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Interiors of Giant Planets Inside and Outside the Solar System

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Science  01 Oct 1999:
Vol. 286, Issue 5437, pp. 72-77
DOI: 10.1126/science.286.5437.72

Abstract

An understanding of the structure and composition of the giant planets is rapidly evolving because of (i) high-pressure experiments with the ability to study metallic hydrogen and define the properties of its equation of state and (ii) spectroscopic and in situ measurements made by telescopes and satellites that allow an accurate determination of the chemical composition of the deep atmospheres of the giant planets. However, the total amount of heavy elements that Jupiter, Saturn, Uranus, and Neptune contain remains poorly constrained. The discovery of extrasolar giant planets with masses ranging from that of Saturn to a few times the mass of Jupiter opens up new possibilities for understanding planet composition and formation. Evolutionary models predict that gaseous extrasolar giant planets should have a variety of atmospheric temperatures and chemical compositions, but the radii are estimated to be close to that of Jupiter (between 0.9 and 1.7 Jupiter radii), provided that they contain mostly hydrogen and helium.

Constraints on the interior structure of the giant planets of our solar system—Jupiter, Saturn, Uranus, and Neptune—are derived from knowledge of their mass M, equatorial radiusa, and gravitational moments J 2,J 4, and J 6. Measurements of these quantities go back to the Pioneer and Voyager spacecraft missions (1). Improvements in measurements of the gravitational moments of Saturn must await the arrival of the Cassini-Huygens mission in the saturnian system in 2004, and measurements for the other planets must await future space missions. The past years have nevertheless been rich in advances in giant planet research: Galileo measured the composition and structure of Jupiter's atmosphere with unprecedented accuracy (2), compression experiments succeeded in pressurizing hydrogen above a pressure of 1011 Pa (100 GPa, or 1 Mbar) (3, 4), and giant planets were discovered orbiting other stars (5). This review describes our present understanding of the internal structure of giant planets both inside and outside of our solar system.

At the foundation of any understanding of the interiors of the giant planets and brown dwarfs (6) lies knowledge about the behavior of chemical species at high pressures, and of hydrogen in particular, it being the most abundant element. At low pressures and temperatures, hydrogen is an insulator in the form of a strongly bound diatomic molecule. At high pressures (∼100 GPa) and moderate temperatures (≲105 K), it dissociates and eventually ionizes to transform into an alkali metal. This form of hydrogen, called metallic hydrogen, escaped detection for many years but has now been observed. Shock wave experiments with two-stage gas guns succeeded in measuring electrical conductivities of fluid hydrogen up to 180 GPa and 3000 K (3). In these experiments, an increase in the measured conductivity by four orders of magnitude was observed when pressure increased from 90 to 140 GPa. The conductivity then became constant, which was initially interpreted as a sign that metallic hydrogen had been formed. However, the conductivity was still smaller than theoretical estimates for a fully ionized hydrogen metal (7). In fact, the fluid still retained a strong pairing character at these pressures. Other experiments (4) used a high-intensity laser to compress deuterium to even greater pressures (300 GPa), but at higher temperatures (up to ∼70000 K). The liquid was found to be more compressible than expected, and for the first time the hydrogen isotope was compressed to a fully dissociated, partially ionized, metallic fluid state. In both sets of experiments, no discontinuous behavior revealing a first-order insulator-metal transition was observed.

These results cannot yet be included in actual interior models of the giant planets without an appropriate equation of state, which still needs to be calculated. The last theoretical effort to model the behavior of hydrogen at high pressures in this astrophysical context, the widely used Saumon-Chabrier equation of state (8), agrees with the experiments at low and high pressures but needs to be improved in the 50 to 300 GPa (0.5 to 3 Mbar) region. Furthermore, it predicts the presence of a first-order (discontinuous) phase transition for temperatures up to 15300 K (the critical point), which is questioned by the experiments. Recent calculations (9) using softer interaction potentials, as indicated by the laser experiments, predict a lower critical temperature (by ∼700 K). This would imply that the laser experiments are supercritical, whereas the gas-gun experiments have not attained a high enough pressure to reach the metallic phase. Laboratory results thus reveal that the hydrogen phase transition is even much more complex than previously thought, as molecules, atoms, protons, itinerant electrons, and even clusters (10) can coexist over an extended pressure range (100 to 300 GPa). The corresponding uncertainties on the predicted density profiles have to be included within interior model calculations (11).

Jupiter and Saturn

The interiors of Jupiter and Saturn have traditionally been divided into three distinct, quasi-homogeneous regions (12): a central dense ice and rock core, a fluid metallic hydrogen region, and (at pressures lower than about 100 GPa) a fluid molecular hydrogen shell. Spectroscopic and in situ measurements can only probe the upper levels of the planets' atmospheres, but the inferred chemical composition is generally thought to apply to the entire molecular region (after allowing for changes due to chemical reactions and condensation processes). In particular, Jupiter's and Saturn's atmospheres, and therefore their molecular regions, are believed to lack some of the helium that was present at their formation. Indeed, the helium mass mixing ratio Y, accurately measured in the jovian atmosphere by the Galileo probe, is such thatY/(X + Y) = 0.238 ± 0.007 (13), X being the hydrogen mass mixing ratio. This value is lower than that in the protosolar nebula, for which it is inferred from solar models thatY/(X + Y) = 0.280 ± 0.005 (14). Saturn's atmosphere probably has even less helium than Jupiter, as indicated by Voyager 2 data (15). Because there is no known physical process that can decrease the He/H ratio to this extent, the missing helium is believed to be hidden deeper inside the planets.

The removal of the atmospheric helium is explained by a H-He phase separation (16), by a first-order transition from molecular to metallic hydrogen (17), or by both. From the point of view of interior models, the presence of a helium-poor and a helium-rich region is at least as important as the molecular-to-metallic transition itself. This distinction between the two regions is needed to determine the amount of heavy elements (that is, any species other than hydrogen and helium) that the planets hold and has direct consequences for their evolution, as gravitational energy is transformed into heat during helium sedimentation (18). However, because any H-He phase separation is expected near the molecular-to-metallic transition of hydrogen (19), it is convenient to equate the helium-poor and helium-rich regions with the molecular and metallic regions, respectively.

Another important feature of present-day models of Jupiter and Saturn is the assumption that the molecular and metallic regions are quasi-homogeneous. This is because the planets emit significant intrinsic heat fluxes, and are therefore hot, fluid, and mainly convective (18, 20). The assumption probably breaks down at several locations (21), as follows: (i) Where a minimum in the mean radiative opacities of the fluid at temperatures of 1300 to 1800 K (22) probably yields the presence of a radiative region in Jupiter and possibly Saturn (23). In such a radiative zone, a variation of chemical abundance is in principle possible, either through gravitational settling or through the slow mixing of material that struck the planet after its formation. Gravitational settling is expected to be small because it is inhibited by turbulent diffusion (24). Helium (and tentatively any late supply of heavy elements to the outermost layers) should be able to sink through the radiative zone thanks to a salt-finger type of instability (25), thus ensuring an almost uniform chemical composition of the radiative zone. (ii) In the region of varying helium concentration, in which convection may be suppressed. The extent of this inhomogeneous region (Fig. 1) is estimated from fully ionized phase separation models (19). In reality, the inhomogeneous region could be narrower or wider. It is not included in any interior models so far, but this seems justified because the gravitational moments only provide constraints on quantities that are averaged over relatively extended regions. More important, this region could be a relatively efficient barrier to the mixing of minor species, because they would have to be transported by slow diffusion processes. The same would occur at the boundary of a first-order transition from the molecular to the metallic phase (18).

Figure 1

Schematic representation of the interiors of Jupiter, Saturn, Uranus, and Neptune. The hashed region indicates a possible radiative zone [in Jupiter, it corresponds toP ∼ 0.15 to 0.6 GPa, T ∼ 1450 to 1900 K, andR ∼ 0.990 to 0.984 R J; in Saturn, it is located around P ∼ 0.5 GPa, T ∼ 1700 K, and R ∼ 0.965 R S, but it is probably very marginal (23)]. The range of temperatures for Jupiter and Saturn is for models neglecting the presence of the inhomogeneous region. Helium mass mixing ratios Yare indicated. In the case of Saturn, it is assumed thatY/(X + Y) = 0.16 in the molecular region. The size of the central rock and ice cores of Jupiter and Saturn is very uncertain (see text). Two representative models of Uranus and Neptune are shown, but their actual interior structure may be significantly different (34). The figure is adapted and updated from (19).

Interior models of Jupiter and Saturn are calculated by solving the standard quasi-hydrostatic differential equations, including the rotational potential calculated within the theory of figures (26). In recent calculations, only models that match all observational constraints are considered. Uncertainties in the equation of state, surface temperature, opacities, internal rotation, and observational error bars on the gravitational moments are taken into account to determine the allowed range of internal compositions of these planets. The space of parameters is then extensively studied within the three-layer assumption. Additional constraints are provided by planetary evolution calculations, because they should yield model ages that are in agreement with that of the solar system (23). A critical improvement of the evolutionary models lies in the ability to account for helium differentiation, because it can considerably slow down the contraction and cooling of a given planet (27). In fact, helium sedimentation is required to explain Saturn's intrinsic heat flux and may be significant in Jupiter as well. The characteristics of typical Jupiter and Saturn models are shown in Fig. 1, including corresponding uncertainties in the temperature profiles.

The resulting constraints on the enrichment in heavy elements of Jupiter and Saturn's metallic regions relative to solar composition (Fig. 2) are weak. However, the enrichments of the molecular regions can be usefully compared to other observations. Galileo probe measurements are compatible with an enrichment of Jupiter's deep atmosphere [pressure (P) ≳ 15 bar] of two to four times the solar values in C, N, and S (28). The Galileo probe results are thus consistent with an abundance of major gases [except helium, neon (16), and water] that is two to four times larger than in the sun, which is in agreement with interior models using the new helium mixing ratio but not the one derived from Voyager data (Fig. 2). The lack of abundant water in the Galileo measurements is thought to be due to jovian meteorology, and its bulk abundance is therefore still unknown (28, 29). On the basis of the Galileo measurements, interior models also rule out water abundances larger than 10 times solar in Jupiter's deep atmosphere. In Saturn, spectroscopic measurements indicate enrichments of CH4 on the order of three to five times solar (30). The lower measured abundance of NH3 (Fig. 2) is certainly due to condensation, because the planet is cooler than Jupiter. The global enrichments calculated with the Voyager helium mass mixing ratio (15) are incompatible with the observed CH4 abundance (Fig. 2). Instead, static and evolutionary models favor a higher value ofY/(X + Y) = 0.11 − 0.25 (23, 27).

Figure 2

Constraints on the mass mixing ratio of heavy elements, in solar units [assuming the mass mixing ratio of heavy elements in the sun (Z ) = 0.0192 (58)] of the molecular (red rectangles) and metallic (purple rectangles) regions of Jupiter and Saturn. The helium mixing ratios used for the calculation are the Galileo value for Jupiter (13) and Y/(Y +X) = 0.16 ± 0.05 for Saturn (see text). The enrichments in the molecular regions that would have been found with the old Voyager values (13, 15) are indicated by blue areas. When available, the observed abundances of C, N, O, and S are indicated. The maximum value for the heavy element enrichment of Saturn's metallic region is 20 Z .

Table 1 gives the total mass of heavy elements in Jupiter and Saturn and shows how they are distributed as core mass in the metallic and molecular envelopes. It is not required that Jupiter have a central core in order to fit the gravitational moments, but that solution is not the preferred one because it implies a rather extreme equation of state and also yields high heavy-element enrichments (in the upper range of Fig. 2). In any case, Jupiter's core must be smaller than 10 Earth masses (M). Furthermore, it is generally found that Saturn has a bigger core than Jupiter, but the constraints are relatively weak because some of the material in the deep metallic envelope could be accounted for as core mass, and vice versa. It is important to note that heavy elements in Jupiter's and Saturn's molecular regions, and some of those in their metallic regions, were probably brought in after their formation (after they had captured most of their hydrogen and helium). It is as yet unclear whether material was exchanged between the molecular and metallic regions. Models of giant planet formation should account for the planetesimals captured during and after formation (31).

Table 1

Amount of heavy elements (inM ) in Jupiter and Saturn.

View this table:

Uranus and Neptune

The structure of the “ice giants” Uranus and Neptune is more difficult to grasp, notably because they contain a relatively smaller fraction of hydrogen and helium, and because their gravitational moments are known with a lower accuracy. Spectroscopic measurements indicate that their hydrogen-helium atmospheres contain a large proportion of heavy elements, mainly CH4, which is enriched by a factor of ∼30 as compared to solar composition (32). The two planets have similar masses (14.53M for Uranus and 17.14M for Neptune) and radii. Neptune's larger mean density is partly due to greater compression but could also be the result of a slightly different composition. The gravitational moments require that the density profiles lie close to that of “ice” (a mixture initially composed of H2O, CH4, and NH3 but whose composition most probably does not consist of intact molecules in the planetary interior), except in the outermost layers, which have a density closer to that of hydrogen and helium (33). Three-layer models of Uranus and Neptune consisting of a central “rock” core (magnesium-silicate and iron material), an ice layer, and a hydrogen-helium gas envelope have been calculated (Fig. 1) (34).

The fact that models of Uranus assuming homogeneity of each layer and adiabatic temperature profiles fail to reproduce its gravitational moments seems to imply that substantial parts of the planetary interior are not homogeneously mixed (35). This could explain the fact that Uranus' heat flux is so small: Its heat would not be allowed to escape to space by convection but through a much slower diffusive process in the regions with a high molecular weight gradient. Such regions would also be present in Neptune but much deeper, thus allowing more heat to be transported outward. The existence of these nonhomogeneous partially mixed regions is further confirmed by the fact that if hydrogen is supposed to be confined solely to the hydrogen-helium envelope, models predict ice/rock ratios on the order of 10 or more, which is much larger than the protosolar value of ∼2.5. On the other hand, if we impose the constraint that the ice/rock ratio be protosolar, the overall composition of both Uranus and Neptune is, by mass, about 25% rock, 60 to 70% ice, and 5 to 15% hydrogen and helium (34, 35).

The Radii of Extrasolar Giant Planets

The discovery of planets outside our solar system represents an opportunity to learn even more about the formation of planets in general and to determine how unique our solar system may be. Although the present constraints on the interior structures of Jupiter, Saturn, Uranus, and Neptune are weak, obtaining the characteristics of extrasolar giant planets with different masses and orbital parameters will enlighten us about their composition. Measurements of radii are within reach, most notably with programs designed to detect planetary transits by photometry (through the slight dimming of a star when an orbiting planet happens to cross the line of sight) (36). The radius of a planet is a function of its mass, age, degree of insolation by the parent star, and composition (37). Let us suppose that the mass is accurately known (for example, by the combination of transit detection and radial velocity measurements) and that the age and albedo can be independently estimated. For a given helium/hydrogen ratio, the amount of heavy elements in the planet can then be determined.

The radii of extrasolar giant planets can be predicted with the same equations that govern the evolution of stars. The evolution of giant planets in isolation or relatively far from their parent star has been studied extensively and now includes detailed treatments of the atmosphere (38). These calculations can be extended to planets orbiting close to their stars (39), with a lesser precision because of uncertainties about how much of the incoming stellar light is absorbed by the planetary atmosphere. Figure 3 gives examples of effective temperatures and radii predicted for some of the recently found extrasolar giant planets and brown dwarfs, assuming solar composition and a factor of 2 uncertainty on the mass (due to the fact that radial velocity measurements only yield M sin i, wherei is the inclination of the orbital plane), and including uncertainties on the age (40) and albedo (between 0.1 and 0.5). It illustrates the diversity of planets detected so far. Because of the range of temperatures, many different condensates (from ammonia to silicates) are expected in planetary atmospheres (41,42). However, the calculated radii are always close to that of Jupiter, until the mass is large enough to sustain hydrogen fusion, at about 75 Jupiter masses (M J) (38,43). A local maximum of the radius at a mass of ∼4M J for isolated planets is due to the competition between additional volume and increased gravity. (This is because, when considering planets of larger masses, the degenerate metallic hydrogen region grows at the expense of the molecular region.) Planets that are significantly heated by their star have larger radii for smaller masses because the outermost layers are substantially puffed up when gravity is small.

Figure 3

Predicted effective temperatures and radii (in R J, ∼70,000 km) of some extrasolar planets and brown dwarfs, including reasonable uncertainties for their mass, albedo, and age (see text) and assuming solar composition. Actual radii could be significantly smaller if the planets contain large proportions of heavy elements. The dashed line is for isolated H-He (Y = 0.25) objects after 10 gigayears of evolution. The upper panel also shows potentially important chemical species expected to condense near the photosphere in the indicated range of effective temperatures.

An important feature of giant planets at close orbital distances, or “hot Jupiters,” is that they have already entered an evolutionary stage in which they become progressively more radiative (that is, less convective), as they strive to attain complete equilibrium with the star (ideally, they will eventually become isothermal). This will also happen for planets that are further away, such as Jupiter and Saturn, but at later times (44). This radiative zone is expected to appear in the outer layers of the planet and to progressively spread over its inner regions (39). In that phase, the evolution of the planet is essentially governed by the ability of the radiative region to transport the still-significant intrinsic heat (the intrinsic luminosity is generally, after a few gigayears, of the same order of magnitude as that of Jupiter: 1024 erg s−1 to 1025 erg s−1). Depending on whether one uses opacities including the presence of grains (45) or opacities that assume that grains are removed by gravitational settling (46), cooling and contraction time scales can differ by factors 2 to 3.

Figure 4 shows typical estimates of model uncertainties in radii, depending on physical parameters (age and albedo) and input physics (equation of state and opacities). The age of the planetary system (inferred from that of the star) will remain fraught with uncertainty. However, planetary albedos will be determined by either accurate photometry of the eclipsing system or by future direct observations capable of resolving the star-planet system. Theoretical models are also expected to provide better constraints on the albedo (47), but the presence of clouds and grains makes this a complex problem. Hopefully, uncertainties associated with the input physics will be reduced by the calculation of new equations of state that include the latest deuterium compression experiments and by improved opacity calculations. At present, the expected theoretical uncertainty in model radii is about 15% for a1-MJ planet, translating into an accuracy of ∼43 M regarding the mass of heavy elements present in the planet. Interestingly enough, this is about the minimal quantity of heavy elements necessary to form such a planet in situ (48). In the case of a 10-MJ planet, the fractional uncertainty is smaller, but the absolute precision regarding the mass of heavy elements is ∼170M. Systems of planets with small masses at short orbital distances are interesting because they should experience significant mass loss and therefore contain a large proportion of heavy elements. Radii measurements and corresponding theoretical models would therefore go beyond a simple answer to the question of whether extrasolar giant planets are mainly formed with hydrogen and helium or are mainly rocks and ices [the limiting radius then being on the order of 1/3 Jupiter radius (RJ) (39)].

Figure 4

Fractional uncertainty in radii of extrasolar giant planets (at 0.05 astronomical units from solar-type stars) due to uncertainties in physical parameters (top) and input physics (bottom), as a function of mass. The corresponding absolute uncertainty about the fraction of the planetary mass that is due to heavy elements is directly proportional to the radii uncertainty [a 10% uncertainty in model radii corresponds to a ∼9% uncertainty about the mass of heavy elements; that is, in that case and for a 1-M J (318 M ) planet, the mass of heavy elements would be known with an accuracy of ∼30M ]. The albedo was assumed to lie between 0.1 and 0.5; the age between 3 and 7 gigayears.

Quantity of Heavy Elements and the Formation of Giant Planets

The planets in our solar system formed in the so-called protosolar nebula, a flattened disk of hydrogen, helium, and solid planetesimals (49). Jupiter, Saturn, Uranus, and Neptune are believed to have formed through accretion of a solid core followed by the capture of surrounding gaseous hydrogen and helium (50), but direct gravitational instability of the gas in the disk has been proposed as a mechanism for forming Jupiter and Saturn (51). Saturn's relatively high core mass seems to rule out the latter hypothesis. The extrasolar giant planets discovered so far could have formed by any of these processes. It has been proposed that those at small orbital distances either formed at further distances and then migrated inward (52) or formed in situ within a massive protoplanetary disk (48). An important test of these theories can be provided by a calculation of the quantity of heavy elements captured after the first formation stages.

In our solar system, the first 10 million years after the giant planets reached an appreciable fraction of their current masses were crucial for planetesimal delivery. Between 80 and 90% of the planetesimals that remained in the outer solar system at that time were acquired by the planets or were ejected from the solar system during that period. Dynamic calculations using present-day radii and an initial 50-M disk of planetesimals suggest that less than 2% of the mass of giant planets (6 M for Jupiter and 2 M for Saturn) is due to late-arriving planetesimals (53). However, at these early epochs, the growing planets possessed effective capture radii that were larger than their present radii (54) and were thus able to capture incoming planetesimals more efficiently while ejecting fewer of them out of the solar system. It is estimated that Jupiter, Saturn, Uranus, and Neptune could have captured by that process up to ∼17, 10, 2, and 2M of heavy elements, respectively (55). Massive extrasolar planets (≳5 M J) are able to efficiently eject material out of the system and are therefore expected to acquire a fractionally smaller inventory of “late heavy elements”.

Prospects for improving our knowledge of the composition of giant planets and their formation will depend on the following future developments. The calculation of a new hydrogen and helium equation of state consistent with the recent compression experiments is essential. The Cassini orbiter will accurately measure the chemical composition and temperature structure of Saturn's atmosphere (and hopefully of Jupiter as well, although with a lesser accuracy), but it would be crucial for interior models that the final stages of its orbital tour allow for a better determination of the gravitational momentsJ 4 and J 6. Such a measurement could yield constraints on the core mass and abundance of heavy elements in the metallic region that are two to three times stronger (23). A polar Jupiter orbiter would yield an accurate determination of the gravitational field of the planet, including high-order gravitational moments, hence constraining its global composition and dynamic structure (56). Finally, important steps in understanding planet formation will come from spectroscopic measurements of the atmospheres of extrasolar giant planets, and from transit detections that would allow the determination of their radii (57) and hence of the global composition of extrasolar planets.

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