The role of the magnetic field in the formation of the filamentary structures
observed in the interstellar medium (ISM) is a debated topic. The Planck
all-sky maps of linearly polarized emission from dust at 353GHz provide the
required combination of imaging and statistics to study the correlation between
the structures of the Galactic magnetic field and of interstellar matter, both
in the diffuse ISM and in molecular clouds. The data reveal structures, or
ridges, in the intensity map with counterparts in the Stokes Q and/or U maps.
We focus on structures at intermediate and high Galactic latitudes with column
density from 1020 to 1022 cm−2. We measure the magnetic field
orientation on the plane of the sky from the polarization data, and present an
algorithm to estimate the orientation of the ridges from the dust intensity
map. We use analytical models to account for projection effects. Comparing
polarization angles on and off the structures, we estimate the mean ratio
between the strengths of the turbulent and mean components of the magnetic
field to be between 0.6 and 1.0, with a preferred value of 0.8. We find that
the ridges are preferentially aligned with the magnetic field measured on the
structures. This trend becomes more striking for increasing polarization
fraction and decreasing column density. We interpret the increase of alignment
with polarization fraction as a consequence of projections effects. The
decrease of alignment for high column density is not due to a loss of
correlation between the structures and the geometry of the magnetic field. In
molecular complexes, we observe structures perpendicular to the magnetic field,
which cannot be accounted for by projection effects. We discuss our results in
the context of models and MHD simulations, which describe the formation of
structures in the magnetized ISM
