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The advent of new sub-millimeter observational facilities has stimulated thedesire to model the sub-mm line emission of galaxies within cosmological galaxyformation models. This is typically done in post-processing by applyingsub-resolution recipes to describe the properties of the unresolvedinterstellar medium. At the same time, while there is freedom in how oneimplements these sorts of recipes, the impact of various choices has yet to besystematically explored in simulations. In this paper, we do just that. Wecombine a semi-analytic model of galaxy formation with chemical equilibriumnetworks and numerical radiative transfer models and explore how differentchoices for the sub-grid modeling affect the predicted CO, [CI], and [CII]emission of galaxies. We find that a key component for a successful modelincludes a molecular cloud mass-size relation and scaling for the ultravioletand cosmic ray radiation field that varies based on local ISM properties. Ourmost successful model adopts a Plummer profile for the radial densitydistribution of gas within molecular clouds. On the other hand, differentassumptions for the clumping of gas within molecular clouds and changes in theslope of the molecular cloud mass distribution function hardly affect the CO,[CI], and [CII] luminosities of galaxies. At fixed star-formation rate the[CII]-SFR ratio of galaxies scales inversely with the pressure acting onmolecular clouds, increasing the molecular clouds density and hence decreasingthe importance of [CII] line cooling. Overall we find that it is essential thata wide range of sub-mm emission lines arising in vastly different phases of theISM are used as model constraints in order to limit the freedom in sub-gridchoices and we present the details of the most successful model variant.

The art of modeling CO, [CI], and [CII] in cosmological galaxy formation models