On the Self-similarity of Unstable Magnetic Discontinuities in Solar Active Regions

We investigate the statistical properties of possible magnetic discontinuities in two solar active regions over the course of several hours. We use linear force-free extrapolations to calculate the three-dimensional magnetic structure in the active regions. Magnetic discontinuities are identified using various selection criteria. Independently of the selection criterion, we identify large numbers of magnetic discontinuities whose free magnetic energies and volumes obey well-formed power-law distribution functions. The power-law indices for the free energies are in the range [ 1.6, 1.35], in remarkable agreement with the power-law indices found in the occurrence frequencies of solar flare energies. This agreement and the strong self-similarity of the volumes that are likely to host flares suggest that the observed statistics of flares may be the natural outcome of a preexisting spatial selforganization accompanying the energy fragmentation in solar active regions. We propose a dynamical picture of flare triggering consistent with recent observations by reconciling our results with the concepts of percolation theory and self-organized criticality. These concepts rely on self-organization, which is expected from the fully turbulent state of the magnetic fields in the solar atmosphere. Subject headings: Sun: activity — Sun: flares — Sun: magnetic fields