RADEX models (with ΔV = 20 km s^-1) of ¹²CO line ratios plotted against T_kin: the left panel shows ¹²CO(2–1)/¹²CO(1–0) and the right ¹²CO(3–2)/¹²CO(1–0). The observations of NGC 1140, shown as a (black) filled circle, have been corrected for beam dilution assuming an exponential source distribution as described in Sect. 4 (see also Figs. 3 and 4). The approximate best-fit RADEX model for NGC 1140 (see Sect. 7.3) is shown in both panels as (purple) solid curves that coincide very well with the observations of NGC 1140. Also shown are three additional parameter combinations of ¹²CO column density N_12CO and volume density n_H2. The R₃₁ parameter space occupied by the other galaxies (like Fig. 4, no beam corrections) is shown in the right-hand panel as a hatched region and solid horizontal lines (NGC 7077, UM 448, and an upper limit for Mrk 996).