A multilevel implementation of the Goldreich-Kylafis effect into the radiative transfer code PyRaTE

Among all the available observational techniques for studying magnetic fields in the dense cold phase of the interstellar medium, linear polarization of spectral lines, referred to in the literature as the Goldreich-Kylafis effect (Goldreich & Kylafis 1981; hereafter "GK effect"), remains one of the most underutilized methods. In this study, we implement the GK effect into the multilevel, non-local thermodynamic equilibrium radiative transfer code PyRaTE. Different modes of polarized radiation are treated individually with separate optical depths computed for each polarization direction. We benchmark our implementation against analytical results and provide tests for various limiting cases. In agreement with previous theoretical results, we find that in the multilevel case the amount of fractional polarization decreases when compared to the two-level approximation, but this result is subject to the relative importance between radiative and collisional processes. Finally, we post-process an axially symmetric, non-ideal magnetohydrodynamic chemo-dynamical simulation of a collapsing prestellar core and provide theoretical predictions regarding the shape (as a function of velocity) of the polarization fraction of CO during the early stages in the evolution of molecular clouds. The code is freely available to download.