Detectability-Aware Screening of Post-Merger Gravitational-Wave Damping Anomalies in Real Detector Noise: A Graph-Spectral Approach with Empirical Null Calibration

The post-merger phase of binary neutron star (BNS) coalescences may encode information about matter at extreme densities and could, in principle, be sensitive to non-standard energy-loss channels, including scenarios motivated by dark-sector physics. Deviations in the effective damping time of post-merger oscillations have been proposed as phenomenological proxies for such channels, but identifying short, high-frequency transients in real, non-stationary detector noise remains difficult, and standard statistical assumptions used to calibrate detection thresholds often do not hold in that regime.

We present a two-stage screening framework for a phenomenological damped-sinusoid post-merger proxy, h(t) = A·exp(−t/τ)·sin(2πf_peak·t + φ), injected directly into real LIGO Livingston (L1) background noise. Stage 1 builds a local time-frequency coherence graph from a Constant-Q representation of each whitened candidate window and computes its leading eigenvalue as a detectability statistic, motivated by the detectability-transition logic of spiked random matrices (the Baik–Ben Arous–Péché transition) rather than a closed-form Gaussian-noise assumption. We validate the matched-filter SNR normalization with a synthetic Gaussian-noise control, and separately validate the graph statistic with power-comparison and tile-shuffling tests showing sensitivity to local time-frequency organization beyond total integrated power, with the effect strongest for the shortest, most compact injected transients. Its null distribution is calibrated empirically on real detector noise, since we find directly that real LIGO noise does not satisfy the Gaussian assumptions a closed-form threshold would require. Stage 2 estimates an effective damping time for Stage-1-passing candidates using an interpretable ridge/energy-decay fit and a classical nonlinear least-squares fit, and compares each against a threshold calibrated on the standard damping-time distribution (τ = 5–40 ms).

All thresholds and models are fixed on independent calibration and training data and evaluated once, after the design was frozen, on a held-out real-noise segment untouched during development. The least-squares estimator is the strongest Stage-2 discriminator (AUC = 0.943); the ridge/energy- decay estimator is a secondary, model-light, time-frequency-native alternative with competitive ranking-level separation but lower recall at a matched low-false-positive operating point. A simple total-power baseline is shown to be a real but substantially weaker, direction-sensitive discriminator.