Probing Eccentricity of Black Hole Binaries: From Surrogate Modeling to Data Analysis

Orbital eccentricity is one of the cleanest tracers of the astrophysical origins of compact binaries, yet it remains absent from routine LIGO--Virgo--KAGRA (LVK) analyses due to the limited availability of accurate as well as computationally efficient eccentric waveform models. As part of our ESIGMA framework for modeling moderately eccentric, non-precessing black hole binaries, we present two recent developments. First, we present a novel surrogate modeling approach that produces over an order of magnitude more compressed and several orders of magnitude more accurate eccentric surrogate models by representing the complex eccentric waveform features in terms of an orbital angular element called the mean anomaly, instead of time. This formulation simplifies the waveform morphology and enables scalable and rapid generation of long-duration eccentric waveforms. Second, we report a re-analysis of the LVK gravitational wave events to search for signatures of orbital eccentricity. While most events appear consistent with quasi-circular orbits, we identify hints of measurable eccentricity in a few cases, potentially suggesting dynamical formation pathways. Together, these studies demonstrate the expanding capabilities of the ESIGMA framework, thus making it a valuable resource for the current and future data analysis needs.