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

TL;DR

This paper explores how solar active regions act as natural laboratories for studying complex magnetic phenomena, revealing self-organized criticality and fractal structures that influence energy release and particle acceleration.

Contribution

It demonstrates that active regions exhibit self-similar fractal structures and follow power-law distributions, supporting models of self-organized criticality in solar magnetic activity.

Findings

Active regions form fractal structures with power-law area distributions.

Energy release follows a power-law distribution with exponent ~1.6-1.8.

Magnetic fields may follow percolation and SOC models.

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.