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 Self-Organized 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
compex, 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.
Subject headings: Sun: activity - Sun: corona - Sun: flares -
Sun: magnetic fields - Sun: X-rays
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