“…Other low-J CO lines may be of practical interest, because these levels remain significantly excited in star-forming galaxies; and thus, the associated lines (CO(2-1), CO(3-2), CO(4-3)) are typically brighter and easier to detect than the ground-state transition CO(1-0). There have been various predictions of the CO luminosity functions both for the J= 1 0 transition and for intermediate and high-J lines, using either theoretical models (e.g., Lagos et al 2011Lagos et al , 2012Lagos et al , 2014Popping et al 2014aPopping et al , 2014bPopping et al , 2016 or empirical relations (e.g., Sargent et al 2012Sargent et al , 2014da Cunha et al 2013;Vallini et al 2016).…”