1. Calibration of Solar Magnetograms and 180 degree ambiguity resolution Moon, Yong-Jae ( 文 鎔 梓 ) (Korea Astronomy and Space Science Institute)

2. Acknowledgement 1994 : Huairou, Dr. Ai, Dr. J. Wang, Dr. Zhang 1997 : Mitaka, Dr. Ichimoto, Dr. Sakurai 1999 : MEES, HSP, Dr. Mickey 2001 : BBSO, Dr. H. Wang 2002 : ASP, Dr. Pevtsov, Dr. Skumanich 2005 : talk2.ppt from WWW by Dr. J. Wang (srg.bao.ac.cn/weihailect/wangjx/TALK2.PPT )

3. Outline Introduction Calibration of filter-based magnetograms : non-linear calibration, k-factor problem Calibration of spectrometer-based magnetograms : Stokes V signal anomaly Comparison of magnetograms A new 180 ambiguity resolution method : Uniform Shear Method Conclusions

4. Introduction Magnetic field is the source of solar explosions Routine observations available at the photosphere We need 4 dimensional data (x,y,wavelength, Stokes Vector) at a given time Two types of solar magnetographs 1) filter-based : MSFC, BBSO, Huairou, Mitaka, IVM - narrow band filtergram (2D spatial, Stokes) - high time res., wide field of view 2) Spectrometer-based : ASP, HSP …… - Spectrometer (1D spatial +Stokes, spatial scan) - accurate field measurements with fill fraction

5. Radiative Transfer of Stokes Parameters (Weak Field Approximation, Jefferies et al. 1989)  

6. where are calibration coefficients for line-of-sight and transverse components, respectively, and 2.Calibration of Filter-based Magnetograms

7. Hagyard and Kineke(1995) developed an iterative procedure to improve the calibration using analytic solution of Stokes radiative equations Fe 5250 line

8. Moon et al.(1999) : Fe I 6302.5 line

9. k-factor problem : Underestimation of magnetic field strength Gary et al(1987) : 8.1 to match Mount Wilson data Gary et al.(1991) : instrumental depolarization MSFC usually adopt k=4. Chae(1996) : seeing corrected fields still require a k-factor (k=2.2 ) Mitaka : to match both Bot and Bpt Huairou : non-linear calibration curves

10. Lites et al.(1994) The k-factor seems to be due to magnetic fill fraction: k=1/f

11. Non-linear Least square method (Skumanich and Lites 1987) : Magnetic fields vectors and thermodynamical parameters are simultaneously determined. Basic assumption : Milne Eddington Atmosphere (All parameters do not depend on optical depth) 3. Calibration of Spectrometer -based Magnetograms

12. ASP data, Bt=688 G, Bl= 971 G, i=35 degree

13. Bt=436 G, Bl= -10 G, i=89 degree

14. Community Inversion Code http://www.hao.ucar.edu/public/research/cic/ 1. Melanie : Milne Eddington line analysis 2. Lilia : LTE inversion, stratification, individual lines 3. Dianne (beta) : Direct inversion using Neural Network

15. 4. Comparison of different magnetograms Wang et al.(1992)

16. Ronan et al.(1992)

17. Two anti-parallel polarization signals of the transverse fields are identical. The only way to remove the ambiguity is to employ a new constraint from other physical or observational assumptions which are independent from Zeeman effect. Importance : for a meaningful understanding of several important physical parameters such as vertical current density, shear angle etc. 5. A new 180 ambiguity resolution method

18. - Potential field assumption -  Best assumption : Minimize the difference between observation and extrapolation -Magnetic charge method : Wang (1993) -Synthesized Method : Wang and Lin (1993) -Multi-step method : Canfield et al.(1993) - Functional Minimization (J or ): Metcalf(1994), Gary and Demoulin (1995) Georgoulis et al.(2004) -H  observations : fibril alignment and/or chirality

19. 1) Potential Field Method 2) : vector with most probable shear Uniform Shear Method (Moon et al. 2003, Solar Physics, 217, 79) 3) : mean neighboring transverse vector Shear Angle Distribution

20. Potential Field Uniform Shear

21. Canfield et al.(1993) Moon et al.(2003) AR5747

22. Uniform Shear Canfield et al.(1993)

23. Moon et al.(2003) Canfield et al.(1993) AR6233

24. Shear Angle Distribution AR5747 AR6233

25. 1. Filter-based and Spectrometer-based magnetographs are complementary each other : Imaging Vector Magnetograph (MEES, BBSO) 2. Cross-comparison is recommended : ASP data for quantitative measurements MDI data for seeing effect 3. New missions : NST, SDO, Solar-B, ATST …. 4. What is a reasonable criterion to determine which ambiguity resolution method is correct. : current minimization, Jz comparison 6. Concluding Remarks