Model-independent search of gravitational wave echoes in LVK data

Abstract

Gravitational wave echoes offer a unique probe of the near-horizon structure of astrophysical black holes, beyond the standard ''black hole spectroscopy''. Theoretical waveform predictions, however, remain uncertain, motivating robust searches that avoid specific echo modeling. We present a model-independent search framework targeting long-lived quasinormal modes (QNMs) expected from strong interior reflection. By employing a generalized phase-marginalized likelihood that coherently combines data for each QNM across a detector network, our method enhances sensitivity to the signals. To handle real detector noise, we implement an optimized notching procedure to suppress instrumental spectral lines and refine the Bayesian parameter settings. We validate the performance of this framework using injection studies on O1 background data, demonstrating reliable signal recovery in realistic noise conditions. We then apply this method to three binary black hole merger events with high ringdown signal-to-noise ratios (SNR) from observing runs O1 to O4: GW150914, GW231226, and the recently detected GW250114. No statistically significant evidence for postmerger echoes is found. Consequently, we derive 90% upper limits on the network SNR and the average amplitude of the long-lived QNMs, setting the first model-independent constraints on late-time echo signatures from LVK data.

Figures (12)

• Figure 1: Comparison of background log Bayes factor distributions with and without notch filtering for detector noise around GW150914. The blue and orange histograms show the notched distributions obtained with the new and old likelihoods, respectively; gray histograms correspond to the results before notching. The vertical dotted lines mark the distribution medians. Each histogram is constructed from $150$ independent noise realizations.
• Figure 2: The injected echo waveform in the frequency domain (top panel) and time domain (bottom panel). The top panel inset shows a zoomed-in view around the peak of amplitude. The blue and orange curve represent the absolute value and the phase of the waveform, respectively. The bottom panel displays a zoomed-in view around the $1$-st and the $30$-th echo wavelets. The red solid and blue dashed curve represent the real part and the imaginary part of the waveform, respectively.
• Figure 3: The log Bayes factor distributions (top), the overall posterior distributions of the inferred network SNR (middle) and the combination $\tau \Delta f$ (bottom) for the injection, as a function of the time duration $T$. For all panels, the upper and lower bars represent the symmetric 90% credible intervals, and the dots denote the median values. In the top panel, the gray band represents the 90% credible interval of the noise distributions. For the middle ones, the green dashed lines denote the theoretical prediction of the SNR.
• Figure 4: Corner plots for the overall posterior distributions for the spacing $\Delta f$, the width $1/\tau$ and the frequency range $f_{\rm min}, f_{\rm max}$ for the injection with $T=5$ s (left) and $49$ s (right). The blue and orange are for new and old likelihoods, respectively. The contours in the bottom-left panels denote the $1\sigma$ and $2\sigma$ ranges of the 2d posteriors.
• Figure 5: Comparison of background log Bayes factor distributions with and without notch filtering for detector noise around GW150914 and GW231226. The blue and orange histograms represent the notched distributions obtained with the new and old likelihoods, using $500$ noise realizations, respectively. The gray histograms correspond to the results before notching, using $150$ noise realizations.