Kinetic models for the exospheres of Jupiter and Saturn

The exospheric theory based on the Kappa velocity distribution function (VDF) is used to model the exosphere of the giant planets Jupiter and Saturn. Such Kappa velocity distribution functions with an enhanced population of suprathermal particles are indeed often observed in space plasmas and in the space environment of the planets. The suprathermal particles have significant effects on the escape flux, density and temperature profiles of the particles in the exosphere of the giant planets. The polar wind flux becomes several orders larger when suprathermal electrons are considered, so that the planetary ionosphere becomes then a significant source for their inner magnetosphere. Moreover, the number density of the particles decreases slower as a function of the altitude when a Kappa distribution is considered instead of a Maxwellian one. Two-dimensional maps of density are calculated for typical values of the temperatures. The exospheric formalism is also applied to study the escape flux from the exospheres of Io and Titan, respectively, moons of Jupiter and Saturn.     

Jupiter and Saturn rotation periods

Anderson and Schubert [2007. Saturn's Gravitational field, internal rotation, and interior structure. Science 317, 1384-1387 (paper I)] proposed that Saturn's rotation period can be ascertained by minimizing the dynamic heights of the 100 mbar isosurface with respect to the geoid; they derived a rotation period of 10 h 32 m 35 s. We investigate the same approach for Jupiter to see if the Jovian rotation period is predicted by minimizing the dynamical heights of its isobaric (1 bar pressure level) surface using zonal wind data. A rotation period of 9 h 54 m 29.7 s is found. Further, we investigate the minimization method by fitting Pioneer and Voyager occultation radii for both Jupiter and Saturn. Rotation periods of 9 h 55 m 30 s and 10 h 32 m 35 s are found to minimize the dynamical heights for Jupiter and Saturn, respectively. Though there is no dynamical principle requiring the minimization of the dynamical heights of an isobaric surface, the successful application of the method to Jupiter lends support to its relevance for Saturn.We derive Jupiter and Saturn rotation periods using equilibrium theory to explain the difference between equatorial and polar radii. Rotation periods of 9 h 55 m 20 s and 10 h 31 m 49 s are found for Jupiter and Saturn, respectively. We show that both Jupiter's and Saturn's shapes can be derived using solid-body rotation, suggesting that zonal winds have a minor effect on the planetary shape for both planets.The agreement in the values of Saturn's rotation period predicted by the different approaches supports the conclusion that the planet's period of rotation is about 10 h 32 m.     

Long slit spectropolarimetry of Jupiter and Saturn

We present ground-based limb polarization measurements of Jupiter and Saturn consisting of full disk imaging polarimetry for the wavelength 7300 Å and spatially resolved (long-slit) spectropolarimetry covering the wavelength range 5200-9350 Å.For the polar region of Jupiter we find for λ = 6000 Å a very strong radial (perpendicular to the limb) fractional polarization with a seeing corrected maximum of about +11.5% in the South and +10.0% in the North. This indicates that the polarizing haze layer is thicker at the South pole. The polar haze layers extend down to 58° in latitude. The derived polarization values are much higher than reported in previous studies because of the better spatial resolution of our data and an appropriate consideration of the atmospheric seeing. Model calculations demonstrate that the high limb polarization can be explained by strongly polarizing (p ≈ 1.0), high albedo (ω ≈ 0.98) haze particles with a scattering asymmetry parameter of g ≈ 0.6 as expected for aggregate particles of the type described by West and Smith (West, R.A., Smith, P.H. [1991]. Icarus 90, 330-333). The deduced particle parameters are distinctively different when compared to lower latitude regions.The spectropolarimetry of Jupiter shows a decrease in the polar limb polarization towards longer wavelengths and a significantly enhanced polarization in strong methane bands when compared to the adjacent continuum. This is a natural outcome for a highly polarizing haze layer above an atmosphere where multiple scatterings are suppressed in absorption bands. For lower latitudes the fractional polarization is small, negative, and it depends only little on wavelength except for the strong CH₄-band at 8870 Å.The South pole of Saturn shows a lower polarization (p ≈ 1.0-1.5%) than the poles of Jupiter. The spectropolarimetric signal for Saturn decrease rapidly with wavelength and shows no significant enhancements in the fractional polarization in the absorption bands. These properties can be explained by a vertically extended stratospheric haze region composed of small particles <100 nm as suggested previously by Karkoschka and Tomasko (Karkoschka, E., Tomasko, M. [2005]. Icarus 179, 195-221).In addition we find in the V- and R-band a previously not observed strong polarization feature (p = 1.5-2.0%) near the equator of Saturn. The origin of this polarization signal is unclear but it could be related to a seasonal effect.Finally we discuss the potential of ground-based limb polarization measurements for the investigation of the scattering particles in the atmospheres of Jupiter and Saturn.     

Stability of jets on Jupiter and Saturn

The linear stability of a zonal jet that decays with depth is investigated under the assumption that the thermal stratification is very small. A westerly cosine jet is found to be more stable than it is in a thin fluid shell with two-dimensional flow. This is in agreement with observations of Jupiter and Saturn, where jet curvature exceeds the barotropic stability criterion. This result constitutes an alternative hypothesis to that of Ingersoll and Pollard [Icarus 52 (1982) 62], who showed that deep jets extending through the interior are also more stable than thin shell jets. The flow regime assumed in the present work requires that a small stratification can exist and persist even in the presence of horizontal temperature gradients. Further work will be needed to test whether this is realistic.     

Phosphine on Jupiter and Saturn from Cassini/CIRS

The global distribution of phosphine (PH₃) on Jupiter and Saturn is derived using 2.5 cm⁻¹ spectral resolution Cassini/CIRS observations. We extend the preliminary PH₃ analyses on the gas giants [Irwin, P.G.J., and 6 colleagues, 2004. Icarus 172, 37-49; Fletcher, L.N., and 9 colleagues, 2007a. Icarus 188, 72-88] by (a) incorporating a wider range of Cassini/CIRS datasets and by considering a broader spectral range; (b) direct incorporation of thermal infrared opacities due to tropospheric aerosols and (c) using a common retrieval algorithm and spectroscopic line database to allow direct comparison between these two gas giants.The results suggest striking similarities between the tropospheric dynamics in the 100-1000 mbar regions of the giant planets: both demonstrate enhanced PH₃ at the equator, depletion over neighbouring equatorial belts and mid-latitude belt/zone structures. Saturn's polar PH₃ shows depletion within the hot cyclonic polar vortices. Jovian aerosol distributions are consistent with previous independent studies, and on Saturn we demonstrate that CIRS spectra are most consistent with a haze in the 100-400 mbar range with a mean optical depth of 0.1 at 10 μm. Unlike Jupiter, Saturn's tropospheric haze shows a hemispherical asymmetry, being more opaque in the southern summer hemisphere than in the north. Thermal-IR haze opacity is not enhanced at Saturn's equator as it is on Jupiter.Small-scale perturbations to the mean PH₃ abundance are discussed both in terms of a model of meridional overturning and parameterisation as eddy mixing. The large-scale structure of the PH₃ distributions is likely to be related to changes in the photochemical lifetimes and the shielding due to aerosol opacities. On Saturn, the enhanced summer opacity results in shielding and extended photochemical lifetimes for PH₃, permitting elevated PH₃ levels over Saturn's summer hemisphere.     

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.     

Significance of gravitational moments for interior structure of Jupiter and Saturn

We present the case for liquid models of Jupiter and Saturn. We then discuss the information which can be obtained about their interior structure from a knowledge of their gravitational moments, and we discuss the nature of presently available data and data which will be necessary to fully exploit future results.     

UV and IR auroral emission model for the outer planets: Jupiter and Saturn comparison

Planetary aurora display the dynamic behavior of the plasma gas surrounding a planet. The outer planetary aurora are most often observed in the ultraviolet (UV) and the infrared (IR) wavelengths. How the emissions in these different wavelengths are connected with the background physical conditions are not yet well understood. Here we investigate the sensitivity of UV and IR emissions to the incident precipitating auroral electrons and the background atmospheric temperature, and compare the results obtained for Jupiter and Saturn. We develop a model which estimates UV and IR emission rates accounting for UV absorption by hydrocarbons, ion chemistry, and non-LTE effects. Parameterization equations are applied to estimate the ionization and excitation profiles in the H₂ atmosphere caused by auroral electron precipitation. The dependences of UV and IR emissions on electron flux are found to be similar at Jupiter and Saturn. However, the dependences of the emissions on electron energy are different at the two planets, especially for low energy (<10 keV) electrons; the UV and IR emissions both decrease with decreasing electron energy, but this effect in the IR is less at Saturn than at Jupiter. The temperature sensitivity of the IR emission is also greater at Saturn than at Jupiter. These dependences are interpreted as results of non-LTE effects on the atmospheric temperature and density profiles. The different dependences of the UV and IR emissions on temperature and electron energy at Saturn may explain the different appearance of polar emissions observed at UV and IR wavelengths, and the differences from those observed at Jupiter. These results lead to the prediction that the differences between the IR and UV aurora at Saturn may be more significant than those at Jupiter. We consider in particular the occurrence of bright polar infrared emissions at Saturn and quantitatively estimate the conditions for such IR-only emissions to appear.     

Time-dependent flexure of the lithospheres on the icy satellites of Jupiter and Saturn

Previous analyses into flexural deformation on the icy satellites of Jupiter and Saturn have assumed static, elastic lithospheres. Viscous creep within the lithosphere, however, can cause evolution over time. Here, we apply a finite-element model that employs a time-dependent elastic–viscous-plastic rheology in order to investigate flexure on icy satellites. Factors that affect this time-dependent response are those that control creep rates; surface temperature, heat flow, and grain size. Our results show that surface temperature is by far the dominant factor. At higher surface temperatures (100–130 K), the evolution of the deformation is such that the thickness of a modeled elastic lithosphere could vary by up to an order of magnitude, depending on the time scale over which the deformation occurred. Because the flexure observed on icy satellites generally indicates transient high heat flow events, our results indicate that the duration of the heat pulse is an important factor. For the icy worlds of Jupiter and Saturn, static models of lithospheric flexure should be used with caution.     

Interaction of moist convection with zonal jets on Jupiter and Saturn

Observations suggest that moist convection plays an important role in the large-scale dynamics of Jupiter's and Saturn's atmospheres. Here we use a reduced-gravity quasigeostrophic model, with a parameterization of moist convection that is based on observations, to study the interaction between moist convection and zonal jets on Jupiter and Saturn. Stable jets with approximately the same width and strength as observations are generated in the model. The observed zonal jets violate the barotropic stability criterion but the modeled jets do so only if the flow in the deep underlying layer is westward. The model results suggest that a length scale and a velocity scale associated with moist convection control the width and strength of the jets. The length scale and velocity scale offer a possible explanation of why the jets of Saturn are stronger and wider than those of Jupiter.     

Hadley circulations and Kelvin wave-driven equatorial jets in the atmospheres of Jupiter and Saturn

We propose a dynamical mechanism that can plausibly explain the origin of the broad prograde equatorial winds observed on Jupiter and Saturn, and examine the feasibility of this mechanism using two- (2D) and three-dimensional (3D) numerical simulation models. The idea is based on combining a narrow Gaussian jet peaking at the equator, which is induced by the momentum transfer from an upward propagating equatorial Kelvin-wave, and a pair of off-equatorial jets due to a meridional-vertical circulation similar to the tropical Hadley circulation on Earth. We employ for this feasibility study a 2D mechanistic mean-flow model which incorporates the influence of prescribed waves, and a 3D general circulation model, based on the generalised primitive equations of atmospheric motion. We then confirm that the dynamical models of both kinds can successfully reproduce theoretically expected flows of a reasonable magnitude, and that when two mechanisms are combined, a broad super-rotating jet is produced with off-equatorial maxima in zonal velocity for both Jupiter and Saturn, approximately in accordance with observations.     

Turbulent convection in rapidly rotating spherical shells: A model for equatorial and high latitude jets on Jupiter and Saturn

The origin of zonal jets on the jovian planets has long been a topic of scientific debate. In this paper we show that deep convection in a spherical shell can generate zonal flow comparable to that observed on Jupiter and Saturn, including a broad prograde equatorial jet and multiple alternating jets at higher latitudes. We present fully turbulent, 3D spherical numerical simulations of rapidly rotating convection with different spherical shell geometries. The resulting global flow fields tend to be segregated into three regions (north, equatorial, and south), bounded by the tangent cylinder that circumscribes the inner boundary equator. In all of our simulations a strong prograde equatorial jet forms outside the tangent cylinder, whereas multiple jets form in the northern and southern hemispheres, inside the tangent cylinder. The jet scaling of our numerical models and of Jupiter and Saturn is consistent with the theory of geostrophic turbulence, which we extend to include the effect of spherical shell geometry. Zonal flow in a spherical shell is distinguished from that in a full sphere or a shallow layer by the effect of the tangent cylinder, which marks a reversal in the sign of the planetary β-parameter and a jump in the Rhines length. This jump is manifest in the numerical simulations as a sharp equatorward increase in jet widths—a transition that is also observed on Jupiter and Saturn. The location of this transition gives an estimate of the depth of zonal flow, which seems to be consistent with current models of the jovian and saturnian interiors.     

Formation of terrestrial planets in a dissipating gas disk with Jupiter and Saturn

We have performed N-body simulations on final accretion stage of terrestrial planets, including the eccentricity and inclination damping effect due to tidal interaction with a gas disk. We investigated the dependence on a depletion time scale of the disk, and the effect of secular perturbations by Jupiter and Saturn. In the final stage, terrestrial planets are formed through coagulation of protoplanets of about the size of Mars. They would collide and grow in a decaying gas disk. Kominami and Ida [Icarus 157 (2002) 43-56] showed that it is plausible that Earth-sized, low-eccentricity planets are formed in a mostly depleted gas disk. In this paper, we investigate the formation of planets in a decaying gas disk with various depletion time scales, assuming disk surface density of gas component decays exponentially with time scale of τ_gas. Fifteen protoplanets with are initially distributed in the terrestrial planet regions. We found that Earth-sized planets with low eccentricities are formed, independent of initial gas surface density, when the condition (τ_cross+τ_growth)/2?τ_gas?τ_cross is satisfied, where τ_cross is the time scale for initial protoplanets to start orbit crossing in a gas-free case and τ_growth is the time scale for Earth-sized planets to accrete during the orbit crossing stage. In the cases satisfying the above condition, the final masses and eccentricities of the largest planets are consistent with those of Earth and Venus. However, four or five protoplanets with the initial mass remain. In the final stage of terrestrial planetary formation, it is likely that Jupiter and Saturn have already been formed. When Jupiter and Saturn are included, their secular perturbations pump up eccentricities of protoplanets and tend to reduce the number of final planets in the terrestrial planet regions. However, we found that the reduction is not significant. The perturbations also shorten τ_cross. If the eccentricities of Jupiter and Saturn are comparable to or larger than present values (∼0.05), τ_cross become too short to satisfy the above condition. As a result, eccentricities of the planets cannot be damped to the observed value of Earth and Venus. Hence, for the formation of terrestrial planets, it is preferable that the secular perturbations from Jupiter and Saturn do not have significant effect upon the evolution. Such situation may be reproduced by Jupiter and Saturn not being fully grown, or their eccentricities being smaller than the present values during the terrestrial planets' formation. However, in such cases, we need some other mechanism to eliminate the problem that numerous Mars-sized planets remain uncollided.     

Accretion of the gaseous envelope of Jupiter around a 5-10 Earth-mass core

New numerical simulations of the formation and evolution of Jupiter are presented. The formation model assumes that first a solid core of several M_⊕ accretes from the planetesimals in the protoplanetary disk, and then the core captures a massive gaseous envelope from the protoplanetary disk. Earlier studies of the core accretion-gas capture model [Pollack, J.B., Hubickyj, O., Bodenheimer, P., Lissauer, J.J., Podolak, M., Greenzweig, Y., 1996. Icarus 124, 62-85] demonstrated that it was possible for Jupiter to accrete with a solid core of 10-30 M_⊕ in a total formation time comparable to the observed lifetime of protoplanetary disks. Recent interior models of Jupiter and Saturn that agree with all observational constraints suggest that Jupiter's core mass is 0-11 M_⊕ and Saturn's is 9-22 M_⊕ [Saumon, G., Guillot, T., 2004. Astrophys. J. 609, 1170-1180]. We have computed simulations of the growth of Jupiter using various values for the opacity produced by grains in the protoplanet's atmosphere and for the initial planetesimal surface density, σinit,Z, in the protoplanetary disk. We also explore the implications of halting the solid accretion at selected core mass values during the protoplanet's growth. Halting planetesimal accretion at low core mass simulates the presence of a competing embryo, and decreasing the atmospheric opacity due to grains emulates the settling and coagulation of grains within the protoplanet's atmosphere. We examine the effects of adjusting these parameters to determine whether or not gas runaway can occur for small mass cores on a reasonable timescale. We compute four series of simulations with the latest version of our code, which contains updated equation of state and opacity tables as well as other improvements. Each series consists of a run without a cutoff in planetesimal accretion, plus up to three runs with a cutoff at a particular core mass. The first series of runs is computed with an atmospheric opacity due to grains (hereafter referred to as ‘grain opacity’) that is 2% of the interstellar value and . Cutoff runs are computed for core masses of 10, 5, and 3 M_⊕. The second series of Jupiter models is computed with the grain opacity at the full interstellar value and . Cutoff runs are computed for core masses of 10 and 5 M_⊕. The third series of runs is computed with the grain opacity at 2% of the interstellar value and . One cutoff run is computed with a core mass of 5 M_⊕. The final series consists of one run, without a cutoff, which is computed with a temperature dependent grain opacity (i.e., 2% of the interstellar value for ramping up to the full interstellar value for ) and . Our results demonstrate that reducing grain opacities results in formation times less than half of those for models computed with full interstellar grain opacity values. The reduction of opacity due to grains in the upper portion of the envelope with has the largest effect on the lowering of the formation time. If the accretion of planetesimals is not cut off prior to the accretion of gas, then decreasing the surface density of planetesimals lowers the final core mass of the protoplanet, but increases the formation timescale considerably. Finally, a core mass cutoff results in a reduction of the time needed for a protoplanet to evolve to the stage of runaway gas accretion, provided the cutoff mass is sufficiently large. The overall results indicate that, with reasonable parameters, it is possible that Jupiter formed at 5 AU via the core accretion process in 1 Myr with a core of 10 M_⊕ or in 5 Myr with a core of 5 M_⊕.     

Search for HD in Jupiter and Saturn

Upper limits are placed on the D/H ratio in the observed portions of the atmospheres of Jupiter and Saturn from observations at high S/N over the region of the 5-0 R(1) line of HD. The upper limits of 4 × 10^?5 and 6 × 10^?5 D/H on Jupiter and Saturn, respectively, are not inconsistent with present models for abundance ratios in the primitive solar nebula or with other estimates of this quantity from observations.     

Seasonal Variations in the North-South Asymmetry of Polarized Light of Jupiter

Over an 18-year period, seasonal changes in the north-south asymmetry of polarization at high latitudes of Jupiter have been revealed by polarimetric observations in blue light. The average seasonal difference in the polarization degree between north and south is positive and equal to about 0.5%. There is some relationship between seasonal variations in the observed difference and the seasonal north-south asymmetry in solar radiation incident on Jupiter's atmosphere. There are two maxima on the observed seasonal curve, falling on the jovian spring and autumn and coinciding correspondingly with positive and negative maxima of the heliographic latitude of Jupiter. Two possible explanations are discussed: seasonal changes in insolation and/or time-dependent magnetospheric influence on the polar events.     

On the formation of Jupiter and Saturn

It is proposed that Jupiter and Saturn were initially formed as small rocks which grew into their present sizes as a result of accretion of matter from the gas-dust cloud surrounding the Sun. The energy released by the accretion of Jupiter and Saturn is computed. It is concluded that the ‘excess’ radiation from these planets is due to simple cooling and that the gravitational contraction from initially extended states most probably never occurred.     

Comparative evolution of Jupiter and Saturn

We present evolutionary sequences for Jupiter and Saturn, based on new non-gray model atmospheres, which take into account the evolution of the solar luminosity and partitioning of dense components to deeper layers. The results are used to set limits on the extent to which possible interior phase separation of hydrogen and helium may have progressed in the two planets. When combined with static models constrained by the gravity field, our evolutionary calculations constrain the helium mass fraction in Jupiter to be between 0.20 and 0.27, relative to total hydrogen and helium. This is consistent with the Galileo determination. The helium mass fraction in Saturn’s atmosphere lies between 0.11 and 0.21, higher than the Voyager determination. Based on the discrepancy between the Galileo and Voyager results for Jupiter, and our models, we predict that revised observational results for Saturn will yield a higher atmospheric helium mass fraction relative to the Voyager value.     

The Cassini-Huygens flyby of Jupiter

The Cassini-Huygens spacecraft flew by Jupiter on December 30, 2000. The instruments aboard the spacecraft started making scientific observations three months earlier. Joint, collaborative observations were carried out with the teams of other spacecraft, notably Galileo, and with Earth-based observers. An operational overview of the flyby is presented and attention drawn to contributions of the eleven papers of this series which follow. Prime achievements of this campaign have been to better define the present state of fundamental elements of the jovian system, confirming many previously tentative conclusions. Particularly noteworthy is that the interactions between the solar wind and the jovian magnetosphere have been explored far deeper than before, along with the link to the morphology and dynamics of the jovian aurora.     

Magnetic reversals of Jupiter and Saturn

We propose that the origin and behavior of the internal magnetic fields of Jupiter and Saturn should be much like the Sun's. Jupiter and Saturn are predominantly gaseous, they have significant internal heat sources, and their surface angular rotation rates vary with latitude. There is also empirical evidence showing that the rotation rates of their magnetic fields vary with latitude. This differential rotation is instrumental in producing solar-type dynamos, which are characterized by quasi-periodic field reversals. When we apply the theory and scaling parameters for the reversal period of the magnetic field of the Sun to Jupiter and Saturn, we derive an estimate for the time interval between magnetic reversals to be on the order of centuries. This time scale is consistent with observed changes in Jupiter's magnetic field over the last 2 decades.