3D Magnetic Free Energy and Flaring Activity Using 83 Major Solar Flares

In this Letter, we examine the relationship between 3D magnetic free energy (MFE) and flaring activity using 83 major solar flares (M-class and X-class) in nine solar active regions (ARs). For this, we use 998 nonlinear force-free field extrapolations compiled by the “Institute for Space-Earth Environmental Research Database” at Nagoya University. These ARs produced at least three major flares with distinct rising and peak phases of 3D MFE. For each phase, the solar flare occurrence rate (FOR) is calculated as a ratio of the number of flares to the duration. The major results from this study are summarized as follows. First, there is no clear linear correlation (CC = 0.15) between 3D MFE and flare peak flux. Second, the FOR (3.4 day⁻¹) of the rising phase is a little higher than that (3.1 day⁻¹) of the peak phase, depending on AR. Third, for several flares, there are noticeable decreases in 3D MFE, which correspond to the typical energy of a major flare (about 10³² erg). Fourth, it is interesting to note that there are noticeable enhancements in FORs at several local maxima of 3D MFE, which may be associated with flux emergence and/or shearing motions. Fifth, the flare index rates, which are defined as the summation of flaring activity divided by the duration, of rising and peak phases are 151 day⁻¹ and 314 day⁻¹, respectively. Our results imply that the traditional and simple “storage and release” model does not apply to flare activities, and the random perturbation may be important for triggering flares.