Solar Physics

, Volume 247, Issue 2, pp 269–299 | Cite as

Nonlinear Force-Free Modeling of Coronal Magnetic Fields. II. Modeling a Filament Arcade and Simulated Chromospheric and Photospheric Vector Fields

  • Thomas R. Metcalf
  • Marc L. DeRosa
  • Carolus J. SchrijverEmail author
  • Graham Barnes
  • Adriaan A. van Ballegooijen
  • Thomas Wiegelmann
  • Michael S. Wheatland
  • Gherardo Valori
  • James M. McTtiernan
Open Access


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.


Nonlinear force-free field modeling Solar magnetic field Coronal magnetic field Methods: numerical 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Thomas R. Metcalf
    • 1
  • Marc L. DeRosa
    • 2
  • Carolus J. Schrijver
    • 2
    Email author
  • Graham Barnes
    • 1
  • Adriaan A. van Ballegooijen
    • 3
  • Thomas Wiegelmann
    • 4
  • Michael S. Wheatland
    • 5
  • Gherardo Valori
    • 6
  • James M. McTtiernan
    • 7
  1. 1.Northwest Research AssociatesColorado Research Associates DivisionBoulderUSA
  2. 2.Lockheed Martin Advanced Technology Center, Dept. ADBSPalo AltoUSA
  3. 3.Smithsonian Astrophysical ObservatoryCambridgeUSA
  4. 4.Max Planck Institut für SonnensystemforschungKatlenburg-LindauGermany
  5. 5.School of PhysicsUniversity of SydneySydneyAustralia
  6. 6.Astrophysical Institute PotsdamPotsdamGermany
  7. 7.Space Sciences LaboratoryUniversity of CaliforniaBerkeleyUSA

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