Spin-orbit interactions in black-hole binaries

TL;DR

This work uses fully nonlinear numerical relativity to quantify spin-orbit interactions in equal-mass black-hole binaries during the final inspiral and merger. It shows that tidal spin-up is too weak to drive corotation, with $a/m$ increasing only by $0.012$ for S0 and $0.006$ for SC, far short of the corotation target, implying corotation is not achieved. It also analyzes spin-to-orbit transfer in near head-on collisions and finds radiated angular momentum and energy to be small and well described by PN/close-limit predictions, providing precise remnant-spin and radiated-energy relations. The results improve gravitational-wave modeling for comparable-mass binaries and highlight the reliability of isolated-horizon spin measurements over horizon-circumference methods in the pre-merger regime.

Abstract

We perform numerical simulations of black-hole binaries to study the exchange of spin and orbital angular momentum during the last, highly nonlinear, stages of the coalescence process. To calculate the transfer of angular momentum from orbital to spin, we start with two quasi-circular configurations, one with initially non-spinning black holes, the other with corotating black holes. In both cases the binaries complete almost two orbits before merging. We find that, during these last orbits, the specific spin (a/m) of each horizon increases by only 0.012 for the initially non-spinning configuration, and by only 0.006 for the initially corotating configuration. By contrast, the corotation value for the specific spin should increase from 0.1 at the initial proper separation of 10M to 0.33 when the proper separation is 5M. Thus the spin-orbit coupling is far too weak to tidally lock the binary to a corotating state during the late-inspiral phase. We also study the converse transfer from spin into orbital motion. In this case, we start the simulations with parallel, highly-spinning non-boosted black holes. As the collision proceeds, the system acquires a non-head-on orbital motion, due to spin-orbit coupling, that leads to the radiation of angular momentum. We are able to accurately measure the energy and angular momentum losses and model their dependence on the initial spins.

Figures (9)

• Figure 1: The measured instantaneous specific spin of the individual horizons, for the S0 configuration, starting from vanishing spin at $t=0$ and up to the merger time. The top panel shows $a/m$ versus time for three resolutions with grid-spacings $h=M/22.5$, $h=M/27$, and $h=M/31.5$, while the lower panel shows the differences in $a/m$ between the low and medium resolutions and the medium and high resolutions (the latter rescaled by 1.9662 to demonstrate third-order convergence). The differences between the low and medium resolutions and medium and high resolutions become large at late times due to the lower resolution runs merging sooner. The curves in the top panel have been cut off at the approximate merger value of $a/m$ (which is independent of resolution).
• Figure 2: The measured instantaneous specific spin of the individual horizons, for the SC configuration, starting from $a/m=0.1$ at $t=0$ and up to the merger time. The top panel shows $a/m$ versus time for three resolutions with grid-spacings $h=M/22.5$, $h=M/27$, and $h=M/31.5$, while the lower panel shows the differences in $a/m$ between the low and medium resolutions and the medium and high resolutions (the latter rescaled by 1.9662 to demonstrate third-order convergence). The differences between the low and medium resolutions and the medium and high resolutions become large at late times due to the lower resolution runs merging sooner. The curves in the top panel have been cut off at the approximate merger value of $a/m$ (which is independent of resolution).
• Figure 3: The specific spin $a/m$ for the SC configuration versus proper binary separation $l$ for three resolutions with grid-spacings $h=M/22.5$, $h=M/27$, and $h=M/31.5$. Note that the large late-time phase errors seen in $a/m$ versus time are not present in this plot. The vertical line shows the proper distance at merger.
• Figure 4: The spin-up of the horizons versus proper binary separation. The continuous line shows $a/m$ for the S0 configuration, the dotted line shows $a/m$ for the SC configuration (initially corotating), and the dot-dash line shows the corotation value for the spin. Note that the S0 configuration shows a slightly larger spin-up and that both spin-ups are much smaller than what is required to tidally lock the binary.
• Figure 5: The final remnant horizon mass versus time for the HS++ configuration. The top panel shows the horizon mass for the three resolutions with grid-spacings $h=M/25$, $h=M/30$, and $h=M/40$, and the two Richardson extrapolations based on leading third-order and leading fourth-order errors. The bottom panel shows the differences in the horizon mass for the $h=M/25$ and $h=M/30$ runs as well as the differences in the mass for the $h=M/30$ and $h=M/40$ runs. This latter difference is rescaled by 1.57052 to demonstrate 3.7-order convergence. The accurate extrapolations (as evident by the agreement of the two extrapolations) to infinite resolution allows for a sufficiently precise determination of the radiated energy to model its dependence on the initial spins.