5 Models with partial freeze-out, time dependent radiative heating and shocks

Figure 2: Evolution of fractional abundances with respect to molecular hydrogen, of species which evaporate at early times for simple models in which freeze-out is incomplete. In each model freeze-out reduces the elemental carbon in gas phase CO to three percent. Top: Results for Model S(0)T(0)3%. Bottom: Results for Model T(0)3%

Figure 3: Evolution of fractional abundances with respect to molecular hydrogen, for species that evaporate at late times for simple models in which freeze-out is incomplete. Top: Results for Model S(0)T(0)3%. Bottom: Results for Model T(0)3%

We have already seen that some abundance ratios of sulphur-bearing species and of HCO to H₂CO are candidate diagnostics of the radiative heating of grains and the hot core dynamical history. We now consider cases in which the radiative heating of the dust and the consequent injection of molecules from the ice into the gas phase, takes place over a finite period of time.

For models T(70)S(20)15%, T(70)S(20)3%, T(70)S(50)3%, T(70)S(50)15%, T(28)S(10)3% and T(28)S(10)15%, freeze-out after the shock passed was assumed not to take place as grains had already reached temperatures that hindered further freeze-out. As stated in Sect. 2, it is assumed that no second freeze-out phase occurred in model S(0)T(0)3%; also, no second freeze-out occurred in model S(0)15%. However, in all other models for which a shock was assumed to pass before the onset of radiative heating, a second freeze-out phase was supposed to occur. We terminated this second phase when the same percentage of carbon was left in gas phase species as after the original freeze-out.

Table 1 gives results for abundance ratios for selected computed models at three different times. We concentrate on results for the time of 5 10⁴ years. We do not present the O/CO, H₂O/O, and O₂/O ratios as those abundance ratios are particularly difficult to measure (note that the SWAS (Bergin et al. 2000) beam is unfortunately much too wide to be of use in observations of a single hot core).

It is evident that the HCO/H₂CO, SO/CS, SO₂/SO, and NS/CS ratios span particularly large ranges for models at this time. The reasons are exactly the same as stated in Sect. 4.

With the exception of model T(70)3%, the models without shocks have HCO to H₂CO abundance ratios of less than 1 10^-2 at 5 10⁴ years. Model T(70)3% has a very high HCO to H₂CO ratio of 0.12; it is the only model without a shock but with slow radiative heating, and high but incomplete depletion. While the presence of a shock in models in which there is less depletion and/or more rapid radiative heating generally leads to a significant increase in the HCO to H₂CO ratio, by itself a high HCO to H₂CO ratio cannot be used to surmise that a shock has passed.

However, the NS to CS abundance ratio at 5 10⁴ years is much lower in model T(70)3% than in many models with shocks. Hence, a high NS to CS abundance ratio and a high HCO to H₂CO abundance ratio together indicate that a shock occurred. Although we reached this conclusion from abundances calculated at a temperature of $\sim$220 K, Table 2 shows that it is still valid at a higher core temperature.

The utility of the abundances of other sulphur-bearing species has been emphasized by previous authors (e.g. Hatchell et al. 1998a), and these species have played a central role in the attempts to derive the "ages'' of hot cores. The models with the lowest CS to CO ratios at 5 10⁴ years are T(28)15%, T(70)15%, and T(70)S(50)15%, which are also the three models having the highest SO to CS ratios at that time; the CS to CO and the SO to CS ratios depend on how much elemental oxygen is in reactive gas phase species, so it is not surprising that models in which the most material is left in the gas phase at the end of a freeze-out phase show low CS to CO and high SO to CS ratios. The passage of a shock early in the development of a hot core with high remnant gas phase abundances of elements more massive than helium greatly alters these two ratios by causing more oxygen to become contained in H₂O.

In the centre of the core, the three models that have the highest SO to CS ratios at 5 10⁴ years also have the highest SO₂ to SO ratios at that time. The SO₂ to SO ratio is reduced if a shock occurs fairly early in a hot core's evolution. Those same three models show the highest H₂S to CS ratios. This result is consistent with CS being removed to form SO in reactions with O sufficiently rapidly that the CS/CO ratio is kept low.