Multi-dimensional Radiative Transfer to Analyze Hanle Effect in Ca II K Line at 3933 Å

Abstract

Radiative transfer (RT) studies of the linearly polarized spectrum of the Sun (the second solar spectrum) have generally focused on line formation, with an aim to understand the vertical structure of the solar atmosphere using one-dimensional (1D) model atmospheres. Modeling spatial structuring in the observations of the linearly polarized line profiles requires the solution of multi-dimensional (multi-D) polarized RT equation and a model solar atmosphere obtained by magnetohydrodynamical (MHD) simulations of the solar atmosphere. Our aim in this paper is to analyze the chromospheric resonance line Ca II K at 3933 Å using multi-D polarized RT with the Hanle effect and partial frequency redistribution (PRD) in line scattering. We use an atmosphere that is constructed by a two-dimensional snapshot of the three-dimensional MHD simulations of the solar photosphere, combined with columns of a 1D atmosphere in the chromosphere. This paper represents the first application of polarized multi-D RT to explore the chromospheric lines using multi-D MHD atmospheres, with PRD as the line scattering mechanism. We find that the horizontal inhomogeneities caused by MHD in the lower layers of the atmosphere are responsible for strong spatial inhomogeneities in the wings of the linear polarization profiles, while the use of horizontally homogeneous chromosphere (FALC) produces spatially homogeneous linear polarization in the line core. The introduction of different magnetic field configurations modifies the line core polarization through the Hanle effect and can cause spatial inhomogeneities in the line core. A comparison of our theoretical profiles with the observations of this line shows that the MHD structuring in the photosphere is sufficient to reproduce the line wings and in the line core, but only line center polarization can be reproduced using the Hanle effect. For a simultaneous modeling of the line wings and the line core (including the line center), MHD atmospheres with inhomogeneities in the chromosphere are required.