Planck intermediate results. XXXVIII. E- and B-modes of dust
  polarization from the magnetized filamentary structure of the interstellar
  medium
  The quest for a B-mode imprint from primordial gravity waves on the
polarization of the cosmic microwave background (CMB) requires the
characterization of foreground polarization from Galactic dust. We present a
statistical study of the filamentary structure of the 353 GHz Planck Stokes
maps at high Galactic latitude, relevant to the study of dust emission as a
polarized foreground to the CMB. We filter the intensity and polarization maps
to isolate filaments in the range of angular scales where the power asymmetry
between E-modes and B-modes is observed. Using the Smoothed Hessian Major Axis
Filament Finder, we identify 259 filaments at high Galactic latitude, with
lengths larger or equal to 2\deg\ (corresponding to 3.5 pc in length for a
typical distance of 100 pc). These filaments show a preferred orientation
parallel to the magnetic field projected onto the plane of the sky, derived
from their polarization angles. We present mean maps of the filaments in Stokes
I, Q, U, E, and B, computed by stacking individual images rotated to align the
orientations of the filaments. Combining the stacked images and the histogram
of relative orientations, we estimate the mean polarization fraction of the
filaments to be 11 %. Furthermore, we show that the correlation between the
filaments and the magnetic field orientations may account for the E and B
asymmetry and the $C_{\ell}^{TE}/C_{\ell}^{EE}$ ratio, reported in the power
spectra analysis of the Planck 353 GHz polarization maps. Future models of the
dust foreground for CMB polarization studies will need to take into account the
observed correlation between the dust polarization and the structure of
interstellar matter.
