1. 2006/4/17-20 Extended 17 th SOT meeting Azimuth ambiguity resolution from dBz/dz M. Kubo (ISAS/JAXA), K. Shimada (University of Tokyo), K. Ichimoto, S. Tsuneta (NAOJ) and SOT-team

2. 2006/4/17-20 Extended 17 th SOT meeting If we can know sign of dBz/dz, the azimuth angle is determined. We calculate the sign of dBz/dz by using (1) two different photospheric line profiles (Fe I 6301.5Å and Fe I 6302.5Å) (2) line-core and wing of one photospheric line profile (Fe I 6301. 5Å) Azimuth ambiguity Resolution of azimuth ambiguity is very important for - determination of magnetic field structure. - calculation of shear angle, current density, and helicity. We try to resolve the azimuth ambiguity from only  B = 0 with no assumption (L. Wu & G. Ai, 1990, ACTA). Magnetic fields must satisfy  B = 0. dBz/dz < 0dBz/dz > 0 Bx, By

3. 2006/4/17-20 Extended 17 th SOT meeting dBz/dz from two different line profiles We obtain two Bz values using Fe I 6301.5Å and Fe I 6302.5Å lines. - SOT/SP obtains full stokes profiles of Fe I 6301.5Å and Fe I 6302.5Å. Milne-Eddington inversion code is applied for each line to derive the magnetic field strengths with different height. Formation height of Fe I 6301.5Å is slightly higher than that of Fe I 6302.5Å. Bz (6301.5Å) - Bz (6302.5Å) >0  dBz/dz > 0 Bz (6301.5Å) - Bz (6302.5Å) <0  dBz/dz < 0 Stokes V profile

4. 2006/4/17-20 Extended 17 th SOT meeting Test Case case# field strength(@160km) [Gauss]250 – 3000 (250 step)12 inclination angle [degree]15, 45, 803 azimuth angle [degree]01 filling factor11 Doppler shift01 dBz/dz  2 Total72 We use Holweger & Muller model atmosphere to make synthesized Stoke profiles. Field strength has height gradient (dB/d  =  300), and inclination does not vary with height. We examine 36 cases for dBz/dz >0 and 36 cases for dBz/dz <0. inclination: 0 = vertical to the solar surface, 90 = horizontal to the solar surface

5. 2006/4/17-20 Extended 17 th SOT meeting dBz/dz > 0 Result1 input parameters: ◇ :  = 10 [deg] △ :  = 45 [deg] × :  = 80 [deg] red: dBz/dz > 0 blue: dBz/dz < 0 dBz/dz < 0 (Filling factor are fixed to 1 in this case.) A percentage of correct answers for both  dBz/dz is 39 % (14/36). When filling factor becomes a free parameter, the percentage increases to 67%. The percentage of correct answers are not improved when thermodynamic parameters are fixed to values derived from both lines or when weight of Stokes-V increases in the ME inversion.

6. 2006/4/17-20 Extended 17 th SOT meeting dBz/dz > 0 Result1 dBz/dz < 0 (Filling factor are fixed to 1 in this case.) input parameters: ◇ :  = 10 [deg] △ :  = 45 [deg] × :  = 80 [deg] red: dBz/dz > 0 blue: dBz/dz < 0 A percentage of correct answers for both  dBz/dz is 39 % (14/36). When filling factor becomes a free parameter, the percentage increases to 67%. The percentage of correct answers are not improved when thermodynamic parameters are fixed to values derived from both lines or when weight of Stokes-V increases in the ME inversion.

7. 2006/4/17-20 Extended 17 th SOT meeting Difference of response function between line-core and wing We investigate difference between two Bz values derived from Stokes profiles around line core and wing. The line core profile represents magnetic fields in the upper atmosphere in comparison with magnetic fields derived from the wing. Bz (line core) - Bz (wing) > 0  dBz/dz > 0 Bz (line core) - Bz (wing) < 0  dBz/dz < 0 The line core is defined as line center  70 mÅ. The wing is defined as -300mÅ to -70 mÅ. We use Fe I 6301.5Å, because a response function of Stokes V to Bz for Fe I 6301.5Å is sharper than that of Fe I 6302.5Å. Response function of Stokes-V to Bz Line center: 6301.5Å Stokes V profile (6301.5 Å )

8. 2006/4/17-20 Extended 17 th SOT meeting dBz/dz > 0 Result2 A percentage of correct answers for both  dBz/dz is 86 % (31/36), and it increase to 97% (29/30) for field strength > 500 Gauss. We may have to change wavelength sampling for line-core and wing with a width of Zeeman splitting. dBz/dz < 0 (Filling factor and Doppler shift are fixed to 1 and 0 respectively in this case.) input parameters: ◇ :  = 10 [deg] △ :  = 45 [deg] × :  = 80 [deg] red: dBz/dz > 0 blue: dBz/dz < 0

9. 2006/4/17-20 Extended 17 th SOT meeting Summary and Future Works Difference between the response functions of Stokes V for line-core and wing would be useful for calculating the sign of dBz/dz. - We have to test this method for (1) many cases with various parameters (Doppler, filling factor..) (2) profiles including noise (3) observed Stokes profile We like to find the best way to calculate the sign of dBz/dz. - We will try to derive the sign of dBz/dz by using (1) Neural network (2) PCA (3) Inversion with height gradient (4) etc

10. 2006/4/17-20 Extended 17 th SOT meeting

11. Stokes V profiles fitted for line core and wing Input parameterResult Field strength [Gauss] Inclination [degree] dBz/dz A200010+OK B225010+NG C225010–OK wing line core input A CB

12. 2006/4/17-20 Extended 17 th SOT meeting Response function of Stokes-V to Bz, FeI6302.5A

13. 2006/4/17-20 Extended 17 th SOT meeting Response function of Stokes-V to Bz, FeI6301.5A

14. 2006/4/17-20 Extended 17 th SOT meeting = -168 ~ +168mA

15. 2006/4/17-20 Extended 17 th SOT meeting 6301.5A 6302.5A

16. 2006/4/17-20 Extended 17 th SOT meeting Residual of ME fit FeI6302.5A Bt=100G