Observed (markers) and modelled (lines) intensity ratios between the HCN J = 1 → 0 and J = 3 → 2 lines as a function of a density measure (Ṁ/ve) of the CSE. Observations of carbon stars are indicated by blue circles, M-type AGB stars by red squares, and S-type AGB stars by green triangles. Model predictions with HCN abundances of 1 × 10-5 (solid line) and 1 × 10-7 (dashed line) are shown for comparison for a circumstellar model as described in the text.
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