5 Discussion

In this paper, we have applied the results of gas-grain chemical models to the problem caused by the low abundances of gaseous O₂and H₂O detected by SWAS in a variety of interstellar sources. In general, the models easily reproduce the O₂ result at almost all times, but reproduce the H₂O result only at late times, when a significant amount of the gas-phase water has accreted onto grain mantles. The molecular oxygen is reproduced at almost all times because its formation in the gas is rather slow and cannot keep up with accretion. Once water and oxygen freeze onto grains, they do not easily desorb at the temperatures considered here.

Our model includes surface reactions and desorption mechanisms for all species, and so is more "complete'' than previous accretion models, such as those of Bergin et al. (2000) and Viti et al. (2001). However, our gas-grain model is at its weakest at late times since the gas-phase abundances are strongly affected by the uncertain desorption rates adopted. Depending on the source, the late-time hypothesis may or may not be in conflict with explanations for the abundances of other molecules. In the dark cloud L134N, our model is most successful in a general sense at a time of $1 \times 10^{6}$ yr, at which time the predicted abundances of water and oxygen are not greater than the SWAS upper limits. Towards the cyanopolyyne peak in the dark cloud TMC-1, our model is most successful in a general sense at early times, but reaches a second era of reasonable, if somewhat less successful agreement, at much later times. The upper limit to the water abundance can only be reproduced at the later times. Moreover, at these times, the predicted CO abundance is falling considerably if not dramatically below the observed value. The worst agreement between theory and observation occurs in denser, warmer regions such as the star-forming region towards $\rho$ Oph observed by SWAS. Here, reproduction of the small water abundance at late times leads to a predicted abundance for CO that can be orders of magnitude below its observed value. Not all star-forming regions have water abundances as low as $\rho$ Oph; its abundance in the extended Orion source is an order of magnitude higher, and so is less difficult to fit simultaneously with a high CO abundance.

It is useful to compare our results with selected other recent approaches directed at explaining the SWAS observations in dark clouds. Two such approaches are those of Viti et al. (2001) and Charnley et al. (2001).

Viti et al. (2001) have constructed many models with gas-phase chemistry and with accretion to study a variety of physical conditions. In some of their models, all heavy species remain on grains while in others, CO and N₂ are returned promptly to the gas following adsorption, while all other heavy species are not. In general, these authors conclude that for dark clouds, the SWAS results and selected other gas-phase abundances are accounted for by a late-time scenario, the duration of which depends on their assumptions. This conclusion is rather similar to ours. They have also run steady-state models under conditions which allow bistability; in this situation, the so-called "high ionization phase'' explains the low abundance of molecular oxygen towards a variety of sites, but the low abundance of water is a problem.

Charnley et al. (2001) have tested a model of shock cycling, in which they follow post-shock gas which is accreting onto grains. Their results are similar to ours, in that they find reasonable agreement with the SWAS limits on H₂O in dark clouds, but fail to match the lower levels observed in other sources. Once again, a type of "late-time'' solution is necessary.

It also should be mentioned that Spaans & van Dishoeck (2001), in their discussion of clumpiness as a source of low average water and oxygen abundances, state that time-dependent chemistry and freeze-out are important to explain the low abundances in dense quiescent objects. A major alternative explanation, that photodissociation can explain the low abundances of water and molecular oxygen (Casu et al. 2001), must be reconciled with the significant abundances of many other molecules.

Since gas-phase water is produced in our models via the dissociative recombination of H₃O⁺, it is useful to see if a change in the uncertain branching fraction for the H₂O + H channel can improve the agreement with the SWAS observations (see also Viti et al. 2001). For the calculations reported in this paper, we have adopted the results of Neau et al. (2000), who found a branching fraction of 0.18 in storage ring experiments. This value is lower than the previous results of 0.33 (Vejby-Christensen et al. 1997) and 0.25 (Jensen et al. 2000), both from a second storage ring. However, Williams et al. (1996) measured a branching ratio for H₂O production of no more than 0.05. Use of this branching fraction, which is 3-4 times lower than adopted in our calculations, does make it somewhat easier to fit the SWAS data. In TMC-1, for example, the predicted water abundance at early time is now only a factor of 3 greater than the current upper limit, although it is not clear that this result is acceptable. For the star-forming region towards $\rho$ Oph, the detected low water abundance and upper limit to the oxygen abundance can be fit at somewhat earlier times than heretofore considered ( $3 \times 10^{5}$ yr), but the predicted gas-phase CO abundance is still much too low at these times. Only at a time of ${\approx} 10^{5}$ yr, when the calculated values for water and oxygen are a factor of a few high, is the prediction for CO reasonable. We conclude that the lower branching fraction is useful but not a panacea.

If our hypothesis that the low abundance of gas-phase water is indeed the result of longer time scales than customarily considered is correct for all sources studied, then it is likely that the desorption of CO and other species in our gas-grain model is not handled adequately. More accurate determinations of the desorption rates, especially for CO, are needed; the CO rate is currently being investigated by both theoretical and experimental means (H. J. Fraser, private communication).

As the revised version of this paper was being submitted, we learned of the unpublished results from the Odin team that the upper limit to the gas-phase O₂ abundance in TMC-1 and L134N is approximately an order of magnitude lower than the SWAS result, depending somewhat upon the spatial extent of the oxygen. From our results in Fig. 4 (TMC-1) and Fig. 5 (L134N), one can see that the new lower limit is met at late time for TMC-1 but requires a time of ${\ge} 2 \times 10^{6}$ yr for L134N. This latter time is somewhat longer than the optimum time of 1- $2\times10^6$ yr discussed in our analysis.

Acknowledgements

The Astrochemistry Program at The Ohio State University is supported by The National Science Foundation (US). We thank the Ohio Supercomputer Center for time on their Cray SV1 machine.