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

Synthetic gravitational-wave dataset generated for eccentricity classification of binary black hole signals Data generation. Strain data were generated with Bilby by injecting simulated waveforms into realistic detector noise, i.e., Gaussian noise coloured by O4 sensitivity curves for the two Advanced LIGO detectors and Advanced Virgo. Eccentric waveforms were produced with the SEOBNRv5EHM approximant, an effective-one-body, multipolar waveform model for eccentric BBH systems with component spins aligned with or against the orbital angular momentum. Unless otherwise stated, all six multipoles available in SEOBNRv5EHM are included. Priors. Intrinsic parameters were sampled with Bilby priors: dimensionless aligned-spin magnitudes a ∈ [0, 0.99]; relativistic anomaly uniform in [0, 2π]; component masses m₁,₂ uniform in [10, 40] M⊙; luminosity distance in [100, 800] Mpc via the default Bilby prior (uniform in comoving volume and source-frame time). The eccentricity at a reference frequency of 10 Hz, e₁₀, was sampled uniformly within each class: eccentric systems with e₁₀ ∈ [0.01, 0.5] and non-eccentric systems with e₁₀ ∈ [0.001, 0.01]. Uniform (rather than log-uniform) sampling ensures balanced class populations for training; the threshold e₁₀ = 0.01 is a practical choice. Signal processing. Waveforms were generated in the frequency domain over 10–1024 Hz (upper cutoff equal to half the sampling rate fₛ) with a duration of 128 s, then transformed to the time domain via inverse FFT. The geocentric merger time was sampled uniformly from 126 ± 0.1 s, and all waveforms were aligned at merger. After injection, an 8 s segment around the merger peak tₘ, [tₘ − 7.8 s, tₘ + 0.2 s], was extracted and whitened. The network signal-to-noise ratio was computed across the three-detector network, and samples with NSNR < 15 were discarded to ensure confident detectability under realistic noise conditions. For full details, see the associated publication.