Clustering analysis of Ca {\sc i} 4227 line polarization using magnetohydrodynamic simulations of the solar atmosphere

Ca {\sc i} 4227 \AA\, line is a strong resonance line formed in the Solar chromosphere. At the limb, it produces the largest scattering polarization signal. So far, modeling the linear polarization in this line has been limited to the use of one-dimensional semi-empirical models of the solar atmosphere. In this paper, we use three-dimensional magnetohydrodynamical models of the solar atmosphere as well as 1.5D radiative transfer to understand the formation of linear polarization profiles due to resonance scattering in this line at a near limb position. Using three-dimensional magnetohydrodynamical models of the solar atmosphere, in this paper, we perform 1.5D radiative transfer calculations to understand the formation of linear polarization profiles due to resonance scattering in this line at a near limb position. We focus on studying the sensitivity of the resonance scattering polarization to the temperature and the density structures in the atmosphere. We do not include the effects of magnetic and velocity fields in this study. We use clustering analysis to identify linear polarization profiles with similar shape and group them accordingly for our study. We analyze the structure of the linear polarization profiles across 14 clusters, each representing different realizations of the solar atmosphere. Using source function ratio plots at various wing and core wavelength positions, we provide a qualitative explanation of linear polarization profiles in these clusters.