Left panel: (inverse of) aperture corrections as given in Eq. (B.5) plotted against Gaussian source FWHM θ_s. Right panel: T_mb corrections (AP_corplotted against θ_s. In both panels, different ¹²CO beams are shown by different colors as line types as described in the legend: ¹²CO(1–0): solid (red); ¹²CO(2–1): dashed (blue); ¹²CO(3–2): dotted (green); ¹²CO(4–3): dot-dashed (purple). The horizontal (light-weighted) lines of the same type correspond to the exponentially-derived quantities for aperture (left panel) and T_mb corrections (right) for NGC 1140. They converge roughly to a common Gaussian beam size of θ_s ~ 26′′ (see main text for more details).