Azimuth ambiguity resolution from dBzdz

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Azimuth ambiguity resolution from dBz/dz

• M. Kubo (ISAS/JAXA),
• K. Shimada (University of Tokyo),
• K. Ichimoto, S. Tsuneta (NAOJ)
• and
• SOT-team

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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 lt 0
dBz/dz gt 0
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)
Bx, By
Bx, By
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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) gt0
• ? dBz/dz gt 0
• Bz (6301.5Å) - Bz (6302.5Å) lt0
• ? dBz/dz lt 0

Stokes V profile
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Test Case

• 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 gt0 and 36 cases
  for dBz/dz lt0.

inclination 0 vertical to the solar surface,
90 horizontal to the solar surface
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Result1

• 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.

dBz/dz gt 0
input parameters ? ? 10 deg ? ? 45
deg ? 80 deg red dBz/dz gt 0 blue
dBz/dz lt 0
dBz/dz lt 0
(Filling factor are fixed to 1 in this case.)
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Result1

• 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.

dBz/dz gt 0
input parameters ? ? 10 deg ? ? 45
deg ? 80 deg red dBz/dz gt 0 blue
dBz/dz lt 0
dBz/dz lt 0
(Filling factor are fixed to 1 in this case.)
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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) gt 0 ? dBz/dz gt 0
• Bz (line core) - Bz (wing) lt 0 ? dBz/dz lt 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)
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Result2

• A percentage of correct answers for both ?
  dBz/dz is 86 (31/36), and
• it increase to 97 (29/30) for field strength gt
  500 Gauss.
• We may have to change wavelength sampling for
  line-core and wing
• with a width of Zeeman splitting.

dBz/dz gt 0
input parameters ? ? 10 deg ? ? 45
deg ? 80 deg red dBz/dz gt 0 blue
dBz/dz lt 0
dBz/dz lt 0
(Filling factor and Doppler shift are fixed to 1
and 0 respectively in this case.)
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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

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Stokes V profiles fitted for line core and wing
A
C
B
input
line core
wing
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Response function of Stokes-V to Bz, FeI6302.5A
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Response function of Stokes-V to Bz, FeI6301.5A
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l -168 168mA
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6301.5A
6302.5A
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FeI6302.5A Bt100G
Residual of ME fit