A search for periodic activity in multi-peaked long gamma-ray bursts

Context. A sizeable fraction of gamma-ray burst (GRB) light curves (LCs) feature a sequence of peaks that hold information on the unknown way energy is released and dissipated into gamma-rays over time. Traditionally, searches for periodic signals in GRB LCs have turned out to be inconclusive, partly because they are challenging as a consequence of the short-lived, coloured-noise, and non-stationary nature of the LCs themselves. Yet, recent claims have revived the issue. Aims. We aim to search for periodic components in GRB LCs through a new approach to GRBs that avoids most of the issues faced by traditional Fourier techniques and periodograms due to the GRB LC nature. Methods. We identified peaks through a well-tested algorithm and selected GRBs with at least ten peaks out of five GRB catalogues (Swift/BAT, CGRO/BATSE, Fermi/GBM, Insight-HXMT, and BeppoSAX/GRBM). At this point, each GRB was simply treated as a discrete point process whose realisation coincides with the sequence of peak times. We searched for possible periodic recurrences based on the multinomial distribution, after accounting for the clustering of peaks due to the non-stationarity of the GRB signals. Results. Accounting for the multiple trial periods, the best candidate has a p value of 3 × 10−4 that there is no periodic recurrence. However, accounting for the multiple trials of 555 searched GRBs, its statistical significance is downgraded to 17%. The overall distribution of the p values obtained for all GRBs is compatible with a uniform distribution in [0, 1]. Our technique is sensitive to the presence of ≳8 periodic peaks and a periodic peak fraction of ∼75% at least. Conclusions. We found no robust evidence for multi-peaked GRBs with periodic recurrences at peak times. We can exclude a sizeable fraction (≳0.75) of peaks of each GRB with at least ten peaks being periodic. While our result does not necessarily clash with claimed periodicities based on Fourier techniques, it constrains the putative recurrent behaviour, which would manifest itself not through the sequence of peaks but, evidently, in a more elusive way.