L_{[CII ]}/L_IR vs. L_IR for our sample of simulated galaxies (grey shaded areas) at z = 4.7. Local galaxies (orange circles) are the GOALS luminous infrared galaxy sample (Díaz-Santos et al. 2017); a mean correction has been applied to their L_{[ CII]} to mimic the effects of CMB heating and attenuation. High-resdhift galaxies (blue circles) are extracted from Table  B.1. We give on the bottom of the figure the mean densities, ISRF, and metallicities (in log), for bins of 0.5 dex in log  L_IR. The [CII] deficit naturally arises in our model. It is well correlated with the intensity of the ISRF.