Sub-mm emission line deep fields: CO and [CII] luminosity functions out to z = 6

Nowthat Atacama Large (Sub)Millimeter Array is reaching its full capabilities, observations of sub-mm emission line deep fields become feasible. We couple a semi-analytic model of galaxy formation with a radiative transfer code to make predictions for the luminosity function of CO J =1-0 out to CO J = 6-5 and [C II] at redshifts z= 0-6. We find that (1) our model correctly reproduces the CO and [C II] emission of low- and high-redshift galaxies and reproduces the available constraints on the CO luminosity function at z ≤ 2.75; (2) we find that the CO and [C II] luminosity functions of galaxies increase from z = 6 to z = 4, remain relatively constant till z = 1 and rapidly decrease towards z = 0. The galaxies that are brightest in CO and [C II] are found at z ~ 2; (3) the CO J = 3-2 emission line is most favourable to study the CO luminosity and global H₂ mass content of galaxies, because of its brightness and observability with currently available sub-mm and radio instruments; (4) the luminosity functions of high-J CO lines show stronger evolution than the luminosity functions of low-J CO lines; (5) our model barely reproduces the available constraints on the CO and [C II] luminosity function of galaxies at z ≥ 1.5 and the CO luminosity of individual galaxies at intermediate redshifts. We argue that this is driven by a lack of cold gas in galaxies at intermediate redshifts as predicted by cosmological simulations of galaxy formation.