The distribution of flares, statistics of magnetohydrodynamic turbulence and coronal heating

In this paper theoretical evidence in favor of the hypothesis that coronal dissipation occurs in bursts at very small spatial scales is presented. Each individual burst, though unobservable and energetically insignificant, is thought to represent the building block of coronal activity. In this framework, a large number of coherently triggered bursts is what appears as one of the many observed solar atmospheric events (i.e., blinkers, heating events, explosive events, flashes, microflares, flares,...). Histograms of such events, when computed, in terms of total energy, duration and peak luminosity appear to display power-law behavior. Simulations of the energy dissipation in the simplest possible forced magnetohydrodynamic (MHD) system, admitting reconnection events, indeed displays such kind of behavior: dissipative events of varying intensity, size and duration may be defined, whose distributions follow power laws. The meaning of cellular automaton models, introduced to describe the power-law statistics of observed energetic events on the Sun, i.e., solar flares, is then discussed. Finally, a minimal set of constraints necessary to render such automaton models more relevant for the description of dynamic phenomena described by magnetohydrodynamic equations is introduced. (C) 1999 American Institute of Physics. [S1070-664X(99)02711-1].