Abstract
It has been widely conjectured that solar flares are energized by the magnetic energy stored in complex active regions. Paradoxically, however, in attempting to show that magnetic changes cause or characterize flares, solar magnetic observations have produced equivocal results.
In previous attempts at resolving the paradox, it has been contended that magnetic measurements are simply imprecise or that magnetic theories of flares are incorrect. We present an alternative explanation: the present use of magnetograms to examine active region structure through numerical integration of miscellaneous field lines (under various force-free assumptions) provides qualitative information only and does not utilize the quantitative information available. Therefore, we propose a new approach to the analysis of magnetograms which is illustrated with a highly symmetrized example that permits integration in closed form. The proposed approach exploits the cellular structure of the flux of field lines present in a complex active region. The various topological connectivities distinguish parent and daughter flux cells. A function F is developed expressing the flux partitioned into the daughter cell of interconnected field lines in a potential field. This F is a function of the location, strength, and relative motions of the photospheric sources. Then dF/dt is used as an EMF in the direct calculation of the stored magnetic energy available for flare production. In carrying out this program the flux partitioning surface (separatrix) is calculated along with its line of self-intersection (separator). The separator is the location of the principal energy release site.
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Baum, P.J., Bratenahl, A., Crockett, G. et al. Magnetic flux of colinear bipolar spot pairs. Sol Phys 62, 53–67 (1979). https://doi.org/10.1007/BF00150131
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DOI: https://doi.org/10.1007/BF00150131