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

We perform a tentative comparison between the statistical properties of cel lular automata statistical flare models including a highly variable non-lin ear external driver and the respective properties of the WATCH flare data b ase, constructed during the maximum of solar cycle 21. The model is based o n the concept of Self-Organized Criticality (SOC): The frequency distributi ons built on the measured X-ray flare parameters show the following charact eristics: (1) The measured parameters (total counts, peak count-rates and, to a lesser extent, total duration) are found to be correlated to each othe r. Overall distribution functions of the first two parameters are robust po wer laws extending over several decades. The total duration distribution fu nction is represented by either two power laws or a power lavi with an expo nential roll-over. (2) By sub-grouping the peak count-rate and the total co unts as functions of duration and constructing frequency distributions on t hese sub-groups, it is found that the slope systematically decreases with i ncreasing duration. (3) No correlation is found between the elapsed time in terval between successive bursts arising from the same active region and th e peak intensity of the flare. Despite the inherent weaknesses of the SOC m odels to simulate realistically a number of physical processes thought to b e at work in solar active regions and in flares' energy release, we show th at the model is able to reproduce the bulk of the above statistical propert ies. We thus underline two main conclusions: (i) A global, statistical appr oach for the study of rapid energy dissipation and magnetic field line anni hilation in complex, magnetized plasmas may be of equal importance with the localized, small-scale Magnetohydrodynamic (MI-ID) simulations, and (ii) r efined SOC models are needed to establish a more physical connection betwee n the cellular automata evolution rules and the observations.