Quantifying the Evolving Magnetic Structure of Active Regions

The topical and controversial issue of parameterizing the magnetic structure of solar active regions has vital implications in the understanding of how these structures form, evolve, produce solar flares, and decay. This interdisciplinary and ill-constrained problem of quantifying complexity is addressed by using a two-dimensional wavelet transform modulus maxima (WTMM) method to study the multifractal properties of active region photospheric magnetic fields. The WTMM method provides an adaptive space-scale partition of a fractal distribution, from which one can extract the multifractal spectra. The use of a novel segmentation procedure allows us to remove the quiet Sun component and reliably study the evolution of active region multifractal parameters. It is shown that prior to the onset of solar flares, the magnetic field undergoes restructuring as Dirac-like features (with a Hölder exponent, h = -1) coalesce to form step functions (where h = 0). The resulting configuration has a higher concentration of gradients along neutral line features. We propose that when sufficient flux is present in an active region for a period of time, it must be structured with a fractal dimension greater than 1.2, and a Hölder exponent greater than -0.7, in order to produce M- and X-class flares. This result has immediate applications in the study of the underlying physics of active region evolution and space weather forecasting.