Nonlinear force-free field
modeling for SDO
T. Wiegelmann, J.K. Thalmann, B. Inhester
and 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-meeting
Napa, 25.-28.03. 2008
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from Gary,
Sol. Phys. 2001
Force-free magnetic field
jxB~0
Vector magnetogram
measurements
SDO-meeting
Napa, 25.-28.03. 2008
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Force-free
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NonLinear Force-Free Fields
Equivalent
• Compute initial a potential field
(Requires only Bn on bottom boundary)
• Iterate for NLFFF-field, Boundary conditions:
- Bn and Jn for positive or negative polarity
on boundary (Grad-Rubin method)
- Magnetic field vector Bx By Bz on boundary
(MHD-relaxation, Optimization method)
SDO-meeting
Napa, 25.-28.03. 2008
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Grad-Rubin method
Amari et al. 1997,2006, Wheatland 2004,06,07
SDO-meeting
Napa, 25.-28.03. 2008
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MHD-relaxation
Optimization
Chodura & Schlueter 1981,
Valori et al. 2005
Wheatland et al. 2000,
Wiegelmann 2004
NLFFF-consortium
(Schrijver et al. 2006):
Optimization most
accurate and
fastest method.
SDO-meeting
Napa, 25.-28.03. 2008
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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-meeting
Napa, 25.-28.03. 2008
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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-meeting
Napa, 25.-28.03. 2008
Wiegelmann et al:
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Vector
magnetogram
H-Alpha
Image
Optional
Preprocessing tool
Chromospheric
Magnetic Field
Nonlinear Force-free code
Coronal
Magnetic Field
SDO-meeting
Napa, 25.-28.03. 2008
Wiegelmann et al:
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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-meeting
Napa, 25.-28.03. 2008
Wiegelmann et al:
Nonlinear force-free fields
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Optimization
Grad-Rubin
MHD-relaxation
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.
SDO-meeting
Napa, 25.-28.03. 2008
Wiegelmann et al:
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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 are
caused by the inconsistent Hinode data set:
Limited FOV for vector-magnetograms and the assumption
of a potential transverse magnetic field outside the
Hinode-FOV, which might be a poor assumption
in a flaring Active Region.
- Ground based vector magnetograms with reasonable FOV
(SFT, SOLIS) are occasionally available and have been
used to study evolution of Active Regions.
SDO-meeting
Napa, 25.-28.03. 2008
Wiegelmann et al:
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Flaring Active Region
(Thalmann & Wiegelmann 2008)
Quiet Active Region
Magnetic M6.1 Flare
energy builds
up and is
releases
during
Plans:
Solar X-ray flux. Vertical blue lines: vector magnetograms available
flare
Study ARs
with higher
time cadence
with SDO.
Magnetic field extrapolations
from Solar Flare telescope
SDO-meeting
Napa, 25.-28.03. 2008
Extrapolated from SOLIS
vector magnetograph
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Quick-look computation: Virial theory
(Metcalf et al. 2008)
• Quick computation (only a 2D-integral
instead 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 not
by NLFFF-computations.
SDO-meeting
Napa, 25.-28.03. 2008
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Computational Requirements
(Rough estimation, similar for the 3 codes)
•
•
•
•
•
Run 3D-boxes of ~ 320*320*256
Might run larger
boxes in future,
Free Memory used ~ 4GB
Advances in Code and
Computing time ~2h on 4 Procs
Computer development
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 (or more)
[Process 1 magnetogram per hour, more for special
campaigns]
SDO-meeting
Napa, 25.-28.03. 2008
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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 measured
with different instruments,
e.g. SDO, SOLIS, Hinode, SFT?
• Run also spherical NLFFF-codes?
SDO-meeting
Napa, 25.-28.03. 2008
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SDO-meeting
Napa, 25.-28.03. 2008
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