We use the POLARIS radiative transport code to generate predictions of the two main observables directly sensitive to the magnetic field morphology and strength in filaments: dust polarization and gas Zeeman line splitting. We simulate generic gas filaments with power-law density profiles assuming two density-field strength dependencies, six different filament inclinations, and nine distinct magnetic field morphologies, including helical, toroidal, and warped magnetic field geometries. We present idealized spatially resolved dust polarization and Zeeman-derived field strengths and directions maps. Under the assumption that dust grains are aligned by radiative torques (RATs), dust polarization traces the projected plane-of-the-sky magnetic field morphology. Zeeman line splitting delivers simultaneously the intensity-weighted line-of-sight field strength and direction. We show that linear dust polarization alone is unable to uniquely constrain the 3D field morphology. We demonstrate that these ambiguities are ameliorated or resolved with the addition of the Zeeman directional information. Thus, observations of both the dust polarization and Zeeman splitting together provide the most promising means for obtaining constraints of the 3D magnetic field configuration. We find that the Zeeman-derived field strengths are at least a factor of a few below the input field strengths due to line-of-sight averaging through the filament density gradient. Future observations of both dust polarization and Zeeman splitting are essential for gaining insights into the role of magnetic fields in star and cluster forming filaments.
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