Representative RADEX CH₃OH minimization plots for IRAS 16293E (see also Figure C1 in Scibelli et al. 2024). Plotted in each panel is the difference in the observed brightness temperature, T_mb, and the RADEX-calculated brightness temperature, T_radex, divided by the noise level, σ_T, versus the RADEX-calculated column density, N. When the RADEX model best fits the observations, |T_mb−T_radex|/σ_T was minimized and the best-fit N was found. In the top panels minimization curves are shown for the CH₃OH E transitions from the ARO 12 m observations at different T_k values (in upper right corner of each plot). In the bottom panels minimization curves are shown for CH₃OH A transitions, from both the ARO 12 m and Yebes 40 m observations, at a fixed T_k = 7 K and for varying θ_src values. In each plot the solid lines indicate when f – 1 was assumed and the dashed lines indicate that a specific θ_src has been used in the fit.