A macroscopic description of a generalized self-organized criticality system: Astrophysical applications
We suggest a generalized definition of self-organized criticality (SOC) systems: SOC is a critical state of a nonlinear energy dissipation system that is slowly and continuously driven toward a critical value of a system-wide instability threshold, producing scale-free, fractal-diffusive, and intermittent avalanches with power law-like size distributions. We develop here a macroscopic description of SOC systems that provides an equivalent description of the complex microscopic fine structure, in terms of fractal-diffusive transport (FD-SOC). Quantitative values for the size distributions of SOC parameters (length scales L, time scales T, waiting times Δt, fluxes F, and fluences or energies E) are derived from first principles, using the scale-free probability conjecture, N(L)dL∝L {sup –d}, for Euclidean space dimension d. We apply this model to astrophysical SOC systems, such as lunar craters, the asteroid belt, Saturn ring particles, magnetospheric substorms, radiation belt electrons, solar flares, stellar flares, pulsar glitches, soft gamma-ray repeaters, black-hole objects, blazars, and cosmic rays. The FD-SOC model predicts correctly the size distributions of 8 out of these 12 astrophysical phenomena, and indicates non-standard scaling laws and measurement biases for the others.