On the distribution of magnetic energy storage in solar active regions

A two-dimensional probabilistic Cellular Automaton is used to model the appearance of active regions at the solar surface. We assume that two main competing processes control the magnetic field evolution at the solar surface (1) the magnetic field is locally enhanced by the flux emergence and/or the coalescence of emerged magnetic flux and (2) it is diminished by flux cancellation or diffusion. The flux emergence follows a basic percolation rule; it is more probable at the points were magnetic flux already exists. The magnetic field is also enhanced when magnetic fields of the same polarity collide. The flux cancellation is due either to the gradual diffusion of the magnetic field, when it is isolated, or to the partial release of energy when opposite magnetic field lines collide. The percolation model proposed in this article is capable of reproducing the statistical properties of the evolving active regions. The evolving simulated magnetograms, derived from our model, are used to estimate the 3-D magnetic fields above the photosphere using constant α force-free extrapolation techniques. Based on the above analysis we are able to estimate a variety of observed statistical characteristics, e.g. the size and flux distribution of the magnetic fields at the solar surface, the fractal dimension of the magnetic structures formed at the photosphere, the energy release frequency distribution, the waiting time distribution of the sporadic energy releases and the statistical properties of the steep horizontal magnetic field gradients in the extrapolated coronal magnetic field. Our main conclusion is that the photospheric driver plays a crucial role in the observed flare statistics, and the solar magnetograms, when interpreted properly, carry important statistical information for the solar coronal activity (coronal heating, flares, CME etc.).