2 Time-dependent chemical models

2.1 The model assumptions

In each of the models that we consider in this section physical and chemical conditions match those inferred from observations during one epoch only; at other times, the physical and chemical conditions in each model are such that the source is undetectable with the sorts of observations already made. Cyclic models of the kind originally suggested by Norman & Silk (1980) have the potential to provide such transient observable conditions (e.g. Williams & Hartquist 1984; Charnley et al. 1988). In this category of models, it is assumed that interstellar and circumstellar gas is continually re-cycled from low to high density, probably by the action of star formation itself. This approach has some attractions, given that the link between interstellar chemistry and dynamics has been frequently discussed.

We model the chemistry of regions of high and low mass star formation and starless cores. For ease of computation a cloud is represented as a single point within a semi-infinite slab with a pseudo-time-dependent chemical simulation. The UMIST chemical database (Millar et al. 1997) was used with some modifications (see Viti et al. 2000), particularly with regard to the gas-grain interaction. In some models, we have included the freeze-out of all gas phase species, except hydrogen and helium, on to dust grains. All the species that deplete on to grains are incorporated in mantles and it is assumed that they are never released. The modified rate file contains 397 species taking part in 4246 reactions (including freeze-out reactions). In all models, except the oxygen poor ones (see later), the initial elemental abundances by number relative to hydrogen were taken to be 7.0 10^-2, 2.2 10^-4, 6.0 10^-5, 4.6 10^-4, 1.3 10^-5, 7.0 10^-9, 2.0 10^-9 and 8.0 10^-9for helium, carbon, nitrogen, oxygen, sulphur, magnesium, sodium, and silicon respectively. As an initial condition we also assumed that half the elemental abundance of carbon is locked in the carbonaceous grains. Our models are time-dependent; this implies that the depletion of each element was not assumed but rather, was derived through a computation of the non-steady state chemical evolution of the gas/dust interaction processes.

We have performed computations for a grid of models. A model is characterized by whether (i) the gas is static or collapsing; the collapse is treated as a "modified'' free-fall as defined by Rawlings et al. (1992) where the density was assumed to increase in a fashion governed by

$$\frac{{\rm d}n_{\rm H}}{{\rm d}t} \!=\! B \left(\frac{n_{\rm ... ...rm H}}{n_{\rm H0}}\right)^{1/3} \!\! - 1\right]\right\}^{1/2}$$ (1)

where t, B, G, and $m_{\rm H}$ are the time, a numerical constant, the gravitational constant, and the mass of a hydrogen atom respectively; in practice, we took B = 1, which corresponds to a free-fall collapse. (ii) the final number density, $n_{\rm H}$ = n(H) + 2n(H₂), is low (10³ cm^-3), medium (10⁴ cm^-3) or high (10⁵, 10⁶ cm^-3); (iii) the initial oxygen abundance is standard or low; (iv) the freeze-out efficiency of gas phase elements onto grains is zero, medium, or high; (v) the temperature is low (10 K) or medium (30 K); (vi) the visual extinction is moderate (2 mag) or high (5 and 15 mag); (vii) the branching ratio for H₃O⁺ dissociative recombination with electrons is higher or lower, according to recent determinations (see below).

Note that the initial density for the models where the final density reaches 10⁶ cm^-3 is slightly higher (10⁴ instead of 10³cm^-3) than employed for the rest of the models where collapse occurs; this was necessary as, in a free-fall collapse from the lower initial density, the final densities are not reached until 1.7 Myr, by which time everything is already frozen on to the grains: this picture is unrealistic. We can justify our choice of having a slightly higher initial value of $n_{\rm H_2}$ if we think of a high mass star as the result of a denser small clump within a much bigger and less dense cloud.

The ambient interstellar radiation field was taken to be that defined by Habing (1968). For the models where collapse occurs, it was assumed that a clump collapses gravitationally within the molecular cloud and that the collapse is a free-fall. When we allowed freeze-out to occur during the collapse phase, gas-phase chemistry and freeze-out on to dust grains with subsequent processing, such as hydrogenation, were assumed to occur. For depletion, we used the parameter FR where FR = 0 implies no freeze-out and FR = 1 means that sticking occurs on every collision. For most of the models we adopted the branching ratios for dissociative recombination of H₃O⁺ (main routes for oxygen chemistry) measured by Vejby-Christensen et al. (1997), but several selected models were also computed with the branching ratios measured by Williams et al. (1996). O'neill & Williams (1999) and Bergin et al. (2000) noted that these two laboratory measurements produce very different amounts of water.

For our "oxygen poor'' models we have halved the oxygen initial elemental abundance: the two initial abundances we chose for oxygen are justified by the interstellar oxygen abundances derived from 14 lines of sight by Meyer et al. (1998, see their Table 2). The oxygen abundance that we use as standard is taken from Snow & Witt (1996), who presented elemental abundances derived from stars in the solar neighbourhood rather than from the Sun.

Our choice of initial physical conditions is based on the parameters suggested by Bergin et al. (2000) representing the various lines of sight observed with SWAS. A total of 67 models have been evaluated, so that the parameter space described here has been thoroughly explored. The results of some of these are presented in the discussion below. A further 30 models, in which higher cosmic ray ionization rates were adopted, were also evaluated but their results are not reported here as none are in harmony with the SWAS observations of the oxygen chemistry in dense cores.

 

 

Table 1: Model parameters: number densities are in cm^-3; the gas temperature is in Kelvin; see text for a full explanation of the nomenclature

	$n_{\rm H_2}$	$T_{\rm gas}$	FR	AV		X(O)	CO-N2	H3O+
							freeze-out	branching ratio
1	104	10	0	15	nc	s	yes	VC97
2	104	10	0.3	15	nc	s	yes	VC97
3	104	10	0.7	15	nc	ns	yes	VC97
4	104	10	0.3	15	nc	ns	yes	VC97
5	104	10	0.3	2	c	s	yes	VC97
6	104	10	0.3	5	c	s	yes	VC97
7	104	10	1	5	c	s	yes	VC97
8	104	10	0.3	15	c	ns	yes	VC97
9	104	10	0.3	15	c	ns	no	VC97*
10	104	10	0.3	15	c	ns	no	VC97
11	104	10	0.3	15	c	ns	yes	W96
12	104	10	0.3	15	c	s	yes	VC97
13	104	10	0.3	15	c	s	yes	W96
14	104	10	0.3	2	nc	s	yes	VC97
15	104	10	0.3	5	nc	s	yes	VC97
16	104	10	0.3	5	c	ns	yes	VC97
17	104	10	0.7	15	nc	ns	no	VC97
18	104	10	0.7	15	nc	ns	yes	W96
19	104	10	0.7	15	nc	s	yes	VC97
20	104	10	0.7	15	nc	s	yes	W96
21	104	10	0	15	nc	ns	yes	VC97
22	104	10	0	2	c	s	yes	VC97
23	104	10	1	15	c	ns	yes	VC97
24	104	10	1	15	c	s	yes	VC97
25	104	10	1	2	nc	s	yes	VC97
26	104	10	1	2	c	s	yes	VC97
27	104	10	1	5	nc	s	yes	VC97
28	104	10	1	5	c	ns	yes	VC97
29	104	30	0.3	2	nc	s	yes	VC97
30	104	30	0.3	5	nc	s	yes	VC97
31	104	30	1	15	c	ns	no	VC97
32	104	30	1	2	nc	s	yes	VC97
33	104	30	1	5	nc	s	yes	VC97
34	105	10	0.3	2	nc	s	yes	VC97
35	105	10	0.3	2	c	s	yes	VC97
36	105	10	0.3	5	nc	s	yes	VC97
37	105	10	0.3	5	c	s	yes	VC97
38	105	10	0.7	15	nc	ns	no	VC97
39	105	10	1	15	c	s	no	VC97
40	105	10	1	2	nc	s	yes	VC97
41	105	10	1	2	c	s	yes	VC97
42	105	10	1	5	nc	s	yes	VC97
43	105	10	1	5	c	s	yes	VC97
44	105	30	0.3	15	c	ns	yes	VC97
45	105	30	0.3	15	c	s	yes	VC97
46	105	30	0.3	2	nc	s	yes	VC97
47	105	30	0.3	2	c	s	yes	VC97
48	105	30	0.3	30	c	ns	yes	VC97
49	105	30	0.3	30	c	s	yes	VC97
50	105	30	0.3	5	nc	s	yes	VC97
51	105	30	0.3	5	c	s	yes	VC97
52	105	30	1	15	c	ns	yes	VC97
53	105	30	1	15	c	ns	no	VC96
* After collapse, the gas is shocked for 200 years

 

Table 1: continued

	$n_{\rm H_2}$	$T_{\rm gas}$	FR	AV		X(O)	CO-N2	H3O+
							freeze-out	branching ratio
54	105	30	1	15	c	s	yes	VC97
55	105	30	1	15	c	s	yes	W96
56	105	30	1	2	nc	s	yes	VC97
57	105	30	1	2	c	s	yes	VC97
58	105	30	1	30	c	s	yes	VC97
59	105	30	1	5	nc	s	yes	VC97
60	105	30	1	5	c	s	yes	VC97
61	106	30	0.3	15	c	ns	yes	VC97
62	106	30	0.3	15	c	s	yes	VC97
63	106	30	0.3	30	c	ns	yes	VC97
64	106	30	0.3	30	c	s	yes	VC97
65	106	30	1	15	c	ns	yes	VC97
66	106	30	1	15	c	s	yes	VC97
67	106	30	1	30	c	s	yes	VC97

2.2 Models in which all massive species freeze-out

Table 1 gives the parameters defining all the computational models we constructed. The fifth and sixth column indicate whether the cloud has undergone collapse (-c-) or is static (-nc-) and whether the initial abundances are standard (-s) or oxygen poor (-ns). In the seventh column, "No'' indicates that CO and N₂are assumed to return instantaneously to the gas phase after freezing-out. The last column indicates whether we adopted the branching ratios measured by Vejby-Christensen et al. (1997, VB97) or the ones measured by Williams et al. (1996, W96). For our discussion we follow the constraints laid out in Bergin et al. (2000), Sect. 4. Generally, SWAS results impose an upper limit for the fractional abundance of molecular oxygen of <10^-6 (Goldsmith et al. 2000), averaged over the SWAS beam, in all regions surveyed. The models therefore need to be capable of satisfying that constraint, together with (i) X(H₂O)< 7 10^-8 for starless cores, (ii) X(H₂O$)\sim$ 10^-6 for low density gas, (iii) 10^-9< X(H₂O) < few $\times$10^-8 in high mass star forming regions.

In this subsection we consider models in which all species containing an element more massive than helium freeze out on collision with dust. We divide the remainder of this subsection into three parts.

2.2.1 Starless cores or cores with little evidence of star-formation

In cores with little evidence of star-formation such as TMC-1 core B ($n_{\rm H}$ $\ge$ 10⁴ cm^-3; $T_{\rm gas}$ = 10 K; A_V > 10 mag) X(H₂O) is found to be <7 10^-8. For these environments, we excluded collapse (a plausible assumption for starless cores). In some models we included freeze out but never with total efficiency. In reality some depletion must occur as the fractional abundance of water ice is observed to be high ($\sim$10^-4) also in starless cores. From the grid, Models 1 to 4 were considered to represent starless cores, and Model 3 was found to be the "best matching" model (defined as the one that best reproduced the observed water and molecular oxygen). In this model, we adopt a high (but not total) freeze out efficiency. In Fig. 1 the Model 3 fractional abundances of selected species versus the logarithmic age of the clump, are plotted. The species selected for inclusion in Fig. 1 correspond to species for which SWAS gave constraints (H₂O and O₂) and species observed previously (see later). In the models considered, X(O₂) is <10^-6 both at early times (<1 Myr) (because of its slow formation) and at late times (>1.7 Myr in these models) where freeze-out on to grains is removing molecules from the gas. Between these two times there is a "peak'' in both species. The duration of these three phases, which we will call "formation'', "equilibrium'' and "depletion'' stages, are model dependent. Water follows a similar behaviour to that of O₂ although X(O₂) often exceeds the limit placed by the SWAS observations. A higher freeze-out efficiency would provide a more efficient loss route for water; however, such a solution would limit the lifetime of the clump to less than 3 Myrs as otherwise almost all molecular species would be frozen out. As expected, an oxygen-poor gas favours lower abundances of water and molecular oxygen, but only by factors comparable to the change in total oxygen abundance.

Figure 1: Fractional abundances (relative to hydrogen) ofselected species versus time (log) Model 3

Also plotted in Fig. 1 are a few selected species detected in core B of TMC-1 (same line of sights as SWAS). Table 2 lists their observed fractional abundances: the HC₃N and NH₃have been calculated from the column densities derived by Takano et al. (1998) at the NH₃ peak (core B) and CS from the column density observed by Hirahara et al. (1992). We also plot the fractional abundance of H₂O $_{\rm ice}$ which is of course entirely created by grain surface chemistry when freeze out is included.

 

 

Table 2: Fractional observed abundances, at A_V = 15 mag, with respect to hydrogen for selected species derived for the column densities of Takano et al. (1998), Hirahara et al. (1992). All the fractional abundances are derived for A_V = 15 mag

	Species
HC3N	2.4 10-9
NH3	1.7 10-8
CS	1.8 10-10

None of the models reproduces the observed abundances of these species during the "formation'' stage when O₂ and H₂O are low. However during the "freeze-out'' stage, before everything is depleted, both HC₃N and NH₃ are close to their observational values. CS would also be close to its observational value if we depleted it by a factor of 100: it should be noted that the abundances of sulphur-bearing species shown in this paper are overestimated because the solar abundance of sulphur has been used in these calculations. Perhaps the actual value should be reduced by a factor of about 100 (e.g. Viti & Williams 1999). However, as the mechanism for sulphur depletion is still unknown (e.g. Ruffle et al. 1999) we have assumed sulphur to have the solar elemental abundance rather than specify an uncertain parameter.

Abundances close to the observed values appear in the "depletion'' phase. HC₃N in particular increases significantly when depletion is effective (cf. Ruffle et al. 1997). Gwenlan et al. (2000) reached a similar conclusion when discussing the chemistry of HC₃N for TMC-1. We have not attempted here to match precisely the abundances of core B in TMC-1, but merely used them as indicative of the chemistry in dark quiescent clouds. We conclude that the general distribution of abundances in starless cores, including those measured in the SWAS observations, could be interpreted as a late-time chemistry in an object in which freeze-out of molecules on to dust is occurring. However, the consequence of this interpretation is that the object has a limited existence, of duration of about 3 My. The close match between our abundances and the SWAS observations is however limited to a very short epoch: it is unlikely that all the cores observed by SWAS are at the same age; in a later section, we therefore explore a modified solution where selective freeze out occurs and we show that this would significantly extend the period over which the abundances of observed species are well reproduced. In general, the implication is that there must be (in this interpretation) a cycle of material in the interstellar medium through stages such as those in the models, on this timescale.

2.2.2 Low density gas

Neufeld et al. (2000) reported observations with SWAS along the line of sight towards Sgr B2 ($n_{\rm H}$ $\le$ 10⁴ cm^-3, $T_{\rm gas}$$\sim$ 10-30 K). This is a long, low-extinction path. They found that water vapour in the foreground gas has a high fractional abundance of $\sim$6 10^-7, significantly higher than found in dense cores. A low fractional abundance of molecular oxygen, less than 10^-6, was also found with SWAS on these lines of sight.

To represent material along this line of sight, we have concentrated our analysis on models of collapsing clouds, as star formation may be present along this line of sight. Model 8 is the model in which collapse is included and CO and N₂ freeze-out occurs with chemical results agreeing most closely with those we consider appropriate for the Sgr B2 line of sight; Fig. 2 shows results for Model 8.

Figure 2: Fractional abundance (relative to hydrogen nuclei) of selected species as a function of age for Model 8

The high visual extinction in this model favours a higher abundance of water at early times because H₂O photodissociation is impeded. Water and molecular oxygen are in harmony with the observed constraints for a brief period around $\sim$1.5 Myrs which is when the final density in the collapse is reached. After that brief period, the H₂O and O₂ abundances rise quickly to unacceptably high values. If the clump is initially oxygen-poor the formation of O₂ is delayed relative to H₂O, probably because oxygen is more easily locked into water than molecular oxygen so a decrease in initial oxygen will delay the formation of O₂.

In the foreground gas along the line of sight of Sgr B2, many species have been observed. We have chosen to compare our models to some of the observational results of NH₃ (Hüttemeister et al. 1993), CS and C₃H₂ (Greaves et al. 1992), and HCO⁺, HCN and HNC (Linke et al. 1981) (see Table 3). Note that while the column densities for NH₃, CS and C₃H₂ are derived from observations of cool components detected at $\sim-40$ kms^-1 the column densities of HCO⁺, HCN and HNC are determined from absorption depths in the $\sim$129 kms^-1 feature of Sgr B2. This should not be a problem as although SWAS observations along the line of sight of Sgr B2 have distinguished various regions kinematically (Neufeld et al. 2000), the water abundances derived was averaged along the line of sight.

 

 

Table 3: Observed fractional abundances with respect to molecular hydrogen for selected species. All are derived for an assumed A_V of 15 mag, and a standard A_Vto hydrogen nuclei ratio

	Species
NH3	3 10-8
CS	1.2 10-9
C3H2	1.1 10-10
HCN	1.1 10-9
HNC	2.6 10-9
HCO+	8.75 10-10

In the region where the Model 8 water and molecular oxygen agree with observations (between 1.5 and 2.1 million years), results for NH₃and HCO⁺ are in reasonable agreement with observations, HCN and HNC are slightly overabundant while CS (depleted by 100) and C₃H₂are overabundant by about one half to 1 order of magnitude. As is the case for cores with little star formation (Sect. 2.2.1), the chemistry of low density gas is very time-dependent. The relatively high H₂O abundance together with the non-detection of O₂provides a severe constraint which can only be met for rather short periods within the scenario described here. High visual extinction and freeze-out lead to better reproduction of the observed abundances, although only for short periods of time. If a typical clump survives for 10 Myr it is unlikely that we would observe the same abundances towards different lines of sight. The short epoch during which model results are compatible with observational results could imply that the clumps are much shorter lived than 10 Myr; perhaps, they are dispersed by stellar outflows or depletion occurs rapidly enough that a clump quickly becomes undetectable.

2.2.3 High-mass star-forming regions

These regions are characterized by the following physical properties: $n_{\rm H}$ $\ge$ 10⁵ cm^-3; $T_{\rm gas} = 20{-}40$ K; A_V > 10 mag. The results from SWAS show that in these regions the water fractional abundance is very low, $10^{-9}< X({\rm H}_2{\rm O})<$ few 10^-8 (Bergin et al. 2000), and the upper limit on X(O₂) is 10^-6. We choose to represent this material with some of the high density models. Figure 3 shows the results for selected species from Model 52 which is the high density model with CO and N₂ freeze-out giving the best agreement with water and molecular oxygen observations for a period of up to 1.5 million years. This timescale varies according to the initial and final densities employed as it is a function of the gas-phase species depletion on the grains.

Figure 3: Fractional abundances (relative to hydrogen nuclei) of selected species as a function of age for Model 52

We note however that none of models reproduce the low water abundance observed with SWAS until freeze-out begins to dominate. High visual extinction and a final density of 10⁵ cm^-3 are favoured.

Bergin et al. (1997) presented results of an observational study covering three giant cloud cores. We use their observational results to compare with our model results for some species (see Table 4 for a list of the species selected with their observational values). We find that there is only a very small period of time during which most of the measured abundances are matched by our models; the best match is reached at $t\sim 1.5$ Myrs, where HCN, CS, C and HC₃N model abundances are close to the observational values, although CH₃OH and SO (depleted by some depletion factor) appear to be underabundant.

 

 

Table 4: Fractional observed abundances with respect to hydrogen for selected species derived from fractional abundances relative to CO from Bergin et al. (1999). We adopted a column density for CO of 3 10¹⁸cm^-2(from core Cepheus in Bergin et al.) and we estimated its fractional abundance with respect to hydrogen assuming a visual extinction of $\sim$15 mag

	Species
CS	4 10-9
CH3OH	2 10-8
HC3N	2 10-10
SO	4 10-9
HCN	1.2 10-8
C	6 10-6-2 10-5

Regions of high density are chemically and dynamically very complex because of the effects of outflows and shocks that excite or heat the gas and the grains: some grain evaporation might occur leading to chemical differentiation due to the different binding energies of the frozen species. The simple studies presented here do not take into account such effects, and cannot be expected to account in any detail for averaged measurements represented by the SWAS results. Nevertheless, one can infer that if the basic chemistry is correct, then for the models to be valid it means that the timescales in high-mass star-forming regions must be very short.

2.3 Selective freeze-out

In all the cases considered so far, it has been assumed that the nature of the gas-grain interaction is the same for all species other than H₂ and He, i.e every species colliding with a grain sticks and is retained. Therefore, the sticking probability has been assumed to be the same for all species (except H₂ and He). Such assumptions may be unjustified, and there have been many studies of systems in which it has been assumed that certain molecules are more readily desorbed into the gas, and not retained on grain surfaces (Millar & Nejad 1985; Hartquist & Williams 1990; Willacy & Williams 1993; Willacy et al. 1994; Gwenlan et al. 2000). The effect of retaining weakly bound molecules such as CO and N₂ in the gas phase is to prolong the epoch of gas-phase chemistry in molecular clouds; the carbon and oxygen in CO, for example, is re-cycled through hydrocarbons and water and these molecules ultimately freeze-out permanently. In particular, the C:O ratio in the chemistry is changed during this phase, and the results are of a chemistry in which [C]/[O] is close to unity (similar to the cyclic models of Nejad & Williams 1992).

Figure 4: Fractional abundances (relative to hydrogen) of selected species versus time for models where CO and N2 are immediately released back into the gas after freezing-out

For models 10, 17, 53, 31, 38 (see Table 1) we assumed that both CO and N₂ are rapidly desorbed, so that the atoms in those molecules feed a late chemistry. Results for the abundances of some species are given in Fig. 4 for Models 10, 17, 31 and 53.

Model 17 may be compared directly to Model 3 (cf. Fig. 1), which we have used to represent starless cores. The consequence of the selective freeze-out which maintains CO and N₂ in the gas is that the period over which the chemistry of observed species, such as H₂CO, NH₃ and HC₃N, is reproduced reasonably well by the models is extended considerably from about 1 My to several Myrs. The Model 17 H₂O and O₂ abundances satisfy the observed constraints for ages greater than $\sim$2 My (cf. Fig. 4). If we increase the density of our clump (Model 38) the H₂O and O₂observational constraints are satisfied already by 0.5 My.

Model 10 may be compared directly to Model 8 (see Fig. 2). The model water fractional abundance rises to near 10^-6, but the O₂ fractional abundance exceeds the SWAS limit by a factor of about 3 for at least part of the chemical evolution. This demonstrates how closely the H₂O and O₂ chemistries are linked. However, in warm (mainly neutral) regions behind shocks the formation of H₂O is rapid while O₂ remains a minor channel and it is in fact destroyed in strong shocks. Hence, it is quite possible that the relatively high water abundance observed towards the Galactic Centre, X(H $_2{\rm O})\sim 10^{-6}$, could be the result of one or more shocks along this line of sight. This line of sight certainly passes through several star-forming regions where shocks may be expected to occur, and in which the H₂O:O₂ balance is strongly increased. In warm post-shock gas, X(H $_2{\rm O})\sim 10^{-4}$, and therefore the fraction of the path towards the Galactic Centre that would be required by the detection of H₂O to be shocked would be around 1%, corresponding to a column density of warm H₂ of $\sim$10²¹ cm^-2.

Model 53 can be compared directly with Model 52 (see Fig. 3). The consequent chemistry has a much extended duration in the case of Model 53 to about 6 My (Fig. 4). However, the freeze-out of CS (which is largely unaffected by this late-phase chemistry) is so rapid at these high densities that it would be undetectable at the levels shown in this model. We have, therefore, examined a very similar case to Model 53, but for a lower density gas (Model 31). Note however that a density of 10⁴ cm^-3 may not be representative of many high mass star forming regions. Model 31 shows that from about 2 My onwards the H₂O and O₂ abundances satisfy the SWAS constraints, while other species such as H₂CO, HCN, NH₃, CS and HCN have levels that are generally around the levels detected; SO and CH₃OH however still remain too low, and this suggests that their chemistries are associated with processes not included in these models.

Figure 5: Steady state stable solutions for a range of densities between 100 and 105 cm-3 when $\zeta$ = 1.3 10-17 s-1 (lower x axis) and for a range of densities between 400 and 4 105 cm-3 when $\zeta$ = 5.2 10-17 s-1 (upper x axis). a) standard elemental depletion of oxygen; b) non standard elemental depletion of oxygen. The dotted horizontal lines correspond to the observed upper limit for O2 and H2O. The short-dashed line corresponds to the observed fractional abundance of water towards Sgr B2

2.4 The branching ratios for H₃O⁺ electronic recombination

We have studied the effect of varying the branching ratios for H₃O⁺ dissociative recombination with electrons. We have chosen one model per scenario and we have recomputed them with the Williams et al. (1996) branching ratios for the dissociative recombination of H₃O⁺ with electrons. The models computed with the Williams et al. (1996) branching ratios are models 11, 13, 18 and 20.

The effect of lowering so dramatically the branching ratio for the main formation channel for water is, as expected, to reduce water abundance for all the three scenarios: for cores with little star formation, this constitutes an improvement as we require water to be very low. However, for low density gas such as along the line of sight of Sgr B2, water is observed to be quite abundant and therefore the SWAS requirements are more poorly matched by this model. For high mass star forming regions a decrease in water formation is desired so models with a low branching ratio are well suited. However, we also obtain a decrease in methanol and SO which is not desired; however, as noted above, these species are not well described in these models. Very recently, new measurements of the H₃O⁺ branching ratios by Jensen et al. (2000) have been published. Their measurements yield a higher branching ratio for OH formation and a lower branching ratio for H₂O formation but both agree within a factor of 1.2 with the Vejby-Christensen et al. (1997) measurements.

Although the use of different branching ratios of H₃O⁺ reduces the production of water and O₂ dramatically, it does not alter the general chemical behaviour of the clump and therefore our previous discussions are not affected.