Radiative transfer in dust clouds - II. Circumstellar dust shells around early M giants and supergiants

The solution of the equation of radiative transfer through dust shells, developed by Rowan-Robinson (1980), is applied to a sample of 27 stars of spectral types M0 to M4 and having appreciable infrared excess. The models, consisting of a star in a spherically symmetric circumstellar 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. The dust grains used are the dirty silicate grains of Jones & Merrill (1976), but we have found it necessary to reduce the absorption efficiency at 8–10 μm in order ot obtain consistency with the detailed spectrophotometry available for $$\alpha\,\text{Ori}\,\mu$$ Cep and PZ Cas. For three stars $$(\alpha\,\text{Ori}\,\mu$$ Cep and TV Gem) the temperature T₁ of the hottest grains is 1000 K, for 12 stars a better fit is obtained with T₁ = 500 K, while for the remainder the available observations are not sufficiently detailed to allow T₁ to be determined. Our model for α Ori is consistent with most of the measurements of infrared size made to date. We compare it also with the models of previous authors. Intensity profiles are given for several models, and we draw attention to the bright rim of radiation expected at all infrared wavelengths at the inner edge of the dust shell; this may contribute to the unresolved component of interferometric observations.