Model dust envelopes around late-type stars

Spectra have been computed for a large number of spherical model circumstellar dust shells, utilizing realistic grain opacities and assuming steady-state radiative equilibrium around cool stars. Results are shown graphically and the important model parameters are evaluated for a wide range of shell optical depths, shell radii, and mass-distribution functions for both silicate and graphite dust grains. For shells containing silicate grains alone, the 10-micron feature can appear in absorption only when there is considerable optical depth at 10 microns in grains colder than about 250 K. This condition can be relaxed somewhat when other warmer grain species coexist. A clearcut distinction exists between models involving 'dirty' silicates, which effectively absorb at short wavelengths, and models involving 'clean' silicates mixed with other more absorptive grains. In the latter case, one must compute a separate energy balance for each grain species, the silicate species generally being much colder. Results indicate that circumstellar silicate grains probably have greater absorptivities for wavelengths between 1 and 5 microns than terrestrial silicates so far indicate.