The Shape of Eccentricity: Rapid Classification of Eccentric Binaries with the Wavelet Scattering Transform

TL;DR

This paper introduces a rapid, wavelet scattering transform-based method to classify gravitational-wave signals as eccentric or quasi-circular, aiding efficient detection of dynamically formed binary mergers.

Contribution

The study demonstrates that the wavelet scattering transform effectively discriminates between eccentric and quasi-circular binaries using simple classifiers, offering a computationally efficient intermediate step before detailed analysis.

Findings

Achieves ~64% detection accuracy at 10% false alarm rate

Provides a compact multi-scale representation of GW signals

Robustly distinguishes eccentricity from spin precession effects

Abstract

The gravitational-wave (GW) detections reported by the LIGO-Virgo-KAGRA (LVK) collaboration have so far been consistent with quasi-circular compact binary coalescences (CBCs). Nevertheless, a small fraction of binaries driven to merge through dynamical interactions in dense stellar environments or in field triples may retain measurable orbital eccentricity when entering the sensitive frequency band of LVK detectors. Confident measurement of eccentricity in the LVK band would provide strong evidence for such dynamically driven mergers; however, eccentric gravitational-waveform models are computationally expensive, and performing production-level inference on all detected signals is not an efficient use of resources when eccentric signals are expected to be rare. An intermediate step between detection and analysis, in which the signal is assessed for the potential presence of eccentricity, could provide quick recommendations for which signals should undergo full eccentric inference. We apply the wavelet scattering transform (WST) to a large set of synthetic waveforms in realistic noise and assess its discriminatory power using simple linear and shallow neural-network classifiers. We find that the WST representation enables effective discrimination between eccentric and quasi-circular binaries and provides a compact multi-scale representation of GW signals. Our approach achieves ~64% percent detection accuracy at a false alarm rate of 10%, with an AUC of 0.844 and an average precision of 0.876. We also examine the ability of our classifiers to distinguish eccentricity from spin-induced precession and find robust performance across a range of spin-precession magnitudes.