Non-Stationary Fast-Driven Self-Organized Criticality in Solar Flares

Abstract

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 \(12\pm6\) 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.