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

1. 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

2. 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

3. 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

4. Grad-Rubin methodAmari et al. 1997,2006, Wheatland 2004,06,07 NJITWiegelmann et al: Nonlinear force-free fields

5. 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

6. 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

7. No net force No net torque Photosphere Smoothness Preprocessed boundary data NJITWiegelmann et al: Nonlinear force-free fields

8. 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

9. 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

10. 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

11. 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

12. We test preprocessing with Aad’s model Prepro- cessing NJITWiegelmann et al: Nonlinear force-free fields

13. Results: Comparison with Aad‘s Model NJITWiegelmann et al: Nonlinear force-free fields

14. 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

15. Flaring Active Region NOAA 10540 NJITWiegelmann et al: Nonlinear force-free fields

16. Magnetic energy buildsup and is releases during flare Plan:Study flaringARs with highertime cadence with SDO NJITWiegelmann et al: Nonlinear force-free fields

17. 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

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