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# Kilohertz quasiperiodic oscillations in short gamma-ray bursts

## Abstract

Short gamma-ray bursts (GRBs) are associated with binary neutron star mergers, which are multimessenger astronomical events that have been observed both in gravitational waves and in the multiband electromagnetic spectrum1. Depending on the masses of the stars in the binary and on details of their largely unknown equation of state, a dynamically evolving and short-lived neutron star may be formed after the merger, existing for approximately 10–300 ms before collapsing to a black hole2,3. Numerical relativity simulations across different groups consistently show broad power spectral features in the 1–5-kHz range in the post-merger gravitational-wave signal4,5,6,7,8,9,10,11,12,13,14, which is inaccessible by current gravitational-wave detectors but could be seen by future third-generation ground-based detectors in the next decade15,16,17. This implies the possibility of quasiperiodic modulation of the emitted gamma rays in a subset of events in which a neutron star is formed shortly before the final collapse to a black hole18,19,20,21. Here we present two such signals identified in the short bursts GRB 910711 and GRB 931101B from archival Burst and Transient Source Experiment (BATSE) data, which are compatible with the predictions from numerical relativity.

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## Data availability

BATSE archival TTE data are available at https://heasarc.gsfc.nasa.gov/FTP/compton/data/batse/ascii_data/batse_tte/.

## Code availability

Details about our codes have been published40, but the code itself is not intended to be used publicly.

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## Acknowledgements

We thank B. Cenko, A. Corsi, E. Hays, F. Lamb, J. Norris, L. Rezzolla, N. Sarin, D. Shoemaker and Z. Wadiasingh for discussions. C.C. acknowledges support by NASA under award numbers 80GSFC17M0002 and TCAN-80NSSC18K1488. M.C.M. was supported in part by NASA ADAP grant 80NSSC21K0649. This work was partially conducted at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Center for Climate Simulation (NCCS) at Goddard Space Flight Center.

## Author information

Authors

### Contributions

C.C. led the project based on her idea of the possibility of a signal. S.D. extracted the Fermi/GBM data and performed the galaxy host search. A.L. extracted the Swift/BAT data and identified cosmic-ray contamination in that data. M.C.M. obtained the BATSE data and performed most of the data analysis. R.P. provided expertise about possible systematic errors in the BATSE data. All authors contributed ideas to the manuscript.

### Corresponding author

Correspondence to Cecilia Chirenti.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature thanks Paul Lasky and﻿ the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Extended data figures and tables

### Extended Data Fig. 1 Differential distribution of Bayes factors for Swift/BAT bursts.

We plot separately the sample of eight short bursts (orange) and 110 long bursts (grey). The light-orange and light-grey distributions include the analysis of segments with spikes in the light curve caused by cosmic-ray contamination. The only case of a short GRB with $${{\mathcal{B}}}_{0}^{1} > 1$$ is GRB 171011A, with $${{\mathcal{B}}}_{0}^{1}\approx 180$$. The moderate Bayes factor in this case was caused by a signal that was identified with the interval between two spikes caused by cosmic rays. By limiting the maximum number of counts in one 100-μs bin to 8, we remove most of the contamination by cosmic rays from both short and long bursts (including 16 more long-burst outliers with $${\log }_{10}{{\mathcal{B}}}_{0}^{1} > 10$$, not shown). After the removal of the cosmic-ray contamination, the single long GRB outlier (dark grey) with Bayes factor of approximately 6,000 is GRB 191004B; the signal was caused by 1,000-Hz calibration pulses on the BAT detectors at nearly 300 s after the trigger, when Swift was slewing.

### Extended Data Fig. 2 Analysis of BATSE segments contaminated by excess red noise.

a, Light curve of a segment near the middle of the approximately 1-s-long burst GRB 980310B. b, Power spectrum of that segment, which shows clear red noise above 500 Hz, and the best fit according to our algorithm. The resulting Bayes factor for one QPO versus none is $${{\mathcal{B}}}_{0}^{1}\approx 1{0}^{214}$$. c, The differential distribution of $${\log }_{10}{{\mathcal{B}}}_{0}^{1}$$ (defined in the main text) for the entire set of BATSE short GRBs (there are four more outliers with large amounts of red noise and $${\log }_{10}{{\mathcal{B}}}_{0}^{1} > 9$$, including the one featured in panels a and b) and for the subset obtained after removing data segments contaminated with red noise above 500 Hz.

### Extended Data Fig. 3 Example of a probably false signal of a QPO.

a, BATSE data from GRB 930110, in which the segment showing the apparent signal is framed by the two vertical dashed lines. Although GRB 930110 has T90 = 220 ms (ref. 58), this segment is effectively an artificially very short GRB with T90 ≈ 10 ms. b, Power spectrum for this segment and the best one-QPO-plus-white-noise fit, along with the 1σ, 2σ and 3σ power levels in the white-noise-only fit (compare with Fig. 3). c, Probability distribution of $${\log }_{10}{{\mathcal{B}}}_{0}^{1}$$ generated with 1,500 realizations of light curves (without QPOs) fitted to the data segment shown in the top panel. The vertical dashed line in the bottom panel shows the value of $${\log }_{10}({{\mathcal{B}}}_{0}^{1})$$ seen in the BATSE data for this segment of GRB 930110, the diagonal dashed line shows an exponential fit to the top 3% of the Bayes factors and the inset number shows the estimated false-positive probability from the exponential fit. See the sections ‘Generating synthetic data’ and ‘Estimates of the significance of signals’ for more details. On the basis of the high probability of a false positive (note also that, in this case, the next half-overlapping data segment has $${{\mathcal{B}}}_{0}^{1}=0.02$$), we remove this segment from our sample. Twelve other segments that presented similarly cropped light curves were also removed from our sample for consistency, although all cases had unremarkable Bayes factors.

### Extended Data Fig. 4 Probability distribution of signal strengths.

Here we show the distribution of $$\Delta ln{{\mathcal{L}}}_{0}^{2}$$ for the BATSE sample of short GRBs analysed in our work, compared with the probability distribution obtained for 15,000 synthetic spectra generated containing independent realizations of Poisson noise. The two outliers are our signals, with $$\Delta ln{{\mathcal{L}}}_{0}^{2}=56.4$$ (GRB 910711) and 33.3 (GRB 931101B). A third outlier with lower significance can also be seen at $$\Delta ln{{\mathcal{L}}}_{0}^{2}=21.3$$. The bulk of the BATSE distribution (excluding the outliers) is well represented by the Poisson noise distribution.

### Extended Data Fig. 5 Real versus synthetic data.

a, Zoom-in on the QPO data segment for GRB 910711, a corresponding smoothed fit given by equation (5) and a representative example of the synthetic light curve obtained by means of Poisson sampling from the smoothed fit (the starting time of the GRB 910711 light curve is shifted here for convenience of presentation). c, Power spectrum of the synthetic light curve shown in a. As in Fig. 3, the red bands show the 1σ, 2σ and 3σ powers expected given the best white-noise-only fits to the data from each burst. e, Probability distribution of $$\Delta ln{{\mathcal{L}}}_{0}^{2}$$ from synthetic data generated from light curve fits to GRB 910711. The vertical dashed line shows the $$\Delta ln{{\mathcal{L}}}_{0}^{2}$$ observed in BATSE data and the diagonal dashed line shows the exponential fit to the top 3% of the synthetic data points (see the section ‘Estimates of the significance of signals’ for details). The inset number gives the estimated false-positive probability for signals as strong as or stronger than that observed. b,d,f, Similarly, for GRB 931101B.

### Extended Data Fig. 6 Hardness–duration plot of BATSE GRBs.

Here we show the hardness ratio (fluence in the 100–300-keV band divided by fluence in the 50–100-keV band) versus T90 for 2704 GRBs in the BATSE catalogue (including both short and long GRBs), highlighting our signals. Error bars represent ±1σ uncertainties. The T90 of some of the shortest bursts was recalculated using the TTE data42. GRB 910711 and GRB 931101B are very short compared with most short GRBs, but the hardness ratios of our bursts do not stand out in the short GRB population.

### Extended Data Fig. 7 Energy dependence of burst properties.

a, Light curves of GRB 910711, in each of the four BATSE TTE channels and combined, over the segment of data (0.131072 s) that contains our strong signal. We see that the higher-energy channels 3 and 4 have greater flux relative to the pre-burst background than the lower-energy channels 1 and 2. b, The power spectra of GRB 910711, in each of the four BATSE TTE energy channels and combined. The energy ranges are 20–50 keV, 50–100 keV, 100–300 keV and >300 keV for channels 1, 2, 3 and 4, respectively. The vertical dashed lines show the centroid frequencies of the QPOs we identify in the summed channel 3 and 4 data (see Extended Data Table 5). c, The spectrogram of GRB 910711, in each energy channel separately as well as in all channels combined, using the same intervals as in Fig. 4. The colour bar on top of each set of plots shows the power scale. The distribution of power, in time and frequency, is complicated. The black arrows indicate the mean values of the QPO frequencies given in Table 1. In some cases (for example, energy channel 3), there may be evidence for substantial power before the main burst. df, The same plots for GRB 931101B.

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Chirenti, C., Dichiara, S., Lien, A. et al. Kilohertz quasiperiodic oscillations in short gamma-ray bursts. Nature 613, 253–256 (2023). https://doi.org/10.1038/s41586-022-05497-0

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