From parallel to perpendicular -- On the orientation of magnetic fields
  in molecular clouds
  We present synthetic dust polarization maps of simulated molecular clouds
(MCs) with the goal to systematically explore the origin of the relative
orientation of the magnetic field ($\bf{B}$) with respect to the MC
sub-structures identified in density ($n$; 3D) and column density ($N$; 2D).
The polarization maps are generated with the radiative transfer code POLARIS,
including self-consistently calculated efficiencies for radiative torque
alignment. The MCs are formed in two sets of 3D MHD simulations: in (i)
colliding flows (CF), and (ii) the SILCC-Zoom simulations. In 3D, for the CF
simulations with an initial field strength below $\sim$5 $\mu$G, $\bf{B}$ is
oriented parallel or randomly with respect to the $n$-structures. For CF runs
with stronger initial fields and all SILCC-Zoom simulations, which have an
initial field strength of 3 $\mu$G, a flip from parallel to perpendicular
orientation occurs at high densities of $n_\text{trans}$ $\simeq$ 10$^2$ -
10$^3$ cm$^{-3}$. We suggest that this flip happens if the MC's mass-to-flux
ratio, $\mu$, is close to or below the critical value of 1. This corresponds to
a field strength around 3 - 5 $\mu$G. In 2D, we use the Projected Rayleigh
Statistics (PRS) to study the orientation of $\bf{B}$. If present, the flip in
orientation occurs at $N_\text{trans}$ $\simeq$ 10$^{21 - 21.5}$ cm$^{-2}$,
similar to the observed transition value from sub- to supercritical magnetic
fields in the ISM. However, projection effects can reduce the power of the PRS
method: Depending on the MC or LOS, the projected maps of the SILCC-Zoom
simulations do not always show the flip, although expected from the 3D
morphology. Such projection effects can explain the variety of recently
observed field configurations, in particular within a single MC. Finally, we do
not find a correlation between the observed orientation of $\bf{B}$ and the
$N$-PDF.
