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Astron. Astrophys. 320, 553-567 (1997)

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1. Introduction

Single stars with an initial mass of less than [FORMULA] solar masses arrive at the end of their life on the asymptotic giant branch (AGB). In this stage of their evolution they are cool supergiant stars with surface temperatures [FORMULA] K and their luminosities are typically of the order of [FORMULA] (Iben 1991). This last phase of stellar life is governed by strong mass loss which is accompanied and probably driven by dust condensation in the stellar wind. The formation of thick circumstellar dust shells makes such stars prominent emitters of infrared emission. Thousands of such objects have been detected by the IRAS satellite. They are the main sites of dust formation in space.

The unraveling of the basic microscopic processes responsible for the formation of dust in these circumstellar shells is still an unsolved problem. Despite much effort (for a review see E. Sedlmayr 1994) no definite conclusion has been arrived at for the basic processes working in the two different main types of cosmic dust making factories:

  • the circumstellar shells around the M-stars with an oxygen rich element mixture which form some kind of iron-magnesium-silicate dust and
  • the circumstellar shells around the C-stars with a carbon rich element mixture which form some kind of carbon dust, probably just ordinary soot.

The main obstacle to further progress is the lack of fundamental data on the basic chemical reactions in the gas phase and at the surfaces of growing clusters and on the properties of the particles involved in the process. The present state and the requirements for future laboratory research is described in Patzer et al. (1995). In this paper we attempt to study one possible process for the nucleation of dust in circumstellar shells around M-stars from the very beginning by calculating the basic properties of the clusters involved in the nucleation process and determining from this the nucleation rate.

The main dust component formed in M-star dust shells consists of some kind of amorphous silicate dust (for a discussion of its structure see Nuth and Hecht 1990) but this dust material cannot nucleate directly from the gas phase as particles with this composition and structure. Instead it requires for its formation the formation of some different kind of seed nuclei (e.g. Gail and Sedlmayr 1987). At first glance the most promising process for this seems to be first nucleating SiO and then growing the magnesium-silicate dust by surface reactions with Mg, Fe and SiO together with the abundant water vapour as an oxidizing agent. A model calculation for the stellar wind, however, indicated that this process yields a lower dust formation temperature than is generally derived from models for the IR-emission from circumstellar shells (Gail and Sedlmayr 1986) and, thus, a different process of formation of seed nuclei seems to be required in most cases. There are some indications of the existence of additional dust components in M-star shells (see the discussion in Henning et al. 1995) which may be pure magnesium-iron oxides. We explore in this paper the possibility that the direct nucleation of MgO from the gas phase occurs in circumstellar shells of M-stars which either forms MgO dust particles of their own or serve as seed nuclei for silicate dust formation.

For this purpose we calculated the properties of MgO using a semi-empirical potential model which extends the classical potential model used for calculating cluster structures of alkali halide ionic clusters to alkaline earth clusters which are not pure ion clusters but for which the bonding shows a marked covalent contribution. The structure of a [FORMULA] -cluster is calculated from the potential model and these results are used to calculate thermodynamic functions for the clusters and their equilibrium abundances. This enables us to determine the nucleation rate of MgO in circumstellar shells.

The plan of this paper is as follows. In Sect. 2 we define the potential model for MgO, in Sect. 3 we present the results of the calculations of the cluster structures, Sect. 4 discusses the cluster size spectrum in a thermodynamic equilibrium state, Sect. 5 shows how this can be used for calculating the nucleation rate. Sect. 6 gives our conclusions and the appendix gives a brief description of the method used for determining the minima of the potential hypersurface.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998