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A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops III. The Free Energy View all abstracts by submitter

Markus J. Aschwanden   Submitted: 2012-11-15 08:03

An analytical approximation of a nonlinear force-free magnetic field (NLFFF) solution was developed in Paper I, while a numerical code that performs fast forward-fitting of this NLFFF approximation to a line-of-sight magnetogram and coronal 3D loops has been described and tested in Paper II. Here we calculate the free magnetic energy E m free=E m N-E m P, ie the difference of the magnetic energies between the nonpotential field and the potential field. A second method to estimate the free energy is obtained from the mean misalignment angle change Deltamu=mu m P-mu m N between the potential and nonpotential field, which scales as E m free/E m P approx an^2{(Deltamu)}. For four active regions observed with STEREO in 2007 we find free energies in the range of q m free=(E m free/E m P) approx 1%-10%, with an uncertainty of less than pm 2% between the two methods, while the free energies obtained from 11 other NLFFF codes exhibit a larger scatter of order approxpm10%. We find also a correlation between the free magnetic energy and the GOES flux of the largest flare that occurred during the observing period, which can be quantified by an exponential relationship, F m GOES propto exp{(q m free/0.015)}, implying an exponentiation of the dissipated currents.

Authors: Markus J. Aschwanden
Projects: STEREO

Publication Status: Solar Physics (in press)
Last Modified: 2012-11-20 20:25
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