Radiative transfer in dust clouds - IV. Circumstellar dust shells around carbon stars

The solution of the equation of radiative transfer developed by Rowan-Robinson is applied to a sample of 41 carbon stars and three others displaying similar characteristics. All of these have appreciable infrared excesses. The models, consisting of a star in a spherically symmetric circum-stellar dust shell (CDS), are compared with the available observational data. All the CDS can be successfully modelled with an $$n(r)\propto r^{-2}$$ density distribution, consistent with steady outflow at a constant velocity. Amorphous carbon-type grains, having a $$Q_\nu \propto \nu$$ absorption efficiency, are found to model the sources with considerably more success than graphite grains, though it has also proved necessary to modify this somewhat at wavelengths λ ≲ 1.4 µm in order to fit the shortest wavelength data where available. We adopt T_s (temperature of central blackbody source) = 2500 K for stars of types C4–C6 and 2000 K for C7–C9. In particular we compare our model of IRC + 10216 with the available infrared size measurements and with the models of other authors.