Self-Organized Criticality Across Thirteen Orders of Magnitude in the Solar-Stellar Connection

Abstract

The observed size distributions of solar and stellar flares is 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 $\alpha_E=(5/3)\approx 1.67$ for the fluence, respectively. In this Letter 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 $L \propto E^{(2/9)}$ for the length scale $L$ as a function of the flare energy $E$, which limits the largest flare size to $L_{max} \lapprox 0.14 R_\odot$ for solar flares, and $L_{stellar} \lapprox 1.04\ R_{\odot}$ for stellar flares on G-type stars. In the 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.