Are Solar Active Regions with Major Flares More Fractal, Multifractal, or Turbulent than Others?

Multiple recent investigations of solar magnetic field measurements have raised claims that the scale-free (fractal) or multiscale (multifractal) parameters inferred from the studied magnetograms may help assess the eruptive potential of solar active regions, or may even help predict major flaring activity stemming from these regions. We investigate these claims here, by testing three widely used scale-free and multiscale parameters, namely, the fractal dimension, the multifractal structure function and its inertial-range exponent, and the turbulent power spectrum and its power-law index, on a comprehensive data set of 370 timeseries of active-region magnetograms (17,733 magnetograms in total) observed by SOHO's Michelson Doppler Imager (MDI) over the entire Solar Cycle 23. We find that both flaring and non-flaring active regions exhibit significant fractality, multifractality, and non-Kolmogorov turbulence but none of the three tested parameters manages to distinguish active regions with major flares from flare-quiet ones. We also find that the multiscale parameters, but not the scale-free fractal dimension, depend sensitively on the spatial resolution and perhaps the observational characteristics of the studied magnetograms. Extending previous works, we attribute the flare-forecasting inability of fractal and multifractal parameters to i) a widespread multiscale complexity caused by a possible underlying self-organization in turbulent solar magnetic structures, flaring and non-flaring alike, and ii) a lack of correlation between the fractal properties of the photosphere and overlying layers, where solar eruptions occur. However useful for understanding solar magnetism, therefore, scale-free and multiscale measures may not be optimal tools for active-region characterization in terms of eruptive ability or, ultimately,for major solar-flare prediction.Comment: 25 pages, 7 figures, 2 tables, Solar Phys., in pres

The Origin, Early Evolution and Predictability of Solar Eruptions

Coronal mass ejections (CMEs) were discovered in the early 1970s when space-borne coronagraphs revealed that eruptions of plasma are ejected from the Sun. Today, it is known that the Sun produces eruptive flares, filament eruptions, coronal mass ejections and failed eruptions; all thought to be due to a release of energy stored in the coronal magnetic field during its drastic reconfiguration. This review discusses the observations and physical mechanisms behind this eruptive activity, with a view to making an assessment of the current capability of forecasting these events for space weather risk and impact mitigation. Whilst a wealth of observations exist, and detailed models have been developed, there still exists a need to draw these approaches together. In particular more realistic models are encouraged in order to asses the full range of complexity of the solar atmosphere and the criteria for which an eruption is formed. From the observational side, a more detailed understanding of the role of photospheric flows and reconnection is needed in order to identify the evolutionary path that ultimately means a magnetic structure will erupt