Interior Of Jupiter Research Articles

Gravitational Tides in the Outer Planets. II. Interior Calculations and Estimation of the Tidal Dissipation Factor

view Abstract Citations (46) References (32) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Gravitational Tides in the Outer Planets. II. Interior Calculations and Estimation of the Tidal Dissipation Factor Ioannou, Petros J. ; Lindzen, Richard S. Abstract The theory of excitation of tidal oscillations in a fluid planetary body is formulated, and separable equations are derived that extend the results of the classical theory of tides to the nonhydrostatic interiors of planets. The theory is applied to the example of the gravitational tidal response of Jupiter to forcing by Io. The tidal response is found to crucially depend on the static stability in the interior of the planet, the response of the planet being as much as two to three orders of magnitude greater than the response with a neutral interior. The tidal dissipation factor Q is calculated for Jupiter and found to agree with the values required by the astronomical arguments only if the interior has finite (though small static stability. We are led to the conclusion that the interior of Jupiter must have regions which are stably stratified. Publication: The Astrophysical Journal Pub Date: March 1993 DOI: 10.1086/172438 Bibcode: 1993ApJ...406..266I Keywords: PLANETS; OUTER PLANETS; GAS PLANETS; GRAVITY EFFECTS; TIDAL EFFECTS; INTERIOR; DISSIPATION; OSCILLATION; THEORETICAL STUDIES; JUPITER; SATELLITES; IO; STABILITY; STRATIFICATION; CALCULATIONS; ROTATION; PARAMETERS; DISTRIBUTION; ATMOSPHERE; MODEL; ENERGY; PLANETS AND SATELLITES: INDIVIDUAL JUPITER; Planets full text sources ADS | Related Materials (1) Part 1: 1993ApJ...406..252I

Electrical conductivity of Jupiter's shallow interior and the formation of a resonant planetary-ionospheric cavity

The hydrogenic ion composition and electrical conductivity are evaluated for the shallow interior of Jupiter extending from the 1-bar surface to a depth of 4000 km below this level. The atmosphere is assumed to be a mixture of hydrogen and helium with a standard mass density ratio of 78/22. The pressure and temperature are modeled assuming the gas is adiabatic, obeys the perfect gas law, and is in hydrostatic equilibrium. In this preliminary study the effects of impurities are ignored. The densities of free electrons, molecular and atomic hydrogen, and their positive and negative ions are computed assuming the atmosphere is in local thermodynamic equilibrium. From these quanteties are evaluated the electron- and ion-neutral collision frequencies and mobilities, and the electrical conductivity. Results of the calculation show that for a hydrogen/helium atmosphere electrical currents within the shallow interior of Jupiter are carried primarily by molecular hydrogen ions, but with nonnegligible contributions from electrons near the surface, and atomic hydrogen ions at greater depths. The electrical conductivity is sufficiently large to form a conducting “boundary” to electromagnetic waves propagating within the shallow interior. The location of this boundary is frequency dependent, ranging from a depth of 1000 km at 1 mHz to 3000 km at 1 MHz. The existence of a conducting boundary suggests that Jupiter possesses a closed planetary-ionosphere cavity similar to the earth-ionosphere cavity. Preliminary calculations yield eigenfrequencies of approximately 0.76, 1.35, and 1.93 Hz for the lowest three transverse-magnetic normal modes, respectively, with corresponding Q-factors of roughly 7. It is speculated that the normal modes of this system may be excited by Jovian lightning in a manner similar to the terrestrial Schumann resonances. Measurements of these modes could be used to diagnose the conductivity of the shallow interior.

Constraints on the formation of giant planets from their atmospheric chemical composition

There are currently two classes of theories of formation of giant planets: the nucleation model and the gas instability model. The comparison of atmospheric compositions of giant planets permits a test of these. The observed enhancement in CNO compounds in all giant planets, and in deuterium in Uranus, compared with the solar abundance, is consistent with the nucleation model in which a core first grows from accretion of planetesimals and subsequently attracts the surrounding gaseous material of the nebula. However, available data do not permit us to definitively exclude the gas instability model. The agreement of the helium abundance observed in Uranus with the solar value and the depletion observed in Jupiter and Saturn is well explained by the differentiation of helium from metallic hydrogen occurring in the interiors of Jupiter and Saturn but not within Uranus where hydrogen cannot become metallic. Accuratein situmeasurements of elemental and isotopic ratios made aboard atmospheric probes descending into atmospheres of giant planets are indispensable for a firm discrimination between various theories of planetary formation.

Interplanetary dust dynamics: III. Dust released from P/Encke: Distribution with respect to the zodiacal cloud

Numerical simulations of the trajectories of over 200 30-μm-radius dust particles released by Comet P/Encke were designed to study the evolution and redistribution of orbital elements as the dust particles spiral in toward the Sun. The dust assumes Jupiter crossing orbits immediately after release due to radiation pressure, while the comet's orbit remains inside Jupiter's orbital path. By the time the dust particles have spiraled past Jupiter, information on their origin from P/Encke is erased from the distribution in orbital elements. The primary objective of this study is to compare the observed spatial distribution of zodiacal/interplanetary dust with that of the model cloud inside Jupiter's orbit. The observed location of the plane of maximum dust density “symmetry plane” of the zodiacal cloud is compared to a least-square-fit plane of the model cloud. A clear correlation between the two planes is found. The variation of the observed inclination and nodes with heliocentric distance agrees also, at least qualitatively, with that found in the model cloud. The hypothesis that short-period comets may have contributed in a major way to the zodiacal cloud is compatible with these results. The study is directly relevant to, and supports, Whipple's suggestion that Comet P/Encke may have been a major source to the zodiacal cloud.

Interrelations between comets and asteroids

AbstractVarious aspects of comet/asteroid distinctions and interrelations are reviewed with emphasis on recent work and paying special attention to the following problems: characteristics of cometary activity at large heliocentric distance and uniqueness of comet P/Schwassmann-Wachmann 1 with respect to physical properties, the rôle of Trojans and other small bodies in the outer planetary system concerning comet/asteroid classification, possibilities for physical evolution of comets into asteroids, orbital and dynamical overlap of the comet and asteroid populations, and the cometary versus asteroidal origin of Earth-approaching asteroids. With regard to these latter questions it is argued that recent discoveries indicate a more substantial probability for Jupiter family comets to develop into asteroidal objects than earlier believed, and several examples of cometary association for newly discovered Apollo-Amor asteroids are also referred to. However, the fractional cometary contribution to the traditional Apollo-Amor asteroid population (aphelia far inside Jupiter’s orbit) apparently can not yet be reliably estimated.

HIGH PRESSURE PHYSICS AND CHEMISTRY IN GIANT PLANETS AND THEIR SATELLITES

The deep interiors of Jupiter, Saturn, Uranus, Neptune, and their satellites are discussed. The important issues relevant to the physics of condensed matter are identified. The discussion emphasizes H_2, H-He, H_2- H_2O, H_2-CH_4, NH_3, and CH_4·5.75H_2O. Present and future theory and experiment are of great benefit to planetary science.

Computation of Jupiter interior models from gravitational inversion theory

A method for deriving a planetary interior model which exactly satisfies a set of N gravitational constraints is implemented. For Jupiter, recent spacecraft measurements provide the mass, radius at a standard pressure level, rotation law, multipole moments of the internal mass distribution, and constraints on the internal composition and temperature distribution. By appropriate iterations, interior models are found which exactly satisfy these constraints. The models are assumed to have constant chemical composition and constant specific entropy in the hydrogenic envelope. The derived pressure-density relation in the outer envelope depends sensitively on the observational uncertainty in the mass multipole moment J 4. Models are not forced to fit the more indirectly derived constraints, which are instead used as consistency checks. For a helium mass fraction in the envelope ( Y) equal to 0.20, the inferred pressure at a mass density ≈ 0.2 g/cm 3 is about a factor of 2 higher than would be indicated by experimental hydrogen shock compression data in the relevant pressure range of 10 5 to 10 6 bar. The inferred pressure distribution is in much better agreement with the shock data for a nominal Y = 0.30 ± 0.05. This value of Y is interpreted in terms of an enhancement in the envelope, by a factor of order 5 over solar abundance, of species primarily consisting of CH 4, NH 3, and possibly H 2O. The same method is applied to Saturn, but existing uncertainties in Saturn's gravitational parameters are still too large to allow useful conclusions about the composition of its envelope.

The helium abundance of Jupiter from Voyager

The helium abundance in the Jovian atmosphere is derived from Voyager 1 data by two methods. The first method uses only infrared spectra from selected locations on the planet while the second method uses a thermal profile independently derived from radio occultation measurements and infrared spectra recorded near the occultation point. A hydrogen mole fraction of 0.897±0.030 is obtained from the first method, while the second method gives 0.880±0.036, corresponding to helium mass fractions of 0.19±0.05 and 0.21±0.06, respectively. The estimated errors for the first method are primarily due to systematic uncertainties in the H2 and He absorption coefficients, while those for the second method result mainly from errors in the radio occultation profile and are less well known. Random errors in the measured infrared spectra are found to be negligible in both cases. The results are consistent with a uniform mix of hydrogen and helium within Jupiter's interior, but a modest amount of helium depletion (ΔY ≤0.05) cannot be excluded.

THE CONDENSED MATTER PHYSICS OF PLANETARY INTERIORS

The deep interiors of Jupiter and Saturn consist of fluid, metallic hydrogen. In Jupiter the metallic hydrogen is uniformly mixed with helium. In Saturn, the incomplete solubility of helium may cause unmixing and energy release. In the interiors of Uranus and Neptune the fluid mixture (of hydrogen, helium, water, methane and ammonia) is metallic or ionic. The terrestral planetary cores are predominantly metallic iron.

Solar heating and internal heat flow on Jupiter

Models of convection in Jupiter's interior are studied to test the hypothesis that internal heat balances the absorbed sunlight at each latitude. Such a balance requires that the ratio of total emitted heat to absorbed sunlight be above a critical value 4/π ≈ 1.27. The necessary horizontal heat transport then takes place in the interior instead of in the atmosphere. Regions of stable stratification can arise in the interior owing to the effects of solar heating and rotation. In such regions, upward heat transfer takes place on sloping surfaces, as in the Earth's atmosphere, provided there are horizontal temperature gradients. Potential temperature gradients are found to be small, and the time constant for the pattern to reach equilibrium is found to be short compared to the age of the solar system. It is suggested that Jupiter and Saturn owe their axisymmetric appearance to internal heat flow, which eliminates differential heating in the atmosphere that would otherwise drive meridional motions.

Photometry and polarimetry of Jupiter at large phase angles: I. Analysis of imaging data of a prominent belt and a zone from pioneer 10

Limb-darkening curves are derived from Pioneer 10 imaging data for Jupiter's STrZ (−18 to −21° latitude) and SEBn (−5 to −8° latitude) in red and blue light at phase angles of 12, 23, 34, 109, 120, 127, and 150°. Inhomogeneous scattering models are computed and compared with the data to constrain the vertical structure and the single-scattering phase functions of the belt and the zone in each color. The very high brightness observed at a 150° phase angle seems to require the presence of at lleast a thin layer of reasonably bright and strongly forward-scattering haze particles at pressure levelsof about 100 mbar or less above both belts and zones. Marginally successful models have been constructed in which a moderate optical thickness ( τ ≥ 0.5) of haze particles was uniformly distributed in the upper 25 km-amagats of H 2. Excellent fits to the data were obtained with models having a thin (optical depths of a few tenths) haze conentraated above most of the gas. Following recent spectrospcopicanalyses, we have placed the main “cloud” layer or layers beneath about 25 km-amagats of H 2, although successful fits to our continuum data probably could be achieved also if the clouds were permitted to extend all the way up to the thin haze layer. Similarly, below the haze level our data cannot distinguish between models having two clouds separated by a clear space as suggested by R. E. Danielson and M. G. Tomasko and models with a single extensive diffuse cloud having an H 2 abundance of a few kilometer-amagats per scattering mean free path as described by W. D. Cochran. In either case, the relative brightness of the planet at each phase angle primarily serves to constrain the single-scattering phase functions of the Jovian clouds at the corresponding scattering angles. The clouds in these models are characterized by single-scattering phase functions having strong forward peaks and modest backward-scattering peaks, indicating cloud particles with dimensions larger than about 0.6 μm. In our models, a lower single-scattering albedo of the cloud particles in the belt relative to the zone accounts for the contrast between these regions. If an increased abundance of absorbing dust above uniformly bright clouds is used to explain the contrast between belts and zones at visible wavelengths, the limb darkening is steeper than that observed for the SEBn in blue light at small phase angles. The phase integral for the planet calculated for either the belt or the zone model in either color lies in the range 1.2 to 1.3. If a value of 1.25 is used with D.J. Taylor's bolometric geometric albedo of 0.28, the planet emits 2.25 or 1.7 times the energy it absorbs from the Sun if it effective temperature is 134 or 125°K, respectively—roughly as expected from current theories of the cooling of Jupiter's interior.

Phase separation for a dense fluid mixture of nuclei

It is shown by Monte Carlo calculations that fluid mixtures of classical point ions in an uniform electron-gas background separate into two phases primarily from potential-energy considerations. For protons and ..cap alpha.. particles the critical temperature over an enormous pressure range is found to be near 1 eV, and only at extremely high pressures (approx.10/sup 8/ Mbar) does the mixture become stable. Phase separation at lower pressures, as in the interior of Jupiter (approx.40 Mbar, 1 eV), is shown to be unlikely on the basis of more realistic models which modify, however crudely, the uniform electron approximation.

Phase separation of metallic hydrogen-helium alloys

Calculations are presented for the thermodynamic functions and phase-separation boundaries of solid metallic hydrogen-helium alloys at temperatures between zero and 19,000 K and at pressures between 15 and 90 Mbar. Expressions for the band-structure energy of a randomly disordered alloy (including third order in the electron-ion interaction) are derived and evaluated. Short- and long-range orders are included by the quasi-chemical method, and lattice dynamics in the virtual-crystal harmonic approximation. It is concluded that at temperatures below 4000 K, there is essentially complete phase separation of hydrogen-helium alloys and that a miscibility gap remains at the highest temperatures and pressures considered. The relevance of these results to models of the deep interior of Jupiter is briefly discussed.

The abundance of water and rock in Jupiter as derived from interior models

Models of Jupiter's interior were computed using a new molecular hydrogen equation of state, and a more precise algorithm for computing gravitational moments. Models with H/H e ratios of 13.5, 11.25, and 10 were computed, and it was found that the models had rocky cores of 16 to 18 Earth masses and envelopes with 20 to 50 Earth masses of water. Models with temperatures of less than 180°K at 1 bar had water-to-rock ratios which were less than the solar value, thus removing a difficulty of previous computations. Models were also constructed in which rock was put into the envelope in place of water. It was found that, to a good approximation, a given mass of rock will replace an equal mass of water. At present the two cases are indistinguishable.

Statistical mechanics of dense ionized matter. VI. Electron screening corrections to the thermodynamic properties of the one-component plasma

The thermodynamic properties of one-component ionic plasmas in a responding (polarized) background of fully degenerate electrons are calculated over a wide range of temperatures and densities. The weak and intermediate screening regimes are treated by two complementary methods which take the one-component plasma in a rigid background as a starting point. Thermodynamic perturbation theory is used in the weakly screened ionic plasma typical of white-dwarf matter; this leads to simple, analytic expressions for the thermodynamic properties. Relativistic effects in the very dense electron gas are considered explicitly. A variational method, based on the Gibbs-Bogolyubov inequality, and the physical idea of an effective charge reduction of the ions, yields satisfactory results in the intermediate screening regime typical of the deep interior of Jupiter. Our results are in good agreement with the available Monte Carlo data and represent a significant improvement over previous calculations based on a hard-sphere reference system.

Heat transport in a stratified two-phase fluid

A self-gravitating fluid, stratified into two phases of appreciably different densities and heated from within is considered. The heat flux, viscosity, and thermal diffusivity are assumed to be small enough to that, away from the interface between the phases, the flux is mainly carried by turbulent convection with a very small superadiabaticity. Different modes are investigated for transporting the heat flux across the interface, and both possible signs of the latent heat L are considered. A thermal boundary layer, distortion of the interface, and the nucleation, growth and motion of droplets and bubbles are included. It is shown that, under a specified range of conditions, the transition region near the interface is thin with a small change in the temperature T across it. The entropy difference between the two phases is then L/T. These considerations probably apply to the interior of Jupiter.

Gravity Field of Jupiter from Pioneer 11 Tracking Data

Significantly improved values of the zonal gravity harmonic coefficients J(39) J(4), and J(6) of Jupiter have been obtained from a preliminary analysis of Pioneer 11 spacecraft Doppler data taken while the spacecraft was near Jupiter. The new results, which will have an important application as boundary conditions for theoretical models of Jupiter's interior. are consistent with a planet in hydrostatic equilibrium.

Interior of Jupiter

Interior of Jupiter

A new nodal expansion for classical plasmas

In calculating the equation of state for plasmas we find that diagrammatic expansions for the free energy become unwieldy at high density. At best, many terms must be retained in order to obtain meaningful results. We present a new expansion technique which can be applied to plasmas in the interiors of Jupiter and white dwarf stars. In such cases the older techniques are unsatisfactory because of the size of the ion coupling parameter. Our work yields expansions for which this parameter is supplanted by ion correlation functions, which can be supplied by external computations. In this paper we assume a two-species plasma of classical particles, thereby focusing on combinatorial techniques. The final result is a new nodal expansion in terms of ion correlation functions and an electron coupling parameter.

Cosmogony of the asteroidal belt

In the plot of asteroids considered the mass density is substituted for the number density. This approach provides a better definition of the limits of the main belt, and demonstrates more clearly that the asteroids, like the Saturnian rings, have condensed from partially corotating plasma. A diagram shows that the whole main belt is located below 2/3 of Jupiter's orbit. This means that the main belt asteroids may have been derived from condensation which took place inside Jupiter's orbit.