Defining eccentricity for spin-precessing binaries

TL;DR

This paper extends a waveform-based eccentricity definition to spin-precessing binary systems, enabling clearer inference of orbital eccentricity in gravitational wave data with a robust filtering method.

Contribution

It introduces a new method for defining eccentricity in spin-precessing binaries by transforming waveforms to the coprecessing frame and filtering spin effects, applicable to various waveform models.

Findings

Method successfully applied to Numerical Relativity waveforms

Robustness demonstrated for generic eccentric spin-precessing binaries

Implementation available in Python package 'gw_eccentricity'

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}.