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

Azimuth ambiguity resolution Azimuth ambiguity resolution from dBz/dzfrom dBz/dz

M. Kubo (ISAS/JAXA), K. Shimada (University of Tokyo),

K. Ichimoto, S. Tsuneta (NAOJ)and

SOT-team

2006/4/17-20 Extended 17th 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 ambiguityAzimuth 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 .

0dzdB

dydB

dxdBB zyx

dBz/dz < 0 dBz/dz > 0

Bx, By Bx, By

2006/4/17-20 Extended 17th 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

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

Test CaseTest Case

case #field strength(@160km) [Gauss] 250 – 3000 (250 step) 12inclination angle [degree] 15, 45, 80 3azimuth angle [degree] 0 1filling factor 1 1Doppler shift 0 1dBz/dz 2Total 72

• 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

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

dBz/dz > 0

Result1Result1

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.

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

dBz/dz > 0

Result1Result1

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.

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

Difference of response function between line-core and wingDifference 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 (6301.5Å)

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

dBz/dz > 0

Result2Result2• 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

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

Summary and Future WorksSummary 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

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

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

Stokes V profiles fitted for line core and wingStokes V profiles fitted for line core and wing

Input parameter Result

Field strength[Gauss]

Inclination[degree]

dBz/dz

A 2000 10 + OK

B 2250 10 + NG

C 2250 10 – OK

wingline coreinput

A

CB

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

Response function of Stokes-V to Bz, FeI6302.5A

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

Response function of Stokes-V to Bz, FeI6301.5A

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

= -168 ~ +168mA

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

6301.5A

6302.5A

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

Residual of ME fit

FeI6302.5ABt=100G