The Self-organized Criticality Behaviors of Two New Parameters in SGR J1935+2154

Abstract: The minimum variation timescale (MVT) and spectral lag of hundreds of X-ray bursts (XRBs) from soft gamma-ray repeater (SGR) J1935+2154 were analyzed in detail for the first time in our recent work, which are important probes for studying the physical mechanism and radiation region. In this work, we investigate their differential and cumulative distributions carefully and find that they follow power-law models. Besides, the distributions of fluctuations in both parameters follow the Tsallis $q$-Gaussian distributions and the $q$ values are consistent for different scale intervals. Therefore, these results indicate that both parameters are scale-invariant, which provides new parameters for the study of self-organized criticality systems. Interestingly, we find that the $q$ values for MVT and spectral lag are similar with duration and fluence, respectively.