# The Signature of Flare Activity in Multifractal Measurements of Active Regions Observed by SDO/HMI

## TL;DR

This study evaluates whether multifractal parameters of active regions can predict flare activity, finding limited discriminative power and significant overlap in parameters across different flare classes, even with high-resolution data.

## Contribution

It provides a comprehensive analysis of high-resolution SDO/HMI data, showing that multifractal parameters are not effective predictors of flare activity across different classes.

## Key findings

- Parameters show distinct averages for different flare classes but overlap significantly.
- No reliable distinction between flare classes based on multifractal parameters.
- Results are consistent across unsigned and signed flux data.

## Abstract

Recent studies indicate that measurements of fractal and multifractal parameters of active regions (ARs) are not efficient tools to discriminate ARs on the basis of the flare activity, as well as to predict flare events. Attempting validation of this result on a large data set of higher spatial and temporal resolution, as well as higher flux sensitivity, observations than employed in previous studies, we analyzed high-cadence time series of line-of-sight magnetograms of 43 ARs characterized by different flare activity, which were observed with SDO/HMI from May 2010 to December 2013. On these data, we estimated four parameters, the generalized fractal dimensions $D_0$ and $D_8$, and the multifractal parameters $C_{\mathrm{div}}$ and $D_{\mathrm{div}}$. We found distinct average values of the parameters measured on ARs that have hosted flares of different class. However, the dispersion of values measured on ARs that have produced same class events is such that the parameters deduced from distinct classes of flaring regions can also largely overlap. Based on the results of our measurements, C- and M-class flaring ARs are practically indistinguishable, as well as M- and X-class flaring ARs. We found consistent changes on the time series of the measured parameters only on $\approx$ 50\% of the studied ARs and $\approx$ 50\% of the M- and X-class events considered. We show that these results hold for fractal and multifractal parameter estimates based on both total unsigned and signed flux data of the analyzed ARs.