Statistical study of free magnetic energy and flare productivity of solar active regions

TL;DR

This study analyzes the relationship between free magnetic energy in solar active regions and their flare productivity, finding weak correlation and limited predictive improvement over magnetic flux alone.

Contribution

It provides a large-scale statistical analysis of free magnetic energy's role in solar flare prediction using over 3000 magnetograms from 61 active regions.

Findings

Weak correlation (<60%) between free magnetic energy and flare index.

FME offers slightly better flare prediction than magnetic flux.

Limited improvement in predicting individual flare activity.

Abstract

Photospheric vector magnetograms from Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory are utilized as the boundary conditions to extrapolate both non-linear force-free and potential magnetic fields in solar corona. Based on the extrapolations, we are able to determine the free magnetic energy (FME) stored in active regions (ARs). Over 3000 vector magnetograms in 61 ARs were analyzed. We compare FME with ARs' flare index (FI) and find that there is a weak correlation ($<60\%$) between FME and FI. FME shows slightly improved flare predictability relative to total unsigned magnetic flux of ARs in the following two aspects: (1) the flare productivity predicted by FME is higher than that predicted by magnetic flux and (2) the correlation between FI and FME is higher than that between FI and magnetic flux. However, this improvement is not significant enough to make a substantial difference in time-accumulated FI, rather than individual flare, predictions.