Planck intermediate results. XXXIII. Signature of the magnetic field
  geometry of interstellar filaments in dust polarization maps
  Planck observations at 353GHz provide the first fully-sampled maps of the
polarized dust emission towards interstellar filaments and their backgrounds.
The polarization data provide insight on the structure of their magnetic field
(B). We present the polarization maps of three nearby star forming filament of
moderate column density (NH~10^22cm^-2): Musca, B211, and L1506. We use the
spatial information to separate Stokes I, Q, and U of the filaments from those
of their backgrounds, an essential step to measure the intrinsic polarization
fraction (p) and angle (psi) of each emission component. We find that the
polarization angles in the three filaments (psi_fil) are coherent along their
lengths and not the same as in their backgrounds (psi_bg). The differences
between psi_fil and psi_bg are 12deg, 6deg, and 54deg for Musca, B211, and
L1506, respectively. These differences for Musca and L1506 are larger than the
dispersions of psi, both along the filaments and in their backgrounds. The
observed changes of psi are direct evidence for variations of the orientation
of the plane of the sky (POS) projection of the B-field. As in previous
studies, we find a decrease of several percent of p with NH. We show that the
drop in p cannot be explained by random fluctuations of the orientation of B
within the filaments because they are too small (sigma_psi<10deg). We recognize
the degeneracy between dust alignment efficiency and the structure of B in
causing variations in p, but we argue that the decrease of p from the
backgrounds to the filaments results in part from depolarization associated
with the 3D structure of B: both its orientation in the POS and with respect to
the POS. We do not resolve the inner structure of the filaments, but at the
smallest scales accessible with Planck (~0.2pc), the observed changes of psi
and p hold information on the B-field structure within filaments.
