SPRITZ is sparkling: Simulated CO and [C II] luminosities

Aims. We present a new prediction for the luminosity functions (LFs) of the [C II] line at 158 mu M, of the CO lines from J = 0 to J = 24, and of the molecular gas mass density up to z = 10, using the Spectro-Photometric Realisations of Infrared-selected Targets at all-z (SPRITz) simulation.Methods. We update the state-of-the-art phenomenological simulation SPRITZ to include both the CO (J <= 24) and the [C II] line luminosities. This has been performed using different empirical and theoretical relations to convert the total infrared luminosity (or star formation rate, SFR) to the [C II] or CO luminosity. The resulting line LFs were compared for validation with a large set of observations available in the literature. We then used the derived CO and [C II] line luminosities to estimate the molecular gas mass density and compare it with available observations.Results. The CO and [C II] LFs presented here are in good agreement with all the available observations. In particular, the best results for [C II] are obtained deriving the [C II] luminosity directly from the SFR, but considering a dependence of this relation on the gas metallicity. For all the CO LFs, the estimates favoured by the data are derived considering different relations, depending on the ionisation mechanism dominating each galaxy, namely star formation or active galactic nuclei, and, moreover, by deriving the J >= 4 CO lines directly from the [C II] luminosity. However, further data are necessary to fully distinguish between models. Finally, the best agreements with observations of the molecular gas mass density are derived by converting the [C II] luminosity to H-2 mass, using a [C II]-to-H-2 conversion similar to 130 M-circle dot/L-circle dot. All the line LFs, useful for planning and interpreting future observations, are made publicly available.