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The determination of the plasma parameters in the sunspot photosphere using the inversion code

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.

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The determination of the plasma parameters in the sunspot photosphere using the inversion code

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  1. The determination of the plasma parameters in the sunspot photosphere using the inversion code

  2. Contents • Introduction to the inversion code • Derivation of the reponse functions • The inversion process • Error estimation • Examples of response functions • Results

  3. 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

  4. 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.

  5. 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

  6. 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 the perturbations of Stokes profiles. If we define the response function we gain

  7. Inversion process

  8. 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 equation is, that the plasma parameters are independent, so changes of one parameter do not influence the remaining ones.

  9. Relative response function of Stokes I

  10. Relative response function of Stokes Q

  11. Relative response function of Stokes U

  12. Relative response function of Stokes V

  13. Averagedmodels of atmosphere

  14. Absolute response functions to temperature

  15. Absolute response functions to magnetic field strength

  16. Absolute response functions to velocity

  17. Individual profiles and corresponding stratification of plasma parameters

  18. Maps of magnetic field configuration(Area 1, horizontal cuts)

  19. Maps of magnetic field configuration(Area 2, horizontal cuts)

  20. The canopy scheme

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