Solar flares and avalanches in driven dissipative systems

The contention of Lu and Hamilton (1991) that the energy release process in solar flares can be understood as avalanches of many small reconnection events is further developed. The dynamics of the complex magnetized plasma of solar active regions is modeled with a simple driven dissipative system, consisting of a vector field with local instabilities that cause rapid diffusion of the field. It is argued that the avalanches in this model are analogous to solar flares. The distributions of avalanches in this model are compared with the solar flare frequency distributions obtained from ISEE 3/ICE satellite observations. Quantitative agreement is found with the energy, peak luminosity, and duration distributions over four orders of magnitude in flare energy, from the largest flares down to the completeness limit of the observations. It is predicted that the power-law solar flare frequency distributions will be found to continue downward with the same logarithmic slopes to an energy of about 3 x 10 exp 25 ergs and duration of about 0.3 s, with deviations from power-law behavior below these values.