Comparison of the average CO[5–4]/CO[2–1] ratio to the average radiation field intensity (⟨ U ⟩, left panel), the star formation efficiency (SFE, center panel), and the star formation surface density (Σ_SFR; right panel), for local spirals (blue), local (U)LIRGs (green), and z = 1.5 normal MS galaxies (black). The best-fitting trend (dashed line) in the left panel is given in Eq. (1), while the relation in the right panel (dotted line) is given in Eq. (3). The cyan trends (right panel) show the predictions of Narayanan & Krumholz (2014) based on their Eq. (19) and Tables 2 and 3, while in red we show the B15 simulation results.