Infrared luminosity (L_IR; 8–1000 μm) as a function of for the z-GAL sample, including the sources from the Pilot Programme (Neri et al. 2020; Stanley et al. 2023). The sources are identified using the same symbols as in Fig. 7. The infrared luminosities are derived from Paper II (Sect. 4.2). For comparison, we also plot high-z lensed and unlensed galaxies, as well as local ultra-luminous infrared galaxies (ULIRGs) from the literature (also shown in Fig. 7) with references and corresponding symbols given in the upper left panel. No correction for amplification was applied to the ¹²CO and infrared luminosities. The dashed line shows the linear relationship between L_IR and for a gas depletion timescale of τ_dep = 0.2 Gyr (Paper III).