Magnetic field inversions from Stokes profiles generated

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Solar Magnetism and Dynamics THEMIS users
meeting, Paris, November 15-17, 2006
Magnetic field inversions from Stokes profiles
generated by MHD simulations.
Elena Khomenko(1,2), Manuel Collados(1)
Instituto de Astrofisica de Canarias, La Laguna,
Spain Main Astronomical Observatory, Kiev
Ukraine.
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Magnetic field strength in IN
Dominance of sub-kG fields Fe I 1.56 ?m
lines Lin (1995) Lin Rimmele (1999) Collados
(2001) Khomenko et al (2003) Sánchez Almeida et
al (2003) Martínez González et al
(2006) Domínguez Cerdeña et al (2006) MnI HFS
lines López Ariste et al (2006a,b)
Dominance of kG fields Fe I 6301/2 A
lines Sánchez Almeida Lites (2000) Lites
(2002) Socas-Navarro Sánchez Almeida
(2002) Sánchez Almeida et al (2003) Dominguez
Cerdeña et al (2003) Dominguez Cerdeña et al
(2006) but Lites et al (1996) B350 G for
horizontal IN fields!
reliability of the inversions?
Stokes V amplitude ratio is a reliable parameter?
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Realistic 3D MHD simulations
see A. Vogler et al (2005)
MURAM code (MPAe/University of Chicago Radiative
MHD by A. Vogler, S. Shelyag, M. Schussler, F.
Cattaneo, Th. Emonet and T. Linde)
Computational domain of 6 ? 6 ? 1.4 Mm, 20 km
resolution
Snapshot
ltBgt 30 G bi-polar 140 G bi-polar
FeI Stokes spectra 6301 (g1.67), 6302 (g2.5),
15648 (g3), 15642 (g1.53), 5247 (g2.0), 5250
(g3.0).
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Line ratio calibration
Amplitude V (smaller geff)
Line ratio
Amplitude V (larger geff)
FeI 5247/5250
FeI 6301/6302
FeI 15652/15648
Stokes V amplitude ratio
thin lines - full resolution, Vmic, Vmac0 thick
lines - reduced resolution, Vmic0.3, Vmac0.7 km
s-1
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Magnetic field strength from the line ratio
original resolution of 20 km
B from MHD 30 G at log ?5-1 Internetwork
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Heights of formation from RFs
centroid of the RFs at the wavelength of the
line core intensity
Ruiz Cobo del Toro Iniesta (1994)
Fe lines formation heights see Shchukina
Trujillo Bueno 2001
Horizontal distace km
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Height variations of RFs of Stokes I to
Temperature
RFs inside the strong magnetic field
concentration
15652
15648
5250
5247
6302
6301
Magnetic field G
Height km
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Magnetic field strength from the line ratio
reduced resolution 0.6 - 0.7 arcsec
Profiles with amplitudes above 5 ?10-3
B from MHD 30 G at log ?5-1, binned 4 ? 4
pxls Internetwork
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Observed line ratio in infrared

• VTT (Tenerife, Isana), July 2000
• Tenerife Infrared Polarimeter
• Full Stokes vector
• Quiet Sun inter-network, disc center
• Scanned area July 20" ? 38 "
• Spectral region containing
• FeI 15648 A (g3)
• FeI 15653 A (geff1.6) lines
• Noise level 2 10-4 IC
• see Khomenko et al (2003)

Magnetic field strength from Stokes V amplitude
ratio
Magnetic field strength from Stokes V splitting
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Conclusions from Line Ratio
The Stokes V amplitude ratio of the FeI 6301-6302
lines does not carry information about the
magnetic field strength since it is affected by
the gradients of the LOS velocity, magnetic field
and thermodynamic parameters.
The Stokes V amplitude ratio of the FeI 5247-5250
lines is likely to reveal weak fields in
inter-network since these lines form high in the
atmosphere.
The Stokes V amplitude ratio of the Fe I
15648-15652 lines gives a reasonable estimate of
B even for the fields with complex internal
structure.
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SIR Inversion of the Stokes spectra at the
original resolution of 20 km
SIR (Ruiz Cobo del Toro Iniesta, ApJ 1992)

• Stokes I, Q, U, V
• No noise
• Filling factor1
• One magnetic component
• Gradients in VLOS and B are allowed
• MHD 140 G, bi-polar

Two separate inversions FeI 15648, 15652 and
FeI 6301, 6302
Free parameters T, B, VLOS, ?
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Magnetic field strength from the inversion
original resolution of 20 km
B from FeI 15648-15652
B from FeI 6301-6302
B from MHD
B G at log? -0.4
FeI 6301-6302 FeI 15648-15652 MHD
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Not surprising!

• The Stokes V amplitude is proportional to the flux

• The simulation does not have structures below 20
  km

filling factor 1
Thus, Stokes V amplitude gives information about B
Inversion is able to recover fields as low as
100-200 G.
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Velocity from the inversion original
resolution of 20 km
V from FeI 15648-15652
V from FeI 6301-6302
V from MHD
Vlos km s-1 at log? -0.4
FeI 6301-6302 FeI 15648-15652 MHD
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Inclination from the inversion original
resolution of 20 km
? from FeI 15648-15652
? from FeI 6301-6302
? ? from MHD
? degr at log? -0.4
FeI 6301-6302 FeI 15648-15652 MHD
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Temperature from the inversion original
resolution of 20 km
T from FeI 15648-15652
T from FeI 6301-6302
T from MHD
T K at log? -0.4
FeI 6301-6302 FeI 15648-15652 MHD
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Example stratifications of B and VLOS
FeI 6301-6302 FeI 15648-15652 MHD
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SIR Inversion of the Stokes spectra at the
reduced resolution of 0.6 arcsec and 1.4 arcsec
SIR (Ruiz Cobo del Toro Iniesta, ApJ 1992)

• Stokes I, V
• Noise 8 x10-4 (mean amplitude 3-5 x10-3)
• Filling factor is a free parameter
• One magnetic component and one non-magnetic
  component
• VLOS and B are constant with ?5
• MHD 30 G, bi-polar

Two separate inversions FeI 15648, 15652 and
FeI 6301, 6302
Free parameters T, B, VLOS, ?, Vmic, Vmac
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Magnetic field strength from the inversion
reduced resolution 0.6 - 0.7 arcsec
B from FeI 6301-6302
B from FeI 15648-15652
B from MHD
B G at log? -1
FeI 6301-6302 FeI 15648-15652 MHD
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Velocity from the inversion reduced
resolution 0.6 - 0.7 arcsec
MAGNETIC COMPONENT
V from FeI 15648-15652
V from FeI 6301-6302
V from MHD
VLOS km s-1 at log? -1
FeI 6301-6302 FeI 15648-15652 MHD
REDSHIFTED!
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Velocity from the inversion reduced
resolution 0.6 - 0.7 arcsec
Non-MAGNETIC COMPONENT
V from FeI 15648-15652
V from FeI 6301-6302
V from MHD
VLOS km s-1 at log? -1
FeI 6301-6302 FeI 15648-15652 MHD
BLUESHIFTED!
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Temperature from the inversion reduced
resolution 0.6 - 0.7 arcsec
T from FeI 15648-15652
T from FeI 6301-6302
T from MHD
T K at log? 0
FeI 6301-6302 FeI 15648-15652 MHD
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Filling factor from the inversion
Order of magnitude difference between 0.6 and 1.4
arcsec resolution!
Resolution 1.4 arcsec
Resolution 0.6 arcsec

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Magnetic field strength from the inversion
reduced resolution 1.4 arcsec
B from FeI 15648-15652
B from FeI 6301-6302
B from MHD
B G at log? -1
FeI 6301-6302 FeI 15648-15652 MHD
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Conclusions from the INVERSIONS
An inversion applied to the Stokes profiles
generated by MHD simulations at the original
resolution of 20 km recovers well the original
distribution of the atmospheric parameters.
If the MHD simulations were the Sun, B could be
recovered fairly good from the FeI 6301, 6302
Stokes profiles at the resolution of 0.6 arcsec,
but not at 1.4 arcsec. The reason is the 10
times difference in the filling factor (Stokes I
does not have information at 1.4 arcsec
resolution).
The magnetic field strength could be recovered
from the FeI 6301, 6302 Stokes profiles only via
complete inversions, not via line ratio, even at
the resolution of 20 km.
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Magnetic field strength from the 5247/5250 line
ratio MHD 200 G
B from MHD 200 G at log ?5-1, binned 4 ? 4 pxls