1. Observations and nonlinear force-free field modeling of active region 10953 Y. Su, A. van Ballegooijen, B. W. Lites, E. E. DeLuca, L. Golub, P. C. Grigis, G. Huang, H. Ji 2009, ApJ, 691, 105

2. AR 10953 Japan sunspot topic for Group 2 in the 180-deg ambiguity workshop small flares (B & C class) and filament activations

3. Abstract Nonlinear force-free field (NLFFF) modeling of AR 10953 SOT/SP and MDI flux rope insertion method comparison between modeled field lines and X-ray loops observed by XRT axial flux : (7±2)×10 20 Mx < 15×10 20 Mx (stable force-free configurations, no eruption) poloidal flux : (0.1-10)×10 10 Mx / cm : wider range X-ray brightenings appeared 20 min earlier than EUV brightenings direct coronal heating due to reconnection energey transported down to the chromosphere is too low to produce EUV emission early flare loop is located above the flux rope the flare started near outer edge, not inner as standard two-ribbon flare model

4. FFF j x B = 0 ; j = curl B = αB : force-free field α= 0; j = 0 : potential field α= constant ≠0 ; linear force free (minimum energy) α≠constant from field line to field line ; nonlinear force-free (stored energy) Flare, prominence eruption, and CME are associated with stored energy in the coronal fields.

5. Flux rope insertion method Magnetic field in the photosphere is not force free highly sheared field in the filament channel is not always visible Here the authors construct NLFFF models using flux rope insertion method which requires radial component of photospheric magnetic fields originally developed by van Ballegooijen (2004) and van Ballegooijen & Mackay (2007)

6. Flux rope insertion method axial flux Φ and poloidal flux F as free parameters estimated by comparison with H-alpha and X-ray coronal loops magnetofrictional relaxation η ～ | j×B | : diffusion occurs with when the state is far from force free hyperdiffusion : topology of magnetic field is nearly conserved

7. Observations X-ray EUV

8. TRACE +XRT XRT +RHESSI much smaller brightenings XRT +PIL Flare

9. Prominence Activation XRT H-alpha +MDI Prominence material flows from northern part to southern part. no feature in X-ray

10. Constraints for Modeling Results some models converge to a NLFFF equilibrium others do not converge and the flux ropes lift off loss of equilibrium, not a numerical problem necessary conditions: best fit the observed highly sheared X-ray loops converge to a stable solution because no large eruption except one small partial eruption is observed in the observations

11. Results red: observed loops blue: best fit model XRT before the C-flare the loop appeared after the partial eruption and disappeared soon

12. Best fit solutions average deviation between a modeled field and an observed loop by measuring the distance on the projected field line unstable (relaxation is unclear) poloidal flux of the best-fit model has a much wider range, so XRT observations do not provide strong constraints on the poloidal flux lift-off

13. Azimuth A small region of the sunspot penumbra NLFFF model show much better fit to the observations than the potential field model. But, the azimuth errors of three NLFFF models are much larger than the measurement errors. The present models do not provide an accurate fit to the vector field data. Potential blue: SOT/SP black: model

14. 3D field configuration and current radial electric current vertical cross section (current density) central part is axial flux highly sheared, but untwisted because of no strong current pink: best fit model at the onset of the flare blue: best fit model before the flare

15. 3D field configuration and current pink line is located beyond the outer edge of the flux rope at the onset of the flare X-ray loop is unsheared and located beyond the outer edge  the flux rope is not the main source for the flare reconnection occurred near the outer edge and directly heated the loop radial electric current vertical cross section (current density)

16. Interpretation of the flare mechanism The initial phase of the flare is caused by interactions of weakly sheared loops near the outer edge of the flux rope Then, during the main phase, the reconnections involved the inner part of the flux rope, which is highly sheared.

17. Conclusion Flux insertion method axial : (7±2)×10 20 Mx, poloidal : 0.1-10 x10 10 Mx free energy 8.5 1031 erg, sufficient to power a B/C flares flare occurred near the outer edge of the flux rope, not the inner or at the bottom seen in standard two-ribbon flares NLFFF models show much better fit to observations but, the azimuth errors is large compared to the measurement errors this is not surprising since the models are mainly constrained by the observed X-ray loops, no attempts was made to fit the observed vector field flux insertion method is quite unlike the other kind of methods (NLFFF by extrapolating observed photospheric vector fields  but, poor match to coronal loops) combination is important for the future