The current Saturn thermal flux is 1.9 Wm~2. Although this is smaller than the corresponding figure for Jupiter, this is due to Saturn's much lower mass and in fact, unlike Jupiter, most models suggest that the figure is too large to be explained by the Kelvin-Helmholtz mechanism alone. Cooling via the Kelvin-Helmholtz mechanism decreases exponentially over time and for Saturn is predicted by most models to have mostly disappeared after approximately 2.5 Gyr. Hence, an additional source of heat seems to be required, which is released later during the planet's evolution as it cools to lower temperatures. Although Saturn has more rocky material than Jupiter, radioactive heating from the 13 Mffi to 28 Mffi of heavy material (Section 2.7.3) in Saturn would account for no more than 1% of this and may be discounted. One possibility is that, like Jupiter, at the lower temperatures found in the metallic-hydrogen region of Saturn, helium becomes slightly immiscible and droplets of helium form, which "rain out'' towards the center. This gradual precipitation, with resultant release of gravitational energy would account for the additional internal heat source, and is also consistent with estimates of the He/H2 ratio of 0.135 which is significantly smaller than the ratio of 0.157 measured in Jupiter's atmosphere.
Saturn may also have a radiative zone in its molecular-hydrogen region and, together with the possible convective barrier at the metallic/molecular-hydrogen boundary (Figure 2.9), these may act to inhibit the transfer of material between the interior and exterior of the planet. The extent of this is unknown.
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