Simulated water-line luminosity as a function of L_FIR. The dashed black line represents the most emitting galaxy in our simulations (ε_SF = 30%, IMF = top-heavy and ), while the dashed gray line corresponds to the least emitting one (ε_SF = 1%, IMF = bottom-heavy and ). The gray-shaded area between these two lines refers to the probed parameter space, and all possible outcomes considered in this study would fall in that regime. Solid blue and red lines refer to the results derived for setups with the top-heavy IMF form for the Galactic and extragalactic M_env − I relations, respectively. Dotted lines show the results for these two correlations, when the standard IMF is applied. In both, i.e., the standard and the top-heavy cases, the free-fall-time scaling factor is set to 1. Circles refer to observational samples (for more details we refer the reader to Sect. 3.1), while the purple line represents the expected relation from Jarugula et al. (2019).