2016A&A...596A..93S

Within four nearby (d<160pc) molecular clouds, we statistically evaluated the structure of the interstellar magnetic field, projected on the plane of the sky and integrated along the line of sight, as inferred from the polarized thermal emission of Galactic dust observed by Planck at 353GHz and from the optical and near-infrared polarization of background starlight. We compared the dispersion of the field orientation directly in vicinities with an area equivalent to that subtended by the Planck effective beam at 353GHz (10') and using the second-order structure functions of the field orientation angles. We found that the average dispersion of the starlight-inferred field orientations within 10'-diameter vicinities is less than 20°, and that at these scales the mean field orientation is on average within 5° of that inferred from the submillimetre polarization observations in the considered regions. We also found that the dispersion of starlight polarization orientations and the polarization fractions within these vicinities are well reproduced by a Gaussian model of the turbulent structure of the magnetic field, in agreement with the findings reported by the Planck Collaboration at scales l>10' and for comparable column densities. At scales l>10', we found differences of up to 14.7 between the second-order structure functions obtained from starlight and submillimetre polarization observations in the same positions in the plane of the sky, but comparison with a Gaussian model of the turbulent structure of the magnetic field indicates that these differences are small and are consistent with the difference in angular resolution between both techniques. The differences between the second-order structure functions calculated with each technique suggests that the increase in the angular resolution obtained with the starlight polarization observations does not introduce significant corrections to the dispersion of polarization orientations used in the calculation of the molecular-cloud-scale magnetic field strengths reported in previous studies by the Planck Collaboration.