1. Stokes Inversion 180  Azimuth Ambiguity Resolution Non-linear Force-free field (NLFFF) Extrapolation of Magnetic Field Progress in Setting up Data Processing Tools for BBSO Vector Magnetogram Data Scientific Research in the Future Spatial distribution of HXR intensity and E rec 3-D Structure and Evolution of Magnetic Fields in a flaring region Establish a relationship model between flare index (FI) and magnetic parameters using Kernel-based Learning Machine (KLM)

2. Motivation: The Infrared Imaging Magnetograph (IRIM) is a new imaging spectro-polarimeter currently being developed by the Big Bear Solar Observatory (Cao et al. 2006). To set up a standard inversion procedure for IRIM data. Some of the main diagnostic features are: magnetic flux, intrinsic field strength, and filling factors. Stokes Inversion

3. Methods Stokesfit.pro (by Thomas R.Metcalf, CORA) An Unno fitting code in ssw. NOAA 10781 on 2005 July 1 NOAA 10781 on 2006 July 1 LILIA (by Hector Socas-Navarro, HAO) Local thermodynamical equilibrium (LTE) Inversion based on the LORIEN Iterative Algorithm (LILIA; Cobo & Iniesta, 1992), written in Fortran 90. LORIEN engine (Lovely Reusable Inversion ENgine) combines the Singular Value Decomposition technique and the Levenberg-Marquardt minimization method. Observed (+) and fitted (—) Stokes V profile. NOAA 10795on 2005 August 9.

4. Future work: What is the actual instrumental profile? De-convolution of Stokes I profile Validity check Estimate of the systematic errors

5. Motivation: To select an objective, robust and automatic ambiguity resolution algorithm for BBSO data set and data sets from new missions (such as Solar-B, STEREO). Methods for Resolution of the 180 o Azimuth Ambiguity Workshop (2005 Sept.26-27, Boulder) 180-Degree Ambiguity Resolution

6. Summary of algorithms (see Table 1 of Metcalf et al. 2006)

7. Improved Minimum Energy Methods (ME2; implemented by T.R. Metcalf) The goal is to minimize The simulated annealing algorithm is very good at finding a global minimum in the presence of many local minima (Metropolis et al., 1953). Advantages – The algorithm is objective, robust, reproducible and fully automated. – The assumptions are physically well motivated. Disadvantages – slow The most promising method!

8. NOAA 0808 on 2005 Sept. 13

9. The codes of ME2 can be downloaded at http://web.njit.edu/~jj4/ambiguity/ current3.tar, README_disambiguity.txt  Generate an IDL-save file containing a structure that presents the vector magnetic field and coordinates in the Imaging Vector Magnetograph data format. bbso2ambi.pro  Resolve the 180-degree ambiguity current3.pro

10. NLFFF Extrapolation Motivation: 3-D non-linear force-free field (NLFFF) allows us to follow the coronal structure before/after solar flares. to determine the amount of free energy present in the corona, and to test hypotheses relating flare activity to free energy.

11. Theory (Yan and Sakurai 2000) The fields are represented by a boundary integral equation based on a specific Green’s function. That is, the magnetic field is expressed in terms of its boundary values and its normal gradients over the boundary.

12. Comparison between TRACE 171Å image and 3-D NLFFF lines of active region NOAA 10759 on 2005 May 13.

13. Quantitative Comparison of Methods of NLFF Modeling Coronal Magnetic Fields (by Schrijver et al. 2006) Optimization algorithm (Wheatland et al. 2000; implemented by McTiernan, and by Wiegelmann) Magnetofrictional algorithm (implemented by Valori) Boundary integral algorithm (Yan & Sakurai 2000) Grad-Rubin algorithm (implemented by Regnier, and by Wheatland) The field is evolved to match the boundary conditions and the force-free and divergence-free conditions in some way that guarantees the volume integral of the Lorentz force plus divergence always decrease

14. Scientific Research in the Future

15. Spatial Distribution of Hard X-ray (HXR) Intensity and E rec along H  Ribbons Electric field in the reconnecting current sheet (RCS) is regarded as one of important measures of magnetic reconnection rate. Temporal correlation between E rec and HXR and microwave lightcurves has been found (e.g., Qiu et al. 2004; Asai et al. 2004; Jing et al. 2005; Isobe et al. 2005; Noglik et al. 2005; Miklenic et al. 2007). Spatial correlation between E rec and HXR sources has been carefully addressed (Asai et al. 2002; Temmer et al. 2007).

16. NOAA 10759 on 2005 May 13

17. E rec HXR SourcesI HXR vs. E rec Until the flare maximum inhomogeneousPoint-likeWeak correlation After the flare maximum inhomogeneousRibbon-likeNo correlation

18. 3-D Structure and Evolution of Magnetic Fields Evolution of AR 10488 (Liu & Zhang. 2006)

19. Establish a relationship model between FI and magnetic parameters using KLM techniques

20. Magnetic parameters Flare Index Kernel-Based Learning Machine (KLM) Relationship model