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

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.

Figures (10)

• Figure 1: Illustrative example of a (left 4 panels) quasi-circular and (right 4 panels) eccentric ($e=0.3$ at 10 Hz) waveform, and their corresponding $(J,Q) = (7,2)$ WST coefficients (on a logarithmic scale). The binary masses are 12 and 18 $M_\odot$, at a luminosity distance of $100$ Mpc. The top row shows two $0.5$ s windows of the waveform, where the first represents the inspiral and the second the merger. The bottom row represents all WST coefficients in the left panel, as well as a slice at two time bins $T_b$ in the right panel, corresponding to the different phases in the top row. From these plots, it is clear that, as expected, the WST coefficients representing the eccentric binary distribute the power across the channels more evenly. It should be noted that the top 15 channels in the bottom row represent first-order scattering coefficients, and the rest second-order.
• Figure 2: Block diagram of the 1D-CNN designed for eccentricity detection. Data from different detectors are encoded separately by a shared Conv1d with three convolutional blocks and intermediate max-pooling for temporal downsampling. Feature maps are averaged into $T_p$ bins, producing fixed-length detector embeddings. These are fused (joined) using first order statistics, and the resulting representation is classified by a shallow MLP to yield the final probability value.
• Figure 3: Confusion matrix obtained for the reference 1D-CNN model and $J=7, Q=2$ WST coefficients, tuned to a target FAR of 10% on the validation set.
• Figure 4: ROC curve and AUC on the test set, for the best fold during training of the 1D-CNN model with $J=7, Q=2$ WST coefficients.
• Figure 5: (left) Histogram of eccentricity values for eccentric samples (i.e. those with $e_{10} > 0.01$) in both the test set and the set of false negatives (FNs), for the reference 1D-CNN with threshold tuned to a FAR of 10%. Additionally, histograms are also shown for the FNs in the subset of binaries with lower $M_{\text{tot}} < 50 M_\odot$, and the subset with lower NSNR $< 30$. (right) Fraction of FNs as a function of the bins on in the left panel. Fractions are calculated within the subsets of lower $M_{\text{tot}}$, NSNR or mass ratio $q$ (where lower $q$ corresponds to $q < 0.6$).