| Abstract: | 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. |
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