Planck intermediate results: XXXII. The relative orientation between the magnetic field and structures traced by interstellar dust

The role of the magnetic field in the formation of the filamentary structures observed in the interstellar medium (ISM) is a debated topic owing to the paucity of relevant observations needed to test existing models. The Planck all-sky maps of linearly polarized emission from dust at 353 GHz provide the required combination of imaging and statistics to study the correlation between the structures of the Galactic magnetic field and of interstellar matter over the whole sky, both in the diffuse ISM and in molecular clouds. We focus our study on structures at intermediate and high Galactic latitudes, which cover two orders of magnitude in column density, from 1020 to 1022 cm-2. We use analytical models to account for projection effects. We discuss our results in the context of models and MHD simulations, which attempt to describe the respective roles of turbulence, magnetic field, and self-gravity in the formation of structures in the magnetized ISM.