Multi-transition spectra (histograms) of HCN line emission (HHT data from Bieging et al. 2000), overlaid by spectra from the best-fit model (solid lines; assuming a Guassian abundance distribution), towards top panels – the carbon star R For using a fractional HCN abundance f0 = 4.0 × 10-5 and an envelope size re = 9.3 × 1015 cm. Middle panels – S-type AGB star W Aql using a fractional HCN abundance f0 = 1.2 × 10-6 and an envelope size re = 1.3 × 1016 cm. Bottom panels – M-type AGB star TX Cam using a fractional HCN abundance f0 = 3.5 × 10-7 and an envelope size re = 2.0 × 1016 cm are also shown (solid lines). The hyperfine splitting of the J = 1 → 0 transition significantly broadens the line. This effect is explicitly taken into account in the modelling. The calibration uncertainty in the observed spectra is ≈±20%.
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