The Fractality and Size Distributions of Astrophysical Self-Organized Criticality Systems

Abstract

The statistics of nonlinear processes in avalanching systems, based on the self-organized criticality (SOC) concept of Bak et al. (1988), predicts power-law-like size (or occurrence frequency) distribution functions. Following up on previous work, we define a standard SOC model in terms of six assumptions: (i) area fractality, (ii) volume fractality, (iii) the flux–volume proportionality, (iv) classical diffusion, (v) the Euclidean maximum at the event peak time, and (vi) the spatiotemporal fluence or energy of an avalanche event. We gather data of the fractal dimension and power-law slopes from 162 publications and assemble them in 28 groups (for instance, solar flare energies, or stellar flare energies), from which we find that 75% of the groups are consistent with the standard SOC model. Alternative SOC models (Lévy flight, flat-world, nonfractal) are slightly less correlated with the data. Outliers are attributed to small number statistics, background definition problems, inadequate fitting ranges, and deviations from ideal power laws.