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What Affects the Power-Law Distribution of the X-Ray Solar Flares? A Theoretical Study Based on a Model of Uniform Normal Field

The power-law distribution of the X-ray solar flares has long been observed, supporting the idea that the solar corona is in a state of self-organized criticality. In this paper, we used a model that simulates the complex relaxation of the coronal magnetic field to study the conditions that affect (1) the very existence of the power-law distribution; and (2) the exponent of the power law. The model consists of a large number of flux tubes arranged in a two-dimensional, square-lattice fashion that undergoes relaxation as any local current exceeds a threshold. We have found that a necessary condition for our model to exhibit a power-law distribution is the conservation of the relative magnetic helicity. The exponent of the power-law distribution is slightly affected by the rule of relaxation chosen, but it is quite insensitive to the pattern of boundary perturbation and the variation of the boundary helicity injection. The power-law exponent is found to be in the range 1.25-1.35.