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Why are coronal magnetic fields important? Models for magnetic field reconstruction.

Coronal magnetic fields Thomas Wiegelmann, MPI for Solar-System Research, (Former: MPI f ü r Aeronomie) Katlenburg-Lindau. Why are coronal magnetic fields important? Models for magnetic field reconstruction. Potential magnetic fields Linear force-free fields Non-linear force-free fields

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Why are coronal magnetic fields important? Models for magnetic field reconstruction.

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  1. Coronal magnetic fieldsThomas Wiegelmann,MPI for Solar-System Research, (Former: MPI für Aeronomie)Katlenburg-Lindau • Why are coronal magnetic fields important? • Models for magnetic field reconstruction. • Potential magnetic fields • Linear force-free fields • Non-linear force-free fields • Magnetic fields and coronal tomography • Conclusions

  2. Why are coronal magnetic fields important? • Magnetic fields couples the solar interior, photosphere and atmosphere. • Magnetic field dominates in the solar corona. (Magnetic pressure >> Plasma pressure). • Knowledge of the coronal B-Field is essentialto understand dynamic phenomena likecoronal mass ejections and flares.

  3. How to obtain coronal B-Fields • Direct measurements are extremely difficult. • Measure B on the photosphere (line of sight Bor vector B) and extrapolate it into the corona. • We need assumptions regarding coronal currents:- No currents  Potential fields-  Linear Force Free Fields •  Non Linear Force Free Fields

  4. Coronal magnetic field models

  5. Global Potential Field reconstruction

  6. Linear Force-Free Fields

  7. Linear Force-Free Fields

  8. Linear Force-Free Fields

  9. Linear Force-Free Fields 3D magnetic field lines withKitt Peak magnetogram EIT-image and projected magnetic field lines. (α · L=2)

  10. Non-linear force-free fields • Why do we need non-linear force-free fields?- In general alpha changes in space.- Potential and linear force-free fields have no free energy to be released during an eruption. • The computation is much more difficult:- Mathematical difficulties due to non-linearity.- Vector magnetograms have ambiguities.- Transversal B-field is very noisy.- Limited field of view for current instruments. (Soon: Full disc vector magnetograph SOLIS.)

  11. Non-linear force-free fields Potential field and non-linear force free reconstruction of a model active region regarding the same line of sight photospheric magnetic field. Our optimization code reconstructs the original analytic solution within the discretisation error.

  12. Magnetic fields and coronal tomography • Coronal tomography uses line of sight integrals of the coronal density from different viewpoints. • Aim: 3D reconstruction of coronal density structure. • Density and magnetic field have to be reconstructedselfconsistently (MHS-equations + observational data).

  13. Magnetic fields and coronal tomography • Use only line of sight density integrals. • Use only magneticfield data. • Use both line of sightdensity integrals andmagnetic field as regularization operator.

  14. Conclusions • Potential magnetic fields and linear force free fields are popular due to their mathematic simplicity and available data. (e.g. from MDI on SOHO, Kitt Peak) • Nonlinear force free fields are necessary todescribe active regions exactly. More challenging both observational and mathematical. • A consistent 3D model of the solar corona requirestomographic inversion and magnetic reconstructionin one model.

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