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

1. Nonlinear force-free field modeling for SDOT. 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 Wiegelmann 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 Wiegelmann 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) Wiegelmann et al: Nonlinear force-free fields

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

7. 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. Wiegelmann et al: Nonlinear force-free fields

8. H-AlphaImage Vector magnetogram Optional Preprocessing tool Chromospheric Magnetic Field Nonlinear Force-free code Coronal Magnetic Field 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. Wiegelmann et al: Nonlinear force-free fields

10. Grad-Rubin MHD-relaxation Optimization 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. 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 showeddifferences 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. Wiegelmann et al: Nonlinear force-free fields

12. Flaring Active Region (Thalmann & Wiegelmann 2008) M6.1 Flare Magnetic energy buildsup and is releases during flare Plans:Study ARswith highertime cadence with SDO. 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 Wiegelmann et al: Nonlinear force-free fields

13. 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. Wiegelmann et al: Nonlinear force-free fields

14. Might run largerboxes in future, Advances in Code and Computer development Computational Requirements(Rough estimation, similar for the 3 codes) • 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] (or more) 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 measuredwith different instruments, e.g. SDO, SOLIS, Hinode, SFT? • Run also spherical NLFFF-codes? Wiegelmann et al: Nonlinear force-free fields

16. Wiegelmann et al: Nonlinear force-free fields