The Limit of Magnetic-Shear Energy in Solar Active Regions

It has been found previously, by measuring from active-region magnetograms a proxy of the free energy in the active region's magnetic field, (1) that there is a sharp upper limit to the free energy the field can hold that increases with the amount of magnetic field in the active region, the active region's magnetic flux content, and (2) that most active regions are near this limit when their field explodes in a coronal mass ejection/flare eruption. That is, explosive active regions are concentrated in a main-sequence path bordering the free-energy-limit line in (flux content, free-energy proxy) phase space. Here, we present evidence that specifies the underlying magnetic condition that gives rise to the free-energy limit and the accompanying main sequence of explosive active regions. Using a suitable free-energy proxy measured from vector magnetograms of 44 active regions, we find evidence that (1) in active regions at and near their free-energy limit, the ratio of magnetic-shear free energy to the non-free magnetic energy the potential field would have is of the order of one in the core field, the field rooted along the neutral line, and (2) this ratio is progressively less in active regions progressively farther below their free-energy limit. Evidently, most active regions in which this core-field energy ratio is much less than one cannot be triggered to explode; as this ratio approaches one, most active regions become capable of exploding; and when this ratio is one, most active regions are compelled to explode.