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Among all the available observational techniques for studying magnetic fieldsin the dense cold phase of the interstellar medium, linear polarization ofspectral lines, referred to in the literature as the Goldreich-Kylafis effect(Goldreich & Kylafis 1981; hereafter "GK effect"), remains one of the mostunderutilized methods. In this study, we implement the GK effect into themultilevel, non-local thermodynamic equilibrium radiative transfer code PyRaTE.Different modes of polarized radiation are treated individually with separateoptical depths computed for each polarization direction. We benchmark ourimplementation against analytical results and provide tests for variouslimiting cases. In agreement with previous theoretical results, we find that inthe multilevel case the amount of fractional polarization decreases whencompared to the two-level approximation, but this result is subject to therelative importance between radiative and collisional processes. Finally, wepost-process an axially symmetric, non-ideal magnetohydrodynamicchemo-dynamical simulation of a collapsing prestellar core and providetheoretical predictions regarding the shape (as a function of velocity) of thepolarization fraction of CO during the early stages in the evolution ofmolecular clouds. The code is freely available to download.

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