Self-organized Criticality across 13 Orders of Magnitude in the Solar–Stellar Connection - Markus J. Aschwanden; Carolus J. Schrijver (The Astrophysical Journal)
The observed size distributions of solar and stellar flares 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 α _F  = (9/5) = 1.80 for the flux, and α _E  = (5/3) ≈ 1.67 for the fluence or energy, respectively. In this study, we explore the solar–stellar connection under this aspect, which extends over an unprecedented dynamic range of 13 orders of magnitude between the smallest detected solar nanoflare event ( E _min  = 10 ^24 erg) and the largest superflare ( E _max  = 10 ^37 erg) on solar-like G-type stars, observed with the Kepler mission. The FD-SOC model predicts a scaling law of L  ∝  E ^(2/9) for the length scale L as a function of the flare energy E , which limits the largest flare size to L _max  ≲ 0.14 R _⊙ for solar flares, and L _stellar  ≲ 1.04 R _⊙ for stellar flares on G-type stars. Overall, we conclude that the universality of power laws (and their slopes) is a consequence of SOC properties (fractality, classical diffusion, scale-freeness, volume-flux proportionality), rather than identical physical processes at different wavelengths.