Hydrogen Eos at Megabar Pressures and the Search for Jupiter’s Core

The interior structure of Jupiter serves as a benchmark for an entire astrophysical class of liquid–metallic hydrogen-rich objects with masses ranging from ~0.1M _J to ~80M _J (1M _J = Jupiter mass = 1.9e30 g), comprising hydrogen-rich giant planets (mass < 13M _J) and brown dwarfs (mass > 13M _J but ~ < 80M _J), the so-called substellar objects (SSOs). Formation of giant planets may involve nucleated collapse of nebular gas onto a solid, dense core of mass ~0.04M _J rather than a stellar-like gravitational instability. Thus, detection of a primordial core in Jupiter is a prime objective for understanding the mode of origin of extrasolar giant planets and other SSOs. A basic method for core detection makes use of direct modeling of Jupiter’s external gravitational potential terms in response to rotational and tidal perturbations, and is highly sensitive to the thermodynamics of hydrogen at multi-megabar pressures. The present-day core masses of Jupiter and Saturn may be larger than their primordial core masses due to sedimentation of elements heavier than hydrogen. We show that there is a significant contribution of such sedimented mass to Saturn’s core mass. The sedimentation contribution to Jupiter’s core mass will be smaller and could be zero.     

Gravitational signature of rotationally distorted Jupiter caused by deep zonal winds

Both deep zonal winds, if they exist, and the basic rotational distortion of Jupiter contribute to its zonal gravity coefficients J_n for n ? 2. In order to capture the gravitational signature of Jupiter that is caused solely by its deep zonal winds, one must take into account the full effect of rotational distortion by computing the coefficients J_n in non-spherical geometry. This represents a difficult and challenging problem because the widely-used spherical-harmonic-expansion method becomes no longer suitable. Based on the model of a polytropic Jupiter with index unity, we compute Jupiter’s gravity coefficients J₂, J₄, J₆, … , J₁₂ taking into account the full effect of rotational distortion of the gaseous planet using a finite element method. For the model of deep zonal winds on cylinders parallel to the rotation axis, we also compute the variation of the gravity coefficients ΔJ₂, ΔJ₄, ΔJ₆, … , ΔJ₁₂ caused solely by the effect of the winds in non-spherical geometry. It is found that the effect of the zonal winds on lower-order coefficients is weak, ∣ΔJ_n/J_n∣ < 1%, for n = 2, 4, 6, but it is substantial for the high-degree coefficients with n ? 8.     

Slow-mode shock candidate in the Jovian magnetosheath

We discuss some interesting plasma observations in the Jovian magnetosheath by the onboard plasma instruments of the Cassini spacecraft during the 2000-2001 Jupiter flyby. We propose that the observations are consistent with a slow-mode shock transition. In the terrestrial magnetosheath, a number of observations have been made that are consistent with slow-mode waves or shocks. In addition, a number of observations have established that, at least occasionally, slow-mode structures form at the plasma sheet-lobe boundary in the terrestrial magnetotail, related to X lines associated with reconnection. There has been only one previously reported observation of a slow-mode shock-like transition in the Jovian plasma environment. This observation was made in the dayside magnetosheath. The observation we report here was made well downstream of the magnetosphere in Jupiter’s magnetosheath, at local time ∼19:10. For our analysis we have used the data from the Cassini Plasma Spectrometer (CAPS) the Magnetospheric Imaging Instrument (MIMI) and the Magnetometer (MAG). The bow shock crossings observed by Cassini ranged downstream to −600 R_J from the planet     

The deep water abundance on Jupiter: New constraints from thermochemical kinetics and diffusion modeling

We have developed a one-dimensional thermochemical kinetics and diffusion model for Jupiter’s atmosphere that accurately describes the transition from the thermochemical regime in the deep troposphere (where chemical equilibrium is established) to the quenched regime in the upper troposphere (where chemical equilibrium is disrupted). The model is used to calculate chemical abundances of tropospheric constituents and to identify important chemical pathways for CO-CH₄ interconversion in hydrogen-dominated atmospheres. In particular, the observed mole fraction and chemical behavior of CO is used to indirectly constrain the jovian water inventory. Our model can reproduce the observed tropospheric CO abundance provided that the water mole fraction lies in the range (0.25-6.0) × 10⁻³ in Jupiter’s deep troposphere, corresponding to an enrichment of 0.3-7.3 times the protosolar abundance (assumed to be H₂O/H₂ = 9.61 × 10⁻⁴). Our results suggest that Jupiter’s oxygen enrichment is roughly similar to that for carbon, nitrogen, and other heavy elements, and we conclude that formation scenarios that require very large (>8× solar) enrichments in water can be ruled out. We also evaluate and refine the simple time-constant arguments currently used to predict the quenched CO abundance on Jupiter, other giant planets, and brown dwarfs.     

Short-term variability of Jupiter’s extended sodium nebula

Ground-based optical observations of D₁ and D₂ line emissions from Jupiter’s sodium nebula, which extend over several hundreds of jovian radii, were carried out at Mt. Haleakala, Maui, Hawaii using a wide field filter imager from May 19 to June 21, 2007. During this observation, the east-west asymmetry of the nebula with respect to the Io’s orbital motion was clearly identified. Particularly, the D₁+D₂ brightness on the western side of Jupiter is strongly controlled by the Io phase angle. The following scenario was developed to explain this phenomenon as follows: First, more ionospheric ions like NaX⁺, which are thought to produce fast neutral sodium atoms due to a dissociative recombination process, are expected to exist in Io’s dayside hemisphere rather than in the nightside one. Second, it is expected that more NaX⁺ ionospheric ions are picked up by the jovian co-rotating magnetic field when Io’s leading hemisphere is illuminated by the Sun. Third, the sodium atom ejection rate varies with respect to Io’s orbital position as a result of the first two points. Model simulations were performed using this scenario. The model results were consistent with the observation results, suggesting that Io’s ionosphere is expected to be controlled by solar radiation just like Earth.     

Galileo in-situ dust measurements in Jupiter’s gossamer rings

Galileo was the first artificial satellite to orbit Jupiter. During its late orbital mission the spacecraft made two passages through the giant planet’s gossamer ring system. The impact-ionization dust detector on board successfully recorded dust impacts during both ring passages and provided the first in-situ measurements from a dusty planetary ring. During the first passage—on 5 November 2002 while Galileo was approaching Jupiter—dust measurements were collected until a spacecraft anomaly at 2.33R_J (Jupiter radii) just 16 min after a close flyby of Amalthea put the spacecraft into a safing mode. The second ring passage on 21 September 2003 provided ring dust measurements down to about 2.5R_J and the Galileo spacecraft was destroyed shortly thereafter in a planned impact with Jupiter. In all, a few thousand dust impacts were counted with the instrument accumulators during both ring passages, but only a total of 110 complete data sets of dust impacts were transmitted to Earth. Detected particle sizes range from about 0.2 to 5 μm, extending the known size distribution by an order of magnitude towards smaller particles than previously derived from optical imaging [Showalter, M.R., de Pater, I., Verbanac, G., Hamilton, D.P., Burns, J.A., 2008. Icarus 195, 361-377; de Pater, I., Showalter, M.R., Macintosh, B., 2008. Icarus 195, 348-360]. The grain size distribution increases towards smaller particles and shows an excess of these tiny motes in the Amalthea gossamer ring compared to the Thebe ring. The size distribution for the Amalthea ring derived from our in-situ measurements for the small grains agrees very well with the one obtained from images for large grains. Our analysis shows that particles contributing most to the optical cross-section are about 5 μm in radius, in agreement with imaging results. The measurements indicate a large drop in particle flux immediately interior to Thebe’s orbit and some detected particles seem to be on highly-tilted orbits with inclinations up to 20°. Finally, the faint Thebe ring extension was detected out to at least 5R_J, indicating that grains attain higher eccentricities than previously thought. The drop interior to Thebe, the excess of submicron grains at Amalthea, and the faint ring extension indicate that grain dynamics is strongly influenced by electromagnetic forces. These findings can all be explained by a shadow resonance as detailed by Hamilton and Krüger [Hamilton, D.P., Krüger, H., 2008. Nature 453, 72-75].     

Keck adaptive optics images of Jupiter’s north polar cap and Northern Red Oval

We present observations at near-infrared wavelengths (1-5 μm) of Jupiter’s north polar region and Northern Red Oval (NN-LRS-1). The observations were taken with the near-infrared camera NIRC2 coupled to the adaptive optics system on the 10-m W.M. Keck Telescope on UT 21 August 2010. At 5-μm Jupiter’s disk reveals considerable structure, including small bright rings which appear to surround all small vortices. It is striking, though, that no such ring is seen around the Northern Red Oval. In de Pater et al. [2010a. Icarus 210, 742-762], we showed that such rings also exist around all small vortices in Jupiter’s southern hemisphere, and are absent around the Great Red Spot and Red Oval BA. We show here that the vertical structure and extent of the Northern Red Oval is very similar to that of Jupiter’s Red Oval BA. These new observations of the Northern Red Oval, therefore, support the idea of a dichotomy between small and large anticyclones, in which ovals larger than about two Rossby deformation radii do not have 5-μm bright rings. In de Pater et al. [2010a. Icarus 210, 742-762], we explained this difference in terms of the secondary circulations within the vortices. We further compare the brightness distribution of our new 5-μm images with previously published radio observations of Jupiter, highlighting the depletion of NH₃ gas over areas that are bright at 5 μm.     

Numerical theory of the motion of Jupiter’s Galilean satellites

A numerical theory of the motion of Jupiter’s Galilean satellites was constructed using 3767 absolute observations of the satellites. The theory was based on the numerical integration of the equations of motion of the satellites. The integration was carried out by Everhart’s method using the ERA software package developed at the Institute of Applied Astronomy (IAA). Perturbations due to the oblateness of the central planet, perturbations from Saturn and the Sun, and the mutual attraction of the satellites were taken into account in the integration. As a result, the coefficients of the Chebyshev series expansion for coordinates and velocities were found for the period from 1962 to 2010. The initial coordinates and velocities of the satellites, as well as their masses, the mass of Jupiter, and the harmonic coefficient J ₂ of the potential of Jupiter, were adjusted. The resulting ephemerides were compared to those of Lieske and Lainey.     

Empirical models of pressure and density in Saturn's interior: Implications for the helium concentration, its depth dependence, and Saturn's precession rate

We present ‘empirical’ models (pressure vs. density) of Saturn's interior constrained by the gravitational coefficients J₂, J₄, and J₆ for different assumed rotation rates of the planet. The empirical pressure-density profile is interpreted in terms of a hydrogen and helium physical equation of state to deduce the hydrogen to helium ratio in Saturn and to constrain the depth dependence of helium and heavy element abundances. The planet's internal structure (pressure vs. density) and composition are found to be insensitive to the assumed rotation rate for periods between 10h:32m:35s and 10h:41m:35s. We find that helium is depleted in the upper envelope, while in the high pressure region (P?1 Mbar) either the helium abundance or the concentration of heavier elements is significantly enhanced. Taking the ratio of hydrogen to helium in Saturn to be solar, we find that the maximum mass of heavy elements in Saturn's interior ranges from ∼6 to 20 M_⊕. The empirical models of Saturn's interior yield a moment of inertia factor varying from 0.22271 to 0.22599 for rotation periods between 10h:32m:35s and 10h:41m:35s, respectively. A long-term precession rate of about ^0.754″ yr⁻¹ is found to be consistent with the derived moment of inertia values and assumed rotation rates over the entire range of investigated rotation rates. This suggests that the long-term precession period of Saturn is somewhat shorter than the generally assumed value of 1.77×¹⁰⁶ years inferred from modeling and observations.     

Jupiter’s radio spectrum from 74 MHz up to 8 GHz

We carried out a brief campaign in September 1998 to determine Jupiter’s radio spectrum at frequencies spanning a range from 74 MHz up to 8 GHz. Eleven different telescopes were used in this effort, each uniquely suited to observe at a particular frequency. We find that Jupiter’s spectrum is basically flat shortwards of 1-2 GHz, and drops off steeply at frequencies greater than 2 GHz. We compared the 1998 spectrum with a spectrum (330 MHz-8 GHz) obtained in June 1994, and report a large difference in spectral shape, being most pronounced at the lowest frequencies. The difference seems to be linear with log(ν), with the largest deviations at the lowest frequencies (ν).We have compared our spectra with calculations of Jupiter’s synchrotron radiation using several published models. The spectral shape is determined by the energy-dependent spatial distribution of the electrons in Jupiter’s magnetic field, which in turn is determined by the detailed diffusion process across L-shells and in pitch angle, as well as energy-dependent particle losses. The spectral shape observed in September 1998 can be matched well if the electron energy spectrum at L = 6 is modeled by a double power law E^−a (1+(E/E₀))^−b, with a = 0.4, b = 3, E₀ = 100 MeV, and a lifetime against local losses τ₀ = 6 × 10⁷ s. In June 1994 the observations can be matched equally well with two different sets of parameters: (1) a = 0.6, b = 3, E₀ = 100 MeV, τ₀ = 6 × 10⁷ s, or (2) a = 0.4, b = 3, E₀ = 100 MeV, τ₀ = 8.6 × 10⁶ s. We attribute the large variation in spectral shape between 1994 and 1998 to pitch angle scattering, coulomb scattering and/or energy degradation by dust in Jupiter’s inner radiation belts.     

A theoretical model of the bow shock and the magnetosphere of Jupiter

Using the data obtained from the Pioneer 10 and 11 observations, a theoretical model is proposed for the bow shock and the magentosphere of Jupiter. This indicates that the distance of the magnetopause from Jupiter on the sunlit side is (50–55) × r_J (r_J: Jupiter radius, = 7 × 10⁹ cm) and that the ratio of the stand-off distance to this distance is about equal to or slightly larger than unity. Hence the Mach number of the solar wind seems to be less than 1.5 at Jupiter's orbit. This result necessarily leads to a blunt body model of the Jovian magnetosphere, the tail region of which is not as extended as observed in the Earth's case.     

Accretion of Jupiter’s atmosphere from a supernova-contaminated molecular cloud

If Jupiter and the Sun both formed directly from the same well-mixed proto-solar nebula, then their atmospheric compositions should be similar. However, direct sampling of Jupiter’s troposphere indicates that it is enriched in elements such as C, N, S, Ar, Kr, and Xe by 2-6× relative to the Sun (Wong, M.H., Lunine, J.I., Atreya, S.K., Johnson, T., Mahaffy, P.R., Owen, T.C., Encrenaz, T. [2008]. 219-246). Most existing models to explain this enrichment require an extremely cold proto-solar nebula which allows these heavy elements to condense, and cannot easily explain the observed variations between these species. We find that Jupiter’s atmospheric composition may be explained if the Solar System’s disk heterogeneously accretes small amounts of enriched material such as supernova ejecta from the interstellar medium during Jupiter’s formation. Our results are similar to, but substantially larger than, isotopic anomalies in terrestrial material that indicate the Solar System formed from multiple distinct reservoirs of material simultaneously with one or more nearby supernovas (Trinquier, A., Birck, J.-L., Allegre, C.J. [2007]. Astrophys. J. 655, 1179-1185). Such temporal and spatial heterogeneities could have been common at the time of the Solar System’s formation, rather than the cloud having a purely well-mixed ‘solar nebula’ composition.     

The equatorial shape and gravity field of Mercury from MESSENGER flybys 1 and 2

On 14 January and 6 October 2008 the MESSENGER spacecraft passed within 200 km of the surface of Mercury. These flybys by MESSENGER provided the first observations of Mercury from a spacecraft since the Mariner 10 flybys in 1974 and 1975. Data from the Mercury Laser Altimeter (MLA) provided new information on the equatorial shape of Mercury, and Doppler tracking of the spacecraft through the flybys provided new data on the planet’s gravity field. The MLA passes were on opposite hemispheres of the planet and span collectively ∼40% of the equatorial circumference. The mean elevation of topography observed during flyby 1, in the longitude range 0-90°E, is greater than that seen during flyby 2 in the longitude range 180-270°E, indicating an offset between centers of mass and figure having a magnitude and phase in general agreement with topography determined by Earth-based radar. Both MLA profiles are characterized by slopes of ∼0.015° downward to the east, which is consistent with a long-wavelength equatorial shape defined by a best-fitting ellipse. The Doppler tracking data show sensitivity to the gravitational structure of Mercury. The equatorial ellipticity of the gravitational field, C_2,2, is well determined and correlates with the equatorial shape. The S_2,2 coefficient is ∼0, as would be expected if Mercury’s coordinate system, defined by its rotational state, is aligned along its principal axes of inertia. The recovered value of the polar flattening of the gravitational potential, J₂, is considerably lower in magnitude than the value obtained from Mariner 10 tracking, a result that is problematic for internal structure models. This parameter is not as well constrained as the equatorial ellipticity because the flyby trajectories were nearly in the planet’s equatorial plane. The residuals from the Doppler tracking data suggest the possibility of mascons on Mercury, but flyby observations are of insufficient resolution for confident recovery. For a range of assumptions on degree of compensation and crustal and mantle densities, the allowable crustal thickness is consistent with the upper limit of about 100 km estimated from the inferred depth of faulting beneath a prominent lobate scarp, an assumed ductile flow law for crustal material, and the condition that temperature at the base of the crust does not exceed the solidus temperature. The MESSENGER value of C_2,2 has allowed an improved estimate of the ratio of the polar moment of inertia of the mantle and crust to the full polar moment (C_m/C), a refinement that strengthens the conclusion that Mercury has at present a fluid outer core.     

The source of widespread 3-μm absorption in Jupiter’s clouds: Constraints from 2000 Cassini VIMS observations

The Cassini flyby of Jupiter in 2000 provided spatially resolved spectra of Jupiter’s atmosphere using the Visual and Infrared Mapping Spectrometer (VIMS). A prominent characteristic of these spectra is the presence of a strong absorption at wavelengths from about 2.9 μm to 3.1 μm, previously noticed in a 3-μm spectrum obtained by the Infrared Space Observatory (ISO) in 1996. While Brooke et al. (Brooke, T.Y., Knacke, R.F., Encrenaz, T., Drossart, P., Crisp, D., Feuchtgruber, H. [1998]. Icarus 136, 1-13) were able to fit the ISO spectrum very well using ammonia ice as the sole source of particulate absorption, Sromovsky and Fry (Sromovsky, L.A., Fry, P.M. [2010]. Icarus 210, 211-229), using significantly revised NH₃ gas absorption models, showed that ammonium hydrosulfide (NH₄SH) provided a better fit to the ISO spectrum than NH₃, but that the best fit was obtained when both NH₃ and NH₄SH were present in the clouds. Although the large FOV of the ISO instrument precluded identification of the spatial distribution of these two components, the VIMS spectra at low and intermediate phase angles show that 3-μm absorption is present in zones and belts, in every region investigated, and both low- and high-opacity samples are best fit with a combination of NH₄SH and NH₃ particles at all locations. The best fits are obtained with a layer of small ammonia-coated particles (r ∼ 0.3 μm) overlying but often close to an optically thicker but still modest layer of much larger NH₄SH particles (r ∼ 10 μm), with a deeper optically thicker layer, which might also be composed of NH₄SH. Although these fits put NH₃ ice at pressures less than 500 mb, this is not inconsistent with the lack of prominent NH₃ features in Jupiter’s longwave spectrum because the reflectivity of the core particles strongly suppresses the NH₃ absorption features, at both near-IR and thermal wavelengths. Unlike Jupiter, Saturn lacks the broad 3-μm absorption feature, but does exhibit a small absorption near 2.965 μm, which resembles a similar jovian feature and suggests that both planets contain upper tropospheric clouds of sub-micron particles containing ammonia as a minor fraction.     

Predictions on the application of the Hanle effect to map the surface magnetic field of Jupiter

In this paper we evaluate the possibility of detecting, for the first time, the surface magnetic field of Jupiter (∼1 bar level) by observing the change of linear polarization induced by the Hanle effect on the H Lyman-alpha (Lyα) emission line of the planet. We find that, indeed, the Hanle effect, which results from the interaction between a local magnetic field and the atomic polarization induced by absorption of anisotropic radiation, is sensitive to relatively weak values of the strength of the magnetic fields expected on planets. First, we show that for the Lyα emission backscattered by atomic H in the presence of a magnetic field, the Hanle effect is polarizing. This new result is in total contrast to the depolarizing effect predicted and observed for emission lines scattered at right angles in solar prominences. Additionally, to estimate the polarization rate for the case of Jupiter, we have considered three magnetic field models: a dipole field for reference, an O₄ based model [Connerney, J.E.P., 1981. The magnetic field of Jupiter—A generalized inverse approach. J. Geophys. Res. 86, 7679-7693], and finally, an O₆ based model [Khurana, K.K., 1997. Euler potential models of Jupiter's magnetospheric field. J. Geophys. Res. 102, 11295-11306]. In all models, we show that for the jovian backscattered Lyα line, the Hanle effect does enhance the Lyα linear polarization; the polarization rate may exceed 2% at specific regions of the jovian disc, making detection possible either remotely or from an orbiter around Jupiter. In general, depending on the instrumental sensitivity and the observing strategy used, we show that accurate mapping of the linear polarization rate at the planetary surface (thermosphere) or off-disc (corona) may provide a rather accurate estimate of the jovian total magnetic field strength on large area scales.     

On Parameters of the Earth-Like Model of Venus

A brief review on the history of constructing Earth-like models of the Venusian interior is presented. Available observational data are analyzed. An explanation for the anomalously large ratio of the quadrupole gravitational moment J₂ to the small parameter of Venus q is proposed. Thus, estimates were obtained for the precession constant and principal moments of inertia for the Earth-like model of Venus.

     

Formation of the regular satellites of giant planets in an extended gaseous nebula I: subnebula model and accretion of satellites

We model the subnebulae of Jupiter and Saturn wherein satellite accretion took place. We expect each giant planet subnebula to be composed of an optically thick (given gaseous opacity) inner region inside of the planet’s centrifugal radius (where the specific angular momentum of the collapsing giant planet gaseous envelope achieves centrifugal balance, located at rCJ ∼ 15R_J for Jupiter and rCS ∼ 22R_S for Saturn) and an optically thin, extended outer disk out to a fraction of the planet’s Roche-lobe (R_H), which we choose to be ∼R_H/5 (located at ∼150 R_J near the inner irregular satellites for Jupiter, and ∼200R_S near Phoebe for Saturn). This places Titan and Ganymede in the inner disk, Callisto and Iapetus in the outer disk, and Hyperion in the transition region. The inner disk is the leftover of the gas accreted by the protoplanet. The outer disk may result from the nebula gas flowing into the protoplanet during the time of giant planet gap-opening (or cessation of gas accretion). For the sake of specificity, we use a solar composition “minimum mass” model to constrain the gas densities of the inner and outer disks of Jupiter and Saturn (and also Uranus). Our model has Ganymede at a subnebula temperature of ∼250 K and Titan at ∼100 K. The outer disks of Jupiter and Saturn have constant temperatures of 130 and 90 K, respectively.Our model has Callisto forming in a time scale ∼10⁶ years, Iapetus in 10⁶-10⁷ years, Ganymede in 10³-10⁴ years, and Titan in 10⁴-10⁵ years. Callisto takes much longer to form than Ganymede because it draws materials from the extended, low density portion of the disk; its accretion time scale is set by the inward drift times of satellitesimals with sizes 300-500 km from distances ∼100R_J. This accretion history may be consistent with a partially differentiated Callisto with a ∼300-km clean ice outer shell overlying a mixed ice and rock-metal interior as suggested by Anderson et al. (2001), which may explain the Ganymede-Callisto dichotomy without resorting to fine-tuning poorly known model parameters. It is also possible that particulate matter coupled to the high specific angular momentum gas flowing through the gap after giant planet gap-opening, capture of heliocentric planetesimals by the extended gas disk, or ablation of planetesimals passing through the disk contributes to the solid content of the disk and lengthens the time scale for Callisto’s formation. Furthermore, this model has Hyperion forming just outside Saturn’s centrifugal radius, captured into resonance by proto-Titan in the presence of a strong gas density gradient as proposed by Lee and Peale (2000). While Titan may have taken significantly longer to form than Ganymede, it still formed fast enough that we would expect it to be fully differentiated. In this sense, it is more like Ganymede than like Callisto (Saturn’s analog of Callisto, we expect, is Iapetus). An alternative starved disk model whose satellite accretion time scale for all the regular satellites is set by the feeding of planetesimals or gas from the planet’s Roche-lobe after gap-opening is likely to imply a long accretion time scale for Titan with small quantities of NH₃ present, leading to a partially differentiated (Callisto-like) Titan. The Cassini mission may resolve this issue conclusively. We briefly discuss the retention of elements more volatile than H₂O as well as other issues that may help to test our model.     

Mercury: Internal structure and thermal evolution

Astronomical observations and cosmochemical calculations suggest that the planet Mercury may be composed of materials which condensed at relatively high temperatures in the primitive solar nebula and may have a basaltic crust similar to parts of the moon. These findings, plus the long standing inference that Mercury is much richer in metallic iron than the other terrestrial planets, provide important constraints which we apply to models of the thermal evolution and density structure of the planet. The thermal history calculations include explicitly the differing thermal properties of iron and silicates and account for core segregation, melting and differentiation of heat sources, and simulated convection during melting. If the U and Th abundances of Mercury are taken from the cosmochemical model of Lewis, then the planet would have fully differentiated a metal core from the silicate mantle for all likely initial temperature distributions and heat transfer properties. Density distributions for the planet are calculated from the mean density and estimates of the present-day temperature. For the fully differentiated model, the moment of inertia C/MR² is 0.325 (J₂=0.302×10^?6). For models with lower heat source abundances, the planet may not yet have differentiated. The density profiles for such models give C/MR²=0.394 (J₂=0.487×10^?6). These results should be useful for preliminary interpretation of the Mariner 10 measurements of Mercury's gravitational field.     

Persistent rings in and around Jupiter’s anticyclones – Observations and theory

We present observations and theoretical calculations to derive the vertical structure of and secondary circulation in jovian vortices, a necessary piece of information to ultimately explain the red color in the annular ring inside Jupiter’s Oval BA. The observations were taken with the near-infrared detector NIRC2 coupled to the adaptive optics system on the 10-m W.M. Keck telescope (UT 21 July 2006; UT 11 May 2008) and with the Hubble Space Telescope at visible wavelengths (UT 24 and 25 April 2006 using ACS; UT 9 and 10 May 2008 using WFPC2). The spatial resolution in the near-IR (∼0.1–0.15″ at 1–5 μm) is comparable to that obtained at UV–visible wavelengths (∼0.05–0.1″ at 250–890 nm). At 5 μm we are sensitive to Jupiter’s thermal emission, whereas at shorter wavelengths we view the planet in reflected sunlight. These datasets are complementary, as images at 0.25–1.8 μm provide information on the clouds/hazes in the troposphere–stratosphere, while the 5-μm emission maps yield information on deeper layers in the atmosphere, in regions without clouds. At the latter wavelength numerous tiny ovals can be discerned at latitudes between ∼45°S and 60°S, which show up as rings with diameters ?1000 km surrounding small ovals visible in HST data. Several white ovals at 41°S, as well as a new red oval that was discovered to the west of the GRS, also reveal 5-μm bright rings around their peripheries, which coincide with dark/blue rings at visible wavelengths. Typical brightness temperatures in these 5-μm bright rings are 225–250 K, indicative of regions that are cloud-free down to at least the ∼4 bar level, and perhaps down to 5–7 bar, i.e., well within the water cloud.Radiative transfer modeling of the 1–2 μm observations indicates that all ovals, i.e., including the Great Red Spot (GRS), Red Oval BA, and the white ovals at 41°S, are overall very similar in vertical structure. The main distinction between the ovals is caused by variations in the particle densities in the tropospheric–stratospheric hazes (2–650 mbar). These are 5–8 times higher above the red ovals than above the white ones at 41°S. The combination of the 5-μm rings and the vertical structure derived from near-IR data suggests anticyclones to extend vertically from (at least) the water cloud (∼5 bar) up to the tropopause (∼100–200 mbar), and in some cases into the stratosphere.Based upon our observations, we propose that air is rising along the center of a vortex, and descending around the outer periphery, producing the 5-μm bright rings. Observationally, we constrain the maximum radius of these rings to be less than twice the local Rossby deformation radius, L_R. If the radius of the visible oval (i.e., the clouds that make the oval visible) is >3000 km, our observations suggest that the descending part of the secondary circulation must be within these ovals. For the Red Oval BA, we postulate that the return flow is at the location of its red annulus, which has a radius of ∼3000 km.We develop a theory for the secondary circulation, where air is (baroclinically) rising along the center of a vortex in a subadiabatic atmosphere, and descending at a distance not exceeding ∼2× the local Rossby deformation radius. Using this model, we find a timescale for mixing throughout the vortex of order several months, which suggests that the chromophores that are responsible for the red color of Oval BA’s red annulus must be produced locally, at the location of the annulus. This production most likely results from the adiabatic heating in the descending part of the secondary circulation. Such higher-than-ambient temperature causes NH₃–ice to sublime, which will expose the condensation nuclei, such as the red chromophores.     

Perturbation of a satellite orbiter by the oblateness of the primary planet

The perturbation of an orbiter around a large satellite of a giant planet (Jupiter, Saturn, Uranus or Neptune) produced by the oblateness of the planet is investigated. The perturbing force of theJ ₂-term (general case) and theJ ₄-term (special case of small eccentricity and inclination) is expanded in an appropriate form and the main term and the parallactic term are given explicitly. The variations of the orbital elements are derived using the stroboscopic method. An example shows that the perturbation of the orbit cannot be neglected.