Possible periodic activity in the short bursts of SGR 1806-20: connection to fast radio bursts

Magnetars are highly magnetized neutron stars that are characterized by recurrent emission of short-duration bursts in soft gamma-rays/hard X-rays. Recently, FRB 200428 were found to be associated with an X-ray burst from a Galactic magnetar. Two fast radio bursts (FRBs) show mysterious periodic activity. However, whether magnetar X-ray bursts are periodic phenomena is unclear. In this paper, we investigate the period of SGR 1806-20 activity. More than 3000 short bursts observed by different telescopes are collected, including the observation of RXTE, HETE-2, ICE and Konus. We consider the observation windows and divide the data into two sub-samples to alleviate the effect of unevenly sample. The epoch folding and Lomb-Scargle methods are used to derive the period of short bursts. We find a possible period about $ 398.20 \pm 25.45 $ days. While other peaks exist in the periodograms. If the period is real, the connection between short bursts of magnetars and FRBs should be extensively investigated.