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 ( B _ { pos } ) as revealed by stellar optical polarimetry with RoboPol .
Dust structures in this translucent cloud show a strong preference for alignment with 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 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 .