A Rosetta Stone for eccentric gravitational waveform models

TL;DR

This paper develops a framework to translate between different definitions of orbital eccentricity in gravitational waveform models, enabling consistent comparisons and interpretations of eccentricity measurements in binary black hole mergers.

Contribution

The authors introduce a systematic method to map eccentricity parameters between two waveform models, aiding in consistent eccentricity estimation across models and simulations.

Findings

A 20-50% smaller eccentricity input in TEOBResumS matches the same eccentricity in SEOBNRE.

The mapping is validated using numerical relativity simulations.

Framework improves comparison of eccentricity measurements across 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 directly compare eccentricity measurements. In this work, we systematically compare two eccentric waveform models, $\texttt{SEOBNRE}$ and $\texttt{TEOBResumS}$, 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 $\texttt{SEOBNRE}$, one must input a $20$-$50\%$ smaller value of eccentricity to $\texttt{TEOBResumS}$ 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 $\texttt{TEOBResumS}$ reports a correspondingly smaller value of eccentricity than $\texttt{SEOBNRE}$.