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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 ingw_eccentricity. 

Abstract Accurate modelling of black hole binaries is critical to achieve the science goals of gravitational-wave detectors. Modelling such configurations relies strongly on calibration to numerical-relativity (NR) simulations. Binaries on quasi-circular orbits have been widely explored in NR, however, coverage of the broader 9-dimensional parameter space, including orbital eccentricity, remains sparse. This article develops a new procedure to control orbital eccentricity of binary black hole simulations that enables choosing initial data parameters with precise control over eccentricity and mean anomaly of the subsequent evolution, as well as the coalescence time. We then calculate several sequences of NR simulations that nearly uniformly cover the 2-dimensional eccentricity--mean anomaly space for equal mass, non-spinning binary black holes. We demonstrate that, for fixed eccentricity, many quantities related to the merger dynamics of binary black holes show an oscillatory dependence on mean anomaly. The amplitude of these oscillations scales nearly linearly with the eccentricity of the system. We find that for the eccentricities explored in this work, the magnitude of deviations in various quantities such as the merger amplitude and peak luminosity can approach $$\sim5\%$$ of their quasi-circular value. We use our findings to explain eccentric phenomena reported in other studies. We also show that methods for estimating the remnant mass employed in the effective-one-body approach exhibit similar deviations, roughly matching the amplitude of the oscillations we find in NR simulations. This work is an important step towards a complete description of eccentric binary black hole mergers, and demonstrates the importance of considering the entire 2-dimensional parameter subspace related to eccentricity.