Quantifying the memory and dynamical stability of magnetar bursts*

Abstract The time series of energy and waiting time in magnetar bursts carry important information about the source activity. In this study, we investigate the memory and dynamical stability of magnetar bursts from four soft gamma repeater (SGR) sources: SGR 1806−20, SGR 1900+14, SGR J1935+2154, and SGR J1550−5418. Based on the rescaled range analysis, we quantify the memory in magnetar bursts for the first time and find that there exists long-term memory in the time series of both waiting time and energy. We investigate the dynamical stability in the context of randomness and chaos. For all four SGR samples, we find that the waiting time is not completely random; however, the energy of two SGRs is consistent with a total random organization. Furthermore, both waiting time and energy exhibit weak chaos. We also find no significant difference between SGRs and repeating fast radio bursts (FRBs) in the randomness-chaos phase space. The statistical similarity between SGRs and repeating FRBs hints that there may be potential physical connection between these two phenomena.