Gravitational waveforms for high spin and high mass-ratio binary black holes: A synergistic use of numerical-relativity codes

Observation and characterization of gravitational waves from binary black holes requires accurate knowledge of the expected waveforms. The late inspiral and merger phase of the waveform is obtained through direct numerical integration of the full 3-dimensional Einstein equations. The Spectral Einstein Code (SpEC) utilizes a multi-domain pseudo-spectral method tightly adapted to the geometry of the black holes; it is computationally efficient and accurate, but—for high mass-ratios and large spins—sometimes requires manual fine-tuning for the merger-phase of binaries. The Einstein Toolkit (ET) employs finite difference methods and the moving puncture technique; it is less computationally efficient, but highly robust. For some mergers with high mass ratio and large spins, the efficient numerical algorithms used in SpEC have failed, whereas the simpler algorithms used in the ET were successful. Given the urgent need of testing the accuracy of waveform models currently used in LIGO and Virgo inference analyses for high mass ratios and spins, we present here a synergistic approach to numerical-relativity: We combine SpEC and ET waveforms into complete inspiral-merger-ringdown waveforms, taking advantage of the computational efficiency of the pseudo-spectral code during the inspiral, and the robustness of the finite-difference code at the merger. We validate our method against a case where complete waveforms from both codes are available, compute three new hybrid numerical-relativity waveforms, and compare them with analytical waveform models currently used in LIGO and Virgo science. All the waveforms and the hybridization code are publicly available.

Figure 1

Gravitational-wave strain. Shown is the real part of the dominant $\ell =2$, $m=2$ multipole for the case (5, 0.9, 0.9) from the SpEC inspiral waveform $h_{\text{insp}}$, the ET merger waveform $h_{\text{merger}}$, and the NR-NR hybrid waveform $h_{\text{hybrid}}$ as a function of retarded time $t$ in units of the total mass $M$ of the binary. The vertical lines indicate the hybridization interval $[t_1,t_2]$, which is enlarged in the inset.

Figure 2

Uncertainties in the NR-NR hybrid waveform from different error sources, in terms of mismatch $\mathcal{M}$ for different total masses $M$, for case (5, 0.9, 0.9).

Figure 3

Mismatch $\mathcal{M}$ between SpEC-ET hybrid and complete SpEC waveforms for the case (3, 0.85, 0.85) where the SpEC waveform includes a merger. The shaded region represents the estimated uncertainty in this computation from errors in the SpEC and ET waveforms.

Figure 4

Mismatch $\mathcal{M}$ between SpEC-ET hybrids and the waveform models SEOBNRv4 (solid lines) and IMRPhenomD (dashed lines) for all the configurations in Table 1.