Evolution of giant gaseous protoplanets embedded in the primitive solar nebula

Evolutionary calculations are presented, in a spherically symmetric approximation, for a protoplanet of 1 Jovian mass with homogeneous solar composition during the early phase of quasi-static contraction prior to the dissociation of molecular hydrogen. In contrast to earlier calculations which assume that protoplanets are isolated, this study invokes a time-dependent surface boundary condition that simulates physical conditions in an evolving primitive solar nebula. In a first set of calculations the protoplanet is surrounded by a “thermal bath” whose temperature varies with time and whose pressure is small and constant in time. Under a wide range of parameters the result is evaporation and complete dispersal of the object. Conditions required for the protoplanet to survive are discussed. In a second set of calculations both the temperature and pressure at the surface vary with time according to models of the solar nebula. In this case the protoplanet is not dispersed, but the evolution is accelerated or retarded relative to that of an isolated protoplanet, depending upon whether the entropy in the nebula is lower than or higher than, respectively, the entropy in the outer layers of the protoplanet. Processes by which terrestrial planets can form in the cores of giant gaseous protoplanets are discussed.     

Core formation in giant gaseous protoplanets

Sedimentation rates of silicate grains in gas giant protoplanets formed by disk instability are calculated for protoplanetary masses between 1 MSaturn to 10 MJupiter. Giant protoplanets with masses of 5 MJupiter or larger are found to be too hot for grain sedimentation to form a silicate core. Smaller protoplanets are cold enough to allow grain settling and core formation. Grain sedimentation and core formation occur in the low mass protoplanets because of their slow contraction rate and low internal temperature. It is predicted that massive giant planets will not have cores, while smaller planets will have small rocky cores whose masses depend on the planetary mass, the amount of solids within the body, and the disk environment. The protoplanets are found to be too hot to allow the existence of icy grains, and therefore the cores are predicted not to contain any ices. It is suggested that the atmospheres of low mass giant planets are depleted in refractory elements compared with the atmospheres of more massive planets. These predictions provide a test of the disk instability model of gas giant planet formation. The core masses of Jupiter and Saturn were found to be ∼0.25 M_⊕ and ∼0.5 M_⊕, respectively. The core masses of Jupiter and Saturn can be substantially larger if planetesimal accretion is included. The final core mass will depend on planetesimal size, the time at which planetesimals are formed, and the size distribution of the material added to the protoplanet. Jupiter's core mass can vary from 2 to 12 M_⊕. Saturn's core mass is found to be ∼8 M_⊕.     

Structure and evolution of isolated giant gaseous protoplanets

The structure and evolution of isolated giant gaseous protoplanets in the mass range 0.3 to 4.5 Jovian masses is investigated. Under the assumptions of the calculations, the following properties are found: (1) The central region of protoplanets of mass less than about 1 Jovian mass is, at some evolutionary epoch, thermodynamically favorable to the liquification of major interstellar grain constituents. Grains in this region can grow and infall to form a planetary core in tens to hundreds of years. (2) All protoplanets studied are convective through-out most of their interior. This property is in contrast to Bodenheimer's fully radiative proto-Jupiter models. We attribute the difference to the use of improved opacities. The presence of convection has at least two important consequences. First, it can mix grains into the central regions during planetary core formation, possibly allowing a core of mass ～ 1 Earth mass to grow. Second, convection can transport angular momentum outward as the protoplanet quasi-statically contracts. (3) The thermal contraction time depends sensitively on the surface opacity (T < 200°K). This opacity is uncertain within a factor of 5. The contraction times imply that some protoplanets can remain stable against tidal disruption by the proto-Sun and solar nebula during core-forming stages.     

Accumulation processes in the primitive solar nebula

Particle accumulation processes are discussed for a variety of physical environments, ranging from the collapse phase of an interstellar cloud to the different parts of the models of the primitive solar nebula constructed by Cameron and Pine. Because of turbulence in the collapsing interstellar gas, it is concluded that interstellar grains accumulate into bodies with radii of a few tens of centimeters before the outer parts of the solar nebula are formed. These bodies can descend quite rapidly through the gas toward midplane of the nebula, and accumulation to planetary size can occur in a few thousand years. Substantial modifications of these processes take place in the outer convection zone of the solar nebula, but again it is concluded that bodies in that zone can grow to planetary size in a few thousand years.From the discussion of the interstellar collapse phase it is concluded that the angular momentum of the primitive solar nebula was predominantly of random turbulent origin, and that it is plausible that the primitive solar nebula should have possessed satellite nebulae in highly elliptical orbits. It is proposed that the comets were formed in these satellite nebulae.A number of other detailed conclusions are drawn from the analysis. It is shown to be plausible that an iron-rich planet should be formed in the inner part of the outer nebular convection zone. Discussions are given of the processes of planetary gas accretion, the formation of satellites, the T Tauri solar wind, and the dissipation of excess condensed material after the nebular gases have been removed by the T Tauri solar wind. It is shown that the present radial distances of the planets (but not Bode's Law) should be predicted reasonably well by a solar nebula model intermediate between the uniform and linear cases of Cameron and Pine.     

Numerical models of the primitive solar nebula

Numerical models have been constructed to represent probable conditions in the primitive solar nebula. A two solar mass fragment of a collapsing interstellar gas cloud has been represented by a uniformly rotating sphere. Two cases have been considered: one in which the internal density of the sphere is uniform and the other in which the density falls linearly from a central value to zero at the surface (the uniform and linear models). These assumptions served to define the distribution of angular momentum per unit mass with mass fraction. The spheres were flattened into disks, and models of the disks were found in which there was a force balance in the radial and vertical directions, subject to certain approximations, and with everywhere the assigned values of angular momentum per unit mass. The radial pressure gradient of the gas was included in the force balance. The energy transport in the vertical direction involved convection and radiative equilibrium; the principal contributors to opacity at lower temperatures were metallic iron grains and ice. The models contained two convection zones, an inner one due to the dissociation of hydrogen molecules, and an outer one in which there was a high opacity due to metallic iron grains. The characteristic semithickness of the disks ranged from about 0.1 astronomical units near the center to about one astronomical unit near the exterior. Characteristic angular momentum transport times and radiation lifetimes for these models of the initial solar nebula were estimated. Both types of characteristic lifetime were as short as a few years near the inner part of the models, and became about 10⁴ years or longer at distances greater than ten astronomical units.     

Secular resonances in the primitive solar nebula

We present here a very simple model that could explain the relatively high eccentricities and inclinations observed in the minor planet belt. This model is based upon the sweeping of the secular resonances ₆ and ₁₆ through the belt due to the gravitational effect of the dissipation of a primitive solar nebula. The sweeping of the ₁₆ secular resonance (responsible for the high inclinations) is very sensitive to the density profile of the nebula. For the model to work we need a density profile proportional to ^–k with between 1.0 and 1.5.     

Clumping of Interstellar grains during formation of the primitive solar nebula

The author has previously shown that a considerable amount of clumping of interstellar grains is likely to take place during the free-fall collapse phase of an interstellar cloud which is forming the primitive solar nebula, with the assumption of sonic turbulence in the gas. The original estimate involved the crude assumption of hierarchal amalgamation of the grains upon collision. A Monte Carlo simulation of this process confirmed the general features of the results, but it was further found that the introduction of a low sticking probability reduced the size of the lumps quite significantly. A more realistic calculation was therefore carried out in which it was assumed that clumps of grains would tend to stick together if their collisions were approximately head-on, but that they would tend to fragment into smaller pieces if the collisions were more tangential. For typical values of the amalgamation parameter, this tends to spread the mass of the interstellar grains over a wide range of clump sizes, ranging from individual grains to objects in the millimeter or centimeter size.     

The role of turbulent convection in the primitive solar nebula: I. Theory

The theoretical framework for modeling the primordial solar nebula is presented in which convection is assumed to be the sole source of turbulence that causes the nebula to evolve. We use a new model of convective turbulence that takes into account the important effects of radiative dissipation, rotation, and anisotropy of convective motions. This model is based on a closure for the nonlinear interactions that employs the growth rates of hydrodynamic instabilities, a procedure that allows one to compute turbulence coefficients for instabilities other than convection. The vertical structure equations in the thin-disk approximation are developed for this new model, and a detailed comparison and critique of previous convective models of the solar nebula are presented. Numerical results are presented in a subsequent paper.     

Contraction of the solar nebula

The concept of Roche limit is applied to the Laplacian theory of the origin of the solar system to study the contraction of a spherical gas cloud (solar nebula). In the process of contraction of the solar nebula, it is assumed that the phenomenon of supersonic turbulent convection described by Prentice (1978) is operative and brings about the halt at various stages of contraction. It is found that the radius of the contracting solar nebula follows Titius-Bode law R _p = Ra^p, where R is the radius of the present Sun and a = 1.442. We call a the Roche's constant. The consequences of the relation are also discussed. The aim, here, is an attempt to explain, on the basis of the concept of Roche limit, the distribution of planets in the solar system and try to understand the physics underlying it.     

The effects of self-gravity on the solar nebula

We study the distribution and transport of angular momentum in a self-gravitating accretion disk formed during the collapse of a rotating gas cloud. Using the surface density for the low-viscosity models and minimum-mass models presented by Cassen and Summers, Poisson's equation is solved explicitly to determine the effects of self-gravitation of the protostellar disk. Analytic expressions for the angular momentum of the central star and other relevant quantities of interest during the formation stage are presented.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.On leave from the City College of the City University of New York, U.S.A.     

The effects of metallicity and grain growth and settling on the early evolution of gaseous protoplanets

Giant protoplanets formed by gravitational instability in the outer regions of circumstellar disks go through an early phase of quasi-static contraction during which radii are large (∼1 AU) and internal temperatures are low (<2000 K). The main source of opacity in these objects is dust grains. We investigate two problems involving the effect of opacity on the evolution of isolated, non-accreting planets of 3, 5, and 7 M_J. First, we pick three different overall metallicities for the planet and simply scale the opacity accordingly. We show that higher metallicity results in slower contraction as a result of higher opacity. It is found that the pre-collapse time scale is proportional to the metallicity. In this scenario, survival of giant planets formed by gravitational instability is predicted to be more likely around low-metallicity stars, since they evolve to the point of collapse to small size on shorter time scales. But metal-rich planets, as a result of longer contraction times, have the best opportunity to capture planetesimals and form heavy-element cores. Second, we investigate the effects of opacity reduction as a result of grain growth and settling, for the same three planetary masses and for three different values of overall metallicity. When these processes are included, the pre-collapse time scale is found to be of order 1000 years for the three masses, significantly shorter than the time scale calculated without these effects. In this case the time scale is found to be relatively insensitive to planetary mass and composition. However, the effects of planetary rotation and accretion of gas and dust, which could increase the timescale, are not included in the calculation. The short time scale we find would preclude metal enrichment by planetesimal capture, as well as heavy-element core formation, over a large range of planetary masses and metallicities.     

Kamacite sulfurization in the solar nebula

Abstract— The kinetics and mechanisms of kamacite sulfurization were studied experimentally at temperatures and H₂S/H₂ ratios relevant to the solar nebula. Pieces of the Canyon Diablo meteorite were heated at 558 K, 613 K, and 643 K in 50 parts per million by volume (ppmv) H₂S-H₂ gas mixtures for up to one month. Optical microscopy and x-ray diffraction analyses show that the morphology and crystal orientation of the resulting sulfide layers vary with both time and temperature. Electron microprobe analyses reveal three distinct phases in the reaction products: monosulfide solid solution (mss), (Fe, Ni, Co)_1-xS, pentlandite (Fe, Ni, Co)_9-xS₈, and a P-rich phase. The bulk composition of the remnant metal was not significantly changed by sulfurization. Kamacite sulfurization at 558 K followed parabolic kinetics for the entire duration of the experiments. Sulfide layers that formed at 613 K grew linearly with time, while those that formed at 643 K initially grew linearly with time then switched to parabolic kinetics upon reaching a critical thickness. The experimental results suggest that a variety of thermodynamic, kinetic, and physical processes control the final composition and morphology of the sulfide layers. We combine morphological, x-ray diffraction, electron microprobe, and kinetic data to produce a comprehensive model of sulfide formation in the solar nebula. Then, we present a set of criteria to assist in the identification of solar nebula condensate sulfides in primitive meteorites.     

The identification of early condensates from the solar nebula

Calcium-aluminum-rich chondrules which are highly deficient in alkalis were extracted from the carbonaceous chondrite Allende and yield a range of compositions with the lowest measured isotopic composition of $\text{(}{}^{87}\text{Sr}\text{/}{}^{86}\text{Sr}\text{)}{}_{\mathrm{<mtext>ALL</mtext>}}\text{= 0.69877±0.00002}$ and identify this material as the earliest known condensate from the solar nebula. Other chondrules suggest the possible presence of even more primitive Sr in this meteorite. This result also shows that some chondritic material formed very near the earliest part of the condensation sequence. Using alkali-deficient planetary objects (Moon, basaltic achondrites, Angra dos Reis, Allende), the Sr data indicate a time interval for condensation of 10 m.y. (from ALL to BABI) if condensation occurred in a solar Rb/Sr environment. A variety of alkali-rich olivine chondrules and CaAl-rich aggregates from Allende fail to determine an isochron and indicate that the element distribution in this meteorite was disturbed later than 3.6ae, possibly recently, in a cometary nucleus. This disturbance requires that the determination of initial ⁸⁷Sr/⁸⁶Sr be done on essentially Rb-free phases. Strontium data from equilibrated chondrites and from an iron meteorite establish an interval for metamorphism or differentiation in protoplanetary objects which followed the condensation process by ≈80 mm.y. The chronology for condensation and early planetary evolution obtained for Sr is in disagreement with the ¹²⁹I chronology but can be brought into agreement, if it is assumed that the high temperature iodine containing phases have not been affected by the metamorphic events determined by Sr.     

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.     

The first ten million years in the solar nebula

Abstract— The ²⁶Al/²⁷Al ratio in a large number of calcium-aluminum inclusions (CAIs) is a rather uniform 5 × 10^?5, whereas in chondrules the ratio is either undetectable or has a much lower value; the simplest interpretation of this is that there was an interval of a few million years between the times that these two meteoritic constituents formed stable solids. The present investigation was undertaken as an exploration of the physics of the processes in the solar nebula during and after the accumulation of the Sun. Understanding the time scales of events in this nebular model, to see if this would cast light on this apparent CAI to chondrule time interval, was the major motivation for the exploration. There were four stages in the history of the solar nebula; in stage 1, a fragment of an interstellar molecular cloud collapsed to form the Sun and solar nebula; in stage 2, the nebula was in approximate steady state balance between infall from the cloud and accretion onto the Sun and was in its FU Orionis accumulation stage; in stage 3, the Sun had been mainly accumulated and there was a slow residual mass flow into the Sun while it was in its classical T Tauri stage; and in stage 4, the nebula had finished accreting material onto the Sun (now a weak-lined T Tauri star) and was in a static condition with no significant dissipation or motions, other than removal at the inner edge due to the T Tauri solar wind and photoevaporation beyond 9 astronomical units (AU). It is found that the energy source keeping the nebula warm during stages 3 and 4 is recombination of ionized H in the ionized bipolar jets and the T Tauri coronal expansion solar wind. The parameters of the heating model were adjusted to locate the ice sublimation line at 5.2 AU. In this work, a nebular model is used with a surface density of 4.25 × 10³ gm/cm² at 1 AU and a variation with radial distance as the inverse first power. Under normal conditions in the nebula, there is a negative pressure gradient that provides partial radial support for the gas, which thus circles the Sun more slowly than large solid objects do. Large objects undergo a slow inward spiral due to the gas drag; very small objects move essentially with the gas but have a slow inward drift; and intermediate objects (e.g., 1 m) have a fairly large inward drift velocity that traverses the full radial extent of the nebula in considerably less than the CAI to chondrule time interval. Such objects are thus lost unless they can grow rapidly to larger sizes. Near the inner edge (bow) of the nebula during stage 4, the pressure gradient becomes positive, creating a narrow zone of zero gas drag toward which solids drift from both directions, facilitating planetesimal formation in the inner solar nebula. Recent theoretical and experimental results on sticking probabilities of solids show that icy surfaces have the best sticking properties, but icy interstellar grains can only stick together when subjected to impact velocities of less than 2000 cm/sec. However, if the solid objects are very underdense, then a collision leads to interpenetration and many points at which the small constituent grains can adhere to one another, and thus coagulation becomes possible for such underdense objects. Simulations were made of such coagulation in the outer solar nebula, and it was found that the central plane of the nebula quickly becomes filled with meter-sized and larger bodies that rapidly accumulated near the top of the nebula and rapidly descended; in a few thousand years this quickly leads to gravitational instabilities that can form planetesimals. These processes led to the rapid formation of Jupiter in the nebula (and the slightly less rapid formation of the other giant planets). The early formation of Jupiter opens an annular gap in the nebula, and thus a second region is created in the nebula with zero gas drag. It is concluded that CAIs were formed at the end of stage 2 of the nebula history and moved out into the nebula for long-term storage, and that most chondrules were formed by magnetic reconnection flares in the bow region of the nebula during stage 4, several million years later. Carbonaceous meteorites should be formed on the far side of the Jovian gap, with the chondrules being heated by flares on the early Jupiter irradiating materials in the nearby zone of zero gas drag, and they should have essentially the same ²⁶Al ages as the CAIs (this will be very hard to confirm owing to scarcity of Al mineral phases in these chondrules).     

The solar oxygen-isotopic composition: Predictions and implications for solar nebula processes

Abstract— The outer layers of the Sun are thought to preserve the average isotopic and chemical composition of the solar system. The solar O-isotopic composition is essentially unmeasured, though models based on variations in meteoritic materials yield several predictions. These predictions are reviewed and possible variations on these predictions are explored. In particular, the two-component mixing model of Clayton and Mayeda (1984) (slightly revised here) predicts solar compositions to lie along an extension of the calcium-aluminum-rich inclusion (CAI) ¹⁶O line between (δ¹⁸O, δ¹⁷O) = (16.4, 11.4)%0 and (12.3, 7.5)%0. Consideration of data from ordinary chondrites suggests that the range of predicted solar composition should extend to slightly lower δ¹⁸O values. The predicted solar composition is critically sensitive to the solid/gas ratio in the meteorite-forming region, which is often considered to be significantly enriched over solar composition. A factor of two solid/gas enrichment raises the predicted solar (δ¹⁸O, δ¹⁷O) values along an extension of the CAI ¹⁶O line to (33, 28)%0. The model is also sensitive to the nebular O gas phase. If conversion of most of the gaseous O from CO to H₂O occurred at relatively low temperatures and was incomplete at the time of CM aqueous alteration, the predicted nebular gas composition (and hence the solar composition) would be isotopically heavier along a slope 1/2 line. The likelihood of having a single solid nebular O component is discussed. A distribution of initial solid compositions along the CAI ¹⁶O line (rather than simply as an end-member) would not significantly change the predictions above in at least one scenario. Even considering these variations within the mixing model, the predicted range of solar compositions is distinct from that expected if the meteoritic variations are due to non-mass-dependent fractionation. Thus, a measurement of the solar O composition to a precision of several permil would clearly distinguish between these theories and should clarify a number of other important issues regarding solar system formation.     

On the evolution of giant protoplanets forming in circumbinary discs

We present the results of hydrodynamic simulations of Jovian mass protoplanets that form in circumbinary discs. The simulations follow the orbital evolution of the binary plus protoplanet system acting under their mutual gravitational forces, and forces exerted by the viscous circumbinary disc. The evolution involves the clearing of the inner circumbinary disc initially, so that the binary plus protoplanet system orbits within a low density cavity. Continued interaction between disc and protoplanet causes inward migration of the planet towards the inner binary. Subsequent evolution can take three distinct paths: (i) the protoplanet enters the 4 : 1 mean motion resonance with the binary, but is gravitationally scattered through a close encounter with the secondary star; (ii) the protoplanet enters the 4 : 1 mean motion resonance, the resonance breaks, and the planet remains in a stable orbit just outside the resonance; (iii) when the binary has initial eccentricity   e _bin≥ 0.2  , the disc becomes eccentric, leading to a stalling of the planet migration, and the formation of a stable circumbinary planet.
These results have implications for a number of issues in the study of extrasolar planets. The ejection of protoplanets in close binary systems provides a source of 'free-floating planets', which have been discovered recently. The formation of a large, tidally truncated cavity may provide an observational signature of circumbinary planets during formation. The existence of protoplanets orbiting stably just outside a mean motion resonance (4 : 1) in the simulations indicate that such sites may harbour planets in binary star systems, and these could potentially be observed. Finally, the formation of stable circumbinary planets in eccentric binary systems indicates that circumbinary planets may not be uncommon.     

Grain motions in the solar nebula

Isotopic analyses of meteorites suggest the possibility that some interaction between supernova ejecta and grains occurred in the solar nebula. In particular, the dynamics of grain motions in the solar nebula can explain the observed mixing of nucleosynthetic components. The effect of a shock wave on the motions of grains are examined. A steady-state, plane shock propagating into a uniform region of gas and dust grains is followed by a zone of gas/grain slip, in which the grains are accelerated by drag forces from the pre-shock to the post-shock gas velocity, i.e. reducing the relative velocity between the gas and grains to zero. On the basis of these calculations, it is estimated that if grains carried the isotopic anomalies investigated by Lee, Papanastassoiu, and Wasserburg (1978), then those grains could be no bigger than 2×10^–4 cm in size. A scenario is suggested in which the sluggishness of grains provides a natural way to concentrate and mix the nucleosynthetic components carried by grains in the ejecta and in the solar nebula.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

Formation of the galilean satellites in a gaseous nebula

A model for Galilean satellite formation was analyzed in which the satellites accrete in the presence of a dense, gaseous disk-shaped nebula and rapidly form optically thick, gravitationally bound primordial atmospheres. Upper-bound temperatures expected during accretion lead to partially differentiated structures for both Ganymede and Callisto, although with Ganymede much more differentiated than Callisto. When allowance is made for the aerodynamic breaking of infalling planetesimal fragments, lower surface temperatures result, and the amount of partial differentiation of Callisto is small, possibly approaching zero for a narrow size distribution of infalling planetesimals. The model is chosen to be consistent with the observed densities of the Galilean satellites and our current understanding of Jupiter formation. The retention of ices more volatile than H₂O is considered but not modeled in detail. A nominal nebula of ～0.1 Jupiter masses is constructed by consideration of likely surface density profiles and existing Jupiter collapse calculations. This nebula is optically thick (even if grain opacity is ignored) in both radial and vertical directions and has a temperature profile T ～ 3600 (R_J/R), where R_J is Jupiter's radius and R is the radial distance in the disk midplane. Satellites accrete very rapidly (dynamical time scales being 10²–10⁴ years) and their optically thick gaseous envelopes are unable to eliminate the heat of accretion by radiation. Water-saturated, convective, adiabatic envelopes form, through which planetesimals fall, break up, and partially disseminate their mass. The resulting satellite surface temperatures during accretion are calculated. Possible implications of these models for the subsequent evolution of Ganymede and Callisto are explored and it is suggested that the extensive differentiation undergone by Ganymede may provide the right environment for subsequent resurfacing, whereas the relative lack of extensive differentiation for Callisto may explain the inferred absence of endogenic tectonism.