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. Eac h individual burst, though unobservable and energetically insignificant, is thought to represent the building block of coronal activity. In this frame work, a large number of coherently triggered bursts is what appears as one of the many observed solar atmospheric events (i.e., blinkers, heating even ts, explosive events, flashes, microflares, flares,...). Histograms of such events, when computed, in terms of total energy, duration and peak luminos ity appear to display power-law behavior. Simulations of the energy dissipa tion in the simplest possible forced magnetohydrodynamic (MHD) system, admi tting reconnection events, indeed displays such kind of behavior: dissipati ve events of varying intensity, size and duration may be defined, whose dis tributions follow power laws. The meaning of cellular automaton models, int roduced to describe the power-law statistics of observed energetic events o n the Sun, i.e., solar flares, is then discussed. Finally, a minimal set of constraints necessary to render such automaton models more relevant for th e description of dynamic phenomena described by magnetohydrodynamic equatio ns is introduced. (C) 1999 American Institute of Physics. [S1070-664X(99)02 711-1].