Exploring black hole superkicks

TL;DR

The paper investigates black-hole recoil (kick) in spinning equal-mass binaries using a highly symmetric superkick setup to isolate spin effects. It links the kick primarily to the asymmetry of the dominant $l=2,m=\pm2$ gravitational-wave modes and shows that most momentum is radiated around the merger, where post-Newtonian approximations break down. By comparing 2.5PN spin evolution with full GR simulations, it finds good agreement for spin precession but significant divergence for the linear-momentum flux near merger, explaining why PN-based kick estimates can severely underestimate the true recoil. The study also reports a final black-hole spin of $a/M_f^2 \approx 0.69$–$0.72$ from ringdown and discusses implications for GW detection and SNR anisotropy due to recoil.

Abstract

Recent calculations of the recoil velocity in black-hole binary mergers have found kick velocities of $\approx2500 $km/s for equal-mass binaries with anti-aligned initial spins in the orbital plane. In general the dynamics of spinning black holes can be extremely complicated and are difficult to analyze and understand. In contrast, the ``superkick'' configuration is an example with a high degree of symmetry that also exhibits exciting physics. We exploit the simplicity of this ``test case'' to study more closely the role of spin in black-hole recoil and find that: the recoil is with good accuracy proportional to the difference between the $(l = 2, m = \pm 2)$ modes of $Ψ_4$, the major contribution to the recoil occurs within $30M$ before and after the merger, and that this is after the time at which a standard post-Newtonian treatment breaks down. We also discuss consequences of the $(l = 2, m = \pm 2)$ asymmetry in the gravitational wave signal for the angular dependence of the SNR and the mismatch of the gravitational wave signals corresponding to the north and south poles.

Figures (16)

• Figure 1: Convergence plots for the puncture separation $r$ and the linear momentum radiation in the $z$-direction, $dP_z/dt$ obtained for model $\alpha=0$ of the $\alpha$-series. The plots are scaled consistent with fourth-order convergence. After merger at about $t = 88M$ convergence in the puncture separation is lost (as expected).
• Figure 2: Convergence of the puncture separation and $dP_z/dt$ as functions of time for evolutions of model D6. Results are scaled for fourth-order convergence. We see that fourth-order convergence is lost in the puncture separation at about $t = 115M$, which corresponds to roughly $t = 165M$ in quantities from waves extracted at $R_{ex} = 50M$, which is about when we see a loss of convergence in $dP_z/dt$. Note that we cut the plot at $t\approx 175~M$ when convergence is lost.
• Figure 3: Puncture separation and $dP_z/dt$ as functions of time for the evolutions of model D6. Results from low, medium and high resolution simulations are shown. Only the highest resolution is shown for $dP_z/dt$.
• Figure 4: Comparison of the kick velocity in km/s according to Eq. (\ref{['eq:p_asym']}), for a range of angles $\alpha$. Data points for the measured kick and the estimate Eq. (\ref{['eq:p_asym']}) are shown, the points corresponding to the energy differences are connected. An analytical fit, $v_z = 2725 \cos(176+\alpha)$, to the measured kick is shown as a dashed line. Note that Eq. (\ref{['eq:p_asym']}) slightly underestimates the kick, which is consistent since it neglects contributions from higher order multipoles $l>2$.
• Figure 5: Excess energy in the $l=2,m=2$ mode, ${2 E_{22}}/{(E_{22}+E_{2-2})}$ plotted for extraction radii $R_{ext} = 30~M$, and $50~M$. The curves are the analytical fits for both extraction radii, see Eq. (\ref{['eq:excess_fit']}) Clearly, there is no significant dependence of this ratio on extraction radius.