Composite periodogram analysis for low-event-count fast radio burst repeaters

Context. Fast radio bursts (FRBs) are a class of transients characterised by their millisecond-scale duration and relatively high dispersion measures. Some FRBs have been observed to repeat. For such repeating FRBs, measuring the period is key to identifying their physical mechanisms. However, periods have only been measured for two FRBs – FRB 20112002A and FRB 20180916B – because most repeating FRBs have a low event count, making it challenging to measure their periods. Aims. We aim to introduce a composite periodogram strategy designed to measure periods of repeating FRBs out of low event counts. Methods. We combined the χ2 periodogram with the inactivity fraction periodogram (F0) to maximise the detection likelihood and minimise noise. Our approach was validated using FRB 20180916B, whereby we successfully recovered the known period with as few as five events. We then applied this method to 17 FRBs whose event counts range from three to 12. Results. A candidate period is identified in FRB 20190804E, FRB 20190915D, FRB 20200223B, FRB 20201130A, and FRB 20201221B, with a probability of chance coincidence ≤0.050. Additionally, we did further checks to eliminate false positives and concluded that the candidate periods for FRB 20190804E (168.39−0.07+3.86 days) and FRB 20201130A (11.38−0.10+0.10 days) are likely close to its true period. These values provide a basis for informed follow-up observations.