Solar flares and avalanches in driven dissipative systems

We further develop an idea presented in a previous paper that the energy release process in solar flares can be understood as avalanches of many small reconnection events. We model the dynamics of the complex magnetized plasma of solar active regions with a simple driven dissipative system, consisting of a vector field with local instabilities that cause rapid diffusion of the field. We drive the system on a time scale much longer than the instability time scale and follow the evolution of the vector field and its statistical properties. Although energy is input to the system at a steady rate, it is released in discrete events, or avalanches. We argue that the avalanches in this model are analogous to solar flares. The frequency distributions of energy release events are power laws over a large dynamic range. The distributions of avalanches in this model are compared with the solar flare frequency distributions obtained from ISEE 3/ICE satellite observations. We find quantitative agreement 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. We predict that the power-law solar flare frequency distributions will be found to continue downward with the same logarithmic slopes to an energy of ∼3 x 10²⁵ ergs and duration of ∼0.3 s, with deviations from power-law behavior below these values. These lower limits are the characteristic energy and time scale of an elementary instability, which we find to have a length scale ∼400 km. Our approach provides a new method of understanding the large-scale dynamics of complex magnetized plasmas.