Total recoil: the maximum kick from nonspinning black-hole binary inspiral

TL;DR

This work provides the first large-scale numerical-relativity survey of nonspinning binary black-hole inspirals across $q=1.0$ to $0.253$ to quantify gravitational recoil and remnant spin. Using the BAM code with moving puncture, the authors map the kick as a function of the symmetric mass parameter $\eta$, obtaining a maximum recoil of $V_{\max} = 175.2 \pm 11$ km s$^{-1}$ near $\eta = 0.195 \pm 0.005$, and show the final spin scales linearly with $\eta$ as $a/M_f = 0.089 \pm 0.003 + 2.4 \pm 0.025\,\eta$. The results agree with analytic predictions and prior studies, while providing a robust error budget ($\lesssim 6\%$ for kicks) across a wide parameter range. This has important implications for astrophysical black-hole demographics and gravitational-wave data analysis, clarifying the expected recoil distributions and remnant spins across diverse mergers.

Abstract

When unequal-mass black holes merge, the final black hole receives a ``kick'' due to the asymmetric loss of linear momentum in the gravitational radiation emitted during the merger. The magnitude of this kick has important astrophysical consequences. Recent breakthroughs in numerical relativity allow us to perform the largest parameter study undertaken to date in numerical simulations of binary black hole inspirals. We study non-spinning black-hole binaries with mass ratios from $q=M_1/M_2=1$ to $q =0.25$ ($η= q/(1 + q)^2$ from 0.25 to 0.16). We accurately calculate the velocity of the kick to within 6%, and the final spin of the black holes to within 2%. A maximum kick of $175.2\pm11$ km s$^{-1}$ is achieved for $η= 0.195 \pm 0.005$.

Figures (4)

• Figure 1: Components $v_x$ and $v_y$ of the kick velocity as function of time, for $\eta=0.19$, for resolutions $h_1 = 1/45$, $h_2 = 1/51$ and $h_3 = 1/58$. Top panels: kick components $v_x$ and $v_y$. Lower panels: demonstration of second-order convergence.
• Figure 2: The kick velocity as a function of mass ratio, with an error of $\pm6$% indicated by the dotted lines. We also indicate previous numerical results from Baker, et alBaker:2006nr, Campanelli Campanelli:2005aa, and Herrmann, et alHerrmann:2006ks, and the analytic estimates of Damour and Gopakumar Damour:2006tr and Sopuerta, et alSopuerta:2006wj.
• Figure 3: Total kick velocity ($v=\sqrt{v_x^2+v_y^2}$) as function of time for $\eta=0.19$. Top panel: for resolutions $h_1, h_2$ and $h_3$ as described in the text. Lower panel: for runs with three initial black-hole separations $r_0 = 6.0M, 7.0M, 8.0M$.
• Figure 4: Left panel: Radiated energy and angular momentum as function of the mass ratio. Right panel: Spin of the final black hole ($a/M_f$) as function of the mass ratio. The spin curves can be fit by $a/M_f = 0.089 (\pm 0.003) + 2.4 (\pm 0.025) \eta$.