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

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3. Chemistry in the accretion disk

As in Paper I we consider that the chemistry in a protoplanetary accretion disk in the outer parts of the disk operates far away from thermodynamic and chemical equilibrium. A kinetical treatment of the possible reaction pathways is necessary in this case. We consider explicitly the reaction kinetics in the gas phase and the dust related processes of vapourisation and chemical sputtering.

3.1. Assumptions

The generally low particle density in an accretion disk as compared to laboratory conditions allows one to restrict the gas phase chemistry essentially to binary reactions between neutral atomic and molecular species only. The only exceptions are ternary reactions between the abundant hydrogen particles H and H2 and ternary reactions involving He for which we included the corresponding three-body association reactions. Though H2 formation by this mechanism is generally inefficient under astrophysical conditions, it becomes important in an accretion disk due to the long available accretion timescale [FORMULA] yr and rather high particle densities.

We neglect the possibility of ionisation or dissociation by UV radiation from the central star because in the viscous phase the disk is optically thick in the radial and vertical directions. Such photo-dissociations and the ion-molecule chemistry driven by photoionisation are probably important in the optically thin outer atmospheric layers of the disk which may be illuminated either directly by the central star or indirectly by scattered starlight. This problem can adequately be treated only on the basis of a vertically stratified model including vertical mixing processes, which is beyond the present computational possibilities. We can make, however, the following qualitative estimation: The mass absorption coefficient of the gas-dust mixture in the short wavelength region is of the order of [FORMULA] cm [FORMULA] g-1. The ionising radiation then penetrates only into a depth corresponding to a mass surface density of the order of [FORMULA] g [FORMULA] cm-2. The surface density of the layer for which the photochemistry may be important is, thus, very small compared to the surface density [FORMULA] of the protoplanetary accretion disk over the whole extension of the present planetary system (cf. Eq. (1)). It seems unlikely, then, that such processes can really affect the chemistry in the midplane of the disk, in which we are mainly interested, since only a very small fraction of the total mass contained in the optically thin outer layers is involved in such photoprocesses.

Another source of ionisation are the ever present cosmic rays. They are stopped and absorbed on a length corresponding to a mass surface density of [FORMULA] g [FORMULA] cm-2. The surface density [FORMULA] of the accretion disk in the region of the terrestrial planets is of the order of several [FORMULA] g [FORMULA] cm-2. Thus, in the inner region of the protoplanetary accretion disk the cosmic rays cannot penetrate deeply into the accretion disk. The ion-molecule chemistry driven by cosmic ray ionisation only affects a thin surface layer of the disk and, again, it seems unlikely that this affects the chemistry in the midplane of the disk. This also holds for X-rays emitted from the T Tauri wind region. The thickness of this layer, however, much exceeds the thickness of the layer for which the photochemistry may be important. From (1) we find that [FORMULA] drops to a value of [FORMULA] g [FORMULA] cm-2 at a distance of [FORMULA] AU. In the outermost region of the protoplanetary accretion disk the cosmic rays penetrate deeply into the disk and may substantially modify the chemistry in this part of the disk. Presently, this ionisation is not included in the calculation since in this paper we are interested in the basic chemical processes in the protoplanetary disk triggered by dust destruction in the region of the terrestrial planets.

A third source of ionisation are the extinct radio nuclides, i.e. unstable nuclides with half lifes of the order of 0.1 to [FORMULA] Myr which have all decayed since the formation of our planetary system [FORMULA] Gyr ago. Such nuclei have been present in the early solar system as we know from studies of the isotopic composition of pristine material from our solar system found in certain meteorites (cf. Wasserburg 1985, Swindle 1993). The most important source of ionisation by such extinct radio nuclides was the decay of 26 Al. The ionisation rate by 26 Al was calculated by Umebayashi and Nakano (1981) and seems to be slightly less than that of the cosmic rays, but this source of ionisation is not shielded by overlying matter as in the previous two cases since these nuclei are part of the matter in the accretion disk. We have not included this process in the present calculation for the same reason as above.

In the innermost part of the disk at temperatures above [FORMULA] K the abundant elements of low ionisation potential start to be ionised either by collisional or radiative processes. These processes also are not included in this calculation. All these ionisation processes and the resulting ion-molecule chemistry will be discussed in a forthcoming paper (Finocchi et al. 1997). In this paper we consider the neutral-neutral chemistry only, which dominates the chemistry in the region of the terrestrial planets and the dust destruction.

3.2. Equations for the gas-phase chemistry

The basic equation governing the time evolution of a specific atomic or molecular species is the continuity equation

[EQUATION]

[FORMULA] is the particle density of the considered species, [FORMULA] is the velocity and [FORMULA] denotes the chemical source and sink terms. The most appropriate coordinate system for the description of the accretion disk is the cylindrical one. If s is the radial distance from the protosun, z the vertical height over the midplane of the disk, and if we assume rotational symmetry with respect to the z -axis, the change of [FORMULA] along a streamline is

[EQUATION]

Then (16) simplifies to the following ordinary differential equation for [FORMULA] in a comoving frame

[EQUATION]

The [FORMULA], [FORMULA] are the rate coefficients of the sink and source terms of binary gas phase reactions, and [FORMULA] and [FORMULA] are the rate coefficients of the sink and source terms of ternary gas phase reactions, respectively. In the one-zone approximation for the thin accretion disk Eq. (18) is averaged with respect to the z -dependence. [FORMULA] and the rate coefficients then are replaced by their values in the midplane of the disk. The averaged [FORMULA] is given by (5) and the averaged z -gradient of [FORMULA] is given by (8).

These rate coefficients [FORMULA] are approximated by the standard Arrhenius form

[EQUATION]

[FORMULA] and [FORMULA] are constants and [FORMULA] is the activation energy barrier.

In principle Eq. (18) has to be complemented by a term describing the infall of matter from the surrounding molecular cloud. In the viscous stage of the evolution of the protoplanetary disk it is assumed that the infall has more or less ceased and, for this reason, we have neglected such source terms in our model calculation. There is some observational indication, however, that there is continued infall of matter at a low rate ([FORMULA] / yr) even in the T Tauri phase (van Langenvelde et al. 1994, Bontemps et al. 1996)). This is probably important for the chemistry in the disk since the infall will feed fresh, chemically unprocessed material into the disk. Without a detailed calculation of the infall process, however, it is difficult to judge whether our neglect of infall is really satisfied or whether a more realistic model calculation should include such source terms.

The differential equation (18) describes the time evolution in a comoving frame for each species i in the gas phase within a specific parcel of matter. We have one such equation for each species i. This system of ordinary differential equations has to be solved together with the equations (3), (4) and (6) for the disk structure and an equation for the opacity. Since

  • the opacity changes due to formation or destruction of absorbers by chemical reactions and since
  • the temperature in the disk changes if the opacity changes and since
  • the rates of the chemical processes change if the temperature changes which in turn strongly influences the further chemical evolution of the system,

the structure of the disk and the chemistry in the disk are closely coupled. For this reason the differential equations for the chemical evolution and the equations for the disk structure need to be solved simultaneously. They form a system of Differential Algebraic Equations which requires special methods for its solution. The method used in our calculation for the solution of such systems is described in detail Paper I.

3.3. The chemical reaction network

In Paper I we modeled the chemistry of the four most abundant elements H, C, N and O. In this work we add the silicon and the sulfur chemistry to our chemical network. The silicon chemistry is initiated by the evaporation of the olivine dust particles, which mainly injects SiO into the gas phase. This SiO then undergoes a lot of gas phase reactions which results in the formation of some other abundant silicon bearing molecular species. The sulfur chemistry becomes active at elevated temperatures, when the troilite particles (FeS) start to evaporate (see Sect. 4.1 for a description of our dust model) which mainly injects Fe and S atoms into the gas phase. The S then undergoes a lot of gas phase reactions to form other abundant sulfur bearing molecules especially H2 S.

For the neutral-neutral reactions of the HCON chemistry we use the gas phase reactions given by Mitchell (1984) 2. The system of Mitchell is extended and updated by some reactions given in Baulch et al. (1992). In the list of Baulch et al. the equilibrium constants of most of the reactions are included. Some backward reactions could then be calculated and added to the system. The reactions for the sulfur chemistry and some reactions for the silicon chemistry are taken from Millar et al. (1991) 3. The silicon chemistry has been completed with the gas phase reactions given in Britten et al. (1990).

In the present work we treat a system of totally 106 molecular and atomic species (i.e. 106 differential equations) coupled by about 600 chemical reactions. The system is complemented by three differential equations for the radius changes of the three different dust components (carbon, olivine and troilite - see Sect. 4.1).

A few ternary reactions are included in our chemical reaction network

[EQUATION]

which lead to the formation of H2. The first reaction is surprisingly active in the outer parts of the disk, where the density of H2 is high. The second is important in the innermost parts of the disks and counteracts for a while the molecular hydrogen dissociation (at [FORMULA] 0.1 AU). The rate coefficients of these reactions are taken from Baulch et al. (1992).

Olivine and troilite particles inject during their thermal decomposition SiO and O (for olivine) and S (for troilite) into the gas phase and additionally corresponding amounts of magnesium and iron atoms. The Mg and Fe atoms are not involved in in our reaction network for the neutral chemistry and remain simply as free atoms in the gas phase.

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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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