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SDO-meetingNapa, 25.-28.03. 2008
Wiegelmann et al: Nonlinear force-free fields
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Nonlinear force-free field modeling for SDO
T. Wiegelmann, J.K. Thalmann, B. Inhesterand the NLFFF-consortium
• Nonlinear Force-Free Fields (NLFFF)• Methods: Grad Rubin, MHD-relaxation, Optimization• Consistency criteria for vector magnetograms and
preprocessing• Evolution of a flaring Active Region• Quick look: energy estimations with Virial Theory• Computational requirements
SDO-meetingNapa, 25.-28.03. 2008
Wiegelmann et al: Nonlinear force-free fields
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Force-free magnetic field
j x B ~ 0
Vector magnetogrammeasurements
from Gary,Sol. Phys. 2001
NOTForce-free
SDO-meetingNapa, 25.-28.03. 2008
Wiegelmann et al: Nonlinear force-free fields
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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 method)- Magnetic field vector Bx By Bz on boundary (MHD-relaxation, Optimization method)
Equivalent
SDO-meetingNapa, 25.-28.03. 2008
Wiegelmann et al: Nonlinear force-free fields
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Grad-Rubin methodAmari et al. 1997,2006, Wheatland 2004,06,07
SDO-meetingNapa, 25.-28.03. 2008
Wiegelmann et al: Nonlinear force-free fields
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MHD-relaxationChodura & Schlueter 1981,Valori et al. 2005
OptimizationWheatland et al. 2000,Wiegelmann 2004
NLFFF-consortium(Schrijver et al. 2006):
Optimization mostaccurate and
fastest method.
SDO-meetingNapa, 25.-28.03. 2008
Wiegelmann et al: Nonlinear force-free fields
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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.
SDO-meetingNapa, 25.-28.03. 2008
Wiegelmann et al: Nonlinear force-free fields
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Preprocessing of vector magnetograms(Wiegelmann, Inhester, Sakurai, Sol. Phys. 2006)
• Use photospheric field vector as input.• Preprocessing provides consistent boundary data
for nonlinear force-free modeling.• 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)
SDO-meetingNapa, 25.-28.03. 2008
Wiegelmann et al: Nonlinear force-free fields
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CoronalMagnetic Field
Nonlinear Force-free code
Preprocessing tool
Vectormagnetogram
H-AlphaImage
ChromosphericMagnetic Field
Optional
SDO-meetingNapa, 25.-28.03. 2008
Wiegelmann et al: Nonlinear force-free fields
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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.
SDO-meetingNapa, 25.-28.03. 2008
Wiegelmann et al: Nonlinear force-free fields
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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
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We have (at least) 3 reliable different NLFFF-codes:• Optimization (Wiegelmann)• Grad-Rubin (Wheatland)• MHD-relaxation (Valori)- Application to Hinode-vectormagnetograms showed
differences in geometry, energy content and force-freeness (Schrijver et al., ApJ, 2008)
- We assume that a main reason for these differences arecaused by the inconsistent Hinode data set: Limited FOV for vector-magnetograms and the assumptionof a potential transverse magnetic field outside theHinode-FOV, which might be a poor assumptionin a flaring Active Region.
- Ground based vector magnetograms with reasonable FOV(SFT, SOLIS) are occasionally available and have beenused to study evolution of Active Regions.
SDO-meetingNapa, 25.-28.03. 2008
Wiegelmann et al: Nonlinear force-free fields
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Flaring Active Region(Thalmann & Wiegelmann 2008)
Quiet Active Region
Solar X-ray flux. Vertical blue lines: vector magnetograms available
Magnetic field extrapolationsfrom Solar Flare telescope
Extrapolated from SOLISvector magnetograph
M6.1 FlareMagneticenergy builds
up and isreleases during
flarePlans:
Study ARswith higher
time cadencewith SDO.
SDO-meetingNapa, 25.-28.03. 2008
Wiegelmann et al: Nonlinear force-free fields
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Quick-look computation: Virial theory(Metcalf et al. 2008)
• Quick computation (only a 2D-integralinstead of 3D-NLFFF-computations)
• Preprocessing of vector magnetograms essential.• Energy in non-force-free domains
(between photosphere and lower chromsphere)cannot be estimated by Virial theory and also notby NLFFF-computations.
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• Run 3D-boxes of ~ 320*320*256
• Free Memory used ~ 4GB
• Computing time ~2h on 4 Procs
• Output-files [IDL-sav-files] ~ 300 MB
• Input vector magnetograms should be calibrated and have ambiguity removed.
• For data analysis (free energy etc.) we might provide NLFFF and Potential fields:(3 or 4) codes*2*300MB*24h ~ 50 GB/day [Process 1 magnetogram per hour, more for special campaigns]
Computational Requirements(Rough estimation, similar for the 3 codes)
Might run largerboxes in future,Advances in Code and Computer development
(or more)
SDO-meetingNapa, 25.-28.03. 2008
Wiegelmann et al: Nonlinear force-free fields
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Points to discuss
• Run different codes for first SDO-data?• Compare magnetic energy-computations of codes
with virial theory estimations?• Investigate free parameters in preprocessing,
α+ and α- solutions for Grad-Rubin code?• Compare computations for same Active Region with
vector magnetograms measuredwith different instruments, e.g. SDO, SOLIS, Hinode, SFT?
• Run also spherical NLFFF-codes?
SDO-meetingNapa, 25.-28.03. 2008
Wiegelmann et al: Nonlinear force-free fields
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