From parallel to perpendicular - On the orientation of magnetic fields in molecular clouds

We present synthetic dust polarization maps of simulated molecular clouds with the goal to systematically explore the origin of the relative orientation of the magnetic field (B) with respect to the cloud sub-structure identified in density (n; 3D) and column density (N; 2D). The polarization maps are generated with the radiative transfer code POLARIS, which includes self-consistently calculated efficiencies for radiative torque alignment. The molecular clouds are formed in two sets of 3D magnetohydrodynamical simulations: (i) in colliding flows (CF), and (ii) in the SILCC-Zoom simulations. In 3D, for the CF simulations with an initial field strength below similar to 5 mu G, B is oriented either parallel or randomly with respect to the n-structures. For CF runs with stronger initial fields as well as 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(trans) similar or equal to 10(2)-10(3) cm(-3). We suggest that this flip happens if the cloud'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, close to the Galactic average. In 2D, we use the method of Projected Rayleigh Statistics (PRS) to study the relative orientation of B. If present, the flip in orientation occurs in the projected maps at N-trans similar or equal to 10(21 - 21.5) cm(-2). This value is similar to the observed transition value from sub- to supercritical magnetic fields in the interstellar medium. However, projection effects can strongly reduce the predictive power of the PRS method: Depending on the considered cloud or line-of-sight, the projected maps of the SILCC-Zoom simulations do not always show the flip, although it is expected given the 3D morphology. Such projection effects can explain the variety of recently observed field configurations, in particular within a single cloud. Finally, we do not find a correlation between the observed orientation of B and the N-PDF.