Excitation temperature of CO as a function of the total CO column density. Black error bars are measurements at z = 0 from Burgh et al. (2007). The red filled circle with error bars is our measurement at z = 2.7 towards J 1237 + 0647 while the blue square represents the measurement at z = 2.4 towards J 1439 + 1117 (Srianand et al. 2008b). Only a large range on T_ex (6–16 K) could be determined for the system at z = 1.64 towards SDSS J160457.50 + 220300.5 (Noterdaeme et al. 2009a), and is therefore not represented in the figure. The vertical dotted line is indicative of a change of behaviour: below this limit there is no correlation between N(CO) and T_ex(CO).