Statistical and Physical Aspects of Self-Organized Criticality : Solar Flares and Astrophysical Phenomena
Abstract
We develop a quantitative model based on fundamental scaling laws that predicts the powerlaw distributions of self-organized criticality (SOC) systems. The fractal-diffusive SOC model is based on three fundamental relationships: (1) The scale-free probability theorem that determines the distribution of spatial scales depending on the Euclidean dimension of the SOC system; (2) a spatio-temporal relationship that is well-approximated with a diffusion equation; and (3) a physical scaling law between the observable and the geometric avalanche volume. The first two properties have universal validity for SOC processes, while the third property depends on the specific observed physical system. Comparing the theoretical predictions with the observed powerlaws of size distributions in astrophysical systems we find acceptable agreement for the cases of lunar craters, asteroid belts, Saturn rings, outer radiation belt electron bursts, solar flares, soft gamma-ray repeaters, and blazars, if we apply the linear flux-volume scaling law. Discrepancies are found for magnetospheric substorms, stellar flares, pulsar glitches, black holes, and cosmic rays, which apparently require a nonlinear flux-volume scaling. We discuss also the role of turbulence, which is related to the spatial scaling law occurring in SOC systems.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2012
- Bibcode:
- 2012AGUFMNG33A..01A
- Keywords:
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- 4480 NONLINEAR GEOPHYSICS / Self-organized criticality