4 Star-forming regions

Figure 7: Predicted gas-phase molecular abundances vs time, from models P1, T = 15 K (left) and P2, T = 20 K (right); n(H2)   = 105 cm-3.

The temperatures of the star-forming regions observed by SWAS are $\sim$20-50 K, and they have higher densities than the dark clouds, $\sim$10⁵ cm^-3. Gas-phase water was observed in these sources, with a fractional abundance significantly below the limits set in TMC-1 and L134N ( $10^{-9}<\rm [H_2O]<$ a few $\times$10^-8; Bergin et al. 2000), while the upper limits on O₂ abundance are an order of magnitude lower than in cold clouds.

The gas-grain chemistry we are using is primarily designed to model dark clouds at 10 K, but, for completeness, we also compare SWAS observations with a few model runs at higher temperatures and densities. We note, however, that results for olivine are uncertain at temperatures significantly greater than 10 K, since the rate modifications may change with temperature (Ruffle & Herbst 2001b). Experimental evidence for H suggests that species on an amorphous carbon surface are more strongly bound (Katz et al. 1999), so that temperatures of $\sim$20 K are required before the grain species are mobile enough for reactions to occur. The binding energies calculated for species on amorphous carbon are similar to those of a pure ice surface (Sandford & Allamandola 1988, 1991), so this model may be more appropriate if reactions occur on the surfaces of dust grains already coated in ice.

4.1 Chemistry on an olivine (silicate) surface

Figure 7 shows gas-phase abundances from models P1 and P2 with temperatures of 15 and 20 K, respectively, and H₂ densities of 10⁵ cm^-3. The results for the two models are similar for the species shown. As was the case for dark clouds, the CO abundance rises for $\sim$10⁵ yr, peaking at $\sim$10^-4 and then decreasing as CO freezes onto the grains. At these higher temperatures, however, there is a "plateau'' between $3 \times 10^{5}$ yr and ${\sim}4\times10^6$ yr where the CO abundance remains at $\sim$10^-6 in model P1 and $\sim$ $3\times10^{-6}$ in model P2. This differs from the models at 10 K, where the CO abundance declines fairly steadily (Fig. 1), because CO desorbs from the grains more efficiently at the higher temperatures.

Figure 8: The ratios of the predicted abundances of H2O, O2 and CO to the limits set/observations made towards $\rho$ Oph. Model P1 uses T=15 K, model P2 uses T=20 K; n(H2)  =105 cm-3.

Figure 8 contains theoretical H₂O and CO abundances, relative to their observed abundances, and O₂ relative to the SWAS upper limit towards $\rho$ Oph, one of the star-forming regions observed by SWAS that possesses a very low detected abundance of water. Again, the observed upper limit on the O₂ abundance does not present a problem, but, as the observed H₂O abundance towards this source is more than ten times lower than the limit set in the cold clouds, it now becomes a more serious problem for the models to reproduce the water observation without predicting a heavy depletion of CO.

   

Table 4: A comparison of molecular abundances observed towards $\rho$ Oph with predictions from gas-grain models.

	Observed	Model P1		Model P2
T (K)		15	15	20	20
(yr)		106	$3\times10^7$	106	$3\times10^7$
H2O	3.0(-9)1	5.2(-9)	2.2(-9)	6.8(-9)	3.7(-9)
O2	<3.(-7)2	2.2(-8)	1.5(-9)	1.1(-8)	3.8(-9)
CO	$\sim$1.(-4)3	1.1(-6)	9.9(-8)	2.9(-6)	3.9(-7)
NH3	3-10(-8)4	1.6(-8)	3.0(-8)	4.8(-8)	5.2(-8)

Note: a(-b) implies $a\times10^{-b}$
Refs.: ¹ Snell et al. (2000a), ² Goldsmith et al. (2000), ³ Myers et al. (1978), ⁴ Mizuno et al. (1990).

The problem is further quantified in Table 4. The models do not predict a heavy depletion of NH₃, so its abundance is in good agreement with observations at all times <10⁸ yr. However, for times between 10⁶ and 10⁷ yr, when the predicted H₂O abundance has fallen to $\sim$twice the SWAS value, the CO abundance is already almost two orders of magnitude lower than the observation. By the time the H₂O abundances from the model are in agreement with the observations, predicted CO abundances are $\sim$10^-7. Even though the CO observation of Myers et al. (1978) may not be in the same direction or at the same resolution as the SWAS beam, the modelled CO abundance does not seem realistic for such an abundant and ubiquitous interstellar molecule.

We have looked at results from model P1 at 20 K, even though the surface rate coefficients are very uncertain at this higher temperature, in order to see whether this would cause more CO desorption and increase its abundance to the levels observed. This is not the case, though; instead the CO abundance declines even more rapidly because at the higher temperature it reacts on freeze-out to make CO₂. We also investigated increasing the elemental C/O ratio to 1, but found that, although there is a significant decrease in O₂ abundance at all times, the H₂O abundance is only reduced by a factor of 3 at its peak abundance, and that, at late times, the gas-phase H₂O abundance is similar to the standard model, with $\rm C/O =0.4$.

4.2 Chemistry on an amorphous carbon surface

Figure 9: The ratios of the predicted abundances of H2O, O2 and CO to the limits set/observations made towards $\rho$ Oph. Models use T=20 K, n(H2)  =105 cm-3. The results are nearly identical for the two models so only three distinct lines are seen.

Figure 9 contains a comparison of the theoretical abundances of H₂O, O₂ and CO from models P1/ac and P2/ac at 20 K with the observations of $\rho$ Oph. For these species, abundances are almost identical in models P1/ac and P2/ac. Once again, there is a discrepancy between the time required for depletion of water, and the fairly high CO abundance that is observed, but this time the gas-phase species freeze out very rapidly after a few $\times$10⁵ yr, because they are more tightly bound to grains and so can't desorb.