Ratio of CO[5–4] to CO[2–1] flux versus the average radiation intensity ⟨ U ⟩ for the four BzK galaxies. They are compared to the MW and a sample of local spirals from Kingfish (Dale et al. 2012) observed with Herschel FTS (Liu et al., in prep.), to the average of (U)LIRGs from P12 and the M83 starburst (Wu et al. 2015), and to starburst-like SMGs. The horizontal line shows the limiting flux ratio of CO[5–4] to CO[2–1] expected for a constant brightness temperature. The dashed line shows the best-fitting trend to the data (Eq. (1)).