Universal Constants in Self-organized Criticality Systems

The occurrence frequency distributions of fluxes (F) and fluences or energies (E) observed in the majority (in 18 out of 23 cases) of astrophysical phenomena are found to be consistent with the predictions of the fractal-diffusive self-organized criticality (FD-SOC) model, which predicts power-law slopes with universal constants of alpha F = (9/5) = 1.80 for the flux and alpha E = (5/3) approximate to 1.67 for the fluence. The theoretical FD-SOC model is based on the fractal dimension, the flux-volume proportionality, and classical diffusion. The universal scaling laws predict the size distributions of numerous astrophysical phenomena, such as solar flares, stellar flares, coronal mass ejections, auroras, blazars, active galactic nuclei, black hole systems, galactic fast radio bursts, gamma-ray bursts, and soft gamma-ray repeaters. In contrast, we identify five outliers of astrophysical phenomena, i.e., coherent solar radio bursts, random solar radio bursts, solar energetic particles, cosmic rays, and pulsar glitches, which are not consistent with the standard FD-SOC model, and thus require different physical mechanisms.