High-accuracy waveforms for binary black hole inspiral, merger, and ringdown

TL;DR

This work demonstrates the first spectral numerical relativity simulation of a binary black hole system undergoing inspiral, merger, and ringdown, achieving high-precision gravitational waveforms for an equal-mass, non-spinning pair. Using a generalized harmonic formulation with a dual-frame, excision-based evolution and carefully designed gauge dynamics, it follows 16 orbits through merger into a Kerr remnant, and extracts waveforms with quantified uncertainties. Key contributions include a rigorous extrapolation-to-infinity procedure that yields phase errors around $5\times10^{-3}$ to $1\times10^{-2}$ rad and amplitude errors near $10^{-2}$ across the inspiral and ringdown, as well as precise remnant properties $M_f/M$ and $S_f/M_f^2$ for the final black hole. The results underscore the importance of gauge control, waveform extrapolation, and high-accuracy methods for producing templates suitable for LIGO/LISA data analysis and future cross-code validations.

Abstract

The first spectral numerical simulations of 16 orbits, merger, and ringdown of an equal-mass non-spinning binary black hole system are presented. Gravitational waveforms from these simulations have accumulated numerical phase errors through ringdown of ~0.1 radian when measured from the beginning of the simulation, and ~0.02 radian when waveforms are time and phase shifted to agree at the peak amplitude. The waveform seen by an observer at infinity is determined from waveforms computed at finite radii by an extrapolation process accurate to ~0.01 radian in phase. The phase difference between this waveform at infinity and the waveform measured at a finite radius of r=100M is about half a radian. The ratio of final mass to initial mass is M_f/M = 0.95162 +- 0.00002, and the final black hole spin is S_f/M_f^2=0.68646 +- 0.00004.

Figures (11)

• Figure 1: Spacetime diagram showing the spacetime volume simulated by the numerical evolutions listed in Table \ref{['tab:Evolutions']}. Each curve represents the worldline of the outer boundary for a particular simulation. The magnified views on the right show that the outer boundary moves smoothly near merger. The transition times $t_g=3917M$ and $t_m=3940M$ are indicated on the right panels.
• Figure 2: Constraint violations of run 30c1. The top panel shows the $L^2$ norm of all constraints, normalized by the $L^2$ norm of the spatial gradients of all dynamical fields. The bottom panel shows the same data, but without the normalization factor. The $L^2$ norms are taken over the portion of the computational volume that lies outside apparent horizons.
• Figure 3: Gravitational waveform extracted at finite radius $r=225M$, for the case 30c1/N6 in Table \ref{['tab:Evolutions']}. The left panel zooms in on the inspiral waveform, and the right panel zooms in on the merger and ringdown.
• Figure 4: Convergence of waveforms with numerical resolution and outer boundary location. Shown are phase and amplitude differences between numerical waveforms $\Psi_4^{22}$ computed using different numerical resolutions. Shown also is the difference between our highest-resolution waveforms using two different outer boundary locations. All waveforms are extracted at $r=60M$, and no time shifting or phase shifting is done to align waveforms.
• Figure 5: Convergence of waveforms with numerical resolution and outer boundary location. Same as Fig. \ref{['fig:WaveformConvergence0']} except waveforms are time-shifted and phase-shifted so that the maximum amplitude occurs at the same time and phase.