Magnetic fields in star forming systems (I): Idealized synthetic
  signatures of dust polarization and Zeeman splitting in filaments
  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.
