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Explore the methods and applications of NLFFF modeling for coronal magnetic fields, including preprocessing criteria, evolution of flaring regions, and comparison with observational data. Enhance your understanding of chromospheric preprocessing and test NLFFF codes for accurate field extrapolations.
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Nonlinear force-free extrapolation of coronal magnetic fieldsT. 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 NJITWiegelmann et al: Nonlinear force-free fields
Force-free magnetic fieldj x B ~ 0 from Gary, Sol. Phys. 2001 NOT Force-free Vector magnetogram measurements NJITWiegelmann et al: Nonlinear force-free fields
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 polarityon boundary (Grad-Rubin method)- Magnetic field vector Bx By Bz on boundary (MHD-relaxation, Optimization method) NJITWiegelmann et al: Nonlinear force-free fields
Grad-Rubin methodAmari et al. 1997,2006, Wheatland 2004,06,07 NJITWiegelmann et al: Nonlinear force-free fields
MHD-relaxation Chodura & Schlueter 1981, Valori et al. 2005 Optimization Wheatland et al. 2000, Wiegelmann 2004 NLFFF-consortium (Schrijver et al. 2006): Optimization most accurate and fastest method. NJITWiegelmann et al: Nonlinear force-free fields
If these relations are NOT fulfilled on the boundary, then the photospheric data are inconsistent with the force-free assumption. NO Force-Free-Field. Consistency criteria for vectormagnetograms (Aly 1989) NJITWiegelmann et al: Nonlinear force-free fields
No net force No net torque Photosphere Smoothness Preprocessed boundary data NJITWiegelmann et al: Nonlinear force-free fields
Preprocessing can be improved by including chromospheric observations. (Wiegelmann, Thalmann, Schrijver, DeRosa, Metcalf, Sol. Phys. 2008) 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 dataare chromospheric like. NJITWiegelmann et al: Nonlinear force-free fields
Chromospheric H-alpha preprocessing • H-alpha fibrils outline magnetic field lines. • With image-recognition techniques we gettangent 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). NJITWiegelmann et al: Nonlinear force-free fields
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. NJITWiegelmann et al: Nonlinear force-free fields
Comparison of NLFFF-codes with Aad’s model Metcalf et al., Sol. Phys. 2008. -Good agreement for extrapolations from chromosphere. -Poor results for using photospheric data directly. -Improvement with preprocessed photospheric data. NJITWiegelmann et al: Nonlinear force-free fields
We test preprocessing with Aad’s model Prepro- cessing NJITWiegelmann et al: Nonlinear force-free fields
Results: Comparison with Aad‘s Model NJITWiegelmann et al: Nonlinear force-free fields
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) NJITWiegelmann et al: Nonlinear force-free fields
Flaring Active Region NOAA 10540 NJITWiegelmann et al: Nonlinear force-free fields
Magnetic energy buildsup and is releases during flare Plan:Study flaringARs with highertime cadence with SDO NJITWiegelmann et al: Nonlinear force-free fields
To Do: Application to Data (STEREO,SDO) Codes work correctly for smooth test cases Magnetohydrostatic optimization code Cartesian: (Wiegelmann, Neukirch, A&A 2006) Spherical: (Wiegelmann, Neukirch, Ruan, Inhester, A&A 2007) Next step: Magnetohydrostatics Lorentz force pressure gradient gravity NJITWiegelmann et al: Nonlinear force-free fields
NJITWiegelmann et al: Nonlinear force-free fields