3. Results of astrochemical simulations
We have performed gas-phase chemical simulations using the entire UMIST RATE95 reaction rate database (Millar et al. 1997). Some relevant parameters have been varied in one dimension at a time [for a multi-dimensional variation see Nilsson (1999)]. The initial elemental abundances were adopted from Bergin et al. (1997), but adding helium and chlorine (see Table 4). The chemical model consists of an average central cloud position characterized by the input parameters. We have solved the coupled ordinary differential equations using the Gear method (Gear 1971a, 1971b; Hindmarsh 1972a, 1972b; Hindmarsh & Gear 1974). Unless otherwise stated the visual extinction has been set to 25 mag, the cloud temperature to T = 20 K, and the cloud density to . We have assumed a standard cosmic ray ionization rate s-1 and a UV-light flux of 1 Habing. Variations in the cosmic-ray ionization rate are used here to model, in an approximate manner, the influence of X-ray irradiation on the chemical evolution. For the adopted visual extinction the influences of the UV-light are negligible. The simulation results are presented in Figs. 4-21.
Table 4. Initial fractional abundances.
The reason why we are studying influences of X-rays in the present context is the fact that young stellar objects (YSO) have been observed to be strong X-ray emitters (e.g. Casanova et al. 1995). In fact, already Krolik & Kallman (1983) have demonstrated that the X-ray sources observed near the core of the Orion molecular cloud would be sufficient to supply the ionization needed to drive the ion-molecule chemistry, even if cosmic ray ionization were not available. The reason is that the secondary ionization caused by Auger and photoelectrons here dominates over the direct X-ray photoionization by more than an order of magnitude [see Krolik & Kallman (1983), and also the discussion by Casanova et al. (1995)]. These authors also argue that in localized regions around the X-ray emitting YSO's the ionization rate would become considerably enhanced. Already the chemical modelling by Krolik & Kallman (1983) demonstrated an accelerated formation of molecules as the ionization rate is increasing. However, for very high ionization rates H2 and most other molecules would be destroyed (cf. Lepp & Dalgarno 1996).
3.1. Temporal evolution
As mentioned in the introduction the original idea behind this project was to find out if the SO/CS abundance ratio could probe the temporal evolution of a molecular cloud. In Fig. 4 we display the abundance variations as a function of time for a number of species relevant to the present project. The time development is just as expected from our earlier discussion (in the introduction) of the dominant formation and destruction mechanisms. While CS and CO reach a high abundance at "early times" the SO and O2 abundances can rise to observable abundances only when their efficient destruction in reactions with free C (reactions 2) is diminished. This happens at "late times" when most C has been locked up in CO. In Fig. 4 we also see that the CS abundance decreases by an order of magnitude at late times. The main reason is efficient CS destruction via
since the amount of free O remains high. For the adopted initial elemental abundances (Table 4) the late time fractional abundances w.r.t. H2 of SO, CS, O2, and CO become , and , respectively. We do indeed confirm the temporal development present in earlier studies including those by Bergin et al. (1995) and Lee et al. (1996). Here the initial elemental abundances have been chosen such that the model will match the observed abundances of CO, CS, SO etc, "as well as possible". A striking consequence of this forced match between modelling and observations is a predicted O2 abundance of ([O2]/[CO] = 0.4), which is more than an order of magnitude above the lowest reported observational limits from ground based (Maréchal et al. 1997a); balloon-borne PIROG 8 (Olofsson et al. 1998); and satellite-borne SWAS (Melnick et al. 1999) observations. We here just note that a "cure" to this problem would be to "adopt" a lower O/C abundance ratio (cf. Figs. 6 and 9), and will return to this question in the comparison of our SO/CS observational data with models. The variations of the O2/SO abundance ratio vs time, as calculated from the model results in Fig. 4, are shown in Fig. 7. In Figs. 5 and 8 we show the time development of the SO/CS and O2/CO abundance ratios, respectively.
3.2. O/C+ variation
The "standard" [C]/[O] interstellar abundance ratio value is 0.4. We have performed calculations to study the sensitivity of the SO/CS and O2/CO abundance ratios to variations in the O/C+ initial abundance ratio. The resulting SO/CS and O2/CO abundance ratios are shown in Figs. 6 and 9, respectively. It is indeed very obvious that these ratios are very sensitive to the initial O/C+ abundance ratio, especially in the range 1-2. High SO and O2 abundances can only develop if O/C 1.5. A decrease below this value rapidly leads to very low SO and O2 abundances. In case of SO this behaviour has been discussed at some length by Bergin et al. (1997) (cf. their Fig. 6).
3.3. Density variations
We also ran simulations for varying H2 number density. The results are displayed in Figs. 10 and 13. The final SO/CS abundance ratio is increased by an order of magnitude as the cloud density (H2 number density) is increased from 103 to 106 cm-3, whereas the O2/CO ratio is not sensitive to the density. We also clearly see a considerably faster chemical evolution as the density increases, which indeed is expected as a result of increasing collision rates between the reaction partners.
3.4. Variations of the (X-ray) ionization level
To study the influence of variations of the X-ray radiation we defined a scaling factor , where is the actual ionization rate and is the standard cosmic ray ionization rate. An increased cosmic ray ionization rate will accomplish the same thing as would an X-ray source, as explained at the beginning of this section.
Figs. 11 and 14 demonstrate the dramatic change of the time dependence resulting from variations of the ionization level. The chemical evolution becomes much faster as the increasing ionization produces a higher abundance (Fig. 16) which leads to more OH (Fig. 19) and a subsequent formation of more SO and O2 (reactions 1). We note that the abundances of , OH, C+ and C increase about linearly with the scaling factor F, and also that the time scale decreases strongly with increasing F. We also note that the late time abundances of SO and O2 decrease with increasing ionization level, however much less pronounced for O2. Such an SO abundance decrease at late times is readily explained by the loss reactions, since the increased ionization level also strongly influences the temporal evolution as well as the late time abundances of C, C+, and CS (Figs. 17, 20, and 18, respectively). The influence of an increased ionization on the H2O concentration is shown in Fig. 21. An increased ionization level leads to a higher abundance of H2O as well as a faster chemistry. Again this is explainable in terms of an increased production of with subsequent formation of H3O+, from which H2O as well as OH are formed via dissociative recombination with electrons. However, this branching ratio still is somewhat uncertain (cf. Herbst & Lee 1997).
Similar results have been obtained by Farquhar et al. (1994). These authors also note, in accordance with our findings, that the SO/CS abundance ratio may be a useful diagnostic of chemical evolution ("cloud age"). However, this clean picture may become rather deteriorated by the very sensitive dependence of the SO abundance upon the initial O/C+ ratio.
3.5. Sulphur variations
Figs. 12 and 15 show that the SO/CS and O2/CO abundance ratios do not depend severely on the initial sulphur content (even though the SO and CS abundances themselves vary rather linearly with the initial S abundance). Only if the S content is increased by a factor of 1000 does the O2/CO abundance ratios decrease by a visible amount (a factor of ).
© European Southern Observatory (ESO) 2000
Online publication: June 26, 2000