Nonlinear Force-Free Modeling of Coronal Magnetic Fields. II. Modeling a Filament Arcade and Simulated Chromospheric and Photospheric Vector Fields |
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| Authors: | Thomas R Metcalf Marc L DeRosa Carolus J Schrijver Graham Barnes Adriaan A van Ballegooijen Thomas Wiegelmann Michael S Wheatland Gherardo Valori James M McTtiernan |
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| Institution: | (1) Northwest Research Associates, Colorado Research Associates Division, 3380 Mitchell Ln., Boulder, CO 80301, USA;(2) Lockheed Martin Advanced Technology Center, Dept. ADBS, Bldg. 252, 3251 Hanover St., Palo Alto, CA 94304, USA;(3) Smithsonian Astrophysical Observatory, 60 Garden St., Cambridge, MA 02138, USA;(4) Max Planck Institut für Sonnensystemforschung, Katlenburg-Lindau, Germany;(5) School of Physics, University of Sydney, Sydney, NSW, 2006, Australia;(6) Astrophysical Institute Potsdam, 14482 Potsdam, Germany;(7) Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA |
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| Abstract: | We compare a variety of nonlinear force-free field (NLFFF) extrapolation algorithms, including optimization, magneto-frictional,
and Grad – Rubin-like codes, applied to a solar-like reference model. The model used to test the algorithms includes realistic
photospheric Lorentz forces and a complex field including a weakly twisted, right helical flux bundle. The codes were applied
to both forced “photospheric” and more force-free “chromospheric” vector magnetic field boundary data derived from the model.
When applied to the chromospheric boundary data, the codes are able to recover the presence of the flux bundle and the field’s
free energy, though some details of the field connectivity are lost. When the codes are applied to the forced photospheric
boundary data, the reference model field is not well recovered, indicating that the combination of Lorentz forces and small
spatial scale structure at the photosphere severely impact the extrapolation of the field. Preprocessing of the forced photospheric
boundary does improve the extrapolations considerably for the layers above the chromosphere, but the extrapolations are sensitive
to the details of the numerical codes and neither the field connectivity nor the free magnetic energy in the full volume are
well recovered. The magnetic virial theorem gives a rapid measure of the total magnetic energy without extrapolation though,
like the NLFFF codes, it is sensitive to the Lorentz forces in the coronal volume. Both the magnetic virial theorem and the
Wiegelmann extrapolation, when applied to the preprocessed photospheric boundary, give a magnetic energy which is nearly equivalent
to the value derived from the chromospheric boundary, but both underestimate the free energy above the photosphere by at least
a factor of two. We discuss the interpretation of the preprocessed field in this context. When applying the NLFFF codes to
solar data, the problems associated with Lorentz forces present in the low solar atmosphere must be recognized: the various
codes will not necessarily converge to the correct, or even the same, solution.
On 07/07/2007, the NLFFF team was saddened by the news that Tom Metcalf had died as the result of an accident. We remain grateful
for having had the opportunity to benefit from his unwavering dedication to the problems encountered in attempting to understand
the Sun’s magnetic field; Tom had completed this paper several months before his death, leading the team through the many
steps described above. |
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| Keywords: | Nonlinear force-free field modeling Solar magnetic field Coronal magnetic field Methods: numerical |
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