Alignment of the magnetic field in star forming regions and why it might be difficult to observe

Magnetic fields are an important component of the interstellar medium (ISM) and exhibit strongly varying field strengths and a non-trivial correlation with the gas density. Its dynamical impact varies between individual regions of the ISM and correlates with the orientation of the field with respect to the gas structures. Using high-resolution magneto-hydrodynamical simulations of the ISM we explore the connection between the orientation of the field and the dynamical state of the gas. We find that the onset of gravitational instability in molecular gas above a density of $\rho\sim10^{-21}\,\mathrm{g\,cm^{-3}}$ $(n\sim400\,\mathrm{cm^{-3}})$ coincides with an alignment of the magnetic field lines and the gas flow. At this transition the gradient of the density changes from mainly perpendicular to preferentially parallel to the field lines. A connection between the three-dimensional alignment and projected two-dimensional observables is non-trivial, because of a large dispersion of the magnetic field orientation along the line of sight. The turbulent correlation lengths can be small compared to the typical integration lengths. As a consequence the small scale signal of the orientation can sensitively depend on the line of sight or the dynamical state of the cloud, can fluctuate stochastically or be completely averaged out. With higher spatial resolution more small scale structures are resolved, which aggravates the link between magneto-hydrodynamical quantities and projected observables.