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

5. Results and interpretation

Fig. 3 shows the chemical composition of the gas phase in the disk's central plane between 7.3 and 0.13 AU. The CO ice already vapourises at 21 AU ( 30 K) and the water ice at 8 AU ( 150 K). At 7.3 AU all the volatile species are in the gas phase. The density of free H atoms is well under the initial concentration of because of H₂ formation by three body collisions (20). At this distance from the protostar the gas phase is composed only of H₂, H, N₂, CO, H₂ O, some H₂ S, and He and this composition prevails until the temperatures required for the onset of dust destruction are reached.

Fig. 3. Run of molecular abundances in the accretion disk in the region of dust destruction.

5.1. Oxidation of the carbon dust

The carbon dust oxidation has dramatic effects on the chemical composition of the gas phase. As a direct consequence of the oxidation process (25) and the follow up reactions (26) and (27), we observe a huge amount of methane as temporary product between 1.5 and 0.8 AU ( 1 000 and 1 200 K) i.e. in the actual vicinity of the Earth. In our previous work (Paper I) we have also observed a maximum for the methane abundance approximately in the same region of the disk but the density of methane was of about a factor 10⁴ lower. We discuss the processes responsible for methane formation and its conversion to CO in some detail.

5.1.1. Methane formation

When the carbon dust is attacked by OH radicals in the first step (25) the ketyl radical HCOO is formed which immediately reacts according to (Eq. 26). This forms (i) a CO molecule which does not further participate in the chemistry of the gas phase due its high bond energy and (ii) a CH₂ radical which reacts rapidly with the abundant H₂ to produce methane according to the reaction chain

These reactions are energetically nearly neutral and involve no substantial activation energy barriers. We have calculated typical reaction timescales at a typical pressure of dyn cm^-2 (cf. Eq. (4)) and temperatures between 1 000 K and 1 500 K (c.f. Eq. (3)) using rate coefficients from Mitchell (1984) and assuming chemical equilibrium abundances of H atoms. The results are shown in Table 3.

Table 3. Relative abundance of CH_n molecules in kinetic equilibrium and timescales (in sec) for reactions with H and H₂ at a pressure of 100 dyn cm^-2 at different temperatures

An inspection of Table 3 shows that reaction timescales range between s and s for the hydrogen abstraction reactions with H and between s and s for the hydrogen addition reactions with H₂. These timescales are short compared to the characteristic timescale for changes of pressure and temperature s. Thus, there quickly establishes an equilibrium where the CH₂ initially injected into the gas phase is distributed over the compounds C, CH, CH₂, CH₃ and CH₄. Most of the carbon remains as CH₄ in the gas phase since hydrogen addition reactions occur much more frequently than hydrogen abstraction reactions due to the high abundance of molecular H₂. Only if the temperature has climbed to 1500K, a substantial fraction of the carbon would be converted into CH₃ because then there is a considerable abundance of free hydrogen atoms. Since the reactions with hydrogen are so rapid, any reaction involving one of the considerably less abundant heavier elements cannot significantly disturb this equilibrium state between the compounds and we can safely assume that the abundance of these molecules always equals their abundance according to a stationary state between the reactions (38)

Table 3 shows the abundances of () relative to CH₄ in kinetical equilibrium with H and H₂. Since we assumed dissociation equilibrium for hydrogen in the gas phase, these abundance ratios are as in chemical equilibrium. Even if the hydrogen dissociation is far from a chemical equlibrium state the reaction timescales are so short compared to the hydrodynamic timescale that their density ratios always equal their stationary equlibrium ratios given by (39).

The molecules form the starting point for further reactions which may lead finally to CO.

5.1.2. Reactions with oxygen bearing compounds

The most abundant oxygen bearing compounds prior to dust destruction are H₂ O and CO (cf. Fig. 3). Reactions with the CO molecule are energetically forbidden by the high bond energy of the CO molecule. Reactions with H₂ O, however, are possible.

The CH_n for exchange a hydrogen atom in reactions with the water molecule:

These reactions are rapid, but they cannot compete with the rapid reactions (38) and do not significantly modify the equilibrium between the . Reactions between water and the , in which an OH group would be attached to the carbon atom are slightly endothermic ( 1 eV) and cannot occur. Reactions between H₂ O and in which the formaldehyde molecule H₂ CO or the formyl radical HCO are formed are strongly exothermic but seem not to occur, probably since the alternative reaction (40) is easier.

The next abundant oxygen bearing molecule is OH, which is formed by the reaction

at the onset of hydrogen dissociation. The OH easely reacts with hydrocarbons by the reactions (40), but this does not form a bond between C and O. Possible reactions which do form a C-O-bond result in formaldehyde

or formyl

The reverse of reactions (41) and (42) are endothermic by 69.3 and 90.3 kcal/ mol, respectively, and thus are energetically forbidden. The resulting formaldehyde is readily transformed into formyl by the hydrogen abstraction reaction

and the formyl is readily transformed into CO by

These reactions are rapid. The reverse of reaction (44) is forbidden since it is endothermic by  kcal/ mol and forms a one way to CO. Characteristic timescales for these reactions have been computed with the rate coefficients given by Mitchell (1984) with the assumption that dissociation of H₂ and H₂ O is as in chemical equilibrium. The results are shown in Table 4. An inspection of this table shows that only reaction (41) is a possible pathway to convert the molecules by reactions wit OH into CO. The abundance of CH is much too low for the reaction (42) to compete with (41), except for the highest temperature.

Table 4. Reaction timescales for reactions important for the conversion of hydrocarbons to CO at a pressure of 100 dyn cm^-2 at different temperatures. This is the average time required for the first molecule to react with the second one

Finally we have to consider reactions with free oxygen atoms. One possible type of reaction with is

Such reactions are fast, but they do not lead to CO formation and they cannot compete with the much more frequent reactions (40), i.e., they are unimportant. Possible reactions leading to formation of a C-O-bond are

These reactions are strongly exothermic and only occur in the indicated direction. Calculated timescales for these reactions using data from Mitchell (1984) are given in Table 4. Since the abundance of O is quite small, the timescales are rather long for low temperatures and only become short at a temperature of 1500 K due to the increasing degree of dissociation of water molecules. In any case, the reactions (42) and (45), ..., (47) cannot compete with the much more frequent reaction (41) and are unimportant for the CO formation.

We conclude that the dominant direct pathway from sputtering products of carbon dust to CO is the reaction chain (41), (43), and (44). Inspection of Table 4 shows that the rate determining step is reaction (41). Every CH₂ reacting with OH rapidly reacts further to CO. However, since the reaction from the products of carbon sputtering to CO requires a reaction path involving the rare molecules CH₂ and OH, the reaction to CO is slow and the CH₄ and the unsaturated molecules accumulate in the gas phase until their abundance has raised to a level where subsequent reactions to CO operate with a rate comparable to the sputtering rate. In this case, a high abundance of molecules develops in the gas phase. This can clearly be seen from Fig. 3. A reaction between the saturated CH₄ molecules is not possible, but if the radicals () have formed in sufficient amounts then reactions between such radicals become important. As a consequence of this, there exists a more efficient indirect pathway to CO formation.

Fig. 4. Run of molecular abundances in the accretion disk in the innermost region of molecule dissociation.

5.1.3. The pathway to acetylene

Reactions, in which a hydrogen atom is exchanged between and are rapid, but they do not significantly modify the equilibrium between these hydrocarbons and hydrogen and, thus, can be neglected. However, there exist some condensation reactions which form higher hydrocarbons:

The formation of C₂ H₅ is slightly endothermic ( 10 kcal/ mol) and occurs preferentially from the right to the left. If we arbitrarily assume that 10% of the carbon grain material is present in the gas phase as CH₄ we can calculate the reaction timescales. We use the rate coefficient for the forward reaction as given by Mitchell (1984) and calculate that for the reverse direction from a Milne relation. Results for the timescales are given in Table 4. We can see that every C₂ H₅ molecule formed in the forward reaction (48) is immediately destroyed by the backwards reaction. Thus, any further reaction path starting at C₂ H₅ will be inefficient and we do not consider this case further.

The reactions (49) and (50) are strongly exothermic and occur only in the direction of formation of a C-C-bond. Calculated timescales are given in Table 4. These reactions convert some of the CH₃ to ethylene C₂ H₄. The ethylene will be subject to the following sequence of reactions with hydrogen

Reactions (51) and (53) are mildly exothermic ( 4.4 and 15.5 kcal/ mol, respectively) and preferentially occur in the backwards direction. Reaction (52) is exothermic by kcal/ mol and acts only in the direction of acetylene formation. Reaction timescales using rate coefficients given by Frenklach and Feigelson (1989) are given in Table 4. The reactions (51) and (53) are rapid and each establishes an equilibrium between C₂ H₄ and C₂ H₃ or between C₂ H₂ and C₂ H, respectively. Most of the carbon will be in ethylene and acetylene. Additionally, reactions with OH are possible in which a hydrogen is exchanged but these cannot compete with the more frequent reactions with H.

5.1.4. The pathway to CO

Reactions with O to form a C-O-bond are possible for C₂ H₄ and C₂ H

The acetylene is known from flame chemistry only to form OH in reactions with O but not to close a C-O-bond. Calculated timescales for these reactions using rate coefficients from Baulch et. al. (1992) are given in Table 4. These reactions are inefficient unless the temperature has increased sufficiently and free oxygen is formed by dissociation.

All these qualitative conclusions are confirmed by our model calculation for the gas phase chemistry following sputtering of carbon grains by OH radicals, which considers most hydrocarbons with up to four carbon atoms and a big number of reactions. The dominating sequence of reactions involved in the conversion of the hydrocarbons into CO is shown in Fig. 5.

Fig. 5. The chemical pathway for CO formation following the formation of CH2 in the reaction

This reaction path to a large extent is identical with the chemical pathway found to be dominating in the combustion of methane in air (e.g. Warnatz 1983 , 1992). There are two major differences however: First, the hydrogen liberated in several elementary steps is not converted into H₂ O as in ordinary combustion but remains due to the big hydrogen excess in the protoplanetary disk as H₂ molecule in the gas phase. The oxidation process of the carbon grains in the disk, then, resembles more closely the watergas reaction than an ordinary combustion process. Second, the direct pathway to CO from CH₂ via H₂ CO and HCO is not very efficient in the protoplanetary disk but is often efficient in flames.

Our present results show that the vapourisation process (which was the carbon destruction process considered in Paper I) is completely negligible in comparison to the oxidation process since vapourisation requires a much higher temperature than oxidation.

From the intermediate products of the carbon sputtering and conversion into CO only CH₄ reaches a high abundance. From all other intermediates only CH₃ and C₂ H₄ are present as temporary products with a noticeable abundance, but their abundances are lower by a factor of at least 10³. The destruction reactions of all the gas-phase hydrocarbons are mainly oxidation reactions with the injected oxygen bearing species during olivine evaporation. The different pathways are the same with and without oxidation and can be found in Paper I. All the liberated carbon accumulates in CO until CO itself is destroyed by collisional dissociation with hydrogen. Close to the central star only free C atoms are present.

5.2. The sulfur chemistry

Troilite is the first dust component to be destroyed by the slowly heating matter. Here we assumed that it thermally decomposes at about 2 AU ( 700 K) and injects according to our assumptions only Fe and S into the gas phase. The liberated sulfur leads to a very rich chemistry between 2 and 1 AU ( 1 000 K). In order to get a better impression of the chemical composition in this region, we have shown on Fig. 6 the sulfur bearing species separately. The iron chemistry is inefficient within the frame of the neutral chemistry and we don't take it into account.

Fig. 6. Sulfur bearing species in the protoplanetary disk. One half of the total sulfur is assumed to enter the disk as gas phase H2 S. The remaining part of the sulfur is assumed to be bound in solid FeS. This S is injected into the gas phase on the decomposition of FeS at AU.

The most abundant sulfur bearing species in this region is H₂ S. It forms in two very fast reactions with H₂

This molecule reaches a maximum abundance of more than 10¹⁰ cm^-3 between about 1.4 and 0.8 AU i.e. where the terrestrial planets are presently located. The Earth is just in the middle part of this region.

When the olivine decomposition begins to be efficient at 0.5 AU, H₂ S reacts very fast with the OH radicals and forms in a more complex reaction sequence the SO₂ molecule

Almost all the H₂ S molecules are converted by this pathways into SO₂.

Other sulfur bearing species like HCS, which is quite abundant, too, are present in this domain. It forms when a free S atom reacts with a methylene radical

Smaller amounts of OCS are produced according to the pathway

The intermediate product CS is observable in the parent molecular cloud core, in the protoplanetary disk it is efficiently converted into OCS by reaction with OH (59).

After the olivine particles are destroyed at 0.31 AU, we find besides the abundant SO₂ quite high abundances of HS and free S atoms and smaller amounts of H₂ S.

In the innermost parts of the disk (see Fig. 4), the SO₂ molecules are destroyed in reactions with free oxygen atoms, which are liberated as products of the water dissociation in this region. The pathways from SO₂ to free S atoms are

HS reacts with free O atoms, too, and forms SO, which in turn reacts with a second O atom to form a free S atom

In the vicinity of the disk's center, only the free atoms S and Fe remain.

5.3. The silicon chemistry

The gas phase silicon chemistry is initiated when the olivine particles start to evaporate at 1 AU and inject SiO into the gas phase. We see from Fig. 3 that most of the Si bearing molecules in the gas phase are rare, except the SiO and the SiOOH. The latter is nearly as abundant as SiO at 0.13 AU ( 2 000 K) and below. This molecule is formed in the following reaction sequence

The SiOOH forms as dissociation product of HSiOOH

Fig. 3 clearly shows that the abundance increase of SiOOH is parallel to the abundance increase of OH. The intermediate HSiOOH is never very abundant. This result is interesting since it means that the silicon in the gas phase prior to its dissociation is not quantitatively bound in SiO as is generally assumed.

SiO₂ is present too with a low but non-negligible abundance of at most of the SiO abundance. It is formed by an exchange reaction between SiO and OH

All the silicon bearing molecules disappear in the innermost regions of the disk in the backward reactions of the above defined pathways. Due to its high bond energy SiO is the last molecule to be dissociated. The assumed process is the collisional dissociation by free H atoms and H₂ molecules

The rate coefficients of these reactions are supposed to be the same as the similar carbon monoxide dissociation. Only the energy barrier must be recalculated (Paper I). As expected, only free Si atoms remain close to the central star.

© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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