Defining eccentricity for spin-precessing binaries

Abstract Standardizing the definition of eccentricity is necessary forunambiguous inference of the orbital eccentricity of compact binariesfrom gravitational wave observations. In previous works, we proposed adefinition of eccentricity for systems without spin-precession thatrelies solely on the gravitational waveform, is applicable to anywaveform model, and has the correct Newtonian limit. In this work, weextend this definition to spin-precessing systems. This simple yeteffective extension relies on first transforming the waveform from theinertial frame to the coprecessing frame, and then adopting anamplitude and a phase with reduced spin-induced effects. Our methodincludes a robust procedure for filtering out spin-inducedmodulations, which become non-negligible in the small eccentricity andlarge spin-precession regime. Finally, we apply our method to a set ofNumerical Relativity and Effective One Body waveforms to showcase itsrobustness for generic eccentric spin-precessing binaries. We make ourmethod public via Python implementation in gw\ₑccentricity.