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arXiv · 2507.08345

Defining eccentricity for spin-precessing binaries

Md Arif Shaikh·Vijay Varma·Antoni Ramos-Buades·Harald P. Pfeiffer·Michael Boyle·Lawrence E. Kidder·Mark A. Scheel
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Abstract

Standardizing the definition of eccentricity is necessary for unambiguous inference of the orbital eccentricity of compact binaries from gravitational wave observations. In previous works, we proposed a definition of eccentricity for systems without spin-precession that relies solely on the gravitational waveform, is applicable to any waveform model, and has the correct Newtonian limit. In this work, we extend this definition to spin-precessing systems. This simple yet effective extension relies on first transforming the waveform from the inertial frame to the coprecessing frame, and then adopting an amplitude and a phase with reduced spin-induced effects. Our method includes a robust procedure for filtering out spin-induced modulations, which become non-negligible in the small eccentricity and large spin-precession regime. Finally, we apply our method to a set of Numerical Relativity and Effective One Body waveforms to showcase its robustness for generic eccentric spin-precessing binaries. We make our method public via Python implementation in \texttt{gw\_eccentricity}.

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Md Arif Shaikh, Vijay Varma, Antoni Ramos-Buades, Harald P. Pfeiffer, Michael Boyle, Lawrence E. Kidder, Mark A. Scheel. 2025-07-11. Defining eccentricity for spin-precessing binaries. https://doi.org/10.1088/1361-6382%2Fae085d

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