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The Milne-Eddington approximation provides an analytic and simple solution tothe radiative transfer equation. It can be easily implemented in inversioncodes that are used to fit spectro-polarimetric observations to infer averagevalues of the magnetic field vector and the line-of-sight velocity of the solarplasma. However, it is in principle restricted to spectral lines formed underlocal thermodynamic conditions. We show that a simple modification in thelinear source function of the Milne-Eddington approximation is sufficient toinfer relevant physical parameters from spectral lines that deviate from localthermodynamic equilibrium. This is not a new modification for the solarcommunity but it has been forgotten for quite some time To check the validityof such approximation we make use of the Mg I b2 and the Ca II lines. We firststudy the influence of these new terms on the profile shape by means of theresponse functions. Then, we test the performance of an inversion codeincluding such modification against the presence of noise. The approximation isalso tested with realistic spectral lines generated with the RH numericalradiative transfer code. Finally, we confront the code with synthetic profilesgenerated from magneto-hydrodynamic simulations.

A modified Milne-Eddington approximation for a qualitative interpretation of chromospheric spectral lines