Total intensity (top) and linear polarisation fraction (bottom) as a function of hydrogen column density. All values have been binned within 100 logarithmic bins in N_H. The solid lines always indicate the average of the binned quantity over all six halos and all four observer positions, while the shaded regions indicate the standard deviation across the halos and positions. Different colours correspond to different dust allocation recipes, as indicated in the legend. Top panel: binned quantity is the average total intensity. Bottom panel: the binned quantities for the lower and upper lines correspond to respectively the mean linear polarisation fraction and the 99% percentile of the linear polarisation fraction in the bin.