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.     

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.     

Motion in the interiors and atmospheres of Jupiter and Saturn: scale analysis,anelastic equations,barotropic stability criterion

If Jupiter's and Saturn's fluid interiors were inviscid and adiabatic, any steady zonal motion would take the form of differentially rotating cylinders concentric about the planetary axis of rotation. B. A. Smith et al. [Science215, 504–537 (1982)] showed that Saturn's observed zonal wind profile extends a significant distance below cloud base. Further extension into the interior occurs if the values of the eddy viscosity and superadiabaticity are small. We estimate these values using a scaling analysis of deep convection in the presence of differential rotation. The differential rotation inhibits the convection and reduces the effective eddy viscosity. Viscous dissipation of zonal mean kinetic energy is then within the bounds set by the internal heat source. The differential rotation increases the superadiabaticity, but not so much as to eliminate the cylindrical structure of the flow. Very large departures from adiabaticity, necessary for decoupling the atmosphere and interior, do not occur. Using our scaling analysis we develop the anelastic equations that describe motions in Jupiter's and Saturn's interiors. A simple problem is solved, that of an adiabatic fluid with a steady zonal wind varying as a function of cylindrical radius. Low zonal wavenumber perturbations are two dimensional (independent of the axial coordinate) and obey a modified barotropic stability equation. The parameter analogous to β is negative and is three to four times larger than the β for thin atmospheres. Jupiter's and Saturn's observed zonal wind profiles are close to marginal stability according to this deep sphere criterion, but are several times supercritical according to the thin atmosphere criterion.     

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.     

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.     

Atmospheric superrotation on Saturn and Jupiter

The problem is discussed whether atmospheric superrotation is driven by internal or external torques. An integral constraint is derived which under certain conditions forbids geostrophic flow, and suggests corkscrew-shaped motion along zones of constant latitude. A momentum balance consideration restricts effective viscosities in the upper atmospheres to be much smaller than maximal eddy viscosity, perhaps as small as molecular viscosity.     

For infrared spectrophotometry of Jupiter and Saturn

Infrared spectral observations of Mars, Jupiter, and Saturn were made from 100 to 470 cm^?1 using NASA's G. P. Kuiper Airborne Observatory. Taking Mars as a calibration source, we determined brightness temperatures of Jupiter and Saturn with approximately 5 cm^?1 resolution. The data are used to determine the internal luminosities of the giant planets, for which more than 75% of the thermally emitted power is estimated to be in the measured bandpass: for Jupiter L_J = (8.0 ± 2.0) × 10^?10L_⊙ and for Saturn L_S = (3.6 ± 0.9) × 10^?10. The ratio R of thermally emitted power to solar power absorbed was estimated to be R_J = 1.6 ± 0.2, and R_S = 2.7 ± 0.8 from the observations when both planets were near perihelion. The Jupiter spectrum clearly shows the presence of the rotational ammonia transitions which strongly influence the opacity at frequencies ?250 cm^?1. Comparison of the data with spectra predicted from current models of Jupiter and Saturn permits inferences regarding the structure of the planetary atmospheres below the temperature inversion. In particular, an opacity source in addition to gaseous hydrogen and ammonia, such as ammonia ice crystals as suggested by Orton, may be necessary to explain the observed Jupiter spectrum in the vicinity of 250 cm^?1.     

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 free oscillations of Jupiter and Saturn

The periods and the eigenfunctions have been calculated for the fundamental modes and for the overtones of spheroidal oscillations of Jupiter and Saturn. Along with ordinary oscillations, the core oscillations appear; these eigenfunctions are localized in the planetary core and have an exponential attenuation to the surface. The rotational splittings of the free oscillations have been calculated. Because of rapid planetary rotation, these splittings were found to be of the order of differences between undisturbed frequences. The idea is proposed that the rotational splitting of the spectrum of Saturn may present in the future the unique possibility of determining the bodily rotation period of the planet.     

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.     

Near-infrared polarization studies of Saturn and Jupiter

Polarization measurements of Jupiter, Saturn, and Saturn's rings from 1 to 3.5 μm are presented. At 1.6 μm on the discs of the two planets, the radially directed limb polarizations observed in the visible undergo, in some cases, a surprising 90° rotation to a tangential direction, particularly on the poles. The only immediate explanation for this effect is double Mie scattering, due to aerosols which must be of the order of a micrometer in size. On Jupiter the patterns are not uniform and are not stable, reflecting variable aerosol concentrations on the two poles. The ring polarization is uniformly negative (E vector parallel to the ecliptic plane) from the visible through 3.5 μm, and is inversely proportional to the albedo. This is as expected from Wolff's model for scattering from rough solid surfaces; but the degree of polarization seems uncommonly high, exceeding 2% at 3.5 μm.     

The upper ionospheres of Jupiter and Saturn

We use a 1-D chemical diffusive model, in conjunction with the measured neutral atmospheric structure, to analyze the Voyager RSS electron density, n_e, profiles for the ionospheres of Jupiter and Saturn. As with previous studies we find serious difficulties in explaining the n_e measurements. The model calculates ionospheres for both Jupiter and Saturn with n_e peaks of 10 times the measured peaks at altitudes which are 900–1000 km lower than the altitude of peaks in the RSS electron densities. Based on our knowledge of neutral atmospheric structure, ionization sources, and known recombination mechanisms it seems that, vibrational excitation of H₂ must play some role in the conversion of slowly radiatively recombining H⁺ ions to the relatively more rapidly recombining H₂⁺ and H₃⁺ ions. In addition, vertical ion flow induced by horizontal neutral winds or electric fields probably also play some role in maintaining the plasma peaks observed both for Jupiter and Saturn to be at high altitudes. For the ionosphere of Saturn, the electron densities are affected by a putative influx of H₂O molecules, Φ_H2O, from the rings. To reproduce the RSS V2 exit n_e results model requires an influx of Φ_H2O 2 × 10⁷ molecules cm⁻² s⁻¹ without invoking H_2f vibrational excitation. To maintain the model n_e peak at the measured altitude vertical plasma drift maintained by meridional winds or vertical electric fields is required. The amounts of H₂O are consistent with earlier estimates of Connerney and Waite (1984) and do not violate any observational constraints.     

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.     

Monochromatic brightness factors of Jupiter and Saturn

The monochromatic brightness factors for morphologically nonuniform cloudy surface fields of Jupiter and Saturn in the visible wavelength range were calculated. In the spectra of both giant planets, the combination (Raman) light scattering feature (a pseudoemission peak) was detected in the range of a strong Fraunhofer line H Ca II; and its intensity was estimated.     

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.     

Imaging spectrometer study of Jupiter and Saturn

Observations with a new near infrared imaging spectrometer with ～15 Å resolution are presented. Twelve spectral images of Saturn in the vicinity of the 8900 Å CH₄ absorption complex were obtained and their interpretation discussed. Spectral images of Jupiter were also obtained and several of these at widely separated wavelengths were subjected to a Minnaert analysis.     

On the origin and evolution of Jupiter and Saturn

Arguments are presented which show that Kumar's (1977) contention that Jupiter and Saturn are unlikely to have formed from an initially extended state by contraction is not valid.     

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.     

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.     

Jupiter and Saturn: Near-infrared spectral albedos

The near-infrared (0.65–2.5μm) spectral albedo of Jupiter and Saturn with 1.5% spectral resolution is presented for the center of disk and for the limb. There is a distinct difference in the continuum slope between Jupiter and Saturn which may be attributed to a difference in the dust content or composition of the two atmospheres. There is an indication of limb brightening in the deepest CH₄ bands on Saturn. No limb brightening is found for Jupiter.