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.     

Deciphering the origin of the regular satellites of gaseous giants - Iapetus: The Rosetta ice-moon

Ever since their discovery the regular satellites of Jupiter and Saturn have held out the promise of providing an independent set of observations with which to test theories of planet formation. Yet elucidating their origins has proven elusive. Here we show that Iapetus can serve to discriminate between satellite formation models. Its accretion history can be understood in terms of a two-component gaseous subnebula, with a relatively dense inner region, and an extended tail out to the location of the irregular satellites, as in the SEMM model of Mosqueira and Estrada (2003a,b) (Mosqueira, I., Estrada, P.R. [2003a]. Icarus 163, 198-231; Mosqueira, I., Estrada, P.R. [2003b]. Icarus 163, 232-255). Following giant planet formation, planetesimals in the feeding zone of Jupiter and Saturn become dynamically excited, and undergo a collisional cascade. Ablation and capture of planetesimal fragments crossing the gaseous circumplanetary disks delivers enough collisional rubble to account for the mass budgets of the regular satellites of Jupiter and Saturn. This process can result in rock/ice fractionation as long as the make up of the population of disk crossers is non-homogeneous, thus offering a natural explanation for the marked compositional differences between outer solar nebula objects and those that accreted in the subnebulae of the giant planets. For a given size, icy objects are easier to capture and to ablate, likely resulting in an overall enrichment of ice in the subnebula. Furthermore, capture and ablation of rocky fragments become inefficient far from the planet for two reasons: the gas surface density of the subnebula is taken to drop outside the centrifugal radius, and the velocity of interlopers decreases with distance from the planet. Thus, rocky objects crossing the outer disks of Jupiter and Saturn never reach a temperature high enough to ablate either due to melting or vaporization, and capture is also greatly diminished there. In contrast, icy objects crossing the outer disks of each planet ablate due to the melting and vaporization of water-ice. Consequently, our model leads to an enhancement of the ice content of Iapetus, and to a lesser degree those of Titan, Callisto and Ganymede, and accounts for the (non-stochastic) compositions of these large, low-porosity outer regular satellites of Jupiter and Saturn. For this to work, the primordial population of planetesimals in the Jupiter-Saturn region must be partially differentiated, so that the ensuing collisional cascade produces an icy population of ?1 m size fragments to be ablated during subnebula crossing. We argue this is likely because the first generation of solar nebula ∼10 km planetesimals in the Jupiter-Saturn region incorporated significant quantities of ²⁶Al. This is the first study successfully to provide a direct connection between nebula planetesimals and subnebulae mixtures with quantifiable and observable consequences for the bulk properties of the regular satellites of Jupiter and Saturn, and the only explanation presently available for Iapetus’ low density and ice-rich composition.     

Characteristic features in the spectra of Europa, Ganymede, and Callisto

The results of ground-based spectrophotometry of the icy Galilean satellites of Jupiter—Europa, Ganymede, and Callisto—are discussed. The observations were carried out in the 0.39–0.92 μm range with the use of the CCD spectrometer mounted on the 1.25-m telescope of the Crimean laboratory of the Sternberg Astronomical Institute in March 2004. It is noted that the calculated reflectance spectra of the satellites mainly agree with the analogous data of the earlier ground-based observations and investigations in the Voyager and Galileo space missions. The present study was aimed at identifying new weak absorption bands (with the relative intensity of ～3–5%) in the reflectance spectra of these bodies with laboratory measurements (Landau et al., 1962; Ramaprasad et al., 1978; Burns, 1993; Busarev et al., 2008). It has been ascertained that the spectra of all of the considered objects contain weak absorption bands of molecular oxygen adsorbed into water ice, which is apparently caused by the radiative implantation of O⁺ ions into the surface material of the satellites in the magnetosphere of Jupiter. At the same time, spectral features of iron of different valence (Fe²⁺ and Fe³⁺) values typical of hydrated silicates were detected on Ganymede and Callisto, while probable indications of methane of presumably endogenous origin, adsorbed into water ice, were found on Europa. The reflectance spectra of the icy Galilean satellites were compared to the reflectance spectra of the asteroids 51 Nemausa (C-class) and 92 Undina (X-class).     

Multiple-satellite-aided capture trajectories at Jupiter using the Laplace resonance

Satellite-aided capture is a mission design concept used to reduce the delta-v required to capture into a planetary orbit. The technique employs close flybys of a massive moon to reduce the energy of the planet-centered orbit. A sequence of close flybys of two or more of the Galilean moons of Jupiter may further decrease the delta-v cost of Jupiter orbit insertion. A Ganymede-Io sequence can save 207 m/s of delta-v over a single Io flyby. A phase angle analysis based on the Laplace resonance is used to find triple-satellite-aided capture sequences involving Io, Europa, and Ganymede. Additionally, the near-resonance of Callisto and Ganymede is used to find triple-satellite-aided capture sequences involving Callisto, Ganymede, and another moon. A combination of these techniques is used to find quadruple-satellite-aided capture sequences that involve gravity-assists of all four Galilean moons. These sequences can save a significant amount of delta-v and have the potential to benefit both NASA’s Jupiter Europa orbiter mission and ESA’s Jupiter Ganymede orbiter mission.     

The Q Values of the Galilean Satellites and their Tidal Contributions to the Deceleration of Jupiter''''s Rotation

The relationship between the k2/Q of the Galilean satellites and the k2J/QJ of Jupiter is derived from energy and momentum considerations. Calculations suggest that the Galilean satellites can be divided into two classes according to their Q values: Io and Ganymede have values between 10 and 50, while Europa and Callisto have values ranging from 200 to 700. The tidal contributions of the Galilean satellites to Jupiter's rotation are estimated. The main deceleration of Jupiter, which is about 99.04% of the total, comes from Io.     

Meteoritical and dynamical constraints on the growth mechanisms and formation times of asteroids and Jupiter

Thermal models and radiometric ages for meteorites show that the peak temperatures inside their parent bodies were closely linked to their accretion times. Most iron meteorites come from bodies that accreted <0.5 Myr after CAIs formed and were melted by ²⁶Al and ⁶⁰Fe, probably inside 2 AU. Rare carbon-rich differentiated meteorites like ureilites probably also come from bodies that formed <1 Myr after CAIs, but in the outer part of the asteroid belt. Chondrite groups accreted intermittently from diverse batches of chondrules and other materials over a 4 Myr period starting 1 Myr after CAI formation when planetary embryos may already have formed at ∼1 AU. Meteorite evidence precludes accretion of late-forming chondrites on the surface of early-formed bodies; instead chondritic and non-chondritic meteorites probably formed in separate planetesimals. Maximum metamorphic temperatures in chondrite groups are correlated with mean chondrule age, as expected if ²⁶Al and ⁶⁰Fe were the predominant heat sources. Because late-forming bodies could not accrete close to large, early-formed bodies, planetesimal formation may have spread across the nebula from regions where the differentiated bodies formed. Dynamical models suggest that the asteroids could not have accreted in the main belt if Jupiter formed before the asteroids. Therefore Jupiter probably reached its current mass >3-5 Myr after CAIs formed. This precludes formation of Jupiter via a gravitational instability <1 Myr after the solar nebula formed, and strongly favors core accretion. Jupiter probably formed too late to make chondrules by generating shocks directly, or indirectly by scattering Ceres-sized bodies across the belt. Nevertheless, shocks formed by gravitational instabilities or Ceres-sized bodies scattered by planetary embryos may have produced some chondrules. The minimum lifetime for the solar nebula of 3-5 Myr inferred from the total spread of CAI and chondrule ages may exceed the median lifetime of 3 Myr for protoplanetary disks, but is well within the 1-10 Myr observed range. Shorter formation times for extrasolar planets may help to explain their unusual orbits compared to those of solar giant planets.     

Formation of the regular satellites of giant planets in an extended gaseous nebula II: satellite migration and survival

For a satellite to survive in the disk the time scale of satellite migration must be longer than the time scale for gas dissipation. For large satellites (∼1000 km) migration is dominated by the gas tidal torque. We consider the possibility that the redistribution of gas in the disk due to the tidal torque of a satellite with mass larger than the inviscid critical mass causes the satellite to stall and open a gap (W.R. Ward, 1997, Icarus 26, 261-281). We adapt the inviscid critical mass criterion to include gas drag, and m-dependent nonlocal deposition of angular momentum. We find that such a model holds promise of explaining the survival of satellites in the subnebula, the mass versus distance relationship apparent in the saturnian and uranian satellite systems, the concentration of mass in Titan, and the observation that the satellites of Jupiter get rockier closer to the planet whereas those of Saturn become increasingly icy. It is also possible that either weak turbulence (close to the planet) or gap-opening satellite tidal torque removes gas on a similar time scale (10⁴-10⁵ years) as the orbital decay time of midsized (200-700 km) regular satellites forming in the inner disk (inside the centrifugal radius (I. Mosqueira and P.R. Estrada, 2003, Icarus, this issue)). We argue that Saturn’s satellite system bridges the gap between those of Jupiter and Uranus by combining the formation of a Galilean-sized satellite in a gas optically thick subnebula with a strong temperature gradient, and the formation of smaller satellites, closer to the planet, in a disk with gas optical depth ?1, and a weak temperature gradient.Using an optically thick inner disk (given gaseous opacity), and an extended, quiescent, optically thin outer disk, we show that there are regions of the disk of small net tidal torque (even zero) where satellites (Iapetus-sized or larger) may stall far from the planet. For our model these outer regions of small net tidal torque correspond roughly to the locations of Callisto and Iapetus. Though the precise location depends on the (unknown) size of the transition region between the inner and outer disks, the result that Saturn’s is found much farther out (at ∼3rcS, where rcS is Saturn’s centrifugal radius) than Jupiter’s (at ∼ 2rcJ, where rcJ is Jupiter’s centrifugal radius) is mostly due to Saturn’s less massive outer disk and larger Hill radius. However, despite the large separation between Ganymede and Callisto and Titan and Iapetus, the long formation and migration time scales for Callisto and Iapetus (I. Mosqueira and P.R. Estrada, 2003, Icarus, this issue) makes it possible (depending on the details of the damping of acoustic waves) that the tidal torque of Ganymede and Titan clears the gas disk out to their location, thus stranding Callisto and Iapetus far from the planet. Either way, our model provides an explanation for the presence of regular satellites outside the centrifugal radii of Jupiter and Saturn, and the absence of such a satellite for Uranus.     

Some dynamical aspects of the accretion of Uranus and Neptune: The exchange of orbital angular momentum with planetesimals

The final stage of the accretion of Uranus and Neptune is numerically investigated. The four Jovian planets are considered with Jupiter and Saturn assumed to have reached their present sizes, whereas Uranus and Neptune are taken with initial masses 0.2 of their present ones. Allowance is made for the orbital variation of the Jovian planets due to the exchange of angular momentum with interacting bodies (“planetesimals”). Two possible effects that may have contributed to the accretion of Uranus and Neptune are incorporated in our model: (1) an enlarged cross section for accretion of incoming planetesimals due to the presence of extended gaseous envelopes and/or circumplanetary swarms of bodies; and (2) intermediate protoplanets in mid-range orbits between the Jovian planets. Significant radial displacements are found for Uranus and Neptune during their accretion and scattering of planetesimals. The orbital angular momentum budgets of Neptune, Uranus, and Saturn turn out to be positive; i.e., they on average gain orbital angular momentum in their interactions with planetesimals and hence they are displaced outwardly. Instead, Jupiter as the main ejector of bodies loses orbital angular momentum so it moves sunward. The gravitational stirring of planetesimals caused by the introduction of intermediate protoplanets has the effect that additional solid matter is injected into the accretion zones of Uranus and Neptune. For moderate enlargements of the radius of the accretion cross section (2–4 times), the accretion time scale of Uranus and Neptune are found to be a few 10⁸ years and the initial amount of solid material required to form them of a few times their present masses. Given the crucial role played by the size of the accretion cross section, questions as to when Uranus and Neptune acquired their gaseous envelopes, when the envelopes collapsed onto the solid cores, and how massive they were are essential in defining the efficiency and time scale of accretion of the two outer Jovian planets.     

Galilean satellites: 1976 radar results

Radar observations of the Galilean satellites, made in late 1976 using the 12.6-cm radar system of the Arecibo Observatory, have yielded mean geometric albedos of 0.04 ± , 0.69 ± 0.17, 0.37 ± 0.09, and 0.15 ± 0.04, for Io, Europa, Ganymede, and Callisto, respectively. The albedo for Io is about 40% smaller than that obtained approximately a year earlier, while the albedos for the outer three satellites average about 70% larger than the values previously reported for late 1975, raising the possibility of temporal variation. Very little dependence on orbital phase is noted; however, some regional scattering inhomogeneities are seen on the outer three satellites. For Europa, Ganymede, and Callisto, the ratios of the echo received in one mode of circular polarization to that received in the other were: 1.61 ± 0.20 1.48 ± 0.27, and 1.24 ± 0.19, respectively, with the dominant component having the same sence of circularity as that transmitted. This behavior has not previously been encountered in radar studies of solar system objects, whereas the corresponding observations with linear polarization are “normal.” Radii determined from the 1976 radar data for Europa and Ganymede are: 1530 ± 30 and 2670 ± 50 km, in fair agreement with the results from the 1975 radar observations and the best recent optical determinations. Doppler shifts of the radar echoes, useful for the improvement of the orbits of Jupiter and some of the Galilean satellites, are given for 12 nights in 1976 and 10 nights in 1975.     

Chaos induced by De Haerdtl inequality in the Galilean system

This paper aims at studying the long-term orbital consequences of the perturbations related to De Haerdtl inequality, a current quasi-commensurability between the Galilean satellites of Jupiter Ganymede and Callisto. We used the method of Frequency Map Analysis to detect a chaotic behavior in a 5-bodies system where every inequality has been dropped, except of De Haerdtl one. We also used Frequency Analysis to draw the behavior of the arguments likely to become resonant, in several numerical integrations. We show that De Haerdtl inequality might have induced chaos in the past if Ganymede's and Callisto's eccentricities have been higher than 4×¹⁰⁻³. Moreover, we enlight the influence of Jupiter's obliquity on this chaos. We also enlight some aspects of this chaotic behavior, showing for instance stable chaos and single resonances. The main result of this study is that De Haerdtl inequality should be taken into account in every study of the long term orbital evolution of the Galilean satellites.     

Planetesimal dissolution in the envelopes of the forming,giant planets

We have assessed the ability of planetesimals to penetrate through the envelopes of growing giant planets that form by a “core-instability” mechanism. According to this mechanism, a core grows by the accretion of solid bodies in the solar nebula and the growing core becomes progressively more effective in gravitationally concentrating gas from the surrounding solar nebula in an envelope until a “runaway” accretion of gas occurs. In performing this assessment, we have considered the ability of gas drag to slow down a planetesimal; the effectiveness of gas dynamical pressure in fracturing and ultimately finely fragmenting it; the ability of its strength and self-gravity to resist such fracturing; and the degree to which it is evaporated due to heating by the surrounding envelope, including shock heating that develops during the supersonic portion of its trajectory. We also consider what happens if the planetesimal is able to reach the core at free-fall velocity and the ability of the envelope to convectively mix dissolved materials to different radial distances. These calculations were performed for various epochs in the growth of a giant planet with the model envelopes derived by Bodenheimer and Pollack (1986,67, 391–408). As might have been anticipated, our results vary significantly with the size of the planetesimal, its composition, and the stage of growth of the giant planet and hence the mass of its envelope. Over much of the growth phase of the core, prior to its reaching its critical mass for runaway gas accretion, icy planetesimals less than about 1 m in size dissolve in the outer region of the envelope, ones larger than about 1 m and smaller than about 1 km dissolve in the middle region of the envelope, ones larger than 1 km either reach the core interface or dissolve in the deeper regions of the envelope. Similarly rocky planetesimals smaller than about a kilometer dissolve in the middle portion of the envelope, while larger ones can penetrate more deeply. Furthermore, the convection zones of the envelopes during this stage are confined to localized regions and hence dissolved materials experience little radial mixing then. Thus, if much of the accreted mass is contained in planetesimals larger than about a kilometer, the critical core mass for runaway accretion is not expected to change significantly when planetesimal dissolution is taken into account. After accretion is terminated and the planet contracts toward its present size, the convection zone grows until it encompasses the entire envelope. Therefore, dissolved material should eventually become well mixed through the envelope. We proposed that the envelopes of the giant planets should contain significant enhancements above solar proportions in the abundances of virtually all elements relative to that of hydrogen, with the magnitude of the enhancement increasing approximately linearly with the ratio of the high Z mass to the (H, He) mass for the bulk of the planet. This prediction is in accord both qualitatively and quantitatively with the systematic increase in the atmospheric C/H ratio from Jupiter to Saturn to Uranus and Neptune and semiquantitatively with the results of recent interior models of the giant planets. It is not clear whether it is consistent with the abundances of H₂O and NH₃ in the atmospheres of some of the outer planets. Finally, the complete reduction of some dissolved materials, especially C containing compounds, is expected to consume some of the H₂ in the envelopes. Consequently, the He/H₂ ratios in the atmospheres of Uranus and Neptune may be slightly enhanced over the solar ratio. We estimate that the He/H₂ ratios for Uranus' and Neptune's atmospheres should be about 6 and 15% larger, respectively, than the solar ratio.     

The eruptive evolution of the Galilean satellites: Implications for the ancient magnetic field of Jupiter

The hypothesis considering the Jupiter-Sun system as a limiting case of a close binary star implies the initial relative ice abundances in all the Galilean satellites to be essentially equal. The satellites move in the Jovian magnetosphere; thus the unipolar current flowing through their bodies subjected their ices to volumetric electrolysis. Explosions of the electrolysis products resulted in a loss of ices. While Callisto did not explode at all, Ganymede exploded once, Europa twice, and Io two or three times. An analysis of the magnetic field changes needed to create the modern ice abundances in the satellite shows:

1. the initial field of Jupiter was ～10² times stronger when compared with the present-day field, and
2. the field had to decrease exponentially with τ_2| ≈ (0.6?1), which means its relic nature.

     

伽利略卫星的平衡形状参数和潮汐耗散因子

木星的四颗大卫星都是同步轨旋卫星，常被称为伽利略卫星，美国发射的伽利略飞船自1995年12月抵达木星系统后，的几年来对木星的四颗伽利略卫星进行了一系列的探测，利用飞船探测的最新资料作为约束条件，建立了伽利略卫星的一组内部结构模型，然后按照同步轨旋卫星的形态理论公式计算了它们的平衡形太参数及潮汐耗散因子等。     

Optical polarimetry of the Galilean satellites of Jupiter

New measurements of the amount of polarization of the Galilean satellites are given and, within the context of other data, are interpreted as follows. The polarization of Europa is consistent with a water-frost surface. Io has a surface of partly absorbing crystals thought to result from evaporates released from the mantle and damaged by radiation. Ganymede has alternating water-frost areas and darker terrain, possibly of a silicaceous nature. Callisto is explained as having a mantle of ice containing embedded blocks of rocks, which occurred when recent evaporation left the blocks piled at the surface in a chaotic manner. This event occurred after the vicinity of Jupiter had been cleared of small orbiting objects able to impact Callisto. Meteorites which continue to enter within the sphere of influence of Jupiter can collide with Callisto only on its leading hemisphere, which is thereby comminuted by impacts. The surface of the trailing hemisphere is not regolithic.     

Radar observations of the icy Galilean satellites

We report 12.6-cm-wavelength radar observations of Europa, Ganymede, and Callisto made at the Arecibo Observatory in November 1977 and February 1979. When combined with previous observations, our results establish firmly the distinguishing radar properties of these satellites: (i) high geometric albedos, α; (ii) circular polarization ratios, μ_C, which anomalously exceed unity; (iii) linear polarization ratios, μ_L, which are approximately 0.5; and (iv) diffuse scattering which varies as cosⁿθ, where θ is angle of incidence and 1 ? n ? 2. We tabulate weighted-mean values of α, μ_C, μ_L, and n derived from observations between 1975 and 1979. The values of μ_C for Ganymede and Europa are nearly identical and significantly larger than that for Callisto. The values of n for Ganymede and Callisto are nearly identical and significantly smaller than that for Europa. Although significant albedo and/or polarization features are common in the radar spectra, the fractional rms fluctuation in disk-integrated properties is only ～10%. No time variation in the radar properties has been evident during 1976–1979.     

Origin,Bulk Chemical Composition And Physical Structure Of The Galilean Satellites Of Jupiter: A Post-Galileo Analysis

The origin of Jupiter and the Galilean satellite system is examinedin the light of the new data that has been obtained by the NASA Galileo Project. In particular, special attention is given to a theory of satellite origin which was put forward at the start of the Galileo Mission and on the basis of which several predictions have now been proven successful (Prentice, 1996a–c). These predictions concern the chemical composition of Jupiter's atmosphere and the physical structure of the satellites. According to the proposed theory of satellite origin, each of the Galilean satellites formed by chemical condensation and gravitational accumulation of solid grains within a concentricfamily of orbiting gas rings. These rings were cast off equatorially by the rotating proto-Jovian cloud (PJC) which contracted gravitationally to form Jupiter some 4 billion years ago. The PJC formed from the gas and grains left over from the gas ring that had been shed at Jupiter's orbit by the contracting proto-solar cloud (PSC). Supersonic turbulentconvection provides the means for shedding discrete gas rings.The temperatures T_n of the system of gas rings shed by the PSCand PJC vary with their respective mean orbital radii R_n (n = 0, 1, 2, Ϊ ) according as T_n ∝ R_n ^-0.9. If the planet Mercury condenses at 1640 K, so accounting for the high density ofthat planet via a process of chemical fractionation between iron and silicates, then T_n at Jupiter's orbit is 158 K. Only 35% of the water vapour condenses out. Thus fractionation between rock and ice, together with an enhancement in the abundance of solids relative to gas which takes place through gravitational sedimentation of solids onto the mean orbit of the gas ring, ensures nearly equal proportions of rock and ice in each of Ganymede and Callisto. Io and Europa condense above the H₂O ice point and consist solely of hydrated rock (h-rock). The Ganymedan condensate consists of h-rock and H₂O ice. For Callisto, NH₃ ice makes up ∼5% of the condensate mass next to h-rock (∼50%) and H₂O ice (∼45%). Detailed thermal and structural models for each of Europa, Ganymedeand Callisto are constructed on the basis of the above initial bulk chemicalcompositions. For Europa (E), a predicted 2-zone model consisting of a dehydrated rock core of mass 0.912M_E and a 150 km thick frozen mantle of salty H₂O yields a moment-of-inertiacoefficient which matches the Galileo Orbiter gravity measurement. For Ganymede (G), a 3-zone model possessing an inner core of solid FeS and mass ∼0.116M_G, and an outer H₂O ice mantle of mass ∼0.502M_G is needed to explain the gravity data.Ganymede's native magnetic field was formed by thermoremanent magnetization of Fe₃O₄. A new Callisto (C) model is proposed consisting of a core of mass 0.826M_C containing a uniform mixture of h-rock (60% by mass) and H₂O and NH₃ ices, and capped by a mantle of pure ice. This model may have the capacity to yield a thin layer of liquid NH₃ċ2H₂O at the core boundary, in line with Galileo's discovery of an induced magnetic field This revised version was published online in July 2006 with corrections to the Cover Date.     

Formation of gas giant planets: core accretion models with fragmentation and planetary envelope

We have calculated formation of gas giant planets based on the standard core accretion model including effects of fragmentation and planetary envelope. The accretion process is found to proceed as follows. As a result of runaway growth of planetesimals with initial radii of ∼10 km, planetary embryos with a mass of ∼10²⁷ g (∼ Mars mass) are found to form in ∼10⁵ years at Jupiter's position (5.2 AU), assuming a large enough value of the surface density of solid material (25 g/cm²) in the accretion disk at that distance. Strong gravitational perturbations between the runaway planetary embryos and the remaining planetesimals cause the random velocities of the planetesimals to become large enough for collisions between small planetesimals to lead to their catastrophic disruption. This produces a large number of fragments. At the same time, the planetary embryos have envelopes, that reduce energies of fragments by gas drag and capture them. The large radius of the envelope increases the collision rate between them, resulting in rapid growth of the planetary embryos. By the combined effects of fragmentation and planetary envelope, the largest planetary embryo with 21M_⊕ forms at 5.2 AU in 3.8×10⁶ years. The planetary embryo is massive enough to start a rapid gas accretion and forms a gas giant planet.     

The formation of iron,stone, and mixed planetesimals in the early solar system

The interaction of dust grains with each other in a finite-temperature solar nebula are examined, taking into account the important fact that such grains would carry net steady-state charges like those of grains in interstellar clouds. This charge is given by the well-known Spitzer relation. It provides a screening mechanism that operates during accretion and results in bodies of differing compositions depending on the local temperature in the nebula. In a typical nebula, it is found that planetesimals of 0.1–10²-cm size form in a time of order 10⁶–10⁷ years. These planetesimals are of iron and stone and mixed composition in the inner solar system, but of mixed composition only in the outer solar system. The predictions of this type of charged-dust accretion can be compared to known data on meteorites and the composition of the planets.     

Models of the protosatellite disk of Saturn: Conditions for Titan’s formation

Models of the protosatellite accretion disk of Saturn are developed that satisfy cosmochemical constraints on the volatile abundances in the atmospheres of Saturn and Titan with due regard for the data obtained with the Cassini orbiter and the Huygens probe, which landed on Titan in January 2005. All basic sources of heating of the disk and protosatellite bodies are taken into account in the models, namely, dissipation of turbulence in the disk, accretion of gaseous and solid material onto the disk from the feeding zone of Saturn in the solar nebula, and heating by the radiation of young Saturn and thermal radiation of the surrounding region of the solar nebula. Two-dimensional (axisymmetric) temperature, pressure, and density distributions are calculated for the protosatellite disk. The distributions satisfy the cosmochemical constraints on the disk temperature, according to which the temperature at the stage of the satellite formation ranged from 60–65 K to 90–100 K at pressures from 10^?7 to ?10^?4 bar in the zone of Titan’s formation (according to estimates, r = 20–35R _Sat). Variations of the basic input parameters (the accretion rate onto the protosatellite disk of Saturn from the feeding zone of the planet ?; the parameter α characterizing turbulent viscosity of the disk; and the mass concentration ratio in the solid/gas system) satisfying the aforementioned temperature constraint are found. The spectrum of models satisfying the cosmochemical constraints covers a considerable range of consistent parameters. A model with a rather small flux of ? = 10^?8 M _Sat/ yr and a tenfold depletion of Saturn’s disk in gas due to gas scattering from the solar nebula is at one side of this range. A model with a much higher flux of ? = 10^?6 M _Sat/yr and a hundredfold decrease in opacity of the disk matter owing to decreased concentration of dust particles and/or their agglomeration into large aggregates and sweeping up by planetesimals is at the other side of the range.