A comparison between statistical properties of solar X-ray flares and avalanche predictions in cellular automata statistical flare models

Abstract

We perform a tentative comparison between the statistical properties of cellular automata statistical flare models including a highly variable non-linear external driver and the respective properties of the WATCH flare data base, constructed during the maximum of solar cycle 21. The model is based on the concept of SelfOrganized Criticality (SOC). The frequency distributions built on the measured X-ray flare parameters show the following characteristics: (1) The measured parameters (total counts, peak count-rates and, to a lesser extent, total duration) are found to be correlated to each other. Overall distribution functions of the first two parameters are robust power laws extending over several decades. The total duration distribution function is represented by either two power laws or a power law with an exponential roll-over. (2) By sub-grouping the peak count-rate and the total counts as functions of duration and constructing frequency distributions on these sub-groups, it is found that the slope systematically decreases with increasing duration. (3) No correlation is found between the elapsed time interval between successive bursts arising from the same active region and the peak intensity of the flare. Despite the inherent weaknesses of the SOC models to simulate realistically a number of physical processes thought to be at work in solar active regions and in flares’ energy release, we show that the model is able to reproduce the bulk of the above statistical properties. We thus underline two main conclusions: (i) A global, statistical approach for the study of rapid energy dissipation and magnetic field line annihilation in complex, magnetized plasmas may be of equal importance with the localized, small-scale Magnetohydrodynamic (MHD) simulations, and (ii) refined SOC models are needed to establish a more physical connection between the cellular automata evolution rules and the observations.