Histogram of the relative orientations (HRO) between the iso-N_H2 contours and the magnetic field orientation inferred from the Planck 353 GHz observations towards the two regions of the Aquila rift illustrated in Fig. C.1. The figures present the HROs for the lowest, an intermediate, and the highest N_H bin (blue, orange, and dark red, respectively). The bins have equal numbers of selected pixels within the N_H-bins ranges labelled. The horizontal dashed line corresponds to the average per angle bin of 15deg. The widths of the shaded areas for each histogram correspond to the 1σ uncertainties related to the histogram binning operation. Histograms peaking at 0deg correspond to predominantly aligned with iso-N_H2 contours. Histograms peaking at 90deg correspond to predominantly perpendicular to iso-N_H2 contours.