Hs

2.4 x 10~5

7.7 x 10~5

3.4 x 10~4

6.2 x 10~4

6.2 x 10~4

Ar

2.9 x 10-6

1.6 x 10-5

?

?

?

ph3

4.3 x 10-7

1.0 x 10-6

5.9 x 10-6

?

?

GeH

6.6 x 10~9

6.0 x 10~10

3.5 x 10-10

?

?

Kr

3.2 x 10-9

8.0 x 10-9

?

?

?

Xe

3.2 x 10-10

7.7 x 10-10

?

?

?

AsH3

3.3 x 10-10

1.9 x 10-10

2.6 x 10-9

?

?

Solar abundances from Grevesse et al. (2007).

Solar abundances from Grevesse et al. (2007).

modeled), or (ii) that Jupiter originally formed as far out as 30 AU and later migrated in. The former scenario does not seem to tie in with the good evidence for high inner solar nebula temperatures and evidence of turbulent mixing, indicated amongst other things by the presence of crystalline silicates in comets. The latter possibility seems at first sight unlikely owing to the excessively long formation time of a Jupiter-sized planet at 30 AU and the difficulty in moving the planet in by almost 25 AU, but we know from Section 2.4.3 from the characteristics of exoplanetary systems and from our own solar system that forming planets do probably migrate. An alternative explanation has been put forward that utilizes crystalline water ice. Here the water ice is assumed to have vaporized on entry into the nebula and then subsequently recondensed at the "ice line''. The partial pressure of water vapor in the nebula was low and thus water initially condensed at about 150 K. Further cooling would have led to more and more water vapor molecules condensing onto the ice grains as the temperature dropped. Water condensing at 150 K is necessarily crystalline and as such may trap other gas molecules, either as hydrates for molecules such as ammonia (NH3-H2O would have formed at approximately 85 K at pressures of 10~8 bar), or clathrate-hydrates for other molecules, where gas molecules are trapped in "cages" of water molecules (Alibert et al., 2005a, b; Gautier et al., 2001a, b; Hersant et al., 2004). There are two classes of clathrate-hydrate depending on the ratio of the number of water molecules to the number of trapped gas molecules in each cage. This ratio is 5.75 for Class I and 5.66 for Class II. As the temperature dropped, more and more ice condensed onto the grains until the temperature was so low that amorphous ice started to form. However, since the saturated vapor pressure decreases exponentially as the temperature reduces it can be seen that the bulk of the condensed ice grains must have been crystalline. Laboratory studies have shown that the heavy molecules in the solar nebula could be trapped in clathrate-hydrates in quantities needed to account for the observed enrichments of the outer planets at far higher temperatures than would be needed to trap equivalent amounts in amorphous ice (Gautier et al., 2001a, b). The clathrate-hydrate formation scenario is consistent with the current turbulent solar system models and is also consistent with observations of a circum-stellar disk where 90% of the ice is observed to be crystalline in a region whose temperature is 30 K to 60K (Malfait et al., 1999). In addition, crystalline ice has also been detected in Comet Hale-Bopp (Lellouch et al., 1998) and it also provides a good explanation of the low Jovian Ne/H ratio since neon is poorly trapped in clathrates, unlike the other noble gases.

Owen and Encrenaz (2006) provide a detailed comparison of the predictions of the clathrate-hydrate model of Gautier et al. (2001a, b) with their own model based on amorphous ice condensed at ~40 K, using the principal of Ockham's Razor (also known as Occam's Razor) that the most simple solution that matches the observed data is most likely to be the correct one. Owen and Encrenaz (2006) note that most elements are enriched on Jupiter to approximately the same degree of ~4x the solar value. We will see later in Section 2.6.3 that the observed 15N/14N ratio strongly suggests that nitrogen was incorporated into Jupiter in the form of N2 and not NH3 and the fact that the observed N/H and Ar/H ratios are also ~4x the solar value argues against the clathrate-hydrate model since temperatures as low as 40 K would be needed to trap these gases in clathrates. Although Owen and Bar-Nun (1995) had suggested that N2 was the most likely form of nitrogen in nebula, they did not anticipate the parity of the N/H and C/H ratios on Jupiter since this had not been observed in any comets. As a result, Owen and Encrenaz (2003) suggested that the icy planetesimals forming Jupiter did not have the same composition as that estimated in current comets, but instead were solar composition icy planetesimals (SCIPs), which contained solar relative abundances of O, N, and other heavy elements, but not solar abundances of H and He, with all the hydrogen atoms present in the form of H2O.

Starting with the assumption that all the giant planets were formed from first accreting SCIPs to form their embryos before collapsing the solar nebula gas, Owen and Encrenaz (2006) use this simple model to calculate the mass of SCIPs that would need to be incorporated into the giant planets to explain the measured enrichments of C/H for Jupiter, Saturn, Uranus, and Neptune. They find that the required mass is similar for all four giant planets and is approximately equal to 10 Me, which matches well the expected embryo mass needed in the core accretion theory to begin Phases 2 and 3. The simple model of Owen and Encrenaz (2006) also predicts well, with the possible exception of Saturn, the D/H ratios of the giant planets (Section 2.6.2) and is also consistent with the measured Jovian 15N/14N ratio (Section 2.6.3).

Owen and Encrenaz (2006) then went on to compare their model with the clathrate-hydrate approach. An implicit assumption of the clathrate-hydrate approach is that the giant planets must have considerably higher O/H ratios than other elements through the need to trap other molecules in the clathrate "cages". While some formation models predict very high enrichments of O/H near the "ice line", where water first condenses at about 5 AU, the clathrate model requires at least 10 x the solar water abundance (whereas the SCIP model would have equal O/H enrichments to the other heavy elements). However, interior models such as those of Guillot (1999b) rule out O/H >10x the solar value. Unfortunately, water condenses in the observable part of the giant planet atmospheres and thus the deep abundance cannot be directly measured. Its abundance can be inferred indirectly, however, from the abundance of other molecules. Estimates of the abundance of CO at Jupiter's tropopause (Bezard et al., 2002) suggests that O/H <9x solar value, which is again inconsistent with the clathrate-hydrate model. While the clathrate-hydrate and SCIP models give similar results for Jupiter, with similar enrichments of all heavy elements, the two models diverge in their predictions for the other giant planets, where the clathrate-hydrate model predicts varying relative enrichments depending on the local thermal conditions in the pre-solar nebula at the distance from the Sun where the planets formed. There are two problems with this. First of all, the clathrate-hydrate model implicitly neglects the migration of planets during formation, which we suspect to be an important effect. Second, although measurements are not yet precise enough from the enrichments of elements on the other giant planets to discriminate between these models for most elements, the clathrate-hydrate model predicts a Saturnian C/H enrichment of ^2.5 x the solar value, which is very much less than that observed by Cassini CIRS of ~11x solar value. Finally, the clathrate model predicts an S/H enrichment for Jupiter that is twice too large. Attempts to explain this by suggesting that H2S corrodes Fe alloy grains in the inner nebula and that this depleted sulfur gas is turbulently mixed out to Jupiter are disputed by Atreya et al. (2003) and Owen and Encrenaz (2003).

Hence, on balance it currently appears that the SCIP model of Owen and Encrenaz (2006) is more consistent with available measurements than the clath-rate-hydrate model (Alibert et al., 2005a, b; Gautier et al., 2001a, b; Hersant et al., 2004). A key discriminator between these models is the O/H ratio, which is not well known for any of the giant planets. However, the arrival of the Juno mission at Jupiter in a low perijove orbit (Section 8.6.1) will be able to constrain the internal structure and finally determine whether the O/H ratio for that planet is >10x the solar value or not. Another discriminator between the SCIP model and others is that the SCIP model predicts equal enhancements for all heavy elements. While the C/N ratio for Jupiter is approximately solar, the estimated C/N ratio for Saturn is considerably supersolar. Fletcher et al. (2008b) suggest that a supersolar C/N ratio on Saturn is consistent with the known deficiencies of N2 in cometary material (Mizuno, 1980), and with the suggestion that N2 could be clathrated at 5AU, but not at 10 AU, so that Saturn's nitrogen content came only from ammonia hydrate

(Hersant et al., 2004). In addition, Fletcher et al. (2008b) find that the C/S and C/P ratios also vary between Jupiter and Saturn and show the opposite trend to the C/N ratio, with the Jovian values being supersolar, and the Saturnian value being subsolar. A caveat to this is that the C/P estimates are poorly known, since the P/H values are determined from the abundance of phosphine, which is a disequilibrium species in the upper tropospheres of the giant planets (as we will see in Chapter 4). The C/S trend, however, suggests that H2S may have been more readily available in the outer nebula, as suggested by Hersant et al. (2004), than closer to the Sun. Given the substantially different C/N, C/S, and C/P ratios on Jupiter and Saturn, Fletcher et al. (2008b) suggest that these planets incorporated icy planetesimals from the immediate vicinity of a nebula whose composition varied with position rather than from a single common reservoir as the SCIP model maintains.

Finally, a key drawback of the SCIP model is the question of where the SCIPs are now. Owen and Encrenaz (2006) suggest that they may perhaps be hiding in the Oort Cloud or in the Kuiper Belt. Alternatively, they suggest that they might have been reprocessed in the same way as the building blocks of inner planets were reprocessed into meteorites and asteroids. As ever, with planetary formation models, the real processes involved in forming planetary systems may in fact incorporate aspects of both ice condensation models. Both models have some advantages and some key drawbacks and until better measurements exist of the planets' bulk composition it will be impossible to discriminate between them. As mentioned earlier, a key discriminator will be the measurement of the deep O/H ratio on Jupiter by the Juno mission, which is planned to arrive in orbit about Jupiter in 2016.

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