Mean 𝒮, p, and 𝒮 × p as a function of N_H, combining results from Planck maps at optimal resolutions for all lines of sight above |b| > 5° (solid curves). For clarity, 𝒮 has been raised vertically by a factor of 2. Upper and lower dashed red curves show the corresponding values using the low and high total intensity offsets, respectively. In contrast to other plots, the running means are computed here for bins of equal logarithmic size, which therefore do not contain the same number of pixels. Error bars correspond to the uncertainty on the mean, , where σ is the statistical dispersion and n is the number of lines of sight in the corresponding bin. Results of the same analysis with different selection criteria on Galactic latitude are shown by thin black dashed (|b| > 10°) and dotted (|b| > 2°) curves. Horizontal coloured bars indicate for each resolution ω the column density interval ℐ(ω) used in the renormalization procedure (see text). The green band highlights a 25% decrease in 𝒮 × p with column density up to 2 × 10²² cm⁻².