Modeling kicks from the merger of non-precessing black-hole binaries

TL;DR

This paper investigates gravitational recoil (kick) from mergers of non-precessing spinning black holes, aiming for a simple parameterized formula usable in astrophysical simulations. It conducts numerical relativity simulations for configurations with mass ratio near $q=\frac{2}{3}$ and spins $\hat{a}_1,\hat{a}_2 \in \{0,0.2\}$ aligned or anti-aligned with the orbital angular momentum, plus an equal-mass case, and extracts kicks from the radiated momentum. The authors propose a PN-inspired two-component kick model that combines mass- and spin-asymmetry contributions with an angular offset $\theta$, and they fit the parameters to match the numerical results within about $10\%$, with best-fit values $V_0=276\,\mathrm{km\,s^{-1}}$, $\theta=0.58\,\mathrm{rad}$, and $k=0.85$; they also discuss the potential for large out-of-plane kicks in configurations beyond their study and the need to explore broader parameter space. The work provides a practical, orbit-averaged prescription for kicks that can be incorporated into N-body and galaxy-merger simulations, and it highlights astrophysical constraints on black hole retention in light of possible large kicks and spin-alignment effects.

Abstract

Several groups have recently computed the gravitational radiation recoil produced by the merger of two spinning black holes. The results suggest that spin can be the dominant contributor to the kick, with reported recoil speeds of hundreds to even thousands of kilometers per second. The parameter space of spin kicks is large, however, and it is ultimately desirable to have a simple formula that gives the approximate magnitude of the kick given a mass ratio, spin magnitudes, and spin orientations. As a step toward this goal, we perform a systematic study of the recoil speeds from mergers of black holes with mass ratio $q\equiv m_1/m_2=2/3$ and dimensionless spin parameters of $a_1/m_1$ and $a_2/m_2$ equal to 0 or 0.2, with directions aligned or anti-aligned with the orbital angular momentum. We also run an equal-mass $a_1/m_1=-a_2/m_2=0.2$ case, and find good agreement with previous results. We find that, for currently reported kicks from aligned or anti-aligned spins, a simple kick formula inspired by post-Newtonian analyses can reproduce the numerical results to better than $\sim$10%.

Figures (3)

• Figure 1: L1 norm of the Hamiltonian constraint for the case of unequal masses with prograde spins (${\rm NE}_{++}$) at two different resolutions, computed on a domain extending to $|x_i|=48M$, which includes our wave-extraction surface. The finest level, containing nonconvergent points near the puncture, has been excluded. The lower resolution, $h_f=3M/160$, has been scaled such that for third-order convergence it should superpose with the $h_f=M/64$ curve.
• Figure 2: The total radiated momentum for the case of unequal masses with prograde spins (${\rm NE}_{++}$) at two different resolutions. The curves have been shifted slightly in time to line up the peaks, for comparison of the merger dynamics. The agreement is better than $5\%$ for most of the evolution and better than $2\%$ through the merger and final kick ($t>300M$).
• Figure 3: Aggregated recoil kicks from all runs listed in Table \ref{['tab:initial']}. The merger time for each binary matches the peak in its kick profile; the relative delay in merger times between data sets differing in initial spins is consistent with the results of Campanelli:2006uy. All configurations show a marked "un-kick" after the peak, with the exception of the equal-mass case, ${\rm EQ}_{+-}$.