A Rosetta Stone for Eccentric Gravitational Waveform Models

Abstract

Orbital eccentricity is a key signature of dynamical binary black hole formation. The gravitational waves from a coalescing binary contain information about its orbital eccentricity, which may be measured if the binary retains sufficient eccentricity near merger. Dedicated waveforms are required to measure eccentricity. Several models have been put forward, and show good agreement with numerical relativity at the level of a few percent or better. However, there are multiple ways to define eccentricity for inspiralling systems, and different models internally use different definitions of eccentricity, making it difficult to compare eccentricity measurements directly. In this work, we systematically compare two eccentric waveform models, SEOBNRE and TEOBResumS, by developing a framework to translate between different definitions of eccentricity. This mapping is constructed by minimizing the relative mismatch between the two models over eccentricity and reference frequency, before evolving the eccentricity of one model to the same reference frequency as the other model. We show that for a given value of eccentricity passed to SEOBNRE, one must input a 20%–50% smaller value of eccentricity to TEOBResumS in order to obtain a waveform with the same empirical eccentricity. We verify this mapping by repeating our analysis for eccentric numerical relativity simulations, demonstrating that TEOBResumS reports a correspondingly smaller value of eccentricity than SEOBNRE.

Four Eccentric Mergers Increase the Evidence that LIGO–Virgo–KAGRA’s Binary Black Holes Form Dynamically

“…This means that an eccentricity inferred with SEOBNRE does not exactly equate to the eccentricity that would be inferred with another model, and that comparisons to predictions made by simulations of dynamical environments should be taken as indicative rather than absolute. Work is ongoing to establish a translation guide between the eccentricities defined by various simulations (Knee et al 2022). 7.…”

“…However, if the parameters preferred by the quasi-circular model are totally removed from the true quasi-circular parameters, then the eccentricity posterior obtained through the reweighting method is unlikely to both recover a high eccentricity and be well sampled; therefore, we use 3.9% as our expected eccentric fraction. The predictions in Zevin et al (2021a) were obtained using a different eccentric waveform model, TEOBResumS (Nagar et al 2018); for an overview of key differences between TEOBResumS and SEOBNRE, see Knee et al (2022). Since the overlap between SEOBNRE and TEOBResumS is 90% >  in LVK noise over the eccentricity range studied here (Knee et al 2022), we assume in this paper that the results of Zevin et al (2021a) are robust to waveform choice.…”

“…The predictions in Zevin et al (2021a) were obtained using a different eccentric waveform model, TEOBResumS (Nagar et al 2018); for an overview of key differences between TEOBResumS and SEOBNRE, see Knee et al (2022). Since the overlap between SEOBNRE and TEOBResumS is 90% >  in LVK noise over the eccentricity range studied here (Knee et al 2022), we assume in this paper that the results of Zevin et al (2021a) are robust to waveform choice. However, we caution that this may not be the case; a repeated study using SEOBNRE is required to obtain waveform-modelspecific predictions.…”

Quiescent and Active Galactic Nuclei as Factories of Merging Compact Objects in the Era of Gravitational Wave Astronomy

“…This led to the development of, on the one hand, numerical relativity simulations aimed at obtaining waveform templates [480], and, on the other hand, approximate methods, or approximants, that greatly reduced the computational cost of data analysis but generally they are generally constructed on the leading order of GW signal expansion [479, e.g.]. A recently developed technique, however, enabled the possibility to retrieve information on the binary eccentricity at a small computational cost [481,482], and permitted to place constrains on the eccentricity of LVC sources, suggesting that up to 4 of them might be eccentric sources [146,148]. In the frequency range of LVC detectors, i.e.…”

“…Placing constraints on the eccentricity of observed mergers became possible only in recently [e.g. [143][144][145][146], and led to place constraints on the eccentricity of up to 4 LVC sources, for which possibly e > 0.1 [147][148][149][150]. Interestingly, for eccentric sources the accuracy on the parameter measurement can significantly increase, e.g.,the chirp mass(localization) accuracy of an eccentric 30 − 30M BBH can be ∼ 10 1 (10 2 ) times higher than for the circular case [151].…”