Saturn meteorology: A diagnostic assessment of thin-layer configurations for the zonal flow

Voyager imaging, infrared, and radio observations for Saturn have been recently interpreted by Smith et al. (1982) as an indication that the jet streams observed at the cloud tops extend to depths greater than the 10⁴-bar level. This analysis assumes a maximum latitudinal temperature contrast of a few percent, a mean atmospheric rotation rate at depth given by Saturn's ratio period, and no variation with latitude of the bottom pressure level for the zonal flow system. These assumptions are not, however, firmly constrained by observation. The diagnostic analysis of plausible alternative configurations for Saturn's atmospheric structure demonstrates that a thin weather layer system (confined at mid to high latitudes to levels above 200 bar) cannot be excluded by any of the available observations. A quantitative estimate of the effects of moisture condensation (including the differentiation of mean molecular weight) suggests that these might provide the buoyancy contrasts necessary to support a thin-layer flow provided that Saturn's outer envelope is enriched approximately 10 times in water abundance relative to a solar composition atmosphere and strongly differentiated with latitude at the condensation level.     

Titan's atmospheric engine: an overview

Heating occurs in Titan's stratosphere from the absorption of incident solar radiation by methane and aerosols. About 10% of the incident sunlight reaches Titan's surface and causes heating there. Thermal radiation redistributes heat within the atmosphere and cools to space. The resulting vertical temperature profile is stable against convection and a state of radiative equilibrium is established. Equating theoretical and observed temperature profiles enables an empirical determination of the vertical distribution of thermal opacity. A uniformly mixed aerosol is responsible for most of the opacity in the stratosphere, whereas collision-induced absorption of gases is the main contributor in the troposphere. Occasional clouds are observed in the troposphere in spite of the large degrees of methane supersaturation found there. Photochemistry converts CH₄ and N₂ into more complex hydrocarbons and nitriles in the stratosphere and above. Thin ice clouds of trace organics are formed in the winter and early spring polar regions of the lower stratosphere. Precipitating ice particles serve as condensation sites for supersaturated methane vapor in the troposphere below, resulting in lowered methane degrees of supersaturation in the polar regions. Latitudinal variations of stratospheric temperature are seasonal, and lag instantaneous response to solar irradiation by about one season for two reasons: (1) an actual instantaneous thermal response to a latitudinal distribution of absorbing gases, themselves out of phase with the sun by about one season, and (2) a sluggish dynamical response of the stratosphere to the latitudinal transport of angular momentum, induced by radiative heating and cooling. Mean vertical abundances of stratospheric organics and aerosols are determined primarily by atmospheric chemistry and condensation, whereas latitudinal distributions are more influenced by meridional circulations. In addition to preferential scavenging by precipitating ice particles from above, the polar depletion of supersaturated methane results from periodic scavenging by short-lived tropospheric clouds, coupled with the steady poleward march of the continuously drying atmosphere due to meridional transport.     

Long-term changes in Saturn's troposphere

We report the results of monitoring Saturn's H₂ quadrupole and CH₄ band absorptions outside of the equatorial zone over one-half of Saturn's year. This interval covers most of the perihelion half of Saturn's elliptical orbit, which happens to be approximately bounded by the equinoxes. Marked long-term changes occur in the CH₄ absorption accompanied by weakly opposite changes in the H₂ absorption. Around the 1980 equinox, the H₂ and CH₄ absorptions in the northern hemisphere appear to be discontinuous with those in the southern hemisphere. This discontinuity and the temporal variation of the absorptions are evidence for seasonal changes. The absorption variations can be attributed to a variable haze in Saturn's troposphere, responding to changes in temperature and insolation through the processes of sublimation and freezing. Condensed or frozen CH₄ is very unlikely to contribute any haze. The temporal variation of the absorption in the strong CH₄ bands at south temperate latitudes is consistent with a theoretically expected phase lag of 60° between the tropopause temperature and the seasonally variable insolation. We model the vertical haze distribution of Saturn's south temperature latitudes during 1971–1977 in terms of a distribution having a particle scale height equal to a fraction of the atmospheric scale height. The results are a CH₄/H₂ mixing ratio of (4.2 ± 0.4) × 10^?3, a haze particle albedo of $\text{ω}\text{= 0.995 ± 0.003}$, and a range of variation in the particle to gas scale-height ratio of 0.6 ± 0.2. The haze was lowest near the time of maximum temperature. We also report spatial measurements of the absorption in the 6450 Å NH₃ band made annually since the 1980 equinox. A 20 ± 4% increase in the NH₃ absorption at south temperate latitudes has occurred since 1973–1976 and the NH₃ absorption at high northern latitudes has increased during spring. Increasing insolation, and the resulting net sublimation of NH₃ crystals, is probably the cause. Significant long-term changes apparently extend to the deepest visible parts of Saturn's atmosphere. An apparently anomalous ortho-para H₂ ratio in 1978 suggests that the southern temperate latitudes experienced an unusual upwelling during that time. This may have signaled a rise in the radiative-convective boundary from deep levels following maximum tropospheric temperature and the associated maximum radiative stability. This would be further evidence that the deep, visible atmosphere is governed by processes such as dynamics and the thermodynamics of phase changes, which have response times much shorter than the radiative time constant.     

Small-scale temperature fluctuations seen by the VeRa Radio Science Experiment on Venus Express

The Venus Express Radio Science Experiment VeRa retrieves atmospheric profiles in the mesosphere and troposphere of Venus in the approximate altitude range of 40–90 km. A data set of more than 500 profiles was retrieved between the orbit insertion of Venus Express in 2006 and the end of occultation season No. 11 in July 2011. The atmospheric profiles cover a wide range of latitudes and local times, enabling us to study the dependence of vertical small-scale temperature perturbations on local time and latitude.Temperature fluctuations with vertical wavelengths of 4 km or less are extracted from the measured temperature profiles in order to study small-scale gravity waves. Significant wave amplitudes are found in the stable atmosphere above the tropopause at roughly 60 km as compared with the only shallow temperature perturbations in the nearly adiabatic region of the adjacent middle cloud layer, below.Gravity wave activity shows a strong latitudinal dependence with the smallest wave amplitudes located in the low-latitude range, and an increase of wave activity with increasing latitude in both hemispheres; the greatest wave activity is found in the high-northern latitude range in the vicinity of Ishtar Terra, the highest topographical feature on Venus.We find evidence for a local time dependence of gravity wave activity in the low latitude range within ±30° of the equator. Gravity wave amplitudes are at their maximum beginning at noon and continuing into the early afternoon, indicating that convection in the lower atmosphere is a possible wave source.The comparison of the measured vertical wave structures with standard linear-wave theory allows us to derive rough estimates of the wave intrinsic frequency and horizontal wavelengths, assuming that the observed wave structures are the result of pure internal gravity waves. Horizontal wavelengths of the waves at 65 km altitude are on the order of ≈300–450 km with horizontal phase speeds of roughly 5–10 m/s.     

Insolation in Titan’s troposphere

Seasonality in Titan’s troposphere is driven by latitudinally varying insolation. We show that the latitudinal distributions of insolation in the troposphere and at the surface, based on Huygens DISR measurements, can be approximated analytically with nonzero extinction optical depths τ, and are not equivalent to that at the top of the atmosphere (τ = 0), as has been assumed previously. This has implications for the temperature distribution and the circulation, which we explore with a simple box model. The surface temperature maximum and the upwelling arm of thermally-direct meridional circulation reach the midlatitudes, not the poles, during summertime.     

Saturn’s zonal wind profile in 2004-2009 from Cassini ISS images and its long-term variability

Five years of Cassini Imaging Science Subsystem images, from 2004 to 2009, are analyzed in this work to retrieve global zonal wind profiles of Saturn’s northern and southern hemispheres in the methane absorbing bands at 890 and 727 nm and in their respective adjacent continuum wavelengths of 939 and 752 nm. A complete view of Saturn’s global circulation, including the equator, at two pressure levels, in the tropopause (60 mbar to 250 mbar with the MT filters) and in the upper troposphere (from ∼350 mbar to ∼500 mbar with the CB filter set), is presented. Both zonal wind profiles (available at the Supplementary Material Section), show the same structure but with significant differences in the peak of the eastward jets and the equatorial region, including a region of positive vertical shear symmetrically located around the equator between the 10° < |φ_c| < 25° where zonal velocities close to the tropopause are higher than at 500 mbar. A comparison of previously published zonal wind sets obtained by Voyager 1 and 2 (1980-1981), Hubble Space Telescope, and ground-based telescopes (1990-2004) with the present Cassini profiles (2004-2009) covering a full Saturn year shows that the shape of the zonal wind profile and intensity of the jets has remained almost unchanged except at the equator, despite the seasonal insolation cycle and the variability of Saturn’s emitted power. The major wind changes occurred at equatorial latitudes, perhaps following the Great White Spot eruption in 1990. It is not evident from our study if the seasonal insolation cycle and its associated ring shadowing influence the equatorial circulation at cloud level.     

Meteorological assessment of the surface temperatures on Titan: constraints on the surface type

The latitudinal profile of near-surface air temperature on Titan retrieved by Voyager 1 has been difficult to understand and raised several speculations about possible exotic processes that might be occurring near Titan's surface, while the thermal properties of the surface itself are unknown. This study systematically investigates the seasonal and spatial variation of the surface temperature and air temperature in the lower troposphere by a 3-dimensional general circulation model for different putative surface types (porous icy regolith, rock-ice mixture, hydrocarbon lakes). For any viable surface type the surface temperature is unlikely to be constant through the year and should more or less vary seasonally and even diurnally, most likely by a few K. Recent observations of tropospheric clouds may be evidence of seasonal variation of the surface temperature and the model predicts in the case of solid surface the development of a convective layer with superadiabatic lapse rates near the surface exactly at those latitudes and seasons where clouds have been identified. The latitudinal profile of the surface temperature retrieved from Voyager 1 infrared spectra can be explained without invoking exotic effects, provided the thermal inertia of the surface is relatively small and/or the surface albedo is low. A dominance of water ice (high thermal inertia and high albedo) at the surface is unfavorable to reproduce the observation. The latitudinal gradient of the surface temperature is particularly large at the hydrocarbon lake surface due to low albedo and small surface drag. Local anomalies of the surface albedo or surface thermal inertia are likely to cause substantial inhomogeneities of the surface temperature. Quasi-permanent accumulation of stratospheric haze at both poles would create a perennial equator-to-pole contrast of the surface temperature, but also a substantially lower global-mean surface temperature due to an enhanced anti-greenhouse effect in summer. The air temperature in the lower troposphere exhibits a tiny latitudinal gradient and a pole-to-pole gradient due to the presence of a pole-to-pole Hadley circulation, indicating that the temperature within the planetary boundary layer may exhibit a vertical profile characteristic of season, location and scenario. There may be a shallow near-surface inversion layer in cold seasons and a shallow convective layer in warm seasons.     

Fresh Ammonia Ice Clouds in Jupiter: I. Spectroscopic Identification, Spatial Distribution, and Dynamical Implications

We report the first spectroscopic detection of discrete ammonia ice clouds in the atmosphere of Jupiter, as discovered utilizing the Galileo Near-Infrared Mapping Spectrometer (NIMS). Spectrally identifiable ammonia clouds (SIACs) cover less than 1% of the globe, as measured in complete global imagery obtained in September 1996 during Galileo's second orbit. More than half of the most spectrally prominent SIACs reside within a small latitudinal band, extending from 2° to 7° N latitude, just south of the 5-μm hot spots. The most prominent of these are spatially correlated with nearby 5-μm-bright hot spots lying 1.5°-3.0° of latitude to the north: they reside over a small range of relative longitudes on the eastward side of hot spots, about 37% of the longitudinal distance to the next hot spot to the east. This strong correlation between the positions of hot spots and the most prominent equatorial SIACs suggests that they are linked by a common planetary wave. Good agreement is demonstrated between regions of condensation predicted by the Rossby wave model of A. J. Friedson and G. S. Orton (1999, Bull. Am. Astron. Assoc31, 1155-1156) and the observed longitudinal positions of fresh ammonia clouds relative to 5-μm hot spots. Consistency is also demonstrated between (1) the lifetime of particles as determined by the wave phase speed and cloud width and (2) the sedimentation time for 10-μm radius particles consistent with previously reported ammonia particle size by T. Y. Brooke et al. (1998, Icarus136, 1-13). A young age (<two days) for most SIAC cloud particles is indicated. To the south, the most prominent SIACs are located to the northwest of the Great Red Spot, in a region where a westward flow of jovian air, diverted approximately 10° of latitude northward by the Great Red Spot, encounters a large eastward flow. SIACs have been observed repeatedly by NIMS at this location during Galileo's first four years in Jupiter orbit. It is speculated that due to the three-dimensional interactions of these flows, relatively large amounts of ammonia gas are steadily transported from the sub-cloud troposphere (below the ∼600-mbar level) to the high troposphere, nearly continuously forming fresh ammonia ice clouds to the northwest of the Great Red Spot.     

Net thermal radiation in the atmosphere of Venus

The four entry probes of the Pioneer Venus mission measured the radiative net flux in the atmosphere of Venus at latitudes of 60°N, 31°S, 27°S, and 4°N. The three higher latitude probes carried instruments (small probe net flux radiometers; SNFR) with external sensors. The measured SNFR net fluxes are too large below the clouds, but an error source and correction scheme have been found (H. E. Revercomb, L. A. Sromovsky, and V. E. Suomi, 1982, Icarus52, 279–300). The near-equatorial probe carried an infrared radiometer (LIR) which viewed the atmosphere through a window in the probe. The LIR measurements are reasonable in the clouds, but increase to physically unreasonable levels shortly below the clouds. The probable error source and a correction procedure are identified. Three main conclusions can be drawn from comparisons of the four corrected flux profiles with radiative transfer calculations: (1) thermal net fluxes for the sounder probe do not require a reduction in the Mode 3 number density as has been suggested by O. B. Toon, B. Ragent, D. Colburn, J. Blamont, and C. Cot (1984, Icarus57, 143–160), but the probe measurements as a whole are most consistent with a significantly reduced mode 3 contribution to the cloud opacity; (2) at all probe sites, the fluxes imply that the upper cloud contains a yet undetected source of IR opacity; and (3) beneath the clouds the fluxes at a given altitude increase with latitude, suggesting greater IR cooling below the clouds at high latitudes and water vapor mixing ratios of about 2–5 × 10^?5 near 60°, 2–5 × 10^?4 near 30°, and 5 × 10^?4 near the equator. The suggested latitudinal variation of IR cooling is consistent with descending motions at high latitudes, and it is speculated that it could provide an important additional drive for the general circulation.     

Seasonal change on Saturn from Cassini/CIRS observations, 2004-2009

Five years of thermal infrared spectra from the Cassini Composite Infrared Spectrometer (CIRS) are analyzed to determine the response of Saturn’s atmosphere to seasonal changes in insolation. Hemispheric mapping sequences at 15.0 cm⁻¹ spectral resolution are used to retrieve the variation in the zonal mean temperatures in the stratosphere (0.5-5.0 mbar) and upper troposphere (75-800 mbar) between October 2004 (shortly after the summer solstice in the southern hemisphere) and July 2009 (shortly before the autumnal equinox).Saturn’s northern mid-latitudes show signs of dramatic warming in the stratosphere (by 6-10 K) as they emerge from ring-shadow into springtime conditions, whereas southern mid-latitudes show evidence for cooling (4-6 K). The 40-K asymmetry in stratospheric temperatures between northern and southern hemispheres (at 1 mbar) slowly decreased during the timespan of the observations. Tropospheric temperatures also show temporal variations but with a smaller range, consistent with the increasing radiative time constant of the atmospheric response with increasing pressure. The tropospheric response to the insolation changes shows the largest magnitude at the locations of the broad retrograde jets. Saturn’s warm south-polar stratospheric hood has cooled over the course of the mission, but remains present.Stratospheric temperatures are compared to a radiative climate model which accounts for the spatial distribution of the stratospheric coolants. The model successfully predicts the magnitude and morphology of the observed changes at most latitudes. However, the model fails at locations where strong dynamical perturbations dominate the temporal changes in the thermal field, such as the hot polar vortices and the equatorial semi-annual oscillation (Orton, G., and 27 colleagues [2008]. Nature 453, 196-198). Furthermore, observed temperatures in Saturn’s ring-shadowed regions are larger than predicted by all radiative-climate models to date due to the incomplete characterization of the dynamical response to the shadow. Finally, far-infrared CIRS spectra are used to demonstrate variability of the para-hydrogen distribution over the 5-year span of the dataset, which may be related to observed changes in Saturn’s tropospheric haze in the spring hemisphere.     

The haze and methane distributions on Neptune from HST-STIS spectroscopy

We analyzed a data cube of Neptune acquired with the Hubble STIS spectrograph on August 3, 2003. The data covered the full afternoon hemisphere at 0.1 arcsec spatial resolution between 300 and 1000 nm wavelength at 1 nm resolution. Navigation was accurate to 0.004 arcsec and 0.05 nm. We constrained the vertical aerosol structure with radiative transfer calculations. Ultraviolet data confirmed the presence of a stratospheric haze of optical depth 0.04 at 370 nm wavelength. Bright, discrete clouds, most abundant near latitudes −40° and 30°, had their top near the tropopause. They covered 1.7% of the observed disk if they were optically thick. The methane abundance above the cloud tops was 0.0026 and 0.0017 km-am for southern and northern clouds, respectively, identical to earlier observations by Sromovsky et al. (Sromovsky, L.A., Fry, P.M., Dowling, T.E., Baines, K.H., Limaye, S.S., [2001b]. Icarus 149, 459-488). Aside from these clouds, the upper troposphere was essentially clear. Below the 1.4-bar layer, a vertically uniform haze extended at least down to 10 bars with optical depth of 0.10-0.16/bar, depending on the latitude. Haze particles were bright at wavelengths above 600 nm, but darkened toward the ultraviolet, at the equator more so than at mid and high latitudes. A dark band near −60° latitude was caused by a 0.01 decrease of the single scattering albedo in the visible, which was close to unity. A comparison of methane and hydrogen absorptions contradicted the current view that methane is uniformly mixed in latitude and altitude below the ∼1.5-bar layer. The 0.04 ± 0.01 methane mixing ratio is only uniform at low latitudes. At high southern latitudes, it is depressed roughly between the 1.2 and 3.3-bar layers compared to low-latitude values. The maximum depression factor is ∼2.7 at 1.8 bars. We present models with 2° latitude sampling across the full sunlit globe that fit the observed reflectivities to 2.8% rms.     

Neptune’s cloud and haze variations 1994-2008 from 500 HST-WFPC2 images

The analysis of all suitable images taken of Neptune with the Wide Field Planetary Camera 2 on the Hubble Space Telescope between 1994 and 2008 revealed the following results. The activity of discrete cloud features located near Neptune’s tropopause remained roughly constant within each year but changed significantly on the time scale of ∼5 years. Discrete clouds covered 1% of the disk on average, but more than 2% in 2002. The other ∼99% of the disk probed Neptune’s hazes at lower altitudes. At red and near-infrared wavelengths, two dark bands around −70° and 10° latitude were perfectly steady and originated in the upper two scale heights of the troposphere, either by decreased haze opacity or by an increased methane relative humidity. At blue wavelengths, a dark band between −60° and −30° latitude was most obvious during the early years, caused by dark aerosols below the 3-bar level with single scattering albedos reduced by ∼0.04, and this contrast was constant between 410 and 630 nm wavelength. The dark band decayed exponentially with a time constant of 5 ± 1 years, which can be explained by settling of the dark aerosols at a rate of 1 bar pressure difference per year. The other latitudes brightened with the same time constant but lower amplitudes. The only exception was a darkening event in the 15-30° latitude region between 1994 and 1996, which coincides with two dark spots observed in the same region during the same time period, the only dark spots seen since Voyager. The dark aerosols had a similar latitudinal distribution as the discrete clouds near the tropopause, although both were separated by four scale heights. Photometric analysis revealed a phase coefficient of 0.0028 ± 0.0010 mag/deg for the 0-2° phase-angle range observable from Earth. Neptune’s sub-Earth latitude varied by less than 3° throughout the observation period providing a data set with almost constant viewing geometry. The trends observed up to 2008 continued into 2010 based on images taken with the Wide Field Camera 3.     

Solar radiation incident on Mars and the outer planets: Latitudinal,seasonal, and atmospheric effects

Calculations of the daily solar radiation incident at the tops of the atmospheres of Mars and the outer planets and its variability with latitude and season are presented in a series of figures and tables similar to those for Earth in The Smithsonian Meteorological Tables. The changes in the latitudinal and seasonal distributions of daily surface insolation during the great Martian dust storm of 1971 (when Martian atmospheric optical depth increased from about τ = 0.1 to 2.0 were significant and dramatically illustrate the effect of atmospheric aerosols on surface insolation; i.e., the mean annual daily insolation at the poles decreased by more than a factor of 100 as τ increased from 0.1 to 2.0.     

The insolation at Pluto

Calculations of the daily solar radiation incident at the top of Pluto's atmosphere and its variability with latitude and season and of the latitudinal variation of the mean annual daily insolation are presented. The large eccentricity of Pluto produces significant north-south seasonal asymmetries in the daily insolation. As for Uranus, having a similarly large obliquity, the equator receives less annual average energy than the poles.     

Thermal structure of Saturn from Voyager infrared measurements: Implications for atmospheric dynamics

Saturn atmospheric temperatures at the 150-mbar level retrieved from Voyager IRIS measurements indicate the presence of small-scale meridional gradients which are approximately symmetric with respect to the equator, but are superposed on a large-scale hemispheric thermal asymmetry. Under the assumption that the retrieved values at this atmospheric level represent kinetic temperatures on a constant pressure surface, it is suggested that the small-scale structure is produced by a meriodional circulation associated with the dissipative decay of the zonal winds with height, while the hemispheric asymmetry represents a thermal response to the seasonally varying insolation. The small-scale gradients are correlated with zonal winds derived from Voyager images at mid and high latitudes through the thermal wind relation; the calculated thermal wind shears suggest a decay with height of the jet system toward a state of uniform eatward flow. The existence of the approximately symmetric zonal winds and associated temperature gradients in the presence of a large-scale seasonal thermal response suggests that the jet system is driven at depths substantially below the levels where seasonally modulated insolation is important ($\text{p?0.5}\text{bar}$).     

Jupiter's atmosphere: Observations and interpretation of the microwave spectrum near 1.25-cm wavelength

Measurements of Jupiter's disk-temperature spectrum in the 20- to 24-GHz (1.5 cm < λ < 1.25 cm) region are reported. These data are combined with previously published data to produce a uniformly calibrated thermal spectrum of Jupiter in the wavelength interval 0.85 to 2.1 cm. Model studies are carried out to determine optimum pressure-temperature profiles for an assumed radiative-convective temperature structure. We find the temperature at the 1-bar total effective pressure level is between 140 and 165°K, with a most probable value of 153°K, provided that NH₃ is uniformly saturated in the clouds on a global scale. We show that the temperature profile for the microwave model is ～20°K cooler than the profiles derived from infrared data. An explanation of this discrepancy is discussed in terms of a model which invokes different NH₃ distributions in the belts and zones.     

Solar infrared occultation observations by SPICAM experiment on Mars-Express: Simultaneous measurements of the vertical distributions of H2O, CO2 and aerosol

The infrared AOTF spectrometer is a part of the SPICAM experiment onboard the Mars-Express ESA mission. The instrument has a capability of solar occultations and operates in the spectral range of 1-1.7 μm with a spectral resolution of ∼3.5 cm⁻¹. We report results from 24 orbits obtained during MY28 at Ls 130°-160°, and the latitude range of 40°-55° N. For these orbits the atmospheric density from 1.43 μm CO₂ band, water vapor mixing ratio based on 1.38 μm absorption, and aerosol opacities were retrieved simultaneously. The vertical resolution of measurements is better than 3.5 km. Aerosol vertical extinction profiles were obtained at 10 wavelengths in the altitude range from 10 to 60 km. The interpretation using Mie scattering theory with adopted refraction indices of dust and H₂O ice allows to retrieve particle size (reff∼0.5-1 μm) and number density (∼1 cm⁻³ at 15-30 km) profiles. The haze top is generally below 40 km, except the longitude range of 320°-50° E, where high-altitude clouds at 50-60 km were detected. Optical properties of these clouds are compatible with ice particles (effective radius reff=0.1-0.3 μm, number density N∼10 cm−3) distributed with variance νeff=0.1-0.2 μm. The vertical optical depth of the clouds is below 0.001 at 1 μm. The atmospheric density profiles are retrieved from CO₂ band in the altitude range of 10-90 km, and H₂O mixing ratio is determined at 15-50 km. Unless a supersaturation of the water vapor occurs in the martian atmosphere, the H₂O mixing ratio indicates ∼5 K warmer atmosphere at 25-45 km than predicted by models.     

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.     

A calculation of Saturn's gravitational contraction history

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

Plasma clouds in Saturn's rings

The expansion and ionization of vapor produced by impacts of meteorites on Saturn's rings is described. There is an “impact plasma” produced in the initial collision, and a “secondary plasma” produced by subsequent ionization of the neutral gas ejecta. The dynamics of these plasma clouds, their size, density, and life time are calculated. It is suggested that large clouds, produced by meter-sized meteorites (or a collection of such clouds produced, e.g., by the impact of a swarm of meteorites) may lead to the formation of spokes by the mechanism discussed in Goertz, C. K., and Morfill, G. E. (Icarus53, 219–229, 1983).