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Astron. Astrophys. 325, 1264-1279 (1997)

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1. Introduction

The generally accepted model for stellar and solar system formation is the collapse of a rotating molecular cloud. The centrifugal forces lead to the formation of a flat structure, a protostellar accretion disk. Most of the infalling material is first incorporated into this disk and then moves inwards and finally becomes part of the newly forming star. This inwards directed accretion of the matter in the disk is due to some kind of viscous process probably generated by turbulent motions.

The evolution of a protostellar accretion disk can be divided into three distinct phases (Cameron 1988):

During the first stage of formation, the protoplanetary disk is built up by infalling matter from the surrounding molecular cloud. This phase lasts for about 105 years.

In the second phase, the external supply of mass has nearly ceased and most of the mass is concentrated in the young central star. The protoplanetary disk is now formed: a thin disk of matter revolving at nearly the local Keplerian velocity around the protosun. In this disk most of the material drifts inwards while angular momentum is transported outwards causing the disk to spread out (Lynden-Bell and Pringle 1974). The mass of the disk itself is small compared to the central mass and the disk is geometrically thin. A characteristic time scale for the duration of this stage is the viscous time scale, which is [FORMULA] years. In this viscous stage, the formation of planetary bodies due to the agglomeration of dust particles in the middle plane of the accretion disk is possible.

During the third and last stage, the gaseous component (mostly the light elements) of the accretion disk is dispersed, probably by the action of the powerful bipolar stellar wind of the central star in its T Tauri phase. T Tauri stars are the first optically visible stage during formation process of low-mass stars. The heavier metallic elements can be present as newly formed planetary bodies: a solar system, then, is born. The duration of this last phase could be somewhat longer ([FORMULA] years, e.g. Beckwith and Sargent 1993).

In this paper we consider the second stage (the viscous phase) of the accretion disk evolution and calculate the chemical composition of the disk material from the reaction kinetics of the gas phase in the disk's middle plane from the outermost edge of the disk down to a position close to the transition layer between the disk and the protosun. Although the prospects for probing the chemical compositions of accretion disks around young stars are extremely dim at present, the chemical evolution of the disk material in this stage is of fundamental importance for understanding the formation of planetary systems in general, and of our own Solar System in particular. For this we consider a gas parcel drifting inwards to the disk's center. The chemistry in this particular parcel is calculated by solving numerically an extended chemical reactions network for the gas phase chemistry, the vapourisation and chemical destruction of dust grains together with a semi-analytical model for the structure of the accretion disk in a one-zone approximation (in the vertical direction).

The resulting differential-algebraic system is extremely stiff and highly non linear, mainly because of the exponential temperature dependence of the rate coefficients and the close coupling between chemistry and temperature structure in the disk. The equations are solved by using the powerful integrator DAESOL (Bleser 1986, Eich 1987, Bauer 1994) which in our previous work (Bauer et al. 1996, hereafter called Paper I) turned out to be very efficient for this kind of problems.

The plan of this paper is as follows: In Sect. 2 we briefly describe the disk model on which our calculation is based and our approximation for the gas opacity. Section 3 presents the equations of the gas phase chemistry and the chemical network. In Sect. 4 we describe our model for the dust and the ices, their vapourisation and destruction. Our results and interpretations are given in Sect. 5. The results are summarised in Sect. 6.

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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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