ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Collaboration I-Collaboration O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O B-Model I-Model I-Model I-Model B-Model B-Citation I-Citation I-Citation I-Citation O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: We present a quantitative analysis of the relative orientation in a set of nearby (pc) well-known MCs to quantify the role of the magnetic field in the formation of density structures on physical scales ranging from tens of parsecs to approximately one parsec in the nearest clouds. The present work is an extension of previous findings, as reported by the Planck collaboration, on their study of the polarized thermal emission from Galactic dust. Previous studies include an overview of this emission ( Planck Collaboration Int. XIX 2015 ), which reported dust polarization percentages up to 20% at low , decreasing systematically with increasing to a low plateau for regions with cm. Planck Collaboration Int. XX (2015) presented a comparison of the polarized thermal emission from Galactic dust with results from simulations of MHD turbulence, focusing on the statistics of the polarization fractions and angles. Synthetic observations were made of the simulations under the simple assumption of homogeneous dust grain alignment efficiency. Both studies reported that the largest polarization fractions are reached in the most diffuse regions. Additionally, there is an anti-correlation between the polarization percentage and the dispersion of the polarization angle. This anti-correlation is reproduced well by the synthetic observations, indicating that it is essentially caused by the turbulent structure of the magnetic field. Over most of the sky Planck Collaboration Int. XXXII (2016) analysed the relative orientation between density structures, which is characterized by the Hessian matrix, and polarization, revealing that most of the elongated structures (filaments or ridges) have counterparts in the Stokes and maps. This implies that in these structures, the magnetic field has a well-defined mean direction on the scales probed by Planck . Furthermore, the ridges are predominantly aligned with the magnetic field measured on the structures. This statistical trend becomes more striking for decreasing column density and, as expected from the potential effects of projection, for increasing polarization fraction. There is no alignment for the highest column density ridges in the cm sample. Planck Collaboration Int. XXXIII (2016) studied the polarization properties of three nearby filaments, showing by geometrical modelling that the magnetic field in those representative regions has a well-defined mean direction that is different from the field orientation in the surroundings. In the present work, we quantitatively evaluate the relative orientation of the magnetic field inferred from the Planck polarization observations with respect to the gas column density structures, using the histogram of relative orientations (HRO, Soler et al. 2013 ). The HRO is a novel statistical tool that quantifies the relative orientation of each polarization measurement with respect to the column density gradient, making use of the unprecedented statistics provided by the Planck