Calibration of Solar Magnetograms and 180 degree ambiguity resolution

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

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. 3. Calibration of Spectrometer -based Magnetograms Non-linear Least squaremethod (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)

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. 5. A new 180 ambiguity resolution method 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.

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

20. Uniform Shear Potential Field

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

22. Uniform Shear Canfield et al.(1993)

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

24. Shear Angle Distribution AR5747 AR6233

25. 6. Concluding Remarks 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 MDIdata 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