Radiative transfer in dust clouds - III. Circumstellar dust shells around late M giants and supergiants

We have modelled the infrared emission from 85 late-type M stars, essentially all such stars in the AFGL catalogue with substantial circumstellar dust shells and for which adequate observational data are currently available. We have investigated the dependence of the emergent spectrum on the temperature of the stars, the condensation temperature of the grains, and the density distribution, optical depth and extent of the shell. We find consistent models for most stars using dirty silicate grains, with an $$n(r)\propto r^{-2}$$ density distribution and a grain melting temperature of 1000 K. This makes the silicate interpretation of the 10 µm feature far more plausible than that of Hoyle & Wickramasinghe which postulates volatile organic molecules. We have made allowance in an approximate way for the effect of molecular bands. Although these bands have a dramatic effect on the spectrum of late-type stars at visual wavelengths, there is little effect on the infrared emission from the circumstellar shell. Several stars have been modelled at different phases and there is evidence for a phase lag between the radius and temperature variations. All stars in our study except GL 915, VY CMa and NML Cyg are consistent with having spherically symmetric shells. Except for VY CMa and NML Cyg, for which other evidence suggests a disc geometry, the intensity distributions predicted by our models are consistent with interferometric measurements at infrared wavelengths.