the determination of the plasma parameters in the sunspot photosphere using the inversion code
DESCRIPTION
The determination of the plasma parameters in the sunspot photosphere using the inversion code. Contents. Introduction to the inversion code Derivation of the reponse functions The inversion process Error estimation Examples of response functions Results. - PowerPoint PPT PresentationTRANSCRIPT
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The determination of the plasma parameters
in the sunspot photosphere using the
inversion code
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Contents
• Introduction to the inversion code
• Derivation of the reponse functions
• The inversion process
• Error estimation
• Examples of response functions
• Results
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Inversion code SIR(Stokes Inversion based on Response
functions)• one-dimensional code
• local termodinamic equilibrium assumed
• one-component model atmosphere
Ruiz Cobo, B. & del Toro Iniesta, J.C. 1992, ApJ, 398,543
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Response functions
• RTE for polarised light
• Formal solution of RTE
• Both the propagation matrix and the source function are dependent on the atmospheric parameters. The integrand is so-called contribution function, which inform us how the different atmospheric layers contribute to the observed spectrum.
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Response functions
• If we change the input parameters, the propagation matrix and the source functions change at first approximation as
• The asociated changes in the intensities follow the transfer equation. If we neglect the second order terms, we gain
• We define effective source function as
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Response functions• The last equation was formally identical to RTE and therefore the solution must be formally the same
• The integrand is now the contribution function to theperturbations of Stokes profiles. If we define the responsefunction
we gain
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Inversion process
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Error estimation• The error of the plasma parameter is proportional to the merit function (quality of the fit) and to the inverse of the response function
• The basic assumtion required for the derivation of this equationis, that the plasma parameters are independent, so changes of one parameter do not influence the remaining ones.
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Relative response function of Stokes I
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Relative response function of Stokes Q
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Relative response function of Stokes U
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Relative response function of Stokes V
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Averaged models of
atmosphere
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Absolute response
functions to temperature
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Absolute response
functions to magnetic
field strength
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Absolute response
functions to velocity
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Individual profiles and corresponding stratification of plasma parameters
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Maps of magnetic field configuration(Area 1, horizontal cuts)
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Maps of magnetic field configuration(Area 2, horizontal cuts)
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The canopy scheme