Feuchtgruber et al. (1999)
isotopic exchange between neutral molecules in the nebula falls rapidly, and effectively disappears for T < 200 K. This means that the enrichment factor /h2o = (D/H)h 0/(D/H)H in water molecules equilibrating with molecular hydrogen in the solar nebula is unlikely to be greater than 3. For the model where water molecules reformed from the dissociation products of formation, the ratio would be close to 1.0. However, the (D/H)H o ratio of some solar system objects is found to be greatly in excess of the theoretical limit of three times the proto-solar (D/H)H ratio (as can be seen in Table 2.3 and Figure 2.7). This suggests that some other interaction must have taken place to increase the fHi0 ratio.
While the enrichment factor for (D/H)H o,/H20, may not exceed for neutral molecule-molecule interactions, other interactions may occur in the ISM which lead to different enrichments. If the ISM is partially ionized (which is often the case) then ion-molecule reactions can occur where the additional ionization energy serves to get over the activation energy of the fractionation reactions and hence leads to much greater levels of enrichment. In some formation models (Drouart et al., 1999; Mousis et al., 2000) it is assumed that while water ice is probably vaporized when it enters the inner part of the circumstellar disk (out to distances of 30 AU to 50 AU) it is not actually dissociated and thus retains its pristine, high/H20 ratio. Subsequent neutral gas interactions with molecular hydrogen in the hot inner nebula quickly reduce yH o to 1, but farther from the Sun the predicted ratio tends to 1 more slowly, due to the
lower temperatures and through turbulent mixing in the nebula between low-/ ice water near the Sun and high-/ ice farther out. The initial degree of D enrichment of presolar ice grains may be indicated by measurements of the composition of Semar-kona and Bishunpur LL3 meteorites which are thought to have originally condensed at around 3 AU from the Sun. Water is incorporated as clays in these meteorites and these are found to be composed of two components: roughly 15% has an/H2q equal to approximately 25, while the remainder has an/H2q equal to approximately 3. This observation is consistent with the idea of mixing between pristine unvaporized presolar ice grains with fH_i0 = 25, together with water that has equilibrated with the local solar nebula.
Using this initial value of fH o, and making reasonable assumptions about the nebula cooling rate and degree of turbulent mixing, the formation models of Drouart et al. (1999) and Mousis et al. (2000) predict that by the time that Uranus, Neptune, and the comets were forming in the outer solar nebula, the mean D enrichment of water molecules could have fallen to approximately 10 which is what is observed in the Halley, Hyakutake, and Hale-Bopp comets. The D/H ratio observed in the molecular hydrogen outer envelopes of the giant planets comes not only from the D/H of the molecular hydrogen in the presolar cloud but also through mixing and equilibrium with the D-enriched water ices making up the planet. For Jupiter and Saturn, the mass of hydrogen far outweighs that of ice and thus the D/H ratio should be representative of the presolar ratio in molecular hydrogen. For Uranus and
Neptune, however, the observed ratio is much higher and if we assume that the atmospheres have thoroughly mixed throughout their whole depth and that the D/H exchanged between water and molecular hydrogen, then, providing we know the relative masses of hydrogen and ice, we can calculate the D/H ratio of pre-Neptune and pre-Uranus ices. The relative masses may be calculated from interior models and recent estimates of the mass of hydrogen in these planets is 4.2 Mffi for Uranus and 3.2 Mffi for Neptune (Mousis et al., 2000; Podolak et al., 2000), where Mffi is the mass of the Earth. Using these values, the/HjO enrichment of pre-Neptune, pre-Uranus ices is consistent with the cometary value of 10. Similar arguments may be used to estimate the presolar D enrichment in HCN and subsequent evolution.
An alternative to the approach of attempting to model the variable composition of the solar nebula with distance is the SCIP model of Owen and Encrenaz (2006), discussed in Section 2.5. The hydrogen in SCIPs is assumed to be purely in the form of water ice and Owen and Encrenaz (2006) assume that the (D/H)h O in SCIPs was the same as that currently determined in comets coming from the Oort Cloud and estimated to be (3.2 ± 0.3) x 10~4 (Bockelee-Morvan et al., 2005; Meier and Owen, 1999). With this assumption and matching the mass of SCIPs needed to match the observed C/H ratios of the giant planets, Owen and Encrenaz (2006) estimate the global D/H ratio for the giant planets to increase as 2.1, 2.2, 4.6, and 6.8 x 10~5 as we move from Jupiter to Neptune, which match quite well the estimated values shown in Table 2.3. Owen and Encrenaz (2006) also note that models of Uranus and Neptune with more than 100x the solar value (Hersant et al., 2004; Lodders and Fegley, 1994) would give D/H > 9 x 10~5, which is the upper bound of present observations. [NB: A SCIP model would have O/H = C/H (i.e., 40-50).]
The only planet for which the predicted D/H ratio of the SCIP model does not appear to agree with measurements is Saturn, for which the most recent estimates from Cassini CIRS (Fletcher et al., 2008b) put the D/H ratio in methane to be (D/H)ch = 1.6 x 10~5. The equilibration of deuterium in methane is governed by a similar equilibration reaction to that for molecular hydrogen, shown in Equation (2.15); that is
To determine the associated (D/H)^ ratio requires knowledge of the methane fractionation factor fCH_4 = (D/H)C^/(D/H)H , which for Jupiter is estimated to be/CH = 1.25 ± 0.12, and for Saturn is estimated to be/CH4 = 1.34 ± 0.19 (Lellouch et al., 2001). Using this estimate of the/CH4 factor for Saturn, Fletcher et al. (2008b) estimate the (D/H)^ ratio to be 1.2 x 10~5, which is considerably less than that estimated for Jupiter and goes against the expected trend of the SCIP model. Fletcher et al. (2008b) note that this again suggests different origins for the trapped volatiles that formed each planet and argues against the simple SCIP approach.
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