Models of Jupiter and Saturn after Galileo mission

New models of Jupiter are based on observational data provided by the Galileo spaceprobe, which considerably improved previously existing estimates of the helium abundance in the atmosphere of Jupiter. These data yield for Jupiter’s atmosphere 20% of the solar oxygen abundance and do not agree with the results of the analysis of the collision of comet Shoemaker-Levy 9 with Jupiter (10 times the solar value). Therefore, both the models of Jupiter with water-depleted and water-enriched atmosphere are considered. By analogy with Jupiter, trial models of Saturn with a water-depleted external envelope are also developed. The molecular-metallic phase transition pressure of hydrogen P_m was taken to be 1.5, 2 and 3 Mbar. Since Saturn’s internal molecular envelope is noticeably enriched in the IR-component (its weight concentration, 0.25–0.30, being by a factor of 3–4 higher than in Jupiter), the phase transition pressure in Saturn can be lower than in Jupiter. In the constructed models, the IR-core masses are 3–3.5 M_⊕ for Jupiter and 3–5.5 M_⊕ for Saturn. Jupiter’s and Saturn’s IR-cores can be considered embryos onto which the accretion of the gas occurred during the formation of the planets. The mass of the hydrogen–helium component dispersed in the zone of planetary formation constitutes ≈2–5 planetary masses for Jupiter and ≈11–14 planetary masses for Saturn.     

The chemical atmospheric composition of the giant planets

For a long time it was believed that the atmospheres of the giant planets, dominated by molecular hydrogen and helium, were similar in composition to the primordial nebula from which they formed. However, this image has strongly evolved over the past twenty years, due to new developments of ground-based infrared spectroscopy, coupled with the success of the Voyager space mission.Significant differences were measured in the abundances of helium, deuterium and carbon of the four giant planets. The variations in the C/H and D/H ratios have given support to the "nucleation" formation scenario, in which the four giant planets first accreted a nucleus of about ten terrestrial masses, big enough to bind gravitationally the surrounding gaseous nebula; the helium depletion in Saturn has been interpreted as a differentiation effect in Saturn's interior; the apparent helium excess in Neptune, coupled with the recent unexpected detection of CO and HCN in this planet, might imply the presence of molecular nitrogen. In the case of Jupiter and Saturn, disequilibrium species have been detected (CO, PH₃, GeH₄, AsH₃), which are tracers of vertical dynamical motions.In the future, significant progress in our knowledge of the Jovian composition, including the noble gases, should be obtained with the mass spectrometer of the Galileo probe. The ISO mission is expected to provide new far-infrared spectroscopic data which should lead to the detection of new minor species and a better determination of the D/H ratio.     

The effect of dense cores on the structure and evolution of Jupiter and Saturn

We have calculated evolutionary and static models of Jupiter and Saturn with homogeneous solar composition mantles and dense cores of material consisting of solar abundances of SiO₂, MgO, Fe, and Ni. Evolutionary sequences for Jupiter were calculated with cores of mass 2, 4, 6, and 8% of the Jovian mass. Evolutionary sequences for Saturn were calculated with cores of mass 16, 18, 20, and 22% of total mass. Two envelope mixtures, representative of the solar abundances were used: X (mass fraction of hydrogen) = 0.74, Y (mass fraction of helium) = 0.24 and X = 0.77 and Y = 0.21. For Jupiter, the observations of the temperature at 1 bar pressure (T_1bar), radius and internal luminosity were best fit by evolutionary models with a core mass of ～6.5% and chemical composition of X = 0.77, Y = 0.21. The calculated cooling time for Jupiter is approximately 4.9 × 10⁹ years, which is consistent, within our error bars, with the known age of the solar system. For Saturn, the observations of the radius, internal luminosity and T_1BAR can be best fit by evolutionary models with a core mass of ～21% and chemical composition of X = 0.77, Y = 0.21. The cooling time calculated for Saturn is approximately 2.6 × 10⁹ years, almost a factor 2 less than the present age of the solar system. Static models of Jupiter and Saturn were calculated for the above chemical compositions in order to investigate the sensitivity of the calculated gravitational moments, J₂ and J₄, to the mass of the dense core, T_1BAR and hydrogen/helium ratio. We find for Jupiter that a model having a core mass of approximately 7% gives values of J₂, J₄, and T_1BAR that are within observational limits, for the mixture X = 0.77, Y = 0.21. The static Jupiter models are completely consistent with the evolutionary results. For Saturn, the quantities J₂, J₄, and J₆ determined from the static models with the most probable T_1BAR of 140°K, using modeling procedures which result in consistent models for Jupiter, are considerably below the observed values.     

The structure of the planets Jupiter and Saturn

Planetary models for Jupiter and Saturn are computed using a fourth-order theory and a new molecular equation of state. The equation of state for the molecular hydrogen and helium planetary envelopes is taken from the Monte Carlo calculations of Slattery and Hubbard [Icarus 29, 187–192 (1976)]. Models for Jupiter are found that have a small amount of heavy elements either mixed with hydrogen and helium throughout the interior of the planet or concentrated in a small dense core. Saturn is modeled with a solar-composition hydrogen and helium envelope and a small derse core. We conclude that the molecular equation of state linked with suitable interior equations of state can produce Jovian models which satisfy the observational data. The planetary models show that the enrichment of heavy elements (relative to solar composition) is approximately 3 times for Jupiter and 10 times for Saturn.     

A comparison of the interiors of Jupiter and Saturn

Interior models of Jupiter and Saturn are calculated and compared in the framework of the three-layer assumption, which rely on the perception that both planets consist of three globally homogeneous regions: a dense core, a metallic hydrogen envelope, and a molecular hydrogen envelope. Within this framework, constraints on the core mass and abundance of heavy elements (i.e. elements other than hydrogen and helium) are given by accounting for uncertainties on the measured gravitational moments, surface temperature, surface helium abundance, and on the inferred protosolar helium abundance, equations of state, temperature profile and solid/differential interior rotation. Results obtained solely from static models matching the measured gravitational fields indicate that the mass of Jupiter’s dense core is less than 14 M_⊕ (Earth masses), but that models with no core are possible given the current uncertainties on the hydrogen–helium equation of state. Similarly, Saturn’s core mass is less than 22 M_⊕ but no lower limit can be inferred. The total mass of heavy elements (including that in the core) is constrained to lie between 11 and 42 M_⊕ in Jupiter, and between 19 and 31 M_⊕ in Saturn. The enrichment in heavy elements of their molecular envelopes is 1–6.5, and 0.5–12 times the solar value, respectively. Additional constraints from evolution models accounting for the progressive differentiation of helium (Hubbard WB, Guillot T, Marley MS, Burrows A, Lunine JI, Saumon D, 1999. Comparative evolution of Jupiter and Saturn. Planet. Space Sci. 47, 1175–1182) are used to obtain tighter, albeit less robust, constraints. The resulting core masses are then expected to be in the range 0–10 M_⊕, and 6–17 M_⊕ for Jupiter and Saturn, respectively. Furthermore, it is shown that Saturn’s atmospheric helium mass mixing ratio, as derived from Voyager, Y=0.06±0.05, is probably too low. Static and evolution models favor a value of Y=0.11−0.25. Using, Y=0.16±0.05, Saturn’s molecular region is found to be enriched in heavy elements by 3.5 to 10 times the solar value, in relatively good agreement with the measured methane abundance. Finally, in all cases, the gravitational moment J₆ of models matching all the constraints are found to lie between 0.35 and 0.38×10⁻⁴ for Jupiter, and between 0.90 and 0.98×10⁻⁴ for Saturn, assuming solid rotation. For comparison, the uncertainties on the measured J₆ are about 10 times larger. More accurate measurements of J₆ (as expected from the Cassini orbiter for Saturn) will therefore permit to test the validity of interior models calculations and the magnitude of differential rotation in the planetary interior.     

New Constraints on the Composition of Jupiter from Galileo Measurements and Interior Models

Using the helium abundance measured by Galileo in the atmosphere of Jupiter and interior models reproducing the observed external gravitational field, we derive new constraints on the composition and structure of the planet. We conclude that, except for helium which must be more abundant in the metallic interior than in the molecular envelope, Jupiter could be homogeneous (no core) or could have a central dense core up to 12M_⊕. The mass fraction of heavy elements is less than 7.5 times the solar value in the metallic envelope and between 1 and 7.2 times solar in the molecular envelope. The total amount of elements other than hydrogen and helium in the planet is between 11 and 45M_⊕.     

Phase separation in giant planets: inhomogeneous evolution of Saturn

We present the first models of Jupiter and Saturn to couple their evolution to both a radiative-atmosphere grid and to high-pressure phase diagrams of hydrogen with helium and other admixtures. We find that prior calculated phase diagrams in which Saturn's interior reaches a region of predicted helium immiscibility do not allow enough energy release to prolong Saturn's cooling to its known age and effective temperature. We explore modifications to published phase diagrams that would lead to greater energy release, and propose a modified H-He phase diagram that is physically reasonable, leads to the correct extension of Saturn's cooling, and predicts an atmospheric helium mass fraction Y_atmos=0.185, in agreement with recent estimates. We also explore the possibility of internal separation of elements heavier than helium, and find that, alternatively, such separation could prolong Saturn's cooling to its known age and effective temperature under a realistic phase diagram and heavy element abundance (in which case Saturn's Y_atmos would be solar but heavier elements would be depleted). In none of these scenarios does Jupiter's interior evolve to any region of helium or heavy-element immiscibility: Jupiter evolves homogeneously to the present day. We discuss the implications of our calculations for Saturn's primordial core mass.     

Radiative-convective equilibrium models of Jupiter and Saturn

Radiative-convective equilibrium models for Jupiter and Saturn have been produced in a study centered primarily on the stratospheric energy balance and the possible role of aerosol heating. These models are compared directly to the thermal structure profiles obtained from Voyager radio occultation measurements. The method is based on a straightforward flux divergence formulation derived from earlier work (J. S. Hogan, S. I. Rasool, and T. Encrenaz 1969, J. Atmos. Sci.26, 898–905). The balance between absorbed and emitted energies is computed iteratively at each level in the atmosphere, assuming local thermodynamic equilibrium and employing a standard treatment of opacities. Results for Jupiter indicate that a dust-free model (no aerosol heating) furnishes a good mean thermal profile for the stratosphere when compared with the Voyager 1 radio occultation (RSS) measurements. These observations of the equatorial region (0° and 12°S, respectively) exhibit periodic vertical structure. Of course, among many possible complications, the Voyager profiles may not represent typical excursions from the mean. The aerosol heat depositions required to match these profiles exactly, relative to the nominal dust-free model, are reasonably consistent with independent estimates for “continuum” absorbers. Other interpretations are discussed, along with a survey of problems encountered in intercomparing the lower portions (P ? 300 mb) of the models, the RSS profiles, and a recent IRIS equatorial profile. Although aerosol heating cannot be ruled out at low latitudes on Jupiter, our results indicate that it may not be required to reproduce the Voyager 1 RSS profiles. On the other hand, heating by aerosols or some other absorber seems necessary in order to match the high-latitude Voyager 2 RSS temperature profile. The Saturn models are relatively simple and in good-to-excellent agreement with the Voyager 2 RSS profiles at all levels. Our comparisons indicate that aerosol heating played a minor role in Saturn's midlatitude stratospheric energy balance at the time of the Voyager 2 encounter. These models, however, may need to be reassessed once the hydrocarbon concentrations have been more precisely determined.     

The atmospheric composition and structure of Jupiter and Saturn from ISO observations: a preliminary review

Infrared spectra of Jupiter and Saturn have been recorded with the two spectrometers of the Infrared Space Observatory (ISO) in 1995–1998, in the 2.3–180 μm range. Both the grating modes (R=150–2000) and the Fabry-Pérot modes (R=8000–30,000) of the two instruments were used. The main results of these observations are (1) the detection of water vapour in the deep troposphere of Saturn; (2) the detection of new hydrocarbons (CH₃C₂H, C₄H₂, C₆H₆, CH₃) in Saturn’s stratosphere; (3) the detection of water vapour and carbon dioxide in the stratospheres of Jupiter and Saturn; (4) a new determination of the D/H ratio from the detection of HD rotational lines. The origin of the external oxygen source on Jupiter and Saturn (also found in the other giant planets and Titan in comparable amounts) may be either interplanetary (micrometeoritic flux) or local (rings and/or satellites). The D/H determination in Jupiter, comparable to Saturn’s result, is in agreement with the recent measurement by the Galileo probe (Mahaffy, P.R., Donahue, T.M., Atreya, S.K., Owen, T.C., Niemann, H.B., 1998. Galileo probe measurements of D/H and ³He/⁴He in Jupiters atmosphere. Space Science Rev. 84 251–263); the D/H values on Uranus and Neptune are significantly higher, as expected from current models of planetary formation.     

The Structure of Jupiter, Saturn, and Exoplanets: Key Questions for High-Pressure Experiments

We give an overview of our current understanding of the structure of gas giant planets, from Jupiter and Saturn to extrasolar giant planets. We focus on addressing what high-pressure laboratory experiments on hydrogen and helium can help to elucidate about the structure of these planets.     

Benzene and aerosol production in Titan and Jupiter's atmospheres: a sensitivity study

Benzene has recently been observed in the atmosphere of Jupiter, Saturn and also Titan. This compound is required as a precursor for larger aromatic species (PAHs) that may be part of aerosol particles. Several photochemical models have tried to reproduce the observed quantities of benzene in the atmospheres of Jupiter (both low- and high-latitudes regions), Saturn and Titan. In this present work, we have conducted a sensitivity study of benzene and PAHs formation, using similar photochemical schemes both for Titan and Jupiter (low-latitudes conditions). Two different photochemical schemes are used, for which the modeled composition fairly agrees with observational constraints, both for Jupiter and Titan. Some disagreements are specific to each atmospheric case, which may point to needed improvements, especially in kinetic data involved in the corresponding chemical cycles. The observed benzene mole fraction in Titan's stratosphere is reproduced by the model, but in the case of Jupiter, low-latitudes benzene abundance is only 3% of the observed column density, which may indicate a possible influence of latitudinal transport, since abundance of benzene is much higher in auroral regions. Though, the photochemical scheme of C₆ compounds at temperature and pressure conditions of planetary atmospheres is still very uncertain. Several variations are therefore done on key reactions in benzene production. These variations show that benzene abundance is mainly sensitive to reactions that may affect the propargyl radical. The effect of aerosol production on hydrocarbons composition is also tested, as well as possible heterogenous recombination of atomic hydrogen in the case of Titan. PAHs are a major pathway for aerosol production in both models. The mass production profiles for aerosols are discussed for both Titan and Jupiter. Total production mass fluxes are roughly three times the one expected by observational constraints in both cases. Such comparative studies are useful to bring more constraints on photochemical models.     

A comparison of the atmospheres of Jupiter and Saturn: deep atmospheric composition, cloud structure, vertical mixing, and origin.

We present our current understanding of the composition, vertical mixing, cloud structure and the origin of the atmospheres of Jupiter and Saturn. Available observations point to a much more vigorous vertical mixing in Saturn's middle-upper atmosphere than in Jupiter's. The nearly cloud-free nature of the Galileo probe entry site, a 5-micron hotspot, is consistent with the depletion of condensable volatiles to great depths, which is attributed to local meteorology. Somewhat similar depletion of water may be present in the 5-micron bright regions of Saturn also. The supersolar abundances of heavy elements, particularly C and S in Jupiter's atmosphere and C in Saturn's, as well as the progressive increase of C from Jupiter to Saturn and beyond, tend to support the icy planetesimal model of the formation of the giant planets and their atmospheres. However, much work remains to be done, especially in the area of laboratory studies, including identification of possible new microwave absorbers, and modelling, in order to resolve the controversy surrounding the large discrepancy between Jupiter's global ammonia abundance, hence the nitrogen elemental ratio, derived from the earth-based microwave observations and that inferred from the analysis of the Galileo probe-orbiter radio attenuation data for the hotspot. We look forward to the observations from Cassini-Huygens spacecraft which are expected to result not only in a rich harvest of information for Saturn, but a better understanding of the formation of the giant planets and their atmospheres when these data are combined with those that exist for Jupiter.     

Astrophysical Implications of the Recent Shocked Deuterium Experiments

In the last few years, deuterium has been the focus of a high level of laboratory activity that was sparked by a disagreement on the experimental value of the maximum compression along the Hugoniot. Astrophysically, the uncertainty in the EOS of hydrogen is most consequential in models of the interiors of Jupiter and Saturn since a significant fraction of their mass falls in the region where the EOS uncertainty is largest. We present a study of the range of interior structures allowed by the shock-compression experiments on deuterium and constrained by astrophysical observations of the two planets. We find that the EOS uncertainty must be reduced to less than 3% along the planet’s isentrope to get good interior models of Jupiter. These models provide values for the mass of a core of heavy elements (other than H and He) and the total mass of heavy elements in these planets. The amount and distribution of heavy elements are quite sensitive to the EOS of hydrogen and constitute important clues to their formation process.     

The planet Jupiter

Summary. The exploration of Jupiter, the closest and biggest giant planet, has provided key information about the origin and evolution of the outer Solar system. Our knowledge has strongly benefited from the Voyager and Galileo space missions. We now have a good understanding of Jupiter's thermal structure, chemical composition and magnetospheric environment. There is still debate about the nature of the heating source responsible for the high thermospheric temperatures (precipitating particles and/or gravity waves). The measurement of elemental abundance ratios (C/H, N/H, S/H) gives strong support to the “nucleation” formation model, according to which giant planets formed from the accretion of an initial core and the collapse of the surrounding gaseous protosolar nebula. The D/H and He/He ratios are found to be representative of their protosolar value. The helium abundance, in contrast, appears to be slightly depleted in the outer envelope with respect to the protosolar value; this departure is interpreted as an evolutionary effect, due to the condensation of helium droplets in the liquid hydrogen ocean inside Jupiter's interior. The cloud structure of Jupiter, characterized by the belt-zone system, is globally understood; also present are specific features like regions of strong infrared radiation (“hot spots”), colder regions (“white ovals”) and the Great Red Spot (GRS). Clouds were surprisingly absent at the hot spot corresponding to the Galileo probe entry site, and the water abundance measured there was strongly depleted with respect to the solar O/H value. This probably implies that hot spots are dry, cloud-free regions of subsidence, while “normal” air, rich in condensibles, is transported upward by convective motions. As a result, the Jovian meteorology, still based on Halley-type cells, seems to be much more complex than a simple zone-belt system. The nature of the GRS, a giant anticyclonic storm, colder and higher than its environment, has been confirmed by the Galileo observations, but its internal structure appears to be very complex. Strong winds, probably driven by the Jovian internal source, were measured at deep tropospheric levels. The troposphere might be statically stable at pressures higher than 18 bars, but the extent of this putative radiative layer is still unknown. Received 23 November 1998     

Models and theoretical spectrum for the free oscillations of Saturn

We constructed new models of Saturn with an allowance made for a helium mass fraction of ～0.18–0.25 in its atmosphere. Our modeling shows that the composition of Saturn differs markedly from the solar composition; more specifically, during its formation, the planet was ～11–15 planetary masses short of the hydrogen-helium component. Saturn, as well as the other giant planets, must have been formed according to Schmidt’s scenario, through the formation of embryonic nuclei, rather than according to Laplace’s scenario. The masses of the embryonic nuclei themselves lie within the range (3.5–8) M_⊕. We calculated a theoretical free-oscillation spectrum for our models of Saturn, each of which fits all of the available observational data. The results of our calculations are presented graphically and in tables. Of particular interest are the diagnostic potentialities of the discontinuity gravitational modes related to density jumps in the molecular envelope of Saturn and at the interface between its molecular and metallic envelopes. When observational data appear, our results can be used both to identify the observed modes and to improve the models themselves. We discuss some of the cosmogonical aspects associated with the formation of the giant planets.     

Giant magnetospheres in our solar system: Jupiter and Saturn compared

We review the current knowledge about the two biggest magnetospheres in our solar system based on the significant progress made with data from the Cassini spacecraft in orbit around Saturn since 2004, and based on the last mission to Jupiter by the Galileo spacecraft between 1995 and 2003. In addition we take into account new observations of the Hubble Space Telescope and other telescopes as well as the latest computer simulation efforts.     

Models of the giant planets

Models of the giant planets were constructed based on the assumption that the hydrogen to helium ratio is solar in these planets. This assumption, together with arguments about the condensation sequence in the primitive solar nebula, yields models with a central core of rock and possibly ice surrounded by an envelope of hydrogen, helium, methane, ammonia, and water. These last three volatiles may be individually enhanced due to condensation at the period of core formation. Jupiter was found to have a core of about 40 earth masses and a water enhancement in the atmosphere of about 7.5 times the solar value. Saturn was found to have a core of 20 earth masses and a water enhancement in the atmosphere of about 25 times the solar value. Rock plus ice constitute 75–85% of the mass of Uranus and Neptune. Temperatures in the interiors of these planets are probably above the melting points, if there is an adiabatic relation throughout the interiors. Some aspects of the sensitivities of these results to uncertainties in rotational flattening are discussed.     

The Rotation of Europa

Theoretical predictions of non-synchronous rotation and of polar wander on Europa have been tested by comparing tectonic features observed in Voyager and Galileo spacecraft images with tidal stresses. Evidence for non-synchronous rotation comes from studying changes in global scale lineaments formed over time, from the character of strike-slip faults, and from comparison of distinctively shaped cycloidal cracks with the longitudes at which such shapes should have formed, in theory. The study of cycloids constrains the rotation period (relative to the direction of Jupiter) to less than 250 000 years, while direct comparison of the orientation of Europa in Voyager and Galileo images shows the rotation is slow, with a period of >12 000 years. Comparison of strike-slip faults with their theoretical locations of formation provides evidence for substantial polar wander, supported by the distribution of various thermally produced features.     

The hydrogen ortho-to-para ratio in the stratospheres of the giant planets

Observations of the H₂ S(0) and S(1) quadrupole lines in the four giant planets by the short-wavelength spectrometer of the Infrared Space Observatory are analyzed. These lines probe pressure levels located between 10 and 1 mbar and allow us to determine the stratospheric hydrogen para fraction for the first time. In Jupiter and Saturn, the stratospheric para fraction is close to its tropopause value. In the stratosphere of these planets as well as in Neptune’s, the para fraction presents a significant departure from thermodynamic equilibrium. This situation results from a lagged conversion between the ortho and the para states as molecular hydrogen is transported upward under the influence of turbulent eddy diffusion. In contrast, the uranian stratosphere lies close to thermodynamic equilibrium. The magnitude of the departure from thermodynamic equilibrium appears to be anti-correlated with the amount of stratospheric aerosols. To validate this assumption, we estimate the hydrogen equilibration time with a one-dimensional diffusion model for different conversion processes in the gas phase or on aerosols. The comparison between our results and the tropospheric estimates from Conrath et al. (1998, Icarus,135, 501-517) shows that paramagnetic conversion on aerosols matches the estimated tropospheric and stratospheric relaxation times in the four giant planets. In contrast, paramagnetic conversion in the gas phase can only explain the relaxation times measured in Jupiter and Saturn atmospheres. This situation provides quantitative evidence for an equilibration mechanism dominated by conversion on aerosols.     

A calculation of Saturn's gravitational contraction history

A calculation has been made of the gravitational contraction of a homogeneous, quasi-equilibrium Saturn model of solar composition. The calculations begin at a time when the planet's radius is ten times larger than its present size, and the subsequent gravitational contraction is followed for 4.5 × 10⁹ years. For the first million years of evolution, the Saturn model contracts rapidly like a pre-main sequence star and has a much higher luminosity and effective temperature than at present. Later stages of contraction occur more slowly and are analogous to the cooling phase of a degenerate white dwarf star.Examination of the interior structure of the models indicates the presence of a metallic hydrogen region near the center of the planet. Differences in the size of this region for Jupiter and Saturn may, in part, be responsible for Saturn having a weaker magnetic field. While the interior temperatures are much too high for the fluids in the molecular and metallic regions to become solids by the current epoch, the temperature in the outer portion of the metallic zone falls below Stevenson's [Phys. Rev. J. (1975)] phase separation curve for helium after 1.2 billion years of evolution. This would lead to a sinking of helium from the outer to the inner portion of the metallic region, as described by Salpeter [Astrophys. J.181, L83–L86 (1973)].At the current epoch, the radius of the model is about 9% larger, while its excess luminosity is comparable to the observed value of Rieke [Icarus26, 37–44 (1975)], as refined by Wright [Harvard College Obs. Preprint No. 480 (1976)]. This behavior of the Saturn model may be compared to the good agreement with both Jupiter's observed radius and excess luminosity shown by an analogous model of Jupiter [Graboske et al., Astrophys. J.199, 255–264 (1975)]. The discrepancy in radius of our Saturn model may be due to errors in the equations of state and/or our neglect of a rocky core. However, arguments are presented which indicate that helium separation may cause an expansion of the model and thus lead to an even bigger discrepancy in radius. Improvement in the radius may also foster a somewhat larger predicted luminosity. At least part and perhaps most of Saturn's excess luminosity is due to the loss of internal thermal energy that was built up during the early rapid contraction, with a minor contribution coming from Saturn's present rate of contraction. These two sources dominate Jupiter's excess luminosity. If helium separation makes an important contribution to Saturn's excess luminosity, then planetwide segregation is required.Finally, because Saturn's early high luminosity was about an order of magnitude smaller than Jupiter's, water-ice satellites may have been able to form closer to Saturn to Jupiter.