Internal structure of Jupiter and Saturn

The mean internal structures of Jupiter and Saturn are shown in Figure 2.9 after Guillot (1999b). Jupiter is significantly oblate (0.065), and its estimated moment of inertia ratio {C/MR2e) of 0.264 indicates a significant concentration of mass towards the center of the planet. Saturn is even more oblate (0.098) and in fact is the most oblate body in the solar system. Its moment of inertia ratio of 0.21 is the lowest of all the planets suggesting even greater mass concentration. These figures, together with the measured J-coefficients of the gravitational field, may be fitted with internal models that model how the density, pressure, temperature, and composition vary with depth. Hydrostatic equilibrium is assumed, and from the fitted pressure-density profile, conclusions may be drawn on the internal structure (e.g., Guillot 1999a,b; Guillot et al., 2004; Saumon and Guillot, 2004). Internal modeling studies suggest that Jupiter is significantly heavier than would be expected were the elements to be present in solar abundance. The mass of heavy elements (i.e., those with mass greater than helium) is estimated to be in the range 8 Mffi to 39 Mffi (Saumon and Guillot, 2004), which is 1-6 x more than would be expected if Jupiter had a solar composition. Saturn is estimated to be even more enriched in heavy elements containing as much as

Figure 2.9. Interior models of Jupiter and Saturn. From Guillot (1999b). Reprinted with permission of the American Association for the Advancement of Science. Copyright 1999.

13 Mffi to 28 Mffi (Saumon and Guillot, 2004), which is 6-14x more than would be expected if Saturn had a solar composition.

If Saturn is so much less massive than Jupiter, why is its volume approximately the same and thus its density so low? Hydrogen is a light and compressible substance and its compressibility is found to be little affected by temperature (provided that the temperature is not too high). Hence, a low-temperature sphere of hydrogen with a mass similar to Jupiter's has a characteristic radius that is nearly independent of total mass and interior temperature (Hubbard, 1997a). In other words, hydrogen is so compressible that a large increase in mass produces almost no change in radius. For a pure-hydrogen planet in the giant planet mass range the characteristic radius is 80,000 km, for a pure-helium planet it is 35,000 km, and for a "heavy" element planet it is typically 25,000 km. For an approximately solar composition, the characteristic radius would be 70,000 km, close to the observed radii of both Jupiter and Saturn.

Pressures and temperatures rise quickly towards the center of both planets and at temperatures greater than around 3,000 K and pressures greater than around 1.4 Mbar, hydrogen is thought to change to an electron-degenerate state of pressure-ionized protons and electrons called "metallic hydrogen''. Experiments have been performed in the laboratory, using shock compression of hydrogen samples with gas-guns and lasers, which have confirmed this transition (Nellis, 2000; Cauble et al., 2000; Weir et al., 1996; Nellis et al., 1995). The phase transition appears to be continuous rather than first-order and thus there is probably not a sharp boundary between the two phases in the interiors of these planets (Nellis, 2000). Rather, molecular hydrogen begins to dissociate at ~0.4Mbar and is completely dissociated at Mbar. The mid-point pressure of 1.4Mbar corresponds to a fractional radius of

0.9 for Jupiter and 0.5 for the much less compressed Saturn (Nellis, 2000). The transition region between molecular and metallic hydrogen is thus predicted to occur at a depth of ^7,000 km for Jupiter and ^30,000 km for Saturn. Thus, the overwhelming bulk of Jupiter's hydrogen is thought to exist in the metallic phase.

Saturn's low moment of inertia requires a high degree of differentiation (i.e., concentration of the heavy elements towards the center). Approximately 1 Mffi to 8 Mffi of heavy elements are thought to reside in the hydrogen/helium envelope (Saumon and Guillot, 2004), with a considerable mass (9-22 Me) thought to reside in a rocky/icy core. A large part of the uncertainty in Saturn's core mass arises from uncertainties in Saturn's J4 gravitational coefficient. Guillot (1999a) noted that the error in the available value of J4 prior to the arrival of the Cassini spacecraft gave rise to a possible variation of 10 Mffi in the core mass (Baraffe, 2005). Through analyzing the trajectory of Cassini in the Saturnian system, Anderson and Schubert (2007) have revised the gravitational coefficients, improving their accuracy by a factor of 10-20 in the case of J4, which should provide much better constraints to interior models.

Jupiter's higher moment of inertia implies less differentiation and it is estimated that perhaps 0 Mffi to 11 Mffi of heavy elements reside in a dense core, with the remaining 1 Mffi to 39 Mffi of heavy elements evenly distributed throughout the hydrogen/helium envelope. It is interesting to note that models with no core are still consistent with the estimated errors of current gravitational coefficients. One of the main aims of the future Juno mission (Section 8.6.1) will be to better constrain these coefficients through tracking the spacecraft's motion in its low perijove polar orbit, to determine once and for all if Jupiter has a core.

These estimates of the core and heavy element masses are consistent with the core accretion formation model outlined earlier, where an icy embryo forms first which then attracts further ice and gas before entering the final runaway gas collapse phase. Clearly Saturn was able to acquire less hydrogen and helium during this final stage, which accounts for its lighter mass, and greater heavy-element enrichment compared with Jupiter.

The estimated interior convective velocities and the calculated conductivity of metallic hydrogen are more than adequate to sustain a magneto-hydrodynamic dynamo of the size needed to account for Jupiter's very powerful magnetic field, especially since the conducting metallic region extends over 90% of the planetary radius. The convective timescale is estimated to be of the order of 100 yr and thus changes in the field are likely to occur on this timescale also. Long-term monitoring of the magnetic field may eventually provide clues on the deep currents. Charged particles from the solar wind and other sources become trapped and accelerated in this field leading to powerful synchrotron radio wave emission at decametric wavelengths, which are detected at Earth and led to the first measurements of the internal bulk rotation rate as inferred from observations of Jupiter's kilometric radiation (JKR) (System III). This was observable since Jupiter's magnetic field is sufficiently misaligned with respect to the rotation axis that diurnal changes in radio wave emission are easily detectable.

In Saturn the observed heat flux must similarly drive convection in most of the liquid interior. However, it is possible that composition differences across the metallic/molecular hydrogen phase boundary inhibit convection and thus transport of heat across this stably stratified boundary might be via conduction. This might explain why Saturn's magnetic field is so closely aligned to within 1° of the rotation axis since the non-axially symmetric parts of the magnetic field generated via the magneto-hydrodynamic dynamo in the convective interior of the metallic-hydrogen zone (which only accounts for 50% of the radius) may be screened out by a stably stratified conducting layer at the top of this region (Stevenson, 1980). The smaller size of the metallic-hydrogen conducting core may also explain why the magnetic field of Saturn is generally weaker than Jupiter's, and why the higher order field components are more greatly reduced (Hubbard, 1997b; Nellis, 2000). The close alignment between the magnetic and rotation axes makes it difficult to determine Saturn's magnetic field rotation period from the Earth and thus this was not determined until the Pioneer 11 flyby in 1979 (Russell and Luhmann, 1997). The current estimate of the System III rotation rate of 10 h 39min was derived from observations of Saturn's kilometric radiation (SKR) during the Voyager encounters. More recently, during the Cassini approach, the SKR rotation rate was observed to be 10 h 45min (Gurnett et al., 2005). Detailed observations since then of the magnetic field have yielded a magnetospheric rotation rate of 10 h 47min (Giampieri et al., 2006). Clearly, System III, derived from SKR observations, does not seem to be a reliable proxy for the bulk rotation rate of Saturn since the magnetosphere seems to slip relative to the interior, perhaps due to centrifugally driven instabilities in Saturn's plasma disk. Most recently, the gravitational data acquired during the Cassini mission have been analysed by Anderson and Schubert (2007) to yield a bulk internal rotation rate of 10 h 32min, which is now thought to be the most reliable estimate.

The magnetosphere of Jupiter, where Jupiter's magnetic field dominates over the interplanetary magnetic field, is vast and if visible to the naked eye would have a diameter roughly twice that of the Moon as seen from the Earth. This great size is due not only to the high strength of Jupiter's magnetic field, but also to the low density of the solar wind at 5 AU and the additional source of charged particles from Io, which resides within the magnetosphere. The magnetosphere of Saturn is roughly five times smaller than that of Jupiter.

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