The magnetic field and dust filaments in the Polaris Flare

In diffuse molecular clouds, possible precursors of star-forming clouds, the effect of the magnetic field is unclear. In this work we compare the orientations of filamentary structures in the Polaris Flare, as seen through dust emission by Herschel, to the plane-of-the-sky magnetic field orientation ($\rm B_{pos}$) as revealed by stellar optical polarimetry with RoboPol. Dust structures in this translucent cloud show a strong preference for alignment with $\rm B_{pos}$. 70 % of field orientations are consistent with those of the filaments (within 30$^\circ$). We explore the spatial variation of the relative orientations and find it to be uncorrelated with the dust emission intensity and correlated to the dispersion of polarization angles. Concentrating in the area around the highest column density filament, and in the region with the most uniform field, we infer the $\rm B_{pos}$ strength to be 24 $-$ 120 $\mu$G. Assuming that the magnetic field can be decomposed into a turbulent and an ordered component, we find a turbulent-to-ordered ratio of 0.2 $-$ 0.8, implying that the magnetic field is dynamically important, at least in these two areas. We discuss implications on the 3D field properties, as well as on the distance estimate of the cloud.