Espectropolarimetría Milne-Eddington para la cromosfera solar

Abstract

The Milne-Eddington model is one of the most known and useful approximations to solve the Radiative Transfer Equation. It provides an analytical solution that is easy to understand. Its use implies to suppose constant magnetic fields and velocities with height and the assumption of a linear source function. So the main limitation is that this approximation only works under Local Thermodynamic Equilibrium conditions because it is only capable to reproduce symmetric Voigt profiles. In the Solar Physics its use is extended for studying the photosphere, not the chromosphere or the corona, where the conditions depart from Thermodynamic Equilibrium. Lites et al. (1988) proposed to modify this approximation including exponential terms variations with optical depth in the source function. Thus they increased the degrees of freedom in the approximation allowing it to fit chromospheric profiles. In this work we take the idea of Lites et al. (1988) providing an analytical solution of the Radiative Transfer Equation applying this modified Milne-Eddington approximation. We also calculate the response functions to the new parameters, helping us to understand their role. Later, we apply the approximation to standard chromospheric models and to realistic data. In the latter case, we fit intensity and polarization profiles of Mg I b2 and Ca II 854.2 lines using realistic magnetohydrodynamic simulations (Carlsson et al., 2016). We compare the results against those obtained with others like weak field approximation or center of gravity technique. After that, we study the polarization scattering and the Hanle effect which happen in low density plasmas. We do it solving the Statistical Equilibrium Equations for a two level atomic transition. Its solution provides the atomic populations of these levels and we use them to compute the scattering polarization signals. We finish this work analyzing scattering polarization diagrams for the Mg I b2 line under different conditions. We also represent the polarization diagram of a modified Milne-Eddington model giving an interpretation of it based on the previous diagrams. After the study performed about the modified Milne-Eddington approximation and the results that it provides, we can confirm that it can be used to explore solar chromosphere in a fast and easy-to-interpret way, also including scattering polarization and Hanle effect.