Formation of the giant planets

Observational constraints on interior models of the giant planets indicate that these planets were all much hotter when they formed and they all have rock and/or ice cores of ten to thirty earth masses. These cores are probably soluble in the envelopes above, especially in Jupiter and Saturn, and are therefore likely to be primordial. They persist despite the continual upward mixing by thermally driven convection throughout the age of the solar system, because of the inefficiency of double-diffusive convection. Thus, these planets most probably formed by the hydrodynamic collapse of a gaseous envelope onto a core rather than by direct instability of the gaseous solar nebula. Recent calculations by Mizuno (1980, Prog. Theor. Phys.64, 544) show that this formation mechanism may explain the similarity of giant planet core masses. Problems remain however, and no current model is entirely satisfactory in explaining the properties of the giant planets and simultaneously satisfying the terrestrial planet constraints. Satellite systematics and protoplanetary disk nebulae are also discussed and related to formation conditions.     

Oligarchic growth of giant planets

Runaway growth ends when the largest protoplanets dominate the dynamics of the planetesimal disk; the subsequent self-limiting accretion mode is referred to as “oligarchic growth.” Here, we begin by expanding on the existing analytic model of the oligarchic growth regime. From this, we derive global estimates of the planet formation rate throughout a protoplanetary disk. We find that a relatively high-mass protoplanetary disk (∼10 × minimum-mass) is required to produce giant planet core-sized bodies (∼10 M_⊕) within the lifetime of the nebular gas (?10 million years). However, an implausibly massive disk is needed to produce even an Earth mass at the orbit of Uranus by 10 Myrs. Subsequent accretion without the dissipational effect of gas is even slower and less efficient. In the limit of noninteracting planetesimals, a reasonable-mass disk is unable to produce bodies the size of the Solar System’s two outer giant planets at their current locations on any timescale; if collisional damping of planetesimal random velocities is sufficiently effective, though, it may be possible for a Uranus/Neptune to form in situ in less than the age of the Solar System. We perform numerical simulations of oligarchic growth with gas and find that protoplanet growth rates agree reasonably well with the analytic model as long as protoplanet masses are well below their estimated final masses. However, accretion stalls earlier than predicted, so that the largest final protoplanet masses are smaller than those given by the model. Thus the oligarchic growth model, in the form developed here, appears to provide an upper limit for the efficiency of giant planet formation.     

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.     

Effects of mass loss for highly-irradiated giant planets

We present calculations for the evolution and surviving mass of highly-irradiated extrasolar giant planets (EGPs) at orbital semimajor axes ranging from 0.023 to 0.057 AU using a generalized scaled theory for mass loss, together with new surface-condition grids for hot EGPs and a consistent treatment of tidal truncation. Theoretical estimates for the rate of energy-limited hydrogen escape from giant-planet atmospheres differ by two orders of magnitude, when one holds planetary mass, composition, and irradiation constant. Baraffe et al. [Baraffe, I., Selsis, F., Chabrier, G., Barman, T.S., Allard, F., Hauschildt, P.H., Lammer, H., 2004. Astron. Astrophys. 419, L13-L16] predict the highest rate, based on the theory of Lammer et al. [Lammer, H., Selsis, F., Ribas, I., Guinan, E.F., Bauer, S.J., Weiss, W.W., 2003. Astrophys. J. 598, L121-L124]. Scaling the theory of Watson et al. [Watson, A.J., Donahue, T.M., Walker, J.C.G., 1981. Icarus 48, 150-166] to parameters for a highly-irradiated exoplanet, we find an escape rate ∼¹⁰² lower than Baraffe's. With the scaled Watson theory we find modest mass loss, occurring early in the history of a hot EGP. In this theory, mass loss including the effect of Roche-lobe overflow becomes significant primarily for masses below a Saturn mass, for semimajor axes ?0.023 AU. This contrasts with the Baraffe model, where hot EGPs are claimed to be remnants of much more massive bodies, originally several times Jupiter and still losing substantial mass fractions at present.     

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 CH₃D/CH₄ 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 D/H 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 D/H ratio of the planet would then be higher than the value measured in hydrogen. Even in this case, the D/H 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 D/H ratio in the atmosphere of Titan with the value of D/H 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.     

Love numbers of the giant planets

We calculate the Love numbers k_n for n = 2 to 10, and determine the “gravitational noise” from tides. The new values k₂ for Jupiter, Saturn, and Uranus yield new estimates for the planetary dissipation functions: $\text{Q}{}_{\mathrm{<mtext>J</mtext>}}\text{? 2.5 × 10}{}^4$, $\text{Q}{}_{\mathrm{<mtext>S</mtext>}}\text{? 1.4 × 10}{}^4\text{, Q}{}_{\mathrm{<mtext>U</mtext>}}\text{? 5 × 10}{}^3$.     

Stable satellites around extrasolar giant planets

In this work, we study the stability of hypothetical satellites of extrasolar planets. Through numerical simulations of the restricted elliptic three-body problem we found the borders of the stable regions around the secondary body. From the empirical results, we derived analytical expressions of the critical semimajor axis beyond which the satellites would not remain stable. The expressions are given as a function of the eccentricities of the planet, e _P, and of the satellite, e _sat. In the case of prograde satellites, the critical semimajor axis, in the units of Hill's radius, is given by a _E≈ 0.4895   (1.0000 − 1.0305 e _P− 0.2738 e _sat). In the case of retrograde satellites, it is given by a _E≈ 0.9309  (1.0000 − 1.0764 e _P− 0.9812 e _sat). We also computed the satellite stability region ( a _E) for a set of extrasolar planets. The results indicate that extrasolar planets in the habitable zone could harbour the Earth-like satellites.     

Atmospheric thermal structures of the giant planets

Thermal models of planetary atmospheres can be calculated from assumptions of the energy budget of the atmosphere and from the knowledge of the effective temperature of the studied planet. On the other hand, the retrieval of the thermal atmospheric profiles from infrared measurements by means of the numerical inversion of the radiative transfer equation presents the advantages of not requiring such assumptions. The extent of the atmospheric range which can then be sounded is examined and the vertical resolution of the inferred profiles is discussed. Comparisons of thermal models and retrieved thermal profiles are made for the four giant planets. The retrieved profiles lead to brightness temperature spectra which fit all the available infrared measurements fairly well for Jupiter and Saturn but only part of them for Uranus and Neptune. The values of the planetary effective temperatures calculated from the retrieved profiles show that Jupiter, Saturn, and Neptune have strong internal heating sources while Uranus probably has a very small or null one.     

Model bond albedos of extrasolar giant planets

The atmospheres of extrasolar giant planets are modeled with various effective temperatures and gravities, with and without clouds. Bond albedos are computed by calculating the ratio of the flux reflected by a planet (integrated over wavelength) to the total stellar flux incident on the planet. This quantity is useful for estimating the effective temperature and evolution of a planet. We find it is sensitive to the stellar type of the primary. For a 5 M_Jup planet the Bond albedo varies from 0.4 to 0.3 to 0.6 as the primary star varies from A5V to G2V to M2V in spectral type. It is relatively insensitive to the effective temperature and gravity for cloud-free planets. Water clouds increase the reflectivity of the planet in the red, which increases the Bond albedo. The Bond albedo increases by an order of magnitude for a 13 M_Jup planet with an M2V primary when water clouds are present. Silicate clouds, on the other hand, can either increase or decrease the Bond albedo, depending on whether there are many small grains (the former) or few large grains (the latter).     

Migration of giant planets in planetesimal discs

Planets orbiting a planetesimal circumstellar disc can migrate inward from their initial positions because of dynamical friction between planets and planetesimals. The migration rate depends on the disc mass and on its time evolution. Planets that are embedded in long-lived planetesimal discs, having total mass of 10⁻⁴– 0.01 M_⊙ , can migrate inward a large distance and can survive only if the inner disc is truncated or as a result of tidal interaction with the star. In this case the semimajor axis, a , of the planetary orbit is less than 0.1 au. Orbits with larger a are obtained for smaller values of the disc mass or for a rapid evolution (depletion) of the disc. This model may explain not only several of the orbital features of the giant planets that have been discovered in recent years orbiting nearby stars, but also the metallicity enhancement found in several stars associated with short-period planets.     

Capture of planetesimals by the giant planets

We investigate the possibility of gravitational capture of planetesimals as temporary or permanent satellites of Uranus and Neptune during the process of planetary growth. The capture mechanism is based in the enhancement of the Hill's sphere of action not only due to the mass acquired by the planet, but also by the variation of the planet-Sun distance as a consequence of the scattering of planetesimals by the planets of the outer solar system. Our calculations indicate that satellite capture was very important, specially during the first stages of the accretion process, contributing in a significant way to the planetary growth.     

The formation and habitability of terrestrial planets in the presence of close-in giant planets

‘Hot jupiters,’ giant planets with orbits very close to their parent stars, are thought to form farther away and migrate inward via interactions with a massive gas disk. If a giant planet forms and migrates quickly, the planetesimal population has time to re-generate in the lifetime of the disk and terrestrial planets may form [P.J. Armitage, A reduced efficiency of terrestrial planet formation following giant planet migration, Astrophys. J. 582 (2003) L47-L50]. We present results of simulations of terrestrial planet formation in the presence of hot/warm jupiters, broadly defined as having orbital radii ?0.5 AU. We show that terrestrial planets similar to those in the Solar System can form around stars with hot/warm jupiters, and can have water contents equal to or higher than the Earth's. For small orbital radii of hot jupiters (e.g., 0.15, 0.25 AU) potentially habitable planets can form, but for semi-major axes of 0.5 AU or greater their formation is suppressed. We show that the presence of an outer giant planet such as Jupiter does not enhance the water content of the terrestrial planets, but rather decreases their formation and water delivery timescales. We speculate that asteroid belts may exist interior to the terrestrial planets in systems with close-in giant planets.     

The interiors of the giant planets — 1983

The last few years brought progress in our understanding of the interiors of the giant planets especially of the two larger ones which have been visited by Pioneer and Voyager spacecraft. An analysis of the formation of the giant planets also heped to clarify certain important common features. The presently available model of Jupiter is still based on certain somewhat bothersome approximations but it appears to satisfy the main observational constraints. Saturn's interior is much better understood than it was previously although the quantitative aspects of the role of the miscibility gap in the hydrogen-helium system have not yet been entirely resolved. Much attention has been directed at the interiors of Uranus and Neptune and the outstanding question appears to be the location and the amount of ices and methane present in their outer layers. Both the two-and the three-layer models are moderately successful. Serious difficulties arise from the considerable uncertainties concerning the rotational periods of both planets. Also the estimates of the internal heat fluxes and of the magnetic fields of both planets are not sufficiently certain. It is hoped that the forthcoming flyby of these two planets by a Voyager spacecraft will provide important new data for a future study of their interiors.     

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.     

Calculations of the evolution of the giant planets

Evolutionary calculations are presented for spherically symmetric protoplanetary configurations with a homogeneous solar composition and with masses of 10^?3, 1.5 × 10^?3, 2.85 × 10^?4, and 4.2 × 10^?4M_⊙. Recent improvements in equation-of-state and opacity calculations are incorporated. Sequences start as subcondensations in the solar nebula with densities of ～10^?10 to 10^?11 g cm^?3, evolve through a hydrostatic phase lasting 10⁵ to 10⁷ years, undergo dynamic collapse due to dissociation of molecular hydrogen, and regain hydrostatic equilibrium with densities ～1 g cm^?3. The nature of the objects at the onset of the final phase of cooling and contraction is discussed and compared with previous calculations.     

Scaling laws for convection and jet speeds in the giant planets

Three dimensional studies of convection in deep spherical shells have been used to test the hypothesis that the strong jet streams on Jupiter, Saturn, Uranus, and Neptune result from convection throughout the molecular envelopes. Due to computational limitations, these simulations must be performed at parameter settings far from jovian values and generally adopt heat fluxes 5-10 orders of magnitude larger than the planetary values. Several numerical investigations have identified trends for how the mean jet speed varies with heat flux and viscosity in these models, but no previous theories have been advanced to explain these trends. Here, we show using simple arguments that if convective release of potential energy pumps the jets and viscosity damps them, the mean jet speeds split into two regimes. When the convection is weakly nonlinear, the equilibrated jet speeds should scale approximately with F/ν, where F is the convective heat flux and ν is the viscosity. When the convection is strongly nonlinear, the jet speeds are faster and should scale approximately as (F/ν)^1/2. We demonstrate how this regime shift can naturally result from a shift in the behavior of the jet-pumping efficiency with heat flux and viscosity. Moreover, both Boussinesq and anelastic simulations hint at the existence of a third regime where, at sufficiently high heat fluxes or sufficiently small viscosities, the jet speed becomes independent of the viscosity. We show based on mixing-length estimates that if such a regime exists, mean jet speeds should scale as heat flux to the 1/4 power. Our scalings provide a good match to the mean jet speeds obtained in previous Boussinesq and anelastic, three-dimensional simulations of convection within giant planets over a broad range of parameters. When extrapolated to the real heat fluxes, these scalings suggest that the mass-weighted jet speeds in the molecular envelopes of the giant planets are much weaker—by an order of magnitude or more—than the speeds measured at cloud level.     

Models of the millimeter-centimeter spectra of the giant planets

Hitherto Jupiter's spectrum at short millimeter wavelenghts showed a clear discrepancy with model calculations (e.g., G.L. Berge and S. Gulkis, 1976, In Jupiter (T. Gehrels, Ed.), pp. 621–692. Univ. of Arizona Press, Tucson). A similar although less pronounced, discrepancy appears to exist for Uranus and Neptune. One explanation of this discrepancy is that additional absorbers not included in the model calculations are present in the atmosphere. It was suggested that uncertainties in the absorption coefficient of ammonia, especially at millimeter wavelengths, may be responsible for at least part of the discrepancy. A comparison of various model atmosphere calculations with data for all four giant planets is shown. The absorption profile of ammonia at centimeter wavelengths was assumed to be rightly represented by a Ben Reuven line profile, which enabled the derivation of information on the vertical distribution of ammonia in these planets' atmospheres. It appeared that ammonia must be depleted in the upper atmospheres of all four planets by a factor of 4–5 with respect to the solar abundance for Jupiter (and Saturn) and by a factor of 100–200 for Uranus and Neptune. At deeper layers the optical depth is larger, due either to a larger abundance of ammonia or to absorption by the presence of water. Given the vertical ammonia distribution in the atmospheres as derived from the centimeter data, a best fit to the millimeter spectra of all four planets was found by changing the high frequency tail of the ammonium lineshape profile. This, we feel, is legitimate since the profile at millimeter wavelenghts is not or is only poorly known due to the absence of laboratory spectra for ammonia as a trace constituent in an otherwise hydrogen gas. It was found that a line profile which at millimeter wavelenghts more closely resembles a Van Vleck-Weisskopf lineshape than the usually adopted Ben Reuven profile gives a rather satisfactory fit to the data of all four gaseous planets.     

Far-infrared and submillimeter brightness temperatures of the giant planets

We have measured the brightness temperatures of Jupiter, Saturn, Uranus, and Neptune in the range 35 to 1000 μm. The effective temperatures derived from the measurements, supplemented by shorter wavelength Voyager data for Jupiter and Saturn, are 126.8 ± 4.5, 93.4 ± 3.3, 58.3 ± 2.0, and 60.3 ± 2.0°K, respectively. We discuss the implications of the measurements for bolometric output and for atmospheric structure and composition. The temperature spectrum of Jupiter shows a strong peak at ～350 μm followed by a deep valley at ～450 to 500 μm. Spectra derived from model atmospheres qualitatively reproduce these features but do not fit the data closely.     

Aeronomy of extra-solar giant planets at small orbital distances

One-dimensional aeronomical calculations of the atmospheric structure of extra-solar giant planets in orbits with semi-major axes from 0.01 to 0.1 AU show that the thermospheres are heated to over 10,000 K by the EUV flux from the central star. The high temperatures cause the atmosphere to escape rapidly, implying that the upper thermosphere is cooled primarily by adiabatic expansion. The lower thermosphere is cooled primarily by radiative emissions from H⁺₃, created by photoionization of H₂ and subsequent ion chemistry. Thermal decomposition of H₂ causes an abrupt change in the composition, from molecular to atomic, near the base of the thermosphere. The composition of the upper thermosphere is determined by the balance between photoionization, advection, and H⁺ recombination. Molecular diffusion and thermal conduction are of minor importance, in part because of large atmospheric scale heights. The energy-limited atmospheric escape rate is approximately proportional to the stellar EUV flux. Although escape rates are large, the atmospheres are stable over time scales of billions of years.