Scale-invariance in soft gamma repeaters

The statistical properties of the soft gamma repeater SGR J1550--5418 are investigated carefully. We find that the cumulative distributions of fluence, peak flux and duration can be well fitted by a bent power law, while the cumulative distribution of waiting time follows a simple power law. In particular, the probability density functions of fluctuations of fluence, peak flux, and duration have a sharp peak and fat tails, which can be well fitted by a $q$-Gaussian function. The $q$ values keep approximately steady for different scale intervals, indicating a scale-invariant structure of soft gamma repeaters. Those results support that the origin of soft gamma repeaters is crustquakes of neutron stars with extremely strong magnetic fields.