Fractal and Multifractal Properties of Active Regions as Flare Precursors: A Case Study Based on SOHO/MDI and SDO/HMI Observations

Abstract

Several studies indicate that fractal and multifractal parameters inferred from solar photospheric magnetic field measurements may help assessing the eruptive potential of Active Regions (ARs) and also predicting their flare activity. We further investigate this topic, by exploring the sensitivity of some parameters already used in the literature on data and methods employed for their estimation. In particular, we measured the generalized fractal dimensions D 0 and D 8, and the multifractal parameters C div and D div, on the time series of photospheric magnetograms of the flaring AR NOAA 11158 obtained with the SOHO/MDI and SDO/HMI. The observations by the latter instrument are characterized by a higher spatial and temporal resolution, as well as higher flux sensitivity, than the ones obtained from SOHO/MDI, which were widely employed in earlier studies. We found that the average and peak values of complexity parameters measured on the two data sets agree within measurement uncertainties. The temporal evolution of the parameters measured on the two data sets show rather similar trends, but the ones derived from the SOHO/MDI observations show larger and spurious variations over time than those deduced from analysis of the corresponding SDO/HMI data. We also found a larger sensitivity of these measurements to characteristics of the data analyzed than reported by earlier studies. In particular, analysis of the higher resolution and higher cadence SDO/HMI data allows us also to detect slight variations of the complexity indicators that cannot be derived from the analysis of the SOHO/MDI data. These variations occur right after the major events in the analyzed AR. They may be the signature of photospheric effects of coronal magnetic field re-arrangement.