Mapping eccentricity evolutions between numerical relativity and effective-one-body gravitational waveforms

TL;DR

This paper develops a method to accurately measure and map orbital eccentricity in gravitational wave signals from binary black holes, improving waveform models for better astrophysical inference.

Contribution

It introduces a robust pipeline for measuring eccentricity evolution from gravitational waves and demonstrates reliable mapping between numerical relativity and effective-one-body waveforms.

Findings

Eccentricity measurement is reliable even for signals spanning multiple orbits.

Small deviations in initial eccentricity significantly affect waveform phase and amplitude.

The mapping between numerical and analytic waveforms improves eccentric waveform modeling.

Abstract

Orbital eccentricity in compact binaries is considered to be a key tracer of their astrophysical origin, and can be inferred from gravitational-wave observations due to its imprint on the emitted signal. For a robust measurement, accurate waveform models are needed. However, ambiguities in the definition of eccentricity can obfuscate the physical meaning and result in seemingly discrepant measurements. In this work we present a suite of 28 new numerical relativity simulations of eccentric, aligned-spin binary black holes with mass ratios between 1 and 6 and initial post-Newtonian eccentricities between 0.05 and 0.3. We then develop a robust pipeline for measuring the eccentricity evolution as a function of frequency from gravitational-wave observables that is applicable even to signals that span at least $\gtrsim 7$ orbits. We assess the reliability of our procedure and quantify its robustness under different assumptions on the data. Using the eccentricity measured at the first apastron, we initialise effective-one-body waveforms and quantify how the precision in the eccentricity measurement, and therefore the choice of the initial conditions, impacts the agreement with the numerical data. We find that even small deviations in the initial eccentricity can lead to non-negligible differences in the phase and amplitude of the waveforms. However, we demonstrate that we can reliably map the eccentricities between the simulation data and analytic models, which is crucial for robustly building eccentric hybrid waveforms, and to improve the accuracy of eccentric waveform models in the strong-field regime.