2023ApJ...959..109P

Using the gamma-ray flare samples of the Sun and 3C 454.3 observed by the Fermi telescope, we investigate the statistical properties of sizes including fluence (energy), peak flux (luminosity), duration time, and waiting time in this work. We find that the cumulative distribution of the fluctuations of these sizes follow well the Tsallis q-Gaussian function. The obtained q values from q-Gaussian distribution remain stable around 2 without any significant change, implying that there is a scale invariance structure in gamma-ray flares of the Sun and 3C 454.3. This scale invariance characteristics of the Sun and 3C 454.3 indicated by q values are also comparable to those of earthquakes, soft gamma repeaters, fast radio burst (FRB 20121102), and X-ray flares of gamma-ray bursts. On top of that, we verify the relationship between q values and the power-law indices α from the size frequency distributions, which is expressed as q = (α + 2)/α. These statistical findings could be well explained within the physical framework of a self-organizing criticality system.