Top: total ¹³CO column density as estimated over a range of T_ex from each line transition separately using Eq. (4). Bottom: distribution of η₂₁ (Eq. (6)) over the same range of T_ex. Since we have defined η₂₁ as the absolute difference between the two total column density estimates, the T_ex in this voxel is determined by locating the global minimum, as shown by the vertical dotted black line. For this example voxel, we find T_ex = 7.8 K.