Binary black hole merger dynamics and waveforms

TL;DR

This study demonstrates that the final merger and ringdown of equal-mass, non-spinning binary black holes produce highly universal gravitational-wave signals across different initial separations when evolved with moving-puncture techniques and adaptive mesh refinement. The authors achieve ~1% agreement in the merger-ringdown waveform across runs, confirm a final black-hole spin of $a/M_f \approx 0.69$, and show ~10% agreement in the earlier inspiral radiation. The work validates the moving-puncture approach for long, stable simulations, provides insights into the relationship between coordinate trajectories and radiative signals, and establishes a robust framework for comparing numerical relativity waveforms with post-Newtonian predictions and detector data.

Abstract

We study dynamics and radiation generation in the last few orbits and merger of a binary black hole system, applying recently developed techniques for simulations of moving black holes. Our analysis of the gravitational radiation waveforms and dynamical black hole trajectories produces a consistent picture for a set of simulations with black holes beginning on circular-orbit trajectories at a variety of initial separations. We find profound agreement at the level of one percent among the simulations for the last orbit, merger and ringdown. We are confident that this part of our waveform result accurately represents the predictions from Einstein's General Relativity for the final burst of gravitational radiation resulting from the merger of an astrophysical system of equal-mass non-spinning black holes. The simulations result in a final black hole with spin parameter a/m=0.69. We also find good agreement at a level of roughly 10 percent for the radiation generated in the preceding few orbits.

Figures (11)

• Figure 1: The L1 norm of the Hamiltonian constraint violation is shown as a function of time for the three different resolution runs of $R1$ given in Table \ref{['table:r1']}. The high resolution case is shown with a dashed line. The medium (bold dashes) and low (solid) cases are scaled so that, for $2^{\rm nd}-$order convergence all three curves would lie on top of each other. The L1 norm is taken over all levels of the grid inside 48M, including the wave extraction region. This figure indicates satisfactory convergence of the Hamiltonian constraint error in our simulations.
• Figure 2: Gravitational waveforms and a naive convergence test. The top panel shows the $l=2$, $m=2$ mode of $\Psi_4$ for the low (solid), medium (bold dashes), and high (dashes) resolution runs of R1. The lower panel shows the differences between these waveforms; for $2^{\rm nd}-$ order convergence, the curves would lie on top of each other. Phase differences between the waveforms account for the large differences shown. When the phases are shifted appropriately, the convergence of the waves is more manifest, as in Fig. \ref{['fig:WaveConvergeII']}
• Figure 3: Time-shifted gravitational waveforms and a physical convergence test. The labels in the top panel are as in Fig. \ref{['fig:WaveConvergeI']}. In the top panel, the gravitational waveforms have been shifted in time so that the peak amplitude of the radiation occurs at $t = 0$. The differences between these time-shifted waveforms are shown in the bottom panel; these curves are scaled so that they would lie on top of each other for $2^{\rm nd}-$ order convergence.
• Figure 4: Paths of black holes starting from different initial separations. For clarity, we show only the track of one of the black holes from each simulation. The paths are very similar for approximately the last orbit, indicating that the black holes follow the same tracks. The point of merger (estimated by a single connected isosurface of $\alpha=0.3$) is indicated by as an asterisk in the plot.
• Figure 5: Waveforms from runs R1 - R4. The figure shows nearly perfect agreement after $t=-50 M_f$. For the preceding $500M_f$, shown in an inset, the waveforms agree in phase and amplitude within about 10% except for a brief initial pulse at the beginning of each run.