Solar and Stellar Active Regions:Cosmic laboratories for the study of Complexity

Abstract

Solar active regions are driven dissipative dynamical systems. The turbulent convection zone forces new magnetic flux tubes to rise above the photosphere and shuffles the magnetic fields which are already above the photosphere. The driven 3D active region responds to the driver with the formation of Thin Current Sheets in all scales and releases impulsively energy, when special thresholds are met, on the form of nano-, micro-, flares and large scale coronal mass ejections. It has been documented that active regions form self similar structures with area Probability Distribution Functions (PDF's) following power laws and with fractal dimensions ranging from $1.2-1.7$. The energy release on the other hand follows a specific energy distribution law $f(E_T)\sim E_T^{-a}$, where $a \sim 1.6-1.8$ and $E_T$ is the total energy released. A possible explanation for the statistical properties of the magnetogrms and the energy release by the active region is that the magnetic field formation follows rules analogous to \textbf{percolating models}, and the 3D magnetic fields above the photosphere reach a \textbf{Self Organized Critical (SOC) state}. The implications of these findings on the acceleration of energetic particles during impulsive phenomena will briefly be outlined.