Coronal magnetic field models Nonlinear Force-Free Fields (NLFFF)

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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Force-free magnetic field

j x B ~ 0

Vector magnetogrammeasurements

from Gary,Sol. Phys. 2001

NOTForce-free



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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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Grad-Rubin methodAmari et al. 1997,2006, Wheatland 2004,06,07



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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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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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No net force

No net torque

Photosphere

Smoothness

Preprocessed boundary data



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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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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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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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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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Prepro-cessing

We test preprocessing with Aad’s model



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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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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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Flaring Active Region NOAA 10540



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Magneticenergy builds

up and isreleases during

flare

Plan:Study flaring

ARs with highertime cadence

with SDO



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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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Documents

Coronal magnetic field models Nonlinear Force-Free Fields (NLFFF)