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Radiative transfer (RT) studies of the linearly polarized spectrum of the Sun(the second solar spectrum) have generally focused on the line formation, withan aim to understand the vertical structure of the solar atmosphere usingone-dimensional (1D) model atmospheres. Modeling spatial structuring in theobservations of the linearly polarized line profiles requires the solution ofmulti-dimensional (multi-D) polarized RT equation and a model solar atmosphereobtained by magneto-hydrodynamical (MHD) simulations of the solar atmosphere.Our aim in this paper is to analyze the chromospheric resonance line Ca {\scii} K at 3933 \AA\ using multi-D polarized RT with Hanle effect and partialfrequency redistribution in line scattering. We use an atmosphere which isconstructed by a two-dimensional snapshot of the three-dimensional MHDsimulations of the solar photosphere, combined with columns of an 1D atmospherein the chromosphere. This paper represents the first application of polarizedmulti-D RT to explore the chromospheric lines using multi-D MHD atmospheres,with PRD as the line scattering mechanism. We find that the horizontalinhomogeneities caused by MHD in the lower layers of the atmosphere areresponsible for strong spatial inhomogeneities in the wings of the linearpolarization profiles, while the use of horizontally homogeneous chromosphere(FALC) produces spatially homogeneous linear polarization in the line core.

Multi-dimensional radiative transfer to analyze Hanle effect in Ca {\sc ii} K line at 3933 \AA\,