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Abstract Numerical relativity (NR) simulations of binary black hole (BBH) systems provide the most accurate gravitational wave predictions, but at a high computational cost—especially when the black holes have nearly extremal spins (i.e. spins near the theoretical upper limit) or very unequal masses. Recently, the technique of reduced order modeling has enabled the construction of ‘surrogate models’ trained on an existing set of NR waveforms. Surrogate models enable the rapid computation of the gravitational waves emitted by BBHs. Typically these models are used for interpolation to compute gravitational waveforms for BBHs with mass ratios and spins within the bounds of the training set. Because simulations with nearly extremal spins are so technically challenging, surrogate models almost always rely on training sets with only moderate spins. In this paper, we explore how well surrogate models can extrapolate to nearly extremal spins when the training set only includes moderate spins. For simplicity, we focus on one-dimensional surrogate models trained on NR simulations of BBHs with equal masses and equal, aligned spins. We assess the performance of the surrogate models at higher spin magnitudes by calculating the mismatches between extrapolated surrogate model waveforms and NR waveforms, by calculating the differences between extrapolated and NR measurements of the remnant black-hole mass, and by testing how the surrogate model improves as the training set extends to higher spins. We find that while extrapolation in this one-dimensional case is viable for current detector sensitivities, surrogate models for next-generation detectors should use training sets that extend to nearly extremal spins.
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This content will become publicly available on December 1, 2025
Phenomenological gravitational waveform model of binary black holes incorporating horizon fluxes
Subjected to the tidal field of its companion, each component of a coalescing binary suffers a slow change in its mass (tidal heating) and spin (tidal torquing) during the inspiral and merger. For black holes, these changes are associated with their absorption of energy and angular momentum fluxes. This effect modifies the inspiral rate of the binary, and consequently, the phase and amplitude of its gravitational waveform. Numerical relativity (NR) waveforms contain these effects inherently, whereas analytical approximants for the early inspiral phase have to include them manually in the energy balance equation. In this work, we construct IMRPhenomD_Horizon, a frequency-domain gravitational waveform model that incorporates the effects of tidal heating of black holes. This is achieved by recalibrating the inspiral phase of the waveform model IMRPhenomD to incorporate the phase corrections for tidal heating. We also include corrections to the amplitude, but add them directly to the inspiral amplitude model of IMRPhenomD. First we demonstrate that the inclusion of the corrections, especially in the phase, confers an overall improvement in the phase agreement between the analytical inspiral model (uncalibrated SEOBNRv2) and NR data. The model presented here is faithful, with less than 1% mismatches against a set of hybrid waveforms (except for one outlier that barely breaches this limit). The recalibrated model shows mismatches of up to ∼14% with IMRPhenomD for high mass ratios and spins. Amplitude corrections become less significant for higher mass ratios, whereas the phase corrections leave more impact—suggesting that the former is practically irrelevant for gravitational wave data analysis in Advanced LIGO (aLIGO), Virgo and KAGRA. Comparing with a set of 219 numerical relativity waveforms, we find that the median of mismatches decreases by ∼4% in aLIGO zero-detuned high power noise curve, and by ∼1.5% with a flat noise curve. This implies a modest but notable improvement in waveform accuracy.
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- Award ID(s):
- 2309352
- PAR ID:
- 10578933
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review D
- Volume:
- 110
- Issue:
- 12
- ISSN:
- 2470-0010
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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