Binary Black Holes: Spin Dynamics and Gravitational Recoil

TL;DR

The paper investigates spin dynamics and gravitational recoil in equal-mass spinning binary black holes using two spin-series and high-precision numerical relativity. It demonstrates that 2PN spin-precession accurately reproduces NR results up to horizon formation and uses recoil data to calibrate the Kidder kick formula, confirming that the out-of-plane kick scales with $\sin\theta$ while in-plane kicks scale with $\cos\theta$, where $\theta$ is the angle between spin and orbital angular momentum. By analyzing entrance angles at plunge and fitting recoil components, the authors provide quantified kick parameters and show that BH spins can be estimated from isolated-horizon spin measurements on coordinate spheres. The findings have direct implications for SMBH demographics, recoil-driven retention in galaxies, and the utility of PN-based models in predicting gravitational-wave-driven kicks. The work lays groundwork for extending analyses to more generic configurations and improving astrophysical population synthesis models.

Abstract

We present a study of spinning black hole binaries focusing on the spin dynamics of the individual black holes as well as on the gravitational recoil acquired by the black hole produced by the merger. We consider two series of initial spin orientations away from the binary orbital plane. In one of the series, the spins are anti-aligned; for the second series, one of the spins points away from the binary along the line separating the black holes. We find a remarkable agreement between the spin dynamics predicted at 2nd post-Newtonian order and those from numerical relativity. For each configuration, we compute the kick of the final black hole. We use the kick estimates from the series with anti-aligned spins to fit the parameters in the \KKF{,} and verify that the recoil along the direction of the orbital angular momentum is $\propto \sinθ$ and on the orbital plane $\propto \cosθ$, with $θ$ the angle between the spin directions and the orbital angular momentum. We also find that the black hole spins can be well estimated by evaluating the isolated horizon spin on spheres of constant coordinate radius.

Figures (10)

• Figure 1: Comparison of $S^x$ computed on the horizon and from spheres with radius $r$ for a BBH evolution (S-90 model, see Table \ref{['tbl:ID-S-series']}). The vertical line (here and in subsequent Figures) shows the first time a common AH is found.
• Figure 2: Comparison of $d\mathbf{S}_1/dt$ computed from the numerical evolution directly and by using PN formulas for the S-90 run. Kidder describes the dynamics using precession angular frequency given by Eq. (\ref{['eq:kidder-prec']}). Blanchet 1PN denotes the dynamics with $\mathbf{\Omega}_{1}$ given by the first term in Eq. (\ref{['eq:omega']}); Blanchet 2PN denotes the case in which the entire expression in Eq. (\ref{['eq:omega']}) is used. The vertical line around $t=149M$ indicates the formation of a common apparent horizon.
• Figure 3: Comparison of S-15 run numerical to Blanchet 2PN. Left panel shows the results of the comparison for BH$_1$ and the right panel for BH$_2$. The top plots on each panel show with a solid line $dS^i/dt$ from our numerical simulations and with a dashed line the values from Blanchet 2PN. The labels denote each component. The bottom plots on each panel show the difference between the numerical solution and the Blanchet 2PN, with solid, dashed and dotted lines for the $x$, $y$ and $z$ components, respectively.
• Figure 4: Same comparison as in Fig. \ref{['fig:S-15_overview']} but for the model S-45.
• Figure 5: Same comparison as in Fig. \ref{['fig:S-15_overview']} but for the model S-90.