Star-formation rate, specific star-formation rate, and “starburstiness” plotted against the hydrogen column density for 65 sources with XMM-Newton spectra and robust SED fitting (including nine with Herschel upper limits). The grey area in panel c) is the main-sequence, as in Figs. 9 and 10. The errors on the hydrogen column density are in the range of  ≲10% to 30%. We do not detect any significant correlation between the two values, even if we split the sample into redshift or luminosity bins, in any of the three plots.