1. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 1 Nonlinear force-free field modeling for SDO T. Wiegelmann, J.K. Thalmann, B. Inhester and 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

2. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 2 Force-free magnetic field j x B ~ 0 Vector magnetogram measurements from Gary, Sol. Phys. 2001 NOT Force-free

3. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 3 NonLinear Force-Free Fields Compute initial a potential field (Requires only B n on bottom boundary) Iterate for NLFFF-field, Boundary conditions: - B n and J n for positive or negative polarity on boundary (Grad-Rubin method) - Magnetic field vector B x B y B z on boundary (MHD-relaxation, Optimization method) Equivalent

4. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 4 Grad-Rubin method Amari et al. 1997,2006, Wheatland 2004,06,07

5. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann 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.

6. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 6 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.

7. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 7 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)

8. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 8 Coronal Magnetic Field Nonlinear Force-free code Preprocessing tool Vector magnetogram H-Alpha Image Chromospheric Magnetic Field Optional

9. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 9 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.

10. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 10 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-RubinMHD-relaxationOptimization

11. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 11 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 are caused by the inconsistent Hinode data set: Limited FOV for vector-magnetograms and the assumption of a potential transverse magnetic field outside the Hinode-FOV, which might be a poor assumption in a flaring Active Region. - Ground based vector magnetograms with reasonable FOV (SFT, SOLIS) are occasionally available and have been used to study evolution of Active Regions.

12. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 12 Flaring Active Region (Thalmann & Wiegelmann 2008) Quiet Active Region Solar X-ray flux. Vertical blue lines: vector magnetograms available Magnetic field extrapolations from Solar Flare telescope Extrapolated from SOLIS vector magnetograph M6.1 Flare Magnetic energy builds up and is releases during flare Plans: Study ARs with higher time cadence with SDO.

13. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 13 Quick-look computation: Virial theory (Metcalf et al. 2008) Quick computation (only a 2D-integral instead 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 not by NLFFF-computations.

14. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 14 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 larger boxes in future, Advances in Code and Computer development (or more)

15. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 15 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 measured with different instruments, e.g. SDO, SOLIS, Hinode, SFT? Run also spherical NLFFF-codes?

16. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 16