Left: thermal gas pressure plotted against star formation efficiency as indicated by L_IR /M_gas. Filled circles are the H-ATLAS SMGs. We also plot the values of the Milky Way, the Tuffy galaxies, the Antennae galaxies, Arp 220 and HFLS3 in filled triangles for comparison. The colour is coded based on their values of n_H2 . The red line shows the fit to the correlation, which yields a slope of 1.1 ± 0.5 for all the sources. The grey dashed square shows the region where H-ATLAS SMGs reside. Middle: similar correlation plot as in the left panel but only for the cool component from the two-component LVG modelling. There is no correlation found (R_P = 0.01 and p = 0.97). Right: similar correlation plot as in the left panel but only for the warm component in the two-component LVG modelling. The dashed red line is an overlay of exactly the same red line plotted in the left panel. The data points follow the same correlation found in the single component fit with an R_P = 0.37 and p = 0.16. In all the three panels, the legends show the Pearson’s correlation coefficient R_P with corresponding p-value. The values of n_H2 for each point are indicated by the colour bar.