Magnetic Energy and Helicity Budgets in the ActiveRegion Solar Corona. II. Nonlinear ForceFree Approximation 

Manolis K. Georgoulis Submitted: 20120926 02:44
Expanding on an earlier work that relied on linear forcefree magnetic fields, we selfconsistently derive the instantaneous free magnetic energy and relative magnetic helicity budgets of an unknown threedimensional nonlinear forcefree magnetic structure extending above a single, known lowerboundary magnetic field vector. The proposed method does not rely on the detailed knowledge of the threedimensional field configuration but is general enough to employ only a magnetic connectivity matrix on the lower boundary. The calculation yields a minimum free magnetic energy and a relative magnetic helicity consistent with this free magnetic energy. The method is directly applicable to photospheric or chromospheric vector magnetograms of solar active regions. Upon validation, it basically reproduces magnetic energies and helicities obtained by wellknown, but computationally more intensive and nonunique, methods relying on the extrapolated threedimensional magnetic field vector. We apply the method to three active regions, calculating the photospheric connectivity matrices by means of simulated annealing, rather than a modeldependent nonlinear forcefree extrapolation. For two of these regions we correct for the inherent linear forcefree overestimation in free energy and relative helicity that is larger for larger, more eruptive, active regions. In the third studied region, our calculation can lead to a physical interpretation of observed eruptive manifestations. We conclude that the proposed method, including the proposed inference of the magnetic connectivity matrix, is practical enough to contribute to a physical interpretation of the dynamical evolution of solar active regions.
Authors: M. K. Georgoulis, K. Tziotziou, & N.E. Raouafi
Projects: Hinode/SOT

Publication Status: ApJ, in press
Last Modified: 20120926 09:10


