Recoiling from a kick in the head-on collision of spinning black holes

TL;DR

This work investigates gravitational recoil kicks in head-on collisions of spinning binary black holes using moving-puncture simulations with Bowen-York initial data. It finds that spin-induced transverse kicks are substantial even in head-on mergers and scale roughly with the sum of the dimensionless spins $a_1+a_2$, while unequal-mass configurations produce smaller longitudinal kicks. Remarkably, leading-order post-Newtonian predictions for spin-orbit and mass-quadrupole interactions remain informative even as the system enters the nonlinear merger regime, suggesting a simple heuristic for estimating spin-kicks. The results support using PN-inspired scalings to estimate kicks in generic inspirals and have implications for the retention of merged black holes in astrophysical environments and for gravitational-wave event rate predictions. Overall, the study demonstrates that spin contributions can dominate transverse recoil and that PN intuition extends into strong-field merger dynamics.

Abstract

Recoil ``kicks'' induced by gravitational radiation are expected in the inspiral and merger of black holes. Recently the numerical relativity community has begun to measure the significant kicks found when both unequal masses and spins are considered. Because understanding the cause and magnitude of each component of this kick may be complicated in inspiral simulations, we consider these effects in the context of a simple test problem. We study recoils from collisions of binaries with initially head-on trajectories, starting with the simplest case of equal masses with no spin and then adding spin and varying the mass ratio, both separately and jointly. We find spin-induced recoils to be significant relative to unequal-mass recoils even in head-on configurations. Additionally, it appears that the scaling of transverse kicks with spins is consistent with post-Newtonian theory, even though the kick is generated in the nonlinear merger interaction, where post-Newtonian theory should not apply. This suggests that a simple heuristic description might be effective in the estimation of spin-kicks.

Figures (10)

• Figure 1: L1-norm convergence of Hamiltonian (top) and momentum ($x$ component; bottom) constraints for the ${\rm EQ}_{+-}$ run, in two regions of the simulation grid: just outside the horizons (left),and in the primary radiation extraction region (right). The Hamiltonian constraint displays third-order convergence in both regions, while the momentum constraint convergence drops to 1.5-order in the extraction region.
• Figure 2: Convergence of ${\rm Re}(\psi_{4})$, the real part of the dominant $(2,2)$ mode of the waveform for the ${\rm EQ}_{+-}$ run. The upper panel shows the thrust for central resolution $M/32$, extracted at $R_{\rm ext} = 60M$; the lower panel shows the absolute differences $M/32 - M/40$ (solid line) and $M/40 - M/48$, the latter scaled to compare with coarse-medium for 1st- and 2nd-order convergence. The inset focuses on the physical part of the waveform, which shows much smaller resolution errors.
• Figure 3: Convergence of transverse momentum thrust $dP^x/dt$ for the ${\rm EQ}_{+-}$ run. The upper panel shows the thrust for central resolution $M/32$, extracted at $R_{\rm ext} = 60M$; the lower panel shows the absolute differences $M/32 - M/40$ (solid line) and $M/40 - M/48$, the latter scaled to compare with coarse-medium for 1st- and 2nd-order convergence.
• Figure 4: Dominant $(l=2,m=2)$ mode of the waveform $\psi_4$ for the three equal-mass configurations: ${\rm EQ}_{00}$ (solid/black), ${\rm EQ}_{+0}$ (dashed/red), and ${\rm EQ}_{+-}$ (dot-dashed/green). These data were extracted at coordinate distance $R_{\rm ext} = 30 \, M$.
• Figure 5: Longitudinal thrust $dP^y/dt$ (top) and kick $\Delta P^y$ (bottom) for ${\rm NE}_{00}$, at extraction radii $R_{\rm ext}$ of $30 M$, $40 M$, $50 M$ and $60 M$, where the latter three have been time-shifted by $10.6 M$, $21.0 M$ and $31.4 M$, respectively, to align the highest thrust peak with the $30M$ case (consistent with time-shift formula Eq. (14) in Fiske:2005fx).