1. Changes of Magnetic Structure in 3-D Associated with Major Flares X3.4 flare of 2006 December 13 (J. Jing, T. Wiegelmann, Y. Suematsu M.Kubo, and H. Wang, 2008 ApJL, 676, L81) X 5.3 flare of 2001 August 25 (in preparation) X1.6 flare of 2001 October 19 (in preparation) …

2. Background and Motivation Rapid and permanent changes of photosphere magnetic fields associated with solar flares have been reported in at least 16 publications during the past eight years (e.g., Cameron & Sammis 1999; Wang et al. 2002; Spirock et al. 2002; Meunier & Kosovichev 2003; Yurchyshyn et al. 2004; Deng et al. 2005; Liu et al. 2005; Sudol & Harvey 2005, etc.; Chen et al. 2007) the unbalanced magnetic flux the increase in transverse magnetic fields penumbral decay and central feature enhancement the decrease or increase in magnetic shear near the flaring neutral line 3-D magnetic structure and its evolution will provide key understanding of this subject.

3. Data Sets Hinode SP vector magnetograms (FOV: ~300”  160”; Resolution: ~0.2”/pixel) advantages: seeing–free, high-resolution, high-precision disadvantages: poor-cadence BBSO DVMG vector magnetograms (FOV: ~350”  350”; Resolution: ~0.6”/pexel) advantages: high cadence, ~1 min disadvantages: seeing problem, Zeeman saturation * SDO Helioseismic and Magnetic Imager (HMI) vector magnetograms (FOV: full disk; Resolution: ~1”/pixel; Cadence: ~90 s) 180-degree Ambiguity Resolving Tools the Minimum Energy algorithm by Metcalf (1994) NLFFF Modeling Tools the Optimization algorithm implemented by Wiegelmann (2004)

4. X3.4 flare of 2006 December 13 AR#: NOAA 10930 Location: S06W35 Flare non-thermal emission peak time: 2006 December 13, 02:28 UT

5. Data Set: Hinode vector magnetograms taken in two time bins time bin 1 (before the flare): 2006 December 12, 20:30 UT  21:33 UT time bin 2 (after the flare): 2006 December 13, 04:30 UT  05:36 UT Modeling of Coronal Magnetic Fields Potential Fields: Green’s function method – by Tom Metcalf NLFF Fields: optimization method – by Thomas Wiegelmann Magnetic Shear Parameters: Magnetic shear: At each altitude, Weighted mean shear: Total magnetic shear: Where Bi=|Bi| at each pixel i, and the superscripts N and p represent the NLFF field and the potential field, respectively. The sum  is performed over all the pixels in a region.

6. Left: Line-of-sight magnetograms taken before (top) and after (bottom) the flare. The FOV is 140”  140”. The rectangles P mark the area close to the flaring magnetic polarity inversion line. Right: weighted mean shear  w (top) and total magnetic shear  w B (bottom) of area P as a function of altitude for two time bins. The step size of altitude is ~0.46 Mm.

7. Future work: Learn to extrapolate the NLFF fields Test the impact of Zeeman saturation on the NLFFF extrapolation Study the evolution of 3-D magnetic fields during Flares the electric current system from photosphere to corona the evolution of magnetic free energy the evolution of magnetic field lines in peripheral penumbra compare the observational findings with theoretical models Saturation-free magnetograms Saturated magnetograms NLFF fields