Extrapolation of magnetic fields
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Transcript of Extrapolation of magnetic fields
Extrapolation of magnetic fields
Thomas Wiegelmann
• Why study coronal magnetic fields?
• How to obtain the coronal magnetic field vector?
• Linear and non-linear models.
• Computational implementation and tests.
• Recent problems and possible solutions.
• Evolution of coronal fields and flare prediction.
• Outlook: Coronal plasma and dynamics.
Coronal mass ejections and flares are assumed to occur due to instabilities in the coronal magnetic field configuration.
It is importantto investigatethe coronal
magnetic field
Coronal magnetic Fields: Origin of Space weather
Question:Origin of coronal
eruptions
Solar magneticfield measured
routinely only inphotosphere
Aim: Extrapolate measured photospheric magneticfield into the corona under model assumptions.
Lorentz force
pressure gradient
gravity
How to model the stationary Corona?
Force-freeFields
Low plasmaBeta in corona
Neglect plasma pressure+gravity
Force-Free Fields
Equivalent
• Potential Fields (no currents)• Linear force-free fields
(currents globally proportional to B-field)
Relation between currents and magnetic field.Force-free functions is constant along field lines, but varies between field lines. => nonlinear force-free fields
Further simplifications
Easy to computeRequire only
LOS-Magnetograms
Here: global constant linear force-free parameter
Simple potential field models provide already areasonable estimate regarding the global magneticfield structure. Mainly closed loops in activeregions and open field lines in coronal holes.
Potential Field Model EUV-emission
EIT-image and projections of magnetic
field lines for a potential field (α=0) .(bad agreement)
Linear force-free field with α=+0.01 [Mm-1](bad agreement)
Active RegionsWe use a linear force-free model with MDI-data and have the freedomto choose an appropriate value for the force-free parameter α.
Linear force-free field with α=-0.01 [Mm-1](good agreement)
3D-magnetic field lines, linear force-free α=-0.01 [Mm-1]
NonLinear Force-Free Fields
• Compute initial a potential field (Requires only Bn on bottom boundary)
• Iterate for NLFFF-field, Boundary conditions:- Bn and Jn for positive or negative polarityon boundary (Grad-Rubin)- Magnetic field vector Bx By Bz on boundary (Magnetofrictional, Optimization)
Equivalent
Grad-Rubin methodSakurai 1981, Amari et al. 1997,2006,
Wheatland 2004,06,07
MagnetofrictionalChodura & Schlueter 1981,Valori et al. 2005
OptimizationWheatland et al. 2000,Wiegelmann 2004,2007
Test: Model Active Region(van Ballegooijen et al. 2007, Aad’s model)
Model contains the (not force-free) photospheric magnetic field vector and an almost force-free chromosphere and corona.
Comparison paper, Metcalf et al., Sol. Phys. 2008.-Good agreement for extrapolations from chromosphere.-Poor results for using photospheric data directly.-Improvement with preprocessed photospheric data.
Grad-Rubin
MHD-relaxation
Optimization
Force-Free
B-Field Measurements,non-force-free
Consistency criteria for vectormagnetograms (Aly 1989)
If these relations are NOT fulfilled on the boundary, then the
photospheric data are inconsistent with the force-free assumption.
NO Force-Free-Field.
No net force
No net torque
Photosphere
Smoothness
Preprocessed boundary data
Chromospheric H-alpha preprocessing• H-alpha fibrils outline magnetic field lines.• With image-recognition techniques we get
tangent to the chromospheric magnetic fieldvector (Hx, Hy).
• Idea: include a term in the preprocessing tominimize angle of preprocessed magnetic field (Bx,By) with (Hx,Hy).
Preprocessing of vector magnetograms(Wiegelmann, Inhester, Sakurai, Sol. Phys. 2006)
• Use photospheric field vector as input.• Preprocessing removes non-magnetic
forces from the boundary data.• Boundary is not in the photosphere
(which is NOT force-free).• The preprocessed boundary data
are chromospheric like.
Preprocessing can be improved by including chromospheric observations.
(Wiegelmann, Thalmann, Schrijver, DeRosa, Metcalf,Sol. Phys. 2008)
Prepro-cessing
We test preprocessing with Aad’s model
Angle <B,H> inChromosphere
Force-free coronalmagnetic Energy
No pre-processing 19o 65%
Classical pre-
processing 9o 97%
H-Alpha pre-processing 1o 100%
Results: Comparison with Aad‘s Model
CoronalMagnetic Field
Nonlinear Force-free code
Preprocessing tool
Vectormagnetogram
H-AlphaImage
ChromosphericMagnetic Field
Optional
Measured loops in a newly developed AR (Solanki, Lagg, Woch,Krupp, Collados, Nature 2003)
Potential field reconstruction
Linear force-free reconstruction Non-linear force-free reconstruction
Comparison of observed magnetic loops and extrapolationsfrom photospheric measurements
Nonlinear force-free Models are
superior.
Stereoscopy vs. coronal field extrapolation
Hinode FOV
From DeRosa et al. 2009: Blue lines are stereoscopic reconstructed loops (Aschwanden et al 2008), Red lines nonlinear force-freeextrapolated field lines from Hinode/SOT with MDI-skirt.
Stereoscopy vs. coronal field extrapolation
• Vector magnetogram data (here: Hinode/SOT) areessential for nonlinear force-free field modeling.
• Unfortunately Hinode-FOV covered only a smallfraction (about 10%) of area spanned by loopsreconstructed from STEREO-SECCHI images.
• Quantitative comparison was unsatisfactory,NLFFF-models not better as potential fields here.
• In other studies NLFFF-methods have shown to besuperior to potential and linear force-freeextrapolations. (Comparison with coronal images from one viewpoint, NLFFF-models from ground based data)
Results of NLFFF-workshop 2008• When presented with complete and consistent boundary conditions, NLFFF
algorithms succeed in modeling test fields. • For a well-observed dataset (a Hinode/SOT-SP vector-magnetogram
embedded in MDI data) the NLFFF algorithms did not yield consistent solutions. From this study we conclude that one should not rely on a model-field geometry or energy estimates unless they match coronal observations.
• Successful application to real solar data likely requires at least:1. large model volumes at high resolution that accommodate most of the
connectivity within a region and to its surroundings;2. accommodation of measurement uncertainties (in particular in the transverse
field component) in the lower boundary condition;3. 'preprocessing’ of the lower-boundary vector field that approximates the physics
of the photosphere-to-chromosphere interface as it transforms the observed, forced, photospheric field to a realistic approximation of the high-chromospheric, near-force free field.
• See: Schrijver et al. 2006 (Spy 235, 161), 2008 (ApJ 675, 1637), Metcalf et al. 2008 (SPh 247, 269), DeRosa et al. (2009, ApJ 696, 1780).
Temporal Evolution of Active RegionsUse time series of ground based vector magnetograms with sufficient large FOV (Solar Flare Telescope, SOLIS).
Flaring AR-10540(Thalmann & Wiegelmann A&A 2008)
Active Region-10960
Solar X-ray flux. Vertical blue lines: vector magnetograms available
Magnetic field extrapolationsfrom Solar Flare telescope
Extrapolated from SOLISvector magnetograph
M6.1 Flare
Magneticenergy builds
up and isreleases during
flare
Comparison of two Active Regions
Conclusions• Potential and linear force-free fields are popular due to their
mathematic simplicity and because only LOS-magnetogramsare needed as input.
• Non-linear force-free fields model coronal magnetic fields more accurately [energy, helicity, topology etc.].
• Nonlinear models are mathematical very challenging and require high quality photospheric vector magnetograms as input.
• We still need to understand the physics of the interface-region between high beta photosphere, where the magnetic field vectoris measured, and the force-free corona.
• Coronal magnetic field models should be compared andvalidated by coronal observations.
Time-dependentMHD-simulations
Self-consistentequilibrium
Artificialimages
LOS-integration
Where to go in corona modeling?
Force-free code
Vectormagnetogram
MHS code
3D Force-freemagnetic field
3D fieldlines
com
pare
Plasma along magnetic
loops
Scaling laws Tomograp
hy
Stereoscopy STEREOimages
3D EUVloops
consistent?