coronal magnetic fields thomas wiegelmann, mpi for solar-system research, (former: mpi für...
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![Page 1: Coronal magnetic fields Thomas Wiegelmann, MPI for Solar-System Research, (Former: MPI für Aeronomie) Katlenburg-Lindau Why are coronal magnetic fields](https://reader036.vdocuments.us/reader036/viewer/2022081603/56649f2f5503460f94c4889a/html5/thumbnails/1.jpg)
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
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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.
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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 FieldsBJ - Non Linear Force Free FieldsBrJ )(
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Model Mathematics Observationsneeded
Validity
Potential
Fields
Line of sightmagnetogram
(Global) currentfree regions,quiet sun
Linear Force-
Free Fields
LOS magnetogram
+ observations ofplasma structures
Local in activeregions, low-betaplasma
Non Linear Force-Free
Vectormagnetogram
(3 times more data,ambiguities, noise)
Active regions,low beta plasmain low corona
MHS
Equilibrium
Vectormagnetogram
+ Tomographic Inversion of density
Helmet streamer,finite beta plasma,full solar corona
Coronal magnetic field models
0
)()( 0
B
pBB
0
)(
B
BrB
0
B
BB 0
0
B
B
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Global Potential Field reconstruction
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Linear Force-Free Fields
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Linear Force-Free Fields
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Linear Force-Free Fields
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Linear Force-Free Fields
EIT-image and projected magnetic field lines.(α · L=2)
3D magnetic field lines withKitt Peak magnetogram
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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.)
BrJ )(
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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.
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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 reconstructed
selfconsistently (MHS-equations + observational data).
2,
,,
322
320
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||
|)()(|),(
NIIxdBB
xdmNNTkBBNBL
Modelip
ip
obsip
V
V
B
0
)()( 0
B
pBB
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Magnetic fields and coronal tomographya) Use only line of
sight density integrals.
b) Use only magneticfield data.
c) Use both line of sightdensity integrals andmagnetic field as regularization operator.
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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.