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The original concept of self-organized criticality (Bak et al.~1987), applied to solar flare statistics (Lu and Hamilton 1991), assumed a slow-driven and stationary flaring rate, which warrants time scale separation (between flare durations and inter-flare waiting times), it reproduces power-law distributions for flare peak fluxes and durations, but predicts an exponential waiting time distribution. In contrast to these classical assumptions we observe: (i) multiple energy dissipation episodes during most flares, (ii) violation of the principle of time scale separation, (iii) a fast-driven and non-stationary flaring rate, (iv) a power law distribution for waiting times $Delta t$, with a slope of $alpha_{Delta t} approx 2.0$, as predicted from the universal reciprocality between mean flaring rates and mean waiting times; and (v) pulses with rise times and decay times of the dissipated magnetic free energy on time scales of $12pm6$ min, up to 13 times in long-duration ($lapprox 4$ hrs) flares. These results are inconsistent with coronal long-term energy storage (Rosner and Vaiana 1978), but require photospheric-chromospheric current injections into the corona.
Power law size distributions are the hallmarks of nonlinear energy dissipation processes governed by self-organized criticality. Here we analyze 75 data sets of stellar flare size distributions, mostly obtained from the {sl Extreme Ultra-Violet Explo
Stars produce explosive flares, which are believed to be powered by the release of energy stored in coronal magnetic field configurations. It has been shown that solar flares exhibit energy distributions typical of self-organized critical systems. Th
X-ray flares have routinely been observed from the supermassive black hole, Sagittarius A$^star$ (Sgr A$^star$), at our Galactic center. The nature of these flares remains largely unclear, despite of many theoretical models. In this paper, we study t
Shortly after the seminal paper {sl Self-Organized Criticality: An explanation of 1/f noise} by Bak, Tang, and Wiesenfeld (1987), the idea has been applied to solar physics, in {sl Avalanches and the Distribution of Solar Flares} by Lu and Hamilton (
We explore upper limits for the largest avalanches or catastrophes in nonlinear energy dissipation systems governed by self-organized criticality (SOC). We generalize the idealized straight power low size distribution and Pareto distribution function