A gating-and-inpainting perspective on GW150914 ringdown overtone: understanding the data analysis systematics

TL;DR

The paper revisits GW150914's ringdown overtone using a gating-and-inpainting pipeline to isolate the ringdown and study data-analysis systematics. By operating in the frequency domain and testing effects of sampling rate, start time accuracy, and PSD resolution, the authors identify a convergence window around the merger where overtone evidence is robust, with Bayes factors in the range of 10–26. Outside this window, results vary with analysis choices, underscoring the importance of systematic controls. Numerical-relativity injections further validate the approach, supporting the presence of an overtone when the analysis is carefully configured, and the work provides practical diagnostics and reproducible tooling for future ringdown studies.

Abstract

We revisit the recent debate on the evidence for an overtone in the black hole ringdown of GW150914 using an independent data-analysis pipeline. By gating and inpainting the data, we discard the contamination from earlier parts of the gravitational wave signal before ringdown. This enables parameter estimation to be conducted in the frequency domain, which is mathematically equivalent to the time domain method. We keep the settings as similar as possible to the previous studies by Cotesta et al. arXiv:2201.00822 and Isi et al. arXiv:1905.00869 arXiv:2202.02941 which yielded conflicting results on the Bayes factor of the overtone. Our aim is to understand how different data analysis systematics, including sampling rates, erroneous timestamps, and the frequency resolution of the noise power spectrum, would influence the statistical significance of an overtone. Our main results indicate the following: (i) a low-resolution estimation of the noise power spectrum tends to diminish the significance of overtones, (ii) adjusting the start time to a later digitized point reduces the significance of overtones, and (iii) overtone evidence varies with different sampling rates if the start time is too early, indicating that the overtone is a poor model, hence we propose a convergence test to verify the validity of an overtone model. With these issues addressed, we find the Bayes factors for the overtone to range from $10$ to $26$ in a range of times centered at the best-fit merger time of GW150914, which supports the existence of an overtone in agreement with the conclusions of Isi et al. arXiv:1905.00869 arXiv:2202.02941. These results are obtained by keeping the start time and sky location fixed, enabling a direct comparison with other work. Marginalizing over these parameters would lower the Bayes factor to 1 for the evidence of an overtone.

Figures (10)

• Figure 1: The logarithm of Bayes factors comparing the $(2,2,0)+(2,2,1)$ model and the $(2,2,0)$-only model with respect to a variety of starting times for sampling rates $f_s=1024/2048/4096/8192$ Hz. As a comparison, we plot the Bayes factors obtained from Cotesta:2022pciIsi:2022mhy. We also plot symmetric error bars with length $\mathcal{B}_{f_s = 8192}\times\delta$. The shaded regions depict where the results from different sampling rates have not converged, quantified by $\delta > 50\%$, while in the non-shaded region all have $\delta < 50\%$.
• Figure 2: The solid lines present the ringdown overtone waveform generated with the maximum likelihood parameters for four different sampling rates, with the scale shown on the left Y-axis. The dashed lines present the matched-filtering SNR as a function of the frequency upper limit of the integration. The lower frequency limit is 20 Hz. The ringdown starting time is $t_\mathrm{ref} - 0.75$ ms. The grey curve shows the ASD $\sqrt{S_n(f)}$.
• Figure 3: The marginal posterior of $M_f$ and $\chi_f$ for four different sampling rates with analysis starting time $t_\mathrm{ref} - 0.75$ ms. In the background, we plot the value of $\tau_{221}$ as expected in GR as a function of the mass and spin of a Kerr BH. The solid and dashed lines show the $90\%$ and $50\%$ credible regions, respectively.
• Figure 4: A comparison of the posteriors for $A_{221}$ and $\tau_{221}$ using two different sampling rates, 1024 Hz and 8192 Hz, with analysis starting time $t_\mathrm{ref} - 0.75$ ms. The contours denote the $90\%$ and $50\%$ credible regions. The shaded region shows the posterior probability density of the $f_s=1024$ Hz result.
• Figure 5: Reconstructing the subsample corresponding to the starting time of ringdown, $t_\mathrm{ringdown}$. This is done by time shifting the data by an offset of the difference of $t_\mathrm{ringdown}$ and $t_\mathrm{nearest}$ which corresponds to the nearest data sample from LIGO Hanford. In the inset we also plot the absolute value of the data before and after being time shifted in the frequency domain. The figure shows they are identical as expected.