3 Simple models with total freeze-out and shocks

The chemistry during the collapse is an entirely conventional interstellar chemistry (cf. van Dishoeck 1998) in which ion-molecule and neutral reactions create molecules of increasing complexity. Ultimately, freeze-out of atoms and molecules on to dust grains removes all species other than H₂ and He from the gas. It is then assumed that the star switches on and that the core is heated by stellar radiation and possibly shocked by its wind. In this section, we compare the results of two models to explore the consequences of shock chemistry in the core.

For model S(0)T(28)0% a shock was assumed to sputter all mantle material and to maintain the core material at 1000 K for 100 years after which rapid cooling was assumed to occur; we supposed that the shock has a fast-mode Mach number not greatly in excess of unity so that the density remained reasonably constant during and after its passage. After the post-shock cooling, freeze-out was assumed to occur at the same rate as during the initial freeze-out phase. Postshock freeze-out was assumed to be total. Then time dependent heating of mantle material was assumed to increase linearly over 28 000 years.

Model T(28)0% is of a core in which no shock, and therefore no second freeze-out, occurs. Otherwise the evolution is similar to that in model S(0)T(28)0%; that is, time dependent grain heating to 200 K taking 28 000 years is assumed.

Figure 1 gives results for some species of interest for model S(0)T(28)0%. These are the species having results (displayed in Fig. 1a) depending significantly on whether or not a shock is incorporated in the models. The other species (results displayed in Fig. 1b) are those which are important in the chemical network, and an inspection of the time evolution of their abundances provides insight into why the abundances of a number of observable species behave as they do.

Figure 1: Evolution of fractional abundances for S(0)T(28)0%. The fractional abundances are relative to the number of hydrogen molecules. Time is measured from when the grain temperature increase, due to radiative heating, begins

Note that the fractional abundance of HCO does not reach a steady state until the fractional abundance of oxygen starts declining: in fact, the first rise of HCO corresponds to its evaporation from the grain; as soon as oxygen reaches its peak (at $\sim$6000 yrs) HCO is efficiently destroyed, but it also continues to be efficiently formed by H₂CO + O and H₂CO + OH reactions. It finally reaches steady state at $\sim$25 000 yrs when the oxygen abundance starts falling steeply. In general, the non-steady behaviour of many species at early times is due to the selective evaporation treatment. Table 1 gives values of abundance ratios at several times for both models S(0)T(28)0% and T(28)0%. Table 1 shows that the time variation of abundances, after thermal evaporation begins, differs very little between the two models. This is a consequence of the fact that hydrogenation on grain surfaces has been supposed to occur, producing ices such as H₂O, CH₄, NH₃ and H₂S. When these species return to the gas phase due to sputtering in a shock, the high temperature chemistry in the H₂ rich gas does not remove them. Though the qualitative nature of the agreement between the results in Table 1 may not be totally unexpected, the rather precise quantitative agreement between the results from the two models is striking, and illustrates that the evaporated products of surface chemistry and of high temperature shock chemistry can be similar. Abundances of deuterated species may be also used as a way to differentiate between thermal evaporation and shock chemistry as they would be more efficiently destroyed in a shocked hot core. However, at temperatures of the order of 200 K, deuterated species would eventually be destroyed even if a shock has not occurred (Hatchell et al. 1998b); therefore the abundances of deuterated species may not be able to distinguish between a young shocked core and a more evolved thermally heated core unless other species are used as tracers.

 

 

Table 1: Abundance ratios at three times (in years) for selected models at the centre of the core corresponding to A_V = 600 mags and T = 220 K

	HCO/H2CO	SO/CS	SO2/SO	H2S/CS	NS/CS
2.5 104
T(0)3%	0.53(-2)	0.24(+2)	0.14(+3)	0.71(+2)	0.17(+0)
T(28)15%	0.29(-3)	0.61(+4)	0.47(+5)	0.75(+4)	0.48(-4)
T(28)0%	0.11(-1)	0.32(+1)	0.16(+2)	0.66(+1)	0.10(-1)
T(28)S(10)3%	0.44(-1)	0.68(+1)	0.38(+2)	0.18(+2)	0.50(+0)
T(28)S(10)15%	0.56(-1)	0.87(+1)	0.12(+3)	0.27(+2)	0.30(+0)
T(70)3%	0.37(-2)	0.11(+2)	0.64(+1)	0.21(+2)	0.31(-4)
T(70)15%	0.69(-3)	0.26(+2)	0.82(+2)	0.32(+2)	0.30(-5)
T(70)S(20)3%	0.14(-1)	0.57(+1)	0.41(+2)	0.21(+2)	0.56(+0)
T(70)S(20)15%	0.37(-1)	0.12(+2)	0.21(+3)	0.54(+2)	0.74(-1)
T(70)S(50)3%	Same as T(70)3%
T(70)S(50)15%	Same as T(70)15%
S(0)T(0)3%	0.43(-2)	0.38(+1)	0.47(+2)	0.26(+2)	0.18(-1)
S(0)T(28)0%	0.12(-1)	0.32(+1)	0.16(+2)	0.67(+1)	0.10(-1)
5.0 104
T(0)3%	0.47(-2)	0.13(+2)	0.62(+2)	0.29(+2)	0.20(+0)
T(28)15%	0.97(-3)	0.82(+3)	0.65(+4)	0.81(+3)	0.37(-3)
T(28)0%	0.61(-2)	0.34(+1)	0.14(+2)	0.54(+1)	0.34(-1)
T(28)S(10)3%	0.36(-1)	0.52(+1)	0.28(+2)	0.13(+2)	0.57(+0)
T(28)S(10)15%	0.41(-1)	0.53(+1)	0.70(+2)	0.16(+2)	0.76(+0)
T(70)3%	0.12(+0)	0.30(+1)	0.10(+2)	0.32(+1)	0.39(-2)
T(70)15%	0.79(-3)	0.46(+3)	0.23(+4)	0.23(+3)	0.18(-4)
T(70)S(20)3%	0.21(-1)	0.37(+1)	0.30(+2)	0.15(+2)	0.55(+0)
T(70)S(20)15%	0.30(-1)	0.43(+1)	0.92(+2)	0.23(+2)	0.57(+0)
T(70)S(50)3%	0.41(-1)	0.23(+1)	0.93(+1)	0.25(+1)	0.12(+0)
T(70)S(50)15%	0.11(-1)	0.35(+3)	0.18(+4)	0.23(+3)	0.14(-2)
S(0)T(0)3%	0.12(-1)	0.28(+1)	0.34(+2)	0.18(+2)	0.38(-1)
S(0)T(28)0%	0.63(-2)	0.33(+1)	0.14(+2)	0.54(+1)	0.34(-1)
1.0 105
T(0)3%	0.39(-2)	0.82(+1)	0.29(+2)	0.11(+2)	0.19(+0)
T(28)15%	0.35(-2)	0.20(+2)	0.13(+3)	0.13(+2)	0.79(-1)
T(28)0%	0.48(-2)	0.34(+1)	0.11(+2)	0.35(+1)	0.61(-1)
T(28)S(10)3%	0.23(-1)	0.36(+1)	0.19(+2)	0.78(+1)	0.71(+0)
T(28)S(10)15%	0.27(-1)	0.33(+1)	0.42(+2)	0.89(+1)	0.11(+1)
T(70)3%	0.81(-2)	0.28(+1)	0.87(+1)	0.22(+1)	0.26(-1)
T(70)15%	0.32(-2)	0.75(+2)	0.46(+3)	0.33(+2)	0.28(-1)
T(70)S(20)3%	0.20(-1)	0.26(+1)	0.20(+2)	0.90(+1)	0.68(+0)
T(70)S(20)15%	0.22(-1)	0.25(+1)	0.48(+2)	0.12(+2)	0.11(+1)
T(70)S(50)3%	0.34(-1)	0.20(+1)	0.83(+1)	0.21(+1)	0.19(+0)
T(70)S(50)15%	0.25(-1)	0.17(+2)	0.10(+3)	0.12(+2)	0.11(+1)
S(0)T(0)3%	0.42(-2)	0.35(+1)	0.22(+2)	0.99(+1)	0.11(+0)
S(0)T(28)0%	0.43(-2)	0.33(+1)	0.11(+2)	0.36(+1)	0.61(-1)

 

 

Table 2: Abundance ratios at three times (in years) for selected models at the centre of the core corresponding to A_V = 13 mags and T = 275 K

	HCO/H2CO	SO/CS	SO2/SO	H2S/CS	NS/CS
2.5 104
T(0)3%	0.32(-2)	0.35(+2)	0.35(+1)	0.11(+3)	0.51(+0)
T(28)15%	0.35(-2)	0.81(+2)	0.51(+1)	0.91(+2)	0.77(-1)
T(28)0%	0.40(-2)	0.55(+1)	0.42(+1)	0.22(+2)	0.34(-1)
T(28)S(10)3%	0.37(-1)	0.69(+1)	0.40(+1)	0.23(+2)	0.61(+0)
T(28)S(10)15%	0.41(-1)	0.97(+1)	0.92(+1)	0.34(+2)	0.31(+0)
T(70)3%	0.34(-2)	0.76(+1)	0.39(+0)	0.17(+2)	0.34(-4)
T(70)15%	0.64(-3)	0.17(+2)	0.20(+1)	0.23(+2)	0.88(-6)
T(70)S(20)3%	0.17(-1)	0.84(+1)	0.39(+1)	0.27(+2)	0.70(+0)
T(70)S(20)15%	0.36(-1)	0.22(+2)	0.83(+1)	0.71(+2)	0.74(-1)
T(70)S(50)3%	Same as T(70)3%
T(70)S(50)15%	Same as T(70)15%
S(0)T(0)3%	0.37(-2)	0.62(+1)	0.34(+2)	0.45(+2)	0.41(-1)
S(0)T(28)0%	0.45(-2)	0.54(+1)	0.43(+1)	0.22(+2)	0.38(-1)
5.0 104
T(0)3%	0.29(-2)	0.25(+2)	0.24(+1)	0.45(+2)	0.53(+0)
T(28)15%	0.35(-2)	0.81(+2)	0.51(+1)	0.91(+2)	0.77(-1)
T(28)0%	0.27(-2)	0.77(+1)	0.27(+1)	0.17(+2)	0.15(+0)
T(28)S(10)3%	0.23(-1)	0.61(+1)	0.36(+1)	0.18(+2)	0.92(+0)
T(28)S(10)15%	0.32(-1)	0.67(+1)	0.89(+1)	0.22(+2)	0.11(+1)
T(70)3%	0.14(-1)	0.37(+1)	0.30(+1)	0.77(+1)	0.12(-1)
T(70)15%	0.23(-3)	0.44(+4)	0.54(+1)	0.56(+4)	0.91(-4)
T(70)S(20)3%	0.28(-1)	0.59(+1)	0.44(+1)	0.20(+2)	0.72(+0)
T(70)S(20)15%	0.31(-1)	0.90(+1)	0.96(+1)	0.32(+2)	0.64(+0)
T(70)S(50)3%	0.30(-1)	0.34(+1)	0.29(+1)	0.60(+1)	0.27(+0)
T(70)S(50)15%	0.05(-1)	0.42(+1)	0.15(+4)	0.25(+3)	0.14(-1)
S(0)T(0)3%	0.05(-1)	0.39(+1)	0.31(+2)	0.23(+2)	0.55(-1)
S(0)T(28)0%	0.29(-2)	0.76(+1)	0.27(+1)	0.17(+2)	0.16(+0)
1.0 105
T(0)3%	0.25(-2)	0.19(+2)	0.16(+1)	0.16(+2)	0.44(+0)
T(28)15%	0.22(-2)	0.24(+2)	0.36(+1)	0.13(+2)	0.18(+0)
T(28)0%	0.24(-2)	0.10(+2)	0.16(+1)	0.97(+1)	0.25(+0)
T(28)S(10)3%	0.13(-1)	0.49(+1)	0.32(+1)	0.11(+2)	0.15(+1)
T(28)S(10)15%	0.18(-1)	0.39(+1)	0.80(+1)	0.10(+2)	0.21(+1)
T(70)3%	0.41(-2)	0.52(+1)	0.19(+1)	0.52(+1)	0.94(-1)
T(70)15%	0.18(-2)	0.51(+2)	0.43(+1)	0.33(+2)	0.14(+0)
T(70)S(20)3%	0.16(-1)	0.46(+1)	0.38(+1)	0.13(+2)	0.12(+1)
T(70)S(20)15%	0.16(-1)	0.41(+1)	0.86(+1)	0.11(+2)	0.22(+1)
T(70)S(50)3%	0.20(-1)	0.31(+1)	0.28(+1)	0.49(+1)	0.47(+0)
T(70)S(50)15%	0.22(-1)	0.20(+2)	0.08(+3)	0.23(+2)	0.15(+1)
S(0)T(0)3%	0.40(-2)	0.37(+1)	0.20(+2)	1.05(+2)	0.48(+0)
S(0)T(28)0%	0.23(-2)	0.10(+2)	0.16(+1)	0.97(+1)	0.25(+0)

Clearly, if hydrogenation is strongly dominant and freeze-out in the collapse and postshocked phases is total, observations of hot core chemistry will give no insight into the hot core dynamics, nor into the manner in which stellar winds turn on. This is the first important result of this study.