2 The model

We follow the chemical evolution in a cloud that is collapsing in a "modified'' free-fall (Ruffle et al. 1999) in the process of forming a massive star. The collapse is ultimately arrested, and a star is assumed to be formed. Our calculations are space- and time-dependent as described in Viti & Williams (1999) but with only five depth points of increasing visual extinction up to 620 mags, taken to be the collapse centre. The chemical evolution of the remnant core is explored during the collapse and after its arrest, including the passage of a shock. The molecular cloud is assumed to have initial and final densities of 10⁴ H₂ cm^-3 and 10⁷ H₂ cm^-3, respectively, and an initial and final visual extinction at the centre of the core of 1.2 and 620 mags, respectively. We have included 119 gas-phase species and 39 surface species interacting in 1729 chemical reactions taken from the UMIST data base (Millar et al. 1997). The surface reactions included in this calculation have been described by Viti & Williams (1999), and are briefly as follows: It is assumed that all species that can be hydrogenated on dust grain surfaces will be fully saturated, e.g. O atoms are converted to H₂O and C atoms to CH₄, and retained on the surface. In addition, a small fraction of CO, 0.01 per cent (as suggested by models such as those of Charnley et al. 1992), is assumed to be converted to methanol on the surfaces of grains.

The initial elemental abundances by number relative to hydrogen were taken to be 0.14, 4.0 10^-4, 1.0 10^-4, 7.0 10^-5, 1.3 10^-7, 1.0 10^-7 for helium, oxygen, carbon, nitrogen, sulphur and magnesium. Note that, as we start from a purely atomic chemistry (apart from hydrogen) after freeze out is completed, NH₃ will contain much of the nitrogen. The sulphur abundance was chosen to be a factor of one hundred lower than solar (Oppenheimer & Dalgarno 1974). The temperature is held at 10 K throughout the collapse. After the collapse phase, the temperature rises from the initial value of 10 K to a value of 226 K at the centre of the core. In the models explored here, this temperature rise may be instantaneous (as is conventionally assumed) or occur over a period of some tens of thousands of years (as discussed by Viti & Williams 1999). The gas and dust temperatures (assumed to be the same because of the very high densities considered) also vary as a function of depth (Viti & Williams 1999). Hot core kinetic temperatures range from 90 K to 300 K, with a mean value of $\sim$170 K (Kurtz et al. 2000). Most the reactions included in our rate file and discussed in this paper are not significantly affected by the difference between our estimate and the mean value. Away from the centre of the core our temperature is higher, reaching 300 K at the edge (A_V=3.6 mag); if the source of heating is internal, rather than external, the material at a given temperature would be spatially distributed somewhat differently but a range of temperatures, similar to the ones considered here, would be present in either case. Rowan-Robinson (1980) derived an expression for the temperature distribution dependence on depth which we have fitted with an exponential expression and have extended to include a linear dependence on time (see Viti & Williams 1999). However, in this paper we mainly present and discuss the evolution at the centre of the core. For a full discussion of the effect of grain evaporation through the core the reader is referred to Viti & Williams (1999).

We have computed an extensive grid of models to investigate the effects of a shock on the chemistry of the remnant core. Results for selected models are listed in Tables 1 and  2 where we selected species shown to be good shock indicators. In this paper we will mainly discuss results shown in Table 1 (centre of the core) although results for a different depth point in the core where the temperature is $\sim$270 K, are shown for completeness in Table 2 and will be briefly discussed. The shock is low velocity and its consequences are assumed to be two-fold: the removal of all mantles, and the increase of temperature to 1000 K for a period of 100 years, representing the temperature structure of a C-shock. This temperature profile was adopted from the calculation of Bergin et al. (1998) who studied the chemistry of H₂O and O₂ in postshock gas. To designate the models, we use T and S to signify the time dependence of the radiative heating and the presence of the shock. The letter T is always followed by the time (measured in thousands of years) over which the grain temperature attains its maximum. Thus, T(70) means that the grains reach this temperature 70 000 years after the star switches on. Instantaneous heating is represented by T(0). The shock may occur at any time during the warming period or after the grains attain their maximum temperature. Thus, S(0) implies that the shock passed at the moment when radiative heating by the star began. S(20) implies that the shock passed 20 000 years after the onset of radiative heating. Finally, the models were run for different percentages of elemental carbon in all forms remaining in the gas at the end of the collapse phase; these percentages are written at the end of the model name. For instance, T(70)S(20)15% is the model in which the radiative heating rate rises over a period of 70 000 years, after freeze-out left 15% of the elemental carbon in gas phase in all forms, and in which a shock passed 20 000 years after the onset of radiative heating.