  A multi-transition survey of HCN (sub-) millimeter line emission from a large
sample of AGB stars of different chemical type is presented. The data are
analysed and circumstellar HCN abundances are estimated. The sample stars span
a large range of properties such as mass-loss rate and photospheric C/O-ratio.
The analysis of the new data allows for more accurate estimates of the
circumstellar HCN abundances and puts new constraints on chemical models. In
order to constrain the circumstellar HCN abundance distribution a detailed
non-LTE excitation analysis, based on the Monte Carlo method, is performed.
Effects of line overlaps and radiative excitation from dust grains are
included. The median values for the derived abundances of HCN (with respect to
H2) are 3x10-5, 7x10-7 and 10-7 for carbon stars (25 stars), S-type AGB stars
(19 stars) and M-type AGB stars (25 stars), respectively. The estimated sizes
of the HCN envelopes are similar to those obtained in the case of SiO for the
same sample of sources and agree well with previous results from
interferometric observations, when these are available. We find that there is a
clear dependence of the derived circumstellar HCN abundance on the C/O-ratio of
the star, in that carbon stars have about two orders of magnitude higher
abundances than M-type AGB stars, on average. The derived HCN abundances of the
S-type AGB stars have a larger spread and typically fall in between those of
the two other types, however, slightly closer to the values for the M-type AGB
stars. For the M-type stars, the estimated abundances are much higher than what
would be expected if HCN is formed in thermal equilibrium. However, the results
are also in contrast to predictions from recent non-LTE chemical models, where
very little difference is expected in the HCN abundances between the various
types of AGB stars.
