Deuterium enrichment in giant planets

Recently published laboratory measurements of the isotopic exchange rate constant k−(T) between CD4 and H2 are used to calculate f(z)—the isotopic enrichment factor between CH4 and H2—at every level in the outer atmosphere of the giant planets. The variation of f(z) with local vertical velocity, temperature and pressure has been calculated under the assumption that atmospheres are convective and uncertainties have been calculated by error propagation. Considering only the random errors—mainly the uncertainty on k−(T)—the f values in the observable upper atmospheres of giant planets (i.e. at z = 0, P = 1 bar) are: f(0) = 1.25 ± 0.05, 1.38 ± 0.06, 1.68 ± 0.09, and 1.61 ± 0.08 for Jupiter, Saturn, Uranus, and Neptune, respectively. Additional systematic errors due to the uncertainty in calculating the vertical velocity in the framework of the mixing length Prandtl theory lead to an overall uncertainty on f(0) of ±0.12, ±0.15, ±0.23, and ±0.21 for each planet, respectively. The D/H ratios in H2 derived from the measured CH3DCH4 ratios in the upper atmosphere of the four giant planets are then recalculated. Uranus and Neptune seem to be enriched in deuterium with respect to the protosolar nebula but depleted relative to the Standard Mean Oceanic Water on the Earth (SMOW). However calculations based on current interior models of Neptune suggest that ices which formed the core of the planet had a DH ratio of the order of the SMOW. The deuterium abundance in proto-Uranian ices remains uncertain. The case where water is a major constituent of the fluid envelope of Neptune is discussed. It is shown that the DH ratio of the planet would then be higher than the value measured in hydrogen. Even in this case, the DH ratio in proto-Neptunian ices is less than the recently revised value in P/Halley and less than the value measured in water of the Semarkona meteorite. These results suggest that the ices which formed the core of Neptune did not have an interstellar origin. Similarly, the comparison of the most recent determination of the DH ratio in the atmosphere of Titan with the value of DH in P/Halley suggests that this atmosphere was not formed by infalling comets but more likely from grains embedded in the sub-nebula of Saturn.