Post-Newtonian theory-inspired framework for characterizing eccentricity in gravitational waveforms

TL;DR

This paper introduces a new framework for measuring eccentricity in gravitational wave signals from binary black hole mergers, improving accuracy by integrating post-Newtonian calculations and validated with numerical relativity data.

Contribution

The authors develop a post-Newtonian inspired method to characterize eccentricity directly from gravitational waveforms, connecting it smoothly to the relativistic regime and providing an open-source implementation.

Findings

Framework accurately estimates eccentricity up to near merger.

Requires extending post-Newtonian calculations to 0.5PN order for better accuracy.

Provides publicly available Python package for community use.

Abstract

Characterizing eccentricity in gravitational waveforms in a consistent manner is crucial to facilitate parameter estimation, astrophysical population studies, as well as searches for these rare systems. We present a framework to characterize eccentricity directly from gravitational waveforms for non-precessing eccentric binary black hole (BBH) mergers using common modulations that eccentricity induces in all spherical harmonic modes of the signals. Our framework is in the spirit of existing methods that use frequency modulations in the waveforms, but we refine the approach by connecting it to state-of-the-art post-Newtonian calculations of the time evolution of the eccentricity. Using 39 numerical relativity (NR) simulations from the SXS and RIT catalogs, as well as waveforms obtained from the post-Newtonian approximation and effective-one-body (EOB) formalism, we show that our framework provides eccentricity estimates that connect smoothly into the relativistic regime (even up to $\sim 2M$ before merger). We also find that it is necessary to carry existing post-Newtonian calculations to an extra $0.5$PN order to adequately characterize existing NR simulations, and provide fits to the extra coefficient for existing simulations. We make the framework publicly available through the Python-based \texttt{gwModels} package.