $dE/dt$, linear momentum $dP^i/dt$ and angular momentum $dJ/dt$ as a function of time for the $S0.10$ ($a=0.4$) case. The vertical line at $60\,M$ denotes $t_{\mathrm{min}}$, the lower limit of the time integration used to estimates kicks which avoids contamination from the spurious radiation in the initial data.
• Figure 2: Recoil velocity $V^x$ and $V^y$ computed from different detector locations for $S0.10$ with resolution $h=M/40$. The detectors were located at $r_{\mathrm{det}}/M=(30,40,50)$.
• Figure 3: The amplitude of the dominant $\ell=2,\, m=2$ mode of $\Psi_4$ for the case $S0.10$ ($a=0.4$). The top plot shows the mode at three different resolutions ($h/M = 1/32, 1/35, 1/40$), while the bottom shows the small differences between the medium-coarse ("c-m") and the medium-fine ("m-f") simulations rescaled for 2nd, 3rd and 4th order. The waveform is between 3rd- and 4th-order convergent.
• Figure 4: Recoil velocity $V^x$ and $V^y$ versus time computed from equation (\ref{['eq:dPdtpsi4']}) and equation (\ref{['eq:recoil.modes']}) for the $S0.10$ model with resolution $h=M/40$ extracted at $r_{det}=30\,M$. $V^z$ is below 0.2 km/s and hence is not shown. The insets labeled "differences" show the difference between the recoil from equation (\ref{['eq:dPdtpsi4']}) and equation (\ref{['eq:recoil.modes']}) with modes up to and including $\ell=4$
• Figure 5: Magnitude of the recoil velocity $V$ as a function of the dimensionless spin parameter $a$. Solid circles are for resolutions $h=M/40$, diamonds for resolutions $h=M/32$ and inverted triangles for resolutions $h=M/30$. In each case, the results at different resolution cluster more tightly than the conservatively estimated error bars (Table \ref{['tab:radiated']}).