Aims. We study the growth of dust in oxygen-rich stellar outflows in order to find out to which extent dust growth models can quantitatively reconcile with the quantities and nature of dust as derived from observations of the infrared emission from circumstellar dust shells.
Methods. We use a set of nine well-observed massive supergiants with optically thin dust shells as testbeds because of the relatively simple properties of the outflows from massive supergiants, contrary to the case of AGB stars. Models of the infrared emission from their circumstellar dust shells are compared to their observed infrared spectra to derive the essential parameters that rule dust formation in the extended envelope of these stars. The results are compared with a model for silicate dust condensation.
Results. For all objects, the infrared emission in the studied wavelength range, between 6 and 25 μm, can be reproduced rather well by a mixture of non-stoichiometric iron-bearing silicates, alumina, and metallic iron dust particles. For three objects (μ Cep, RW Cyg, and RS Per), the observed spectra can be sufficiently well reproduced by a stationary and (essentially) spherically symmetric outflow in the instantaneous condensation approximation. For these objects, the temperature at the onset of massive silicate dust growth is of the order of 920 K and the corresponding outflow velocity of the order of the sound velocity. This condensation temperature is only somewhat below the vapourisation temperature of the silicate dust and suggests that the silicate dust grows on the corundum dust grains that formed well inside of the silicate dust shell at a much higher temperature. The low expansion velocity at the inner edge of the silicate dust shell further suggests that, for these supergiants, the region inside the silicate dust shell has an only subsonic average expansion velocity, though a high degree of supersonic turbulence is indicated by the widths of spectral lines.
Conclusions. Our results suggest that for the two major problems of dust formation in stellar outflows, that is (i) formation of seed nuclei and (ii) their growth to macroscopic dust grains, we are gradually coming close to a quantitative understanding of the second item.
Temperature distributions in circumstellar dust shells
