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Astron. Astrophys. 332, 1099-1122 (1998)

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1. Introduction

All present theories of the origin of the Solar System require the existence of an accretion disk around the protosun. The disk results from infall of matter from a slowly rotating molecular cloud core. After an initial phase of build up of the disk of duration of roughly [FORMULA] yrs and a subsequent viscous phase of a few [FORMULA] yrs duration where the protostar acquires most of its mass by accretion from the disk there follows the clearing phase when infall from the parent molecular cloud has nearly ceased. It is believed that formation of a planetary system starts at the end of the viscous phase. The disk material in this stage of the evolution of the protoplanetary accretion disk is more or less unprocessed material from the parent molecular cloud which landed at large distances (beyond [FORMULA] AU) from the protosun on the disk (e.g. Cassen 1994) without being substantially modified during the passage of the accretion shock standing on the disk surface. All material which initially entered the disk close to the star, which has been processed there by strong heating, and some fraction of which has been transported by viscous transport processes out to large distances during the early evolution of the accretion disk, has been transported inwards during the late evolution of the disk and is incorporated into the protosun at the time of the onset of planetary formation.

As the dust material with the composition and structure as inherited from the molecular cloud during the disk accretion process slowly spirals inwards towards the protosun it enters disk regions of progressively higher temperatures. At sufficiently high temperatures energetic lattice vibrational states become populated by thermal excitation and less strongly bound atoms or groups of atoms start to diffuse around within the lattice. The resulting conversion of the amorphous structure of interstellar dust grains into an ordered lattice structure is accompanied by a strong modification of the extinction properties of the disk material. This annealing process and its consequences for the disk structure are discussed in this paper.

The dust material entering the disk from the parent molecular cloud is a mixture of many different solid condensates with quite different chemical compositions (cf. Pollak et al. 1994) originating from very different sources like circumstellar shells of late type giant and supergiant stars or from the ejecta of novae and supernovae. Due to the large variations in the formation conditions of the dust and the element abundances in the sources the composition of the dust mixture entering the protoplanetary accretion disk does not correspond to any mixture which can be formed in a single condensation process in an environment with a mixture of elements corresponding to Solar System element abundances. Such a mixture is chemically only metastable in the sense that at low temperatures (up to several 100 K) the dust material does not participate in chemical reactions which changes the amount of condensed material and the chemical composition of the solids. Such reactions are kinetically forbidden at low temperatures due to high activation energy barriers. At elevated temperatures, however, chemical reactions between solids and the gas phase species and (or) vapourisation of the solids becomes possible. In the warm inner parts of the accretion disk the initial dust mixture then starts to be chemically processed into a mixture of condensates corresponding to that mixture which corresponds to a chemical equilibrium state compatible with the pressure and temperature conditions encountered in the protoplanetary disk, and to the specific element mixture which results from equilibrating all compositional differences in the initial mixture.

Some processes which may be responsible for the destruction of the dust at elevated temperatures have been discussed in Duschl et al. (1996). In this paper we consider the multicomponent mixture of several kinds of dust species which can be expected to be formed in the inner parts of the protoplanetary disk in a state of thermodynamic equilibrium from the initial dust mixture of the molecular cloud. The varying composition of the matter in the Solar Nebula by the appearance and disappearance of different condensates from the most abundant elements with changing temperature has been studied several times by applying the concepts of equilibrium thermodynamics (e.g. Grossman 1972, Lattimer et al. 1978, Saxena & Eriksson 1986, Sharp & Huebner 1990). This paper follows to some extent the concepts of such studies, but we prefer to derive explicit expressions for the equilibrium abundance of the various possible condensates since it is convenient to use such expressions in model calculations for the structure of protoplanetary accretion disks. Especially we broadly discuss which type of dust materials formed from the elements O, Si, Mg, and Fe are the thermodynamically stable dust materials in an element mixture with the specific abundances as observed for the Solar System. These dust materials are of special importance since they represent the main sources of opacity in the disk material in the region of their existence and, thus, are crucial for the structure of the disk. The same holds for solid calcium and aluminium compounds which are stable up to quite high temperatures and are the main opacity sources of the disk material in some inner part of the protoplanetary accretion disk. We discuss in this paper which type of condensate can be expected to be present in the inner part of the disk where aluminium compounds are the dominating opacity sources.

The results of these calculations then are used to calculate a model for a stationary protoplanetary accretion disk in the one zone approximation which self consistently yields the disk structure and the chemical composition of the dust mixture in the warm inner parts of the accretion disk .

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© European Southern Observatory (ESO) 1998

Online publication: March 30, 1998