Planck intermediate results: XXXIII. Signature of the magnetic field geometry of interstellar filaments in dust polarization maps

Planck observations at 353 GHz provide the first fully-sampled maps of the polarized dust emission of interstellar filaments and their background (i.e., the emission from outside the filaments, be it associated to the filament or not), offering unprecedented information on the structure of the magnetic field. We present the polarization properties of three nearby filaments, the Musca filament, and the Taurus B211 and L1506 filaments. These three filaments have similar total intensities of dust emission (Stokes I), while the variations of the Stokes Q and U parameters of linear polarization are all different: the Musca filament is visible in both the Q and U maps, B211 and L1506 are seen in the Q map but are not distinguishable in the U map, and the Q increase for L1506 is not spatially coincident with that of I. They all offer 3 pc segments, along which both the background and filament Stokes parameters are almost uniform. In all three cases, the polarization fraction towards the filaments is smaller than that of their background. The polarized emission results from the combination of the three dimensional magnetic field (B) structure and the dust polarization properties. We model the variations of the Stokes parameters across the filaments using variations solely of the orientation of the magnetic field, assuming constant dust polarization fraction (p0). Our modelling shows that the magnetic fields in the filaments and their background have an ordered component with a mean orientation that we can infer from Planck polarization data. We find that for L1506, the depolarization arises only from the rotation by 65 of the plane of the sky (POS) projection of the field (BPOS) in the filament with respect to that of its background. For Musca and B211, the drop in the polarization fraction is due mostly to different orientations of B with respect to the POS inside and outside the filaments, and these relative orientations depend on the choice of p0. The magnetic fields inside the Musca and B211 filaments are nearly orthogonal to their long axes, but almost parallel in the case of the L1506 filament. In all three filaments, the field does not have the same orientation as in the background, with a different configuration in each case. In spite of the degeneracy between p0 and the angle of B with respect to the POS, we find that for Musca and B211 the quality of the fit is better for p0 values larger than 13% and 7%, respectively.