Local thermodynamic equilibrium models of the Q branch of ${\mathrm{C}\mathrm{H}}_3^{+}$ at a column density of $N_{\text{vib }}\left({\mathrm{C}\mathrm{H}}_3^{+}\right)=2\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$ at different excitation temperatures using the set of spectroscopic constants from Changala et al. (2023). The higher the excitation temperature is, the more intense the lines at shorter wavelengths are. The black (resp. gray) arrows point to the peak (resp. base) of the lines we use for the ratios plotted in Fig. 7.