A Reconnection Model for the Distribution of Flare Energies

Abstract

A physically based explanation is given for the distribution of flare energies N(E)∼E ^−α where α≃1.5. In contrast to previous approaches, the present treatment is based on a physical theory of the flare reconnection site. The central assumption is that topological flare energy, although released explosively, is slowly accumulated over several hundred Alfvén timescales. When coupled to the geometric properties of the reconnective flare source, this assumption is shown to lead naturally to a deduction of the flare energy distribution. Current sheet models yield the exponent $\alpha = \frac{3}{2}$ whereas more compact current structures imply steeper spectra $\frac{3}{2} \leqslant \alpha \leqslant 2$.