Magnetic fields in molecular clouds: Limitations of the analysis of
  Zeeman observations
  Context. Observations of Zeeman split spectral lines represent an important
approach to derive the structure and strength of magnetic fields in molecular
clouds. In contrast to the uncertainty of the spectral line observation itself,
the uncertainty of the analysis method to derive the magnetic field strength
from these observations is not been well characterized so far.
  Aims. We investigate the impact of several physical quantities on the
uncertainty of the analysis method, which is used to derive the line-of-sight
(LOS) magnetic field strength from Zeeman split spectral lines.
  Methods. We simulate the Zeeman splitting of the 1665 MHz OH line with the 3D
radiative transfer (RT) extension ZRAD. This extension is based on the line RT
code Mol3D (Ober et al. 2015) and has been developed for the POLArized
RadIation Simulator POLARIS (Reissl et al. 2016).
  Results. Observations of the OH Zeeman effect in typical molecular clouds are
not significantly affected by the uncertainty of the analysis method. We
derived an approximation to quantify the range of parameters in which the
analysis method works sufficiently accurate and provide factors to convert our
results to other spectral lines and species as well. We applied these
conversion factors to CN and found that observations of the CN Zeeman effect in
typical molecular clouds are neither significantly affected by the uncertainty
of the analysis method. In addition, we found that the density has almost no
impact on the uncertainty of the analysis method, unless it reaches values
higher than those typically found in molecular clouds. Furthermore, the
uncertainty of the analysis method increases, if both the gas velocity and the
magnetic field show significant variations along the line-of-sight. However,
this increase should be small in Zeeman observations of most molecular clouds
considering typical velocities of ~1 km/s.
