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Theory of quadrupolar sunspots and the active region of August, 1972 |
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| Authors: | Hai-Shou Yang Hou-Mei Chang J W Harvey |
| Institution: | 1. The University of Alabama in Huntsville, 35899, Huntsville, AL, U.S.A. 2. Visiting Professor from the Astrophysics Division, Geophysics Department, Beijing University, Beijing, People's Republic of China 3. Kitt Peak National Observatory, 85726, Tucson, AZ, U.S.A. |
| Abstract: | Energy is stored when the force-free magnetic field in an active region departs from a potential field, the departure showing up as a shear in the field. As soon as the field untwists, energy will be released to produce flares. Based on this idea, we derived an analytical solution of the equation of force-free field under the assumption of a constant force-free factor, and found expressions for seven important quantities for quadrupolar sunspots: the magnetic energy of the twisted field, that of potential field, the extractable free energy ΔM, the magnetic flux, the total current, the force-free factor and the field decay factor, in terms of three observables: the field intensity, the twist angle and the distance between two spots of the same polarity. The expression for ΔM can be useful in solar prediction work. For the active region of August, 1972, we found ΔM up to 6 × 1032 erg, sufficient to supply the energy of the observed flare activity. Observations of this active region are in good general agreement with our theoretical expectations: in the entire twisting of the quadrupolar sunspot group, each spot assumes the form of a complete spiral in the clockwise direction for each of the four spots. |
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