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

Abstract

The Milne-Eddington approximation provides an analytic and simple solution to the radiative transfer equation. It can be easily implemented in inversion codes that are used to fit spectro-polarimetric observations to infer average values of the magnetic field vector and the line-of-sight velocity of the solar plasma. However, it is in principle restricted to spectral lines formed under local thermodynamic conditions. We show that a simple modification in the linear source function of the Milne-Eddington approximation is sufficient to infer relevant physical parameters from spectral lines that deviate from local thermodynamic equilibrium. This is not a new modification for the solar community but it has been forgotten for quite some time To check the validity of such approximation we make use of the Mg I b2 and the Ca II lines. We first study the influence of these new terms on the profile shape by means of the response functions. Then, we test the performance of an inversion code including such modification against the presence of noise. The approximation is also tested with realistic spectral lines generated with the RH numerical radiative transfer code. Finally, we confront the code with synthetic profiles generated from magneto-hydrodynamic simulations.

arXiv commentAccepted for publication in Astronomy and Astrophysics

References in corpus (7)

• The stellar atmosphere simulation code Bifrost
• A publicly available simulation of an enhanced network region of the Sun
• Inversion of the radiative transfer equation for polarized light
• The usefulness of analytic response functions
• On the weak field approximation for CaII 8542 A
• Study of the polarization produced by the Zeeman effect in the solar Mg I b lines
• On spectropolarimetric measurements with visible lines

Cited by in corpus (3)

• Designing wavelength sampling for Fabry-Pérot observations. Information-based spectral sampling
• Diagnosing the solar atmosphere through the Mg I b${}_2$ 5173 Å line. II. Morphological classification of the intensity and circular polarization profiles
• Multi-height probing of horizontal flows in the solar photosphere