Spin Flips and Precession in Black-Hole-Binary Mergers

TL;DR

This study evolves equal-mass black-hole binaries with misaligned spins using the moving-puncture method to track spin precession and remnant-spin flips during merger. It combines Post-Newtonian expectations with fully nonlinear simulations by measuring spin direction on horizons via approximate Killing vectors and coordinate-based estimators, and by analyzing horizon and gravitational-wave data. The SP3 and SP4 configurations show large spin precessions of $\Theta_p \approx 98^{\circ}$ and $\Theta_p \approx 151^{\circ}$ and spin-flips of $\Theta_{\rm flip} \approx 72^{\circ}$ and $\Theta_{\rm flip} \approx 35^{\circ}$, with remnant spins $S/M_{\mathcal H}^2 \approx 0.72$ and $0.81$ and substantial radiated angular momenta, confirming the spin-flip phenomenon and revealing how spin orientation evolves during merger. The results inform GW waveform modeling and have potential implications for the electromagnetic signatures in accreting systems.

Abstract

We use the `moving puncture' approach to perform fully non-linear evolutions of spinning quasi-circular black-hole binaries with individual spins not aligned with the orbital angular momentum. We evolve configurations with the individual spins (parallel and equal in magnitude) pointing in the orbital plane and 45-degrees above the orbital plane. We introduce a technique to measure the spin direction and track the precession of the spin during the merger, as well as measure the spin flip in the remnant horizon. The former configuration completes 1.75 orbits before merging, with the spin precessing by 98-degrees and the final remnant horizon spin flipped by ~72-degrees with respect to the component spins. The latter configuration completes 2.25 orbits, with the spins precessing by 151-degrees and the final remnant horizon spin flipped ~34-degrees with respect to the component spins. These simulations show for the first time how the spins are reoriented during the final stage of binary black hole mergers verifying the hypothesis of the spin-flip phenomenon. We also compute the track of the holes before merger and observe a precession of the orbital plane with frequency similar to the orbital frequency and amplitude increasing with time.

Figures (21)

• Figure 1: The puncture trajectories along with spin direction (every $4M$) for the SP3 configuration for the $M/30$ resolution run. The spins are initially aligned along the $y$-axis, but rotate by $\sim 90^\circ$ during the 1.25 last orbits and also acquire a non-negligible $z$-component. Note that the $z$-scale is 1/10th the x and y scale.
• Figure 2: The projection of puncture trajectories and spin for the SP3 configuration onto the $xy$ plane along with the individual apparent horizons for the $M/30$ run. The horizons and spins are shown at $t=0, 20M, 40M, ..., 160M, 164M$. The first common horizon (also shown) formed at $t=164.2M$. The spins are initially aligned along the $y$-axis but rotate by $\sim 90^\circ$ during the last 1.25 orbits. The spin of the second black hole (not shown) is equal to the first.
• Figure 3: The spin components and magnitude versus time for the SP3 configuration as calculated using the coordinate rotational vectors (coord) and the poles of the approximate Killing vector (IH) for the $M/30$ resolution. The calculation of the approximate Killing vector breaks down near the merger (which occurs at $t=164.2$), but the purely coordinate based calculation continues to produce reasonable results. Note that the direction obtained from the Killing vector oscillates about the coordinate based direction. Also note the spin has just rotated by $90^\circ$ in the xy plane at the time of merger. The spin magnitude remains essentially constant throughout the merger phase. The magnitude of the spin calculated from the Killing vector is coordinate invariant and, unlike the spin direction, is expected to be more accurate than the coordinate based calculation.
• Figure 4: A convergence plot of the coordinate-base $\vec{S}_{\rm coord}$ calculation for the SP3 configuration. Note that for our choice of resolutions, third-order convergence is demonstrated by $S(M/22.5) - S(M/25) = (S(M/25) - S(M/30)) C$, where $C=0.88$. The spin is initially third-order convergent, with higher order-convergence apparent at later times.
• Figure 5: The $z$-component of the Killing vector based calculation of the spin rescaled by the square of the horizon mass for the three resolutions. The curves have been translated by a distance equal to the difference in merger times of the $M/22.5$ and $M/25$ runs with the merger time of the $M/30$ run. In this configuration, unlike the previously studied aligned-spin binary, the 'spin-up' appears to be large. However, in this case the 'spin-up' is actually the rotation of the nearly-constant spin-vector towards the $z$-axis, rather than an increase in the spin magnitude.