The Maximum Free Magnetic Energy Allowed in a Solar Active Region

Two whole-active-region magnetic quantities that can be measured from a line-of-sight magnetogram are (sup L) WL(sub SG), a gauge of the total free energy in an active region's magnetic field, and sup L(sub theta), a measure of the active region's total magnetic flux. From these two quantities measured from 1865 SOHO/MDI magnetograms that tracked 44 sunspot active regions across the 0.5 R(sub Sun) central disk, together with each active region's observed production of CMEs, X flares, and M flares, Falconer et al (2009, ApJ, submitted) found that (1) active regions have a maximum attainable free magnetic energy that increases with the magnetic size (sup L) (sub theta) of the active region, (2) in (Log (sup L)WL(sub SG), Log(sup L) theta) space, CME/flare-productive active regions are concentrated in a straight-line main sequence along which the free magnetic energy is near its upper limit, and (3) X and M flares are restricted to large active regions. Here, from (a) these results, (b) the observation that even the greatest X flares produce at most only subtle changes in active region magnetograms, and (c) measurements from MSFC vector magnetograms and from MDI line-of-sight magnetograms showing that practically all sunspot active regions have nearly the same area-averaged magnetic field strength: =- theta/A approximately equal to 300 G, where theta is the active region's total photospheric flux of field stronger than 100 G and A is the area of that flux, we infer that (1) the maximum allowed ratio of an active region's free magnetic energy to its potential-field energy is ~1, and (2) any one CME/flare eruption releases no more than a small fraction (less than ~10%) of the active region's free magnetic energy. This work was funded by NASA's Heliophysics Division and NSF's Division of Atmospheric Sciences.