Main physical parameters corresponding to the ¹³CO(2–1) gas (left panel) and the C¹⁸O(2–1) gas (right panel) detected in M31-I(3). The optical depths are shown as function of the ¹³CO(2–1) column density (per km s^-1) and the molecular hydrogen density n_H2. The vertical green-black lines indicate the critical densities computed for a collisional temperature of 20 K (see Table 3). The horizontal thick, full yellow-black lines indicate the ¹³CO(2–1) and the C¹⁸O(2–1) averaged column densities (per unit velocity), while the horizontal thin black lines indicate the corresponding 1σ standard deviation; the hatched area corresponds to the M31-I(3) detection. The horizontal thick, dashed yellow-black lines (thin black lines) correspond to the column densities (1σ standard deviation) computed with standard abundances (Bergin et al. 1995) and the corresponding molecular hydrogen column densities. The full line (dashed and dotted) contour levels correspond to an excitation temperature of 17 K (14 K and 19 K). The optical depths, corresponding to 17 K, are shown as a thick line contour level.