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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann et al: Nonlinear force-free fields
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Nonlinear force-free extrapolation of coronal magnetic fields
T. Wiegelmann, J.K. Thalmann, B. Inhester
• Coronal magnetic field models• Nonlinear Force-Free Fields (NLFFF)• Consistency criteria for vector
magnetograms and preprocessing• Evolution of a flaring Active Region• Non-force-free fields• Conclusions
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann 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
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann 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
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann et al: Nonlinear force-free fields
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Grad-Rubin methodAmari et al. 1997,2006, Wheatland 2004,06,07
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann 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.
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01.04.2008 NJIT-seminarNewark, 01.04. 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.
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann et al: Nonlinear force-free fields
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No net force
No net torque
Photosphere
Smoothness
Preprocessed boundary data
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann 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)
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann et al: Nonlinear force-free fields
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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).
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
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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.
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann et al: Nonlinear force-free fields
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Comparison of NLFFF-codes with Aad’s modelMetcalf et al., Sol. Phys. 2008.-Good agreement for extrapolations from chromosphere.-Poor results for using photospheric data directly.-Improvement with preprocessed photospheric data.
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann et al: Nonlinear force-free fields
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Prepro-cessing
We test preprocessing with Aad’s model
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann et al: Nonlinear force-free fields
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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
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
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Evolution of flaring Active Region NOAA 10540(Extrapolation (optimization) from NAOJ/SFT-vector magnetograms;
Thalmann & Wiegelmann, A&A 2008, in press)
Solar Flare Telescope,Mitaka, Tokyo,(Sakurai et al.1995, operatingsince 1992)
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann et al: Nonlinear force-free fields
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Flaring Active Region NOAA 10540
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann et al: Nonlinear force-free fields
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Magneticenergy builds
up and isreleases during
flare
Plan:Study flaring
ARs with highertime cadence
with SDO
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann et al: Nonlinear force-free fields
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Next step: Magnetohydrostatics
Lorentz force
pressure gradient
gravity
Magnetohydrostatic optimization codeCartesian: (Wiegelmann, Neukirch, A&A 2006)
Spherical: (Wiegelmann, Neukirch, Ruan, Inhester, A&A 2007)
Codes workcorrectly for
smooth test cases
To Do:Application
to Data (STEREO,SDO)
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01.04.2008 NJIT-seminarNewark, 01.04. 2008
NJITWiegelmann et al: Nonlinear force-free fields
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