A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. III. The Free Energy
Abstract
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 Efree=EN−EP, i.e., the difference of the magnetic energies between the non-potential field and the potential field. A second method to estimate the free energy is obtained from the mean misalignment angle change Δμ=μP−μN between the potential and non-potential field, which scales as Efree/EP≈tan2(Δμ). For the four active regions observed with STEREO in 2007 we find free energies in the range of qfree=(Efree/EP)≈1 % - 10 %, with an uncertainty of less than ± 2 % between the two methods, while the free energies obtained from 11 other NLFFF codes exhibit a larger scatter of about ± 10 %. We also find 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, FGOES∝exp(qfree/0.015), implying an exponentiation of the dissipated currents.
- Publication:
-
Solar Physics
- Pub Date:
- October 2013
- DOI:
- 10.1007/s11207-012-0203-6
- arXiv:
- arXiv:1211.1708
- Bibcode:
- 2013SoPh..287..369A
- Keywords:
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- Sun: corona;
- Sun: magnetic fields;
- Astrophysics - Solar and Stellar Astrophysics
- E-Print:
- 23 pages, 8 Figures, 1 Table