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

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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 E free=E NE P, 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=μ Pμ N between the potential and non-potential field, which scales as E free/E P≈tan2μ). For the four active regions observed with STEREO in 2007 we find free energies in the range of q free=(E free/E P)≈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, F GOES∝exp(q free/0.015), implying an exponentiation of the dissipated currents.

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Acknowledgements

The author appreciates the provided data and helpful discussions with Anna Malanushenko and Marc L. DeRosa. Part of the work was supported by NASA contract NNG 04EA00C of the SDO/AIA instrument and the NASA STEREO mission under NRL contract N00173-02-C-2035.

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Correspondence to Markus J. Aschwanden.

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Solar Dynamics and Magnetism from the Interior to the Atmosphere

Guest Editors: R. Komm, A. Kosovichev, D. Longcope, and N. Mansour

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Aschwanden, M.J. A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. III. The Free Energy. Sol Phys 287, 369–389 (2013). https://doi.org/10.1007/s11207-012-0203-6

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Keywords

  • Sun: corona
  • Sun: magnetic fields