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Within ten nearby (d < 450 pc) Gould Belt molecular clouds we evaluatestatistically the relative orientation between the magnetic field projected onthe plane of sky, inferred from the polarized thermal emission of Galactic dustobserved by Planck at 353 GHz, and the gas column density structures,quantified by the gradient of the column density, $N_H$. The selected regions,covering several degrees in size, are analyzed at an effective angularresolution of 10' FWHM, thus sampling physical scales from 0.4 to 40 pc in thenearest cloud. The column densities in the selected regions range from $N_H\approx 10^{21}$ to $10^{23}$ cm$^{-2}$, and hence they correspond to the bulkof the molecular clouds. The relative orientation is evaluated pixel by pixeland analyzed in bins of column density using the novel statistical tool called"Histogram of Relative Orientations". Throughout this study, we assume that thepolarized emission observed by Planck at 353 GHz is representative of theprojected morphology of the magnetic field in each region, i.e., we assume aconstant dust grain alignment efficiency, independent of the local environment.Within most clouds we find that the relative orientation changes progressivelywith increasing $N_H$, from preferentially parallel or having no preferredorientation to preferentially perpendicular. In simulations ofmagnetohydrodynamic turbulence in molecular clouds this trend in relativeorientation is a signature of Alfv\'enic or sub-Alfv\'enic turbulence, implyingthat the magnetic field is significant for the gas dynamics at the scalesprobed by Planck. We compare the deduced magnetic field strength with estimateswe obtain from other methods and discuss the implications of the Planckobservations for the general picture of molecular cloud formation andevolution.

Planck intermediate results. XXXV. Probing the role of the magnetic field in the formation of structure in molecular clouds