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Astron. Astrophys. 336, 309-314 (1998)

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4. Discussion

4.1. Observability

A complication of this analysis is that it is not enough to argue that NH3 family molecules will cover smaller areas of the sky than CS family molecules. We have postulated in Paper 1 that this is the case for NH3 only by assuming that it is at such an abundance that it is undetectable in the CS clumps, and this may not be the case for other molecules of the NH3 family. What can be said, however, is that at similar angular resolution molecules of the NH3 family should show a much steeper decrease in intensity from peak, i.e. a smaller half-power contour. In order to sample fully the area a resolution of [FORMULA] is preferable for mapping purposes, though higher resolution would be required to resolve most of the individual clumps. On the other hand, the excitation conditions for particular transitions are important, so for example a member of the CS family will not appear widespread compared with NH3 if the transition [FORMULA] is so high that it is only significantly excited in the densest of cores (e.g. CS(J=[FORMULA])). Mappings of molecules in low-mass star-forming regions on the [FORMULA] scale are rare in the literature, so this discussion is concerned more with potential observability. In Table 2 we show line information concerning transitions, frequencies and estimated line strengths for the most relevant molecules discussed.


Table 2. Transitions of relevant early- and late-time molecules with the estimated line strength relative to the CS (J=1-0) line intensity, at the time of reaching maximum abundance. Calculations have been made assuming LTE, Tex=10 K and a line width [FORMULA]V=1  km s-1

4.2. Early-time molecules

HCN (J=[FORMULA]) was mapped in two cores in high-mass star-forming regions by Zinchenko et al. (1994), and those authors remark that the spatial extent follows CS rather than ammonia, as predicted here. The molecule is easily observable in low-mass sources as well (e.g van Dishoeck et al. 1995). We anticipate that CN will follow the same distribution.

H2CO is now widely observed since it appears to be a good indicator of infall due to collapse (e.g. Myers et al. 1995). Its emission appears widespread in diffuse clouds (Turner 1994), which may not be star-forming, but mappings of star-forming cores would probably be better in transitions like [FORMULA] (rather than at cm wavelengths) which is at a high enough frequency ([FORMULA] 141 GHz) that the required resolution can be achieved.

H2CS is clearly observable (e.g. Minh et al. 1991) and mapping would be possible. Like H2CO, however, there has been speculation that this molecule is formed on grains rather than in the gas, which could affect our conclusions.

We predict a number of carbon chains to be members of the CS family, most prominantly C3N, HC3N, and C3H. Although their abundances are probably inflated in our models since the chemical network for species with four or more carbon atoms is incomplete, their early-time behaviour should not be affected. The original impetus to this work came from our analysis (Howe, Taylor & Williams 1996) of observations of HC3N and NH3 (together with CCS and C4H) in TMC-1 by Hirahara et al. (1992). This exceptionally rich source shows at least five distinct cores, the carbon chains and ammonia showing intensity peaks in different cores. We interpreted this spatial difference as being due to sequential time evolution. By associating C3H with C4H there does not seem to be any doubt that all three of these molecules could be mapped in other star-forming regions. CCS appears well suited to core observation and, although not included in these models, is also early-time. HC5N ought to follow the distribution of HC3N, and was mapped in four sources by Benson & Myers (1983), however the maps were not extensive and the comparison with NH3 is indeterminate. Our models predict CCN to belong to the CS family, but the molecule is yet to be observed.

4.3. Late-time molecules

HCO+ is another commonly used tracer of infall, though again maps are rare. However, Butner, Lada, & Loren (1995) do show the coverage of DCO+ in a number of sources previously mapped in CS/NH3, and it is apparent that for the most part this molecule is closer to ammonia than CS. Assuming that HCO+ follows DCO+ then these observations are consistent with our prediction that HCO+ is a late-time molecule. Since we presume the late-time molecules to emit from far fewer clumps than the early time molecules (perhaps only one clump), it follows that their peaks of emission ought to coincide. In this respect it is encouraging that HCO+ has been observed in L1251 by Sato et al. (1994) and the emission is smaller than, but coincident with, the NH3 mapped by Morata et al. (1997).

The molecule SO has been mapped by Chernin, Masson, & Fuller (1994) in a number of low to intermediate-mass sources. The 32-21 emission is quiescent (rather than being associated with molecular outflows) and seems to be compact, although none of the sources appear to coincide with those of the CS/NH3 surveys. An understanding of the behaviour of SO is impeded by lack of information on the elemental depletion of sulphur. However, a comparison with CS would be very interesting.

Emission from NO at [FORMULA] 150GHz is clearly detectable (e.g Gerin, Viala & Casoli 1993) and maps ought to be possible at the required resolution, though none appear to exist at present. OCN peaks at 1.9 [FORMULA]yr in our model and so can be classed as late-time, but has not been observed. A number of archetypal late-time molecules (O2, N2, C2H2) are unfortunately not observed in emission because of their lack of dipole moment. The chemistry of C2H2 is unusual in that it exhibits an early-time peak due to formation through C+ and CH4, but experiences a larger late-time peak because its main destruction paths through C and C+ are reduced as these species are removed from the gas-phase.

4.4. Chemistry

A glance at the chemical equations in Sect. 3 confirms that neutral-neutral reactions are surprisingly important, although much of interstellar chemistry is based on ion-molecule chemistry. It is important to confirm that these neutral-neutral reactions proceed at 10K; in fact, most of these reactions have only been studied at room temperature, if they have been studied at all. The CS family chemistry, in particular, depends on efficient neutral-neutral reactions. For the NH3 family, the removal of these predominant pathways will probably lead to even slower formation.

Certain neutral-neutral reactions have indeed been studied at low temperatures. The reaction of CN with C2H2 (reaction 10) has been examined by Sims et al. (1993), and of CN with O2 (reaction 13) by Rowe, Canosa, & Sims (1993). Gerin et al. (1992) show that N with OH (reaction 14) proceeds with a negligible barrier. The reaction C + C2H2 (reaction 7) was studied recently by Kaiser et al. (1997) and found to proceed, and also in the correct ratio of cylic to linear C3H product. The reaction of O with OH is thought to have a barrier of [FORMULA] 30K, low enough to be a significant barrier in cold clouds. For the schemes used here, OH reactions are based on the assumption that atom-radical reactions can in fact proceed without barrier, given the evidence above (cf. Herbst et al. 1994).

The initial condition of the gas that is adopted in these studies has been typical of fairly diffuse interstellar material, and we have further assumed that most of the carbon is in the form of C+. We have, however, also explored the consequences of starting with significant quantities of carbon in CO. The results are not greatly different from those illustrated in Fig. 1. This is because the photodissociation of CO before the collapse dominates (at [FORMULA] yr) always ensures enough free carbon to drive the carbon chemistry, as described in Sect. 3.

The initial condition also sets the sulphur abundance at about 1% of its cosmic value. This is clearly incorrect under the near-diffuse conditions at the start of the collapse; in diffuse clouds sulphur is observed to have a relative abundance close to the cosmic value. However, in calculations that we have made using higher values of the sulphur relative abundance, sulphur-bearing molecules are found to have abundances that are much too high when compared to the observed values. Evidently, these calculations are telling us that sulphur is being heavily depleted during the collapse process. The physical mechanism by which this depletion occurs is unknown, and is currently a topic of study by us. Until this mechanism is understood, we have chosen to adopt a (low) fractional abundance of sulphur that is necessary to give approximately the abundances of the S-bearing family of molecules.

As mentioned earlier (Sect. 3), the dynamical and chemical timescales control the appearance of early and late families of molecules. In this simple model, the dynamical timescale is controlled by the scaling parameter, B (Sect. 2). The value of B has been set equal to unity in the calculations reported here. We have, however, also explored the consequences of a slow collapse (B=0.1). In this case, the early time abundance peaks are suppressed. These peaks are a consequence of the cloud having attained a high density before the gas can respond chemically. With the slower collapse, represented by B=0.1, the chemical timescale is shorter than the dynamical timescale, so these peaks are smoothed out. The arguments of Paper 1 and of Howe et al. (1996) therefore suggest that collapses as slow as those modelled by B=0.1 are excluded.

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Online publication: July 7, 1998