Nonlinear Force-Free Fields (NLFFF) Methods: Grad Rubin, MHD-relaxation, Optimization

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



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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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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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CoronalMagnetic Field

Nonlinear Force-free code

Preprocessing tool

Vectormagnetogram

H-AlphaImage

ChromosphericMagnetic Field

Optional



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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 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.



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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.



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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)



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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?



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Nonlinear Force-Free Fields (NLFFF) Methods: Grad Rubin, MHD-relaxation, Optimization

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