Line response functions in nonlocal thermodynamic equilibrium
Max-Planck-Institut für Sonnersystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
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Received: 31 October 2016
Accepted: 3 February 2017
Context. Response functions provide us with a quantitative measure of sensitivity of the emergent spectrum to perturbations in the solar atmosphere and are thus the method of choice for interpreting spectropolarimetric observations. For the lines formed in the solar chromosphere, it is necessary to compute these responses taking into account nonlocal thermodynamic equilibrium (NLTE) effects.
Aims. We show how to analytically compute the response of the level populations in NLTE to a change of a given physical quantity at a given depth in the atmosphere. These responses are then used to compute opacity and emissivity responses, which are then propagated to obtain the response of the emergent intensity.
Methods. Our method is based on the derivative of the rate equations, where we explicitly incorporate spatial coupling in the radiative rate terms. After considering and collecting all interdependencies, the problem reduces to a linear system of equations with a dimension equal to the product of the number of spatial points and the number of energy levels.
Results. We compare analytically computed response functions with those obtained using a finite difference approach and find very good agreement. In addition, a more accurate way of propagating opacity and emissivity perturbations through the numerical solution of the radiative transfer equation was developed.
Conclusions. This method allows for the fast evaluation of the response of the emergent spectrum to perturbations of a given quantity at a given depth, and thus is a significant step towards more efficient NLTE inversions.
Key words: line: formation / radiative transfer / scattering
© ESO, 2017