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

2. Model

If the telescope beam includes a number of unresolved clumps then the difference in emission may be due to the differences in the physical, and hence chemical, evolution between them. We proposed in Paper 1 that all clumps had collapsed from a relatively diffuse state, in which only hydrogen is predominantly molecular. As the gas collapses, a large amount of free carbon is available to form molecules such as CS, before the carbon is swallowed up in CO. These `early-time' carbon-based molecules (like CS) exhibit a peak in fractional abundance (= n(X)/, where n(X) is the number density per unit volume of the molecule X and is the number density of hydrogen nuclei) before falling off at later times. Other molecules may simply achieve their maximum abundance at the same time as the peak of the early-time molecules and then remain at constant abundance (being in chemical equilibrium), but some termed `late-time' only peak in abundance at significantly later times due to bottlenecks in the their formation routes caused by low reaction rates. Ammonia is an example of this latter type since the reactions involved in its formation

appear to be considerably slower at 10K than other comparable reactions. Only cores that are stable upon the initial collapse will be detectable in these molecules. Other cores, perhaps dispersed quickly because they are too small or are not in pressure equilibrium with the external medium, will not be detectable in "late-time" species.

Our chemical model is described in detail in Paper 1; the important points are reiterated here. In a single point calculation chemical abundances are followed from initial conditions typical of a diffuse cloud (  cm^-3, visual extinction ) through a free-fall collapse (increasing and ) until  cm^-3 and , after which both of these parameters are kept constant. The formula used for this collapse is given in Rawlings et al. (1992), and includes a scaling parameter `B' that we have normally taken to be unity. This description is intended to represent the relaxation to an equilibrium state in magnetohydrodynamic numerical collapse models, which in those simulations is followed by a longer phase in which magnetic support for the core is slowly removed by ambipolar diffusion so that the core can then collapse further to form a star. The formation of a number of such clumps may be the result of the fragmentary collapse of a larger scale ( 1pc) cloud. Observational evidence for such clumps comes from the small scale structure of core D in TMC-1 (Langer et al. 1996), and from the clumpy emission seen ahead of bow shocks in a number of sources (Taylor & Williams 1996).

The observations pertinent to Paper 1 could only be explained if the effective freezeout parameter, FR, was low. This parameter accounts for the efficiency of adsorption of gas molecules onto dust grain surfaces and for the grain size distribution (which affects the surface area available for gas species to stick to), and its low value may be an indication of effective desorption rather than inefficient sticking. There are a number of methods of desorption, described e.g. in Williams & Taylor (1996), and amongst the more recent to be considered are desorption due to the heat emitted from the exothermic formation of molecular hydrogen on the grain surface (Willacy, Williams & Duley 1994), and the desorption of CO by transfer of energy from the O-H vibration at 3.1 µm (Dzegilenko & Herbst 1995). As in Paper 1 we normally take FR=0.01, and we also use the same elemental abundances. However, the chemical data has been updated, and also extended, by increasing the carbon chain chemistry to include species as complex as HC₃N (there are now 138 gas phase species and 1996 reactions), and the revised UMIST ratefile has also been used (Millar, Farquhar & Willacy 1997).

© European Southern Observatory (ESO) 1998

Online publication: July 7, 1998
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