Top panel: observed CO SLEDs for the ULIRGs in our sample. The color coding is shown in the legend on top of the figure. Bottom panel: we compute the average CO SLED of our sample, and compare it to other well-studied galaxies, the starburst galaxy M 82 (Mashian et al. 2015), the nearby ULIRG NGC 6240 (hosting a dual AGN and a SB; Papadopoulos et al. 2014), and the Milky Way inner disk (Fixsen et al. 1999). We also show the average CO SLEDs for a sample of local (U)LIRGs studied by Papadopoulos et al. (2012), and a sample of high-z SMGs (Bothwell et al. 2013). In both panels, the dotted gray line corresponds to a constant brightness temperature in the Rayleigh-Jeans regime (i.e., S​_ν ∼ ν²), which is the trend expected for thermally excited CO emission, in the optically thick limit for all lines. All line fluxes are in units of Jy km s⁻¹, normalized by the CO(2−1) flux measured by APEX.