Similar Scale-invariant Behaviors between Soft Gamma-ray Repeaters and An Extreme Epoch from FRB 121102

The recent discovery of a Galactic fast radio burst (FRB) associated with a hard X-ray burst from the soft gamma-ray repeater (SGR) J1935+2154 has established the magnetar origin of at least some FRBs. In this work, we study the statistical properties of soft gamma-/hard X-ray bursts from SGRs 1806--20 and J1935+2154 and of radio bursts from the repeating FRB 121102. For SGRs, we show that the probability density functions for the differences of fluences, fluxes, and durations at different times have fat tails with a $q$-Gaussian form. The $q$ values in the $q$-Gaussian distributions are approximately steady and independent of the temporal interval scale adopted, implying a scale-invariant structure of SGRs. These features indicate that SGR bursts may be governed by a self-organizing criticality (SOC) process, confirming previous findings. Very recently, 1652 independent bursts from FRB 121102 have been detected by the Five-hundred-meter Aperture Spherical radio Telescope (FAST). Here we also investigate the scale-invariant structure of FRB 121102 based on the latest observations of FAST, and show that FRB 121102 and SGRs share similar statistical properties. Given the bimodal energy distribution of FRB 121102 bursts, we separately explore the scale-invariant behaviors of low- and high-energy bursts of FRB 121102. We find that the $q$ values of low- and high-energy bursts are different, which further strengthens the evidence of the bimodality of the energy distribution. Scale invariance in both the high-energy component of FRB 121102 and SGRs can be well explained within the same physical framework of fractal-diffusive SOC systems.