Combined modeling of thermal evolution and accretion of trans-neptunian objects—Occurrence of high temperatures and liquid water

We have calculated the early thermal evolution of trans-neptunian objects by means of a thermal evolution code that takes into account simultaneous accretion. The set of coupled partial differential equations for ²⁶Al radioactive heating, transformation of amorphous to crystalline ice and melting of water ice was solved numerically for small porous icy (cometary-like) bodies growing to final radii between 2 and 32 km and accreting between 20 and 44 AU. Accretion within a swarm of gravitationally interacting small bodies was calculated self-consistently with a simple accretion algorithm and thermal evolution of a typical member of the swarm was tracked in a parameter-space survey. We find that including accretion in numerical modeling of thermal evolution leads to a broad variety of thermally processed icy bodies and that the early occurrence of liquid water and extended crystalline ice interiors may be a very common phenomenon. The pristine nature of small icy bodies becomes thus restricted to a particular set of initial conditions. Generally, long-period comets should be more thermally affected than short-period ones.     

Thermal evolution of trans‐Neptunian objects,icy satellites,and minor icy planets in the early solar system

Numerical simulations are performed to understand the early thermal evolution and planetary scale differentiation of icy bodies with the radii in the range of 100–2500 km. These icy bodies include trans‐Neptunian objects, minor icy planets (e.g., Ceres, Pluto); the icy satellites of Jupiter, Saturn, Uranus, and Neptune; and probably the icy‐rocky cores of these planets. The decay energy of the radionuclides, ²⁶Al, ⁶⁰Fe, ⁴⁰K, ²³⁵U, ²³⁸U, and ²³²Th, along with the impact‐induced heating during the accretion of icy bodies were taken into account to thermally evolve these planetary bodies. The simulations were performed for a wide range of initial ice and rock (dust) mass fractions of the icy bodies. Three distinct accretion scenarios were used. The sinking of the rock mass fraction in primitive water oceans produced by the substantial melting of ice could lead to planetary scale differentiation with the formation of a rocky core that is surrounded by a water ocean and an icy crust within the initial tens of millions of years of the solar system in case the planetary bodies accreted prior to the substantial decay of ²⁶Al. However, over the course of billions of years, the heat produced due to ⁴⁰K, ²³⁵U, ²³⁸U, and ²³²Th could have raised the temperature of the interiors of the icy bodies to the melting point of iron and silicates, thereby leading to the formation of an iron core. Our simulations indicate the presence of an iron core even at the center of icy bodies with radii ≥500 km for different ice mass fractions.     

Growth and evolution of small porous icy bodies with an adaptive-grid thermal evolution code: I. Application to Kuiper belt objects and Enceladus

We present a new 1-dimensional thermal evolution code suited for small icy bodies of the Solar System, based on modern adaptive grid numerical techniques, and suited for multiphase flow through a porous medium. The code is used for evolutionary calculations spanning 4.6×¹⁰⁹ yr of a growing body made of ice and rock, starting with a 10 km radius seed and ending with an object 250 km in radius. Initial conditions are chosen to match two different classes of objects: a Kuiper belt object, and Saturn's moon Enceladus. Heating by the decay of ²⁶Al, as well as long-lived radionuclides is taken into account. Several values of the thermal conductivity and accretion laws are tested. We find that in all cases the melting point of ice is reached in a central core. Evaporation and flow of water and vapor gradually remove the water from the core and the final (present) structure is differentiated, with a rocky, highly porous core of 80 km radius (and up to 160 km for very low conductivities). Outside the core, due to refreezing of water and vapor, a compact, ice-rich layer forms, a few tens of km thick (except in the case of very high conductivity). If the ice is initially amorphous, as expected in the Kuiper belt, the amorphous ice is preserved in an outer layer about 20 km thick. We conclude by suggesting various ways in which the code may be extended.     

Thermal evolution of Kuiper belt objects, with implications for cryovolcanism

We investigate the internal thermal evolution of Kuiper belt objects (KBOs), small (radii <1000 km), icy (mean densities ) bodies orbiting beyond Neptune, focusing on Pluto's moon Charon in particular. Our calculations are time-dependent and account for differentiation. We review evidence for ammonia hydrates in the ices of KBOs, and include their effects on the thermal evolution. A key finding is that the production of the first melt, at the melting point of ammonia dihydrate, ≈176 K, triggers differentiation of rock and ice. The resulting structure comprises a rocky core surrounded by liquids and ice, enclosed within a >100-km thick undifferentiated crust of rock and ice. This structure is especially conducive to the retention of subsurface liquid, and bodies the size of Charon or larger (radii >600 km) are predicted to retain some subsurface liquid to the present day. We discuss the possibility that this liquid can be brought to the surface rapidly via self-propagating cracks. We conclude that cryovolcanism is a viable process expected to affect the surfaces of large KBOs including Charon.     

Long-Term Evolution of Objects in the Kuiper Belt Zone—Effects of Insolation and Radiogenic Heating

The Kuiper Belt zone is unique insofar as the major heat sources of objects a few tens of kilometers in size—solar radiation on the one hand and radioactive decay on the other—have comparable power. This leads to unique evolutionary patterns, with heat waves propagating inward from the irradiated surface and outward from the radioactively heated interior. A major radioactive source that is considered in this study is ²⁶Al. The long-term evolution of several models with characteristics typical of Kuiper Belt objects is followed by means of a 1-D numerical code that solves the heat and mass balance equations on a spherically symmetric grid. The free parameters considered are radius (10-500 km), heliocentric distance (30-120 AU), and initial ²⁶Al content (0-5×10⁻⁸ by mass). The initial composition assumed is a porous mixture of ices (H₂O, CO, and CO₂) and dust. Gases released in the interior are allowed to escape to the surface. It is shown that, depending on parameters, the interior may reach quite high temperatures (up to 180 K). The models suggest that Kuiper Belt objects are likely to lose the ices of very volatile species during early evolution; ices of less volatile species are retained in a surface layer, about 1 km thick. The models indicate that the amorphous ice crystallizes in the interior, and hence some objects may also lose part of the volatiles trapped in amorphous ice. Generally, the outer layers are far less affected than the inner part, resulting in a stratified composition and altered porosity distribution. These changes in structure and composition should have significant consequences for the short-period comets, which are believed to be descendants of Kuiper Belt objects.     

Some consequences of a phase transition of water ice on the heat balance of comet nuclei

We consider spheres of water ice of about 1 km in radius moving on three different orbits with a common perihelion distance of 8 AU. As evaporation is negligible in these cases, we call them inactive ice bodies. The surface temperature has been numerically calculated for two extreme situations: (1) The spheres are composed of amorphous ice with a heat conduction to the interior presumed to be negligible. (2) The spheres are composed of compact hexagonal ice with a heat conduction coefficient known from laboratory experiments. Whereas in case 1 the temperature is an unambiguous function of heliocentric distance, in case 2 we observe a thermal “hysteresis” and the maximum temperature has a phase lag with respect to perihelion. The perihelion temperature depends on the eccentricity of the orbit. The case of active ice bodies is also discussed. We come to the conclusion that an ice body moving on the orbit of Tempel 2 must contain crystalline ice and the variations of the surface temperature must be smoothed out in an important way. In the case of Halley's orbit, we suppose that the center of the ice body still contains large amounts of amorphous ice.     

Radiation-induced amorphization of crystalline ice

We study radiation-induced amorphization of crystalline ice, analyzing the results of three decades of experiments with a variety of projectiles, irradiation energy, and ice temperature, finding a similar trend of increasing resistance of amorphization with temperature and inconsistencies in results from different laboratories. We discuss the temperature dependence of amorphization in terms of the ‘thermal spike’ model. We then discuss the common use of the 1.65 μm infrared absorption band of water as a measure of degree of crystallinity, an increasingly common procedure to analyze remote sensing data of astronomical icy bodies. The discussion is based on new, high quality near-infrared reflectance absorption spectra measured between 1.4 and 2.2 μm for amorphous and crystalline ices irradiated with 225 keV protons at 80 K. We found that, after irradiation with 10¹⁵ protons cm⁻², crystalline ice films thinner than the ion range become fully amorphous, and that the infrared absorption spectra show no significant changes upon further irradiation. The complete amorphization suggests that crystalline ice observed in the outer Solar System, including trans-neptunian objects, may results from heat from internal sources or from the impact of icy meteorites or comets.     

Hydrated Silicates on Edgeworth-Kuiper Objects – Probable Ways of Formation

Visible-range absorption bands at 600–750 nm were recently detected on two Edgeworth-Kuiper Belt (EKB) objects (Boehnhardt et al., 2002). Most probably the spectral features may be attributed to hydrated silicates originated in the bodies. We consider possibilities for silicate dressing and silicate aqueous alteration within them. According to present models of the protoplanetary disk, the temperatures and pressures at the EKB distances (30–50 AU) at the time of formation of the EKB objects (10⁶ to 10⁸ yr) were very low (15–30 K and 10^-9–10^-10 bar). At these thermodynamic conditions all volatiles excluding hydrogen, helium and neon were in the solid state. An initial mass fraction of silicates (silicates/(ices + dust)) in EKB parent bodies may be estimated as 0.15–0.30. Decay of the short-lived ²⁶Al in the bodies at the early stage of their evolution and their mutual collisions (at velocities ≥1.5 km s^-1) at the subsequent stage were probably two main sources of their heating, sufficient for melting of water ice. Because of the former process, large EKB bodies (R ≥ 100 km) could contain a large amount of liquid water in their interiors for the period of a few 10⁶ yr. Freezing of the internal ocean might have begun at ≈ 5 × 10⁶ yr after formation of the solar nebula (and CAIs). As a result, aqueous alteration of silicates in the bodies could occur. A probable mechanism of silicate dressing was sedimentation of silicates with refractory organics, resulting in accumulation of large silicate-rich cores. Crushing and removing icy covers under collisions and exposing EKB bodies' interiors with increased silicate content could facilitate detection of phyllosilicate spectral features.     

Modeling the morphological diversity of impact craters on icy satellites

Impact craters on icy satellites display a wide range of morphologies, some of which have no counterpart on rocky bodies. Numerical simulation studies have struggled to reproduce the diversity of features, such as central pits and transitions in crater depth with increasing diameter, observed on the icy Galilean satellites. The transitions in crater depth (at diameters of about 26 and 150 km on Ganymede and Callisto) have been interpreted as reflecting subsurface structure. Using the CTH shock physics code, we model the formation of craters with diameters between 400 m and about 200 km on Ganymede using different subsurface temperature profiles. Our calculations include recent improvements in the model equation of state for H₂O and quasi-static strength parameters for ice. We find that the shock-induced formation of dense high-pressure polymorphs (ices VI and VII) creates a gap in the crater excavation flow, which we call discontinuous excavation. For craters larger than about 20 km, discontinuous excavation concentrates a hot plug of material (>270 K and mostly on the melting curve) in the center of the crater floor. The size and occurrence of the hot plug are in good agreement with the observed characteristics of central pit craters, and we propose that a genetic link exists between them. We also derive depth versus diameter curves for different internal temperature profiles. In a 120 K isothermal crust, calculated craters larger than about 30 km diameter are deeper than observed and do not reproduce the transition at about 26 km diameter. Calculated crater depths are shallower and in good agreement with observations between about 30 and 150 km diameter using a warm thermal gradient representing a convective interior. Hence, the depth-to-diameter transition at about 26 km reflects thermal weakening of ice. Finally, simulation results generally support the hypothesis that the anomalous interior morphologies for craters larger than 100 km are related to the presence of a subsurface ocean.     

Comet Grains: Their IR Emission and Their Relation to ISm Grains

Comets and the chondritic porous interplanetary dust particles (CP IDPs) that they shed in their comae are reservoirs of primitive solar nebula materials. The high porosity and fragility of cometary grains and CP IDPs, and anomalously high deuterium contents of highly fragile, pyroxene-rich Cluster IDPs imply these aggregate particles contain significant abundances of grains from the interstellar medium (ISM). IR spectra of comets (3–40 μm) reveal the presence of a warm (near-IR) featureless emission modeled by amorphous carbon grains. Broad andnarrow resonances near 10 and 20 microns are modeled by warm chondritic (50% Feand 50% Mg) amorphous silicates and cooler Mg-rich crystalline silicate minerals, respectively. Cometary amorphous silicates resonances are well matched by IRspectra of CP IDPs dominated by GEMS (0.1 μm silicate spherules) that are thought to be the interstellar Fe-bearing amorphous silicates produced in AGB stars. Acid-etched ultramicrotomed CP IDP samples, however, show that both the carbon phase (amorphous and aliphatic) and the Mg-rich amorphous silicate phase in GEMS are not optically absorbing. Rather, it is Fe and FeS nanoparticles embedded in the GEMS that makes the CP IDPs dark. Therefore, CP IDPs suggest significant processing has occurred in the ISM. ISM processing probably includes in He⁺ ion bombardment in supernovae shocks. Laboratory experiments show He⁺ ion bombardment amorphizes crystalline silicates, increases porosity, and reduces Fe into nanoparticles. Cometary crystalline silicate resonances are well matched by IR spectra of laboratory submicron Mg-rich olivine crystals and pyroxene crystals. Discovery of a Mg-pure olivine crystal in a Cluster IDP with isotopically anomalous oxygen indicates that a small fraction of crystalline silicates may have survived their journey from AGB stars through the ISM to the early solar nebula. The ISM does not have enough crystalline silicates (<5%), however, to account for the deduced abundance of crystalline silicates in comet dust. An insufficient source of ISMMg-rich crystals leads to the inference that most Mg-rich crystals in comets are primitive grains processed in the early solar nebula prior to their incorporation into comets. Mg-rich crystals may condense in the hot (～1450 K), inner zones of the early solar nebula and then travel large radial distances out to the comet-forming zone. On the other hand, Mg-rich silicate crystals may be ISM amorphous silicates annealed at ～1000 K and radially distributed out to the comet-forming zone or annealed in nebular shocks at ～5-10 AU. Determining the relative abundance of amorphous and crystalline silicatesin comets probes the relative contributions of ISM grains and primitive grains to small, icy bodies in the solar system. The life cycle of dust from its stardust origins through the ISM to its incorporation into comets is discussed.     

Dust Grains in the Comae and Tails of Sungrazing Comets: Modeling of Their Mineralogical and Morphological Properties

Observations of sungrazing comets, all of which belong to the Kreutz family, provide the opportunity of studying the properties of dust in the comae and tails of the comets. On the basis of available information on cometary and interplanetary dust as well as observations of dust in the tails of sungrazers, we model dust in sungrazing comets as fluffy silicate aggregates of submicrometer sizes. To better interpret observational data, we numerically calculate the solar radiation pressure, the equilibrium temperature, and the sublimation and crystallization rates of silicate grains near the Sun. Our results show that the dust tails contain aggregates of submicrometer crystal grains, but not amorphous grains, since amorphous silicates mostly crystallize after release from the comets. The peak in the lightcurves of the dust comae observed either at 11.2 or 12.3 solar radii (R_⊙) seems to result from sublimation of fluffy aggregates consisting of crystalline or amorphous olivines, respectively. We attribute an additional enhancement in the lightcurves inside 7 R_⊙ to increasing out-flow of crystalline and amorphous pyroxenes composed fluffy aggregates. According to our model, the observed lightcurves indicate a high abundance of olivine and a low abundance of pyroxene in the comets, which may bear implications about the dynamical and thermal history of the sungrazers and their progenitor.     

The possible formation of a hydrogen coma around comets at large heliocentric distances

An observational test--the detection of a hydrogen coma around comets at large heliocentric distances--is proposed for determining whether comets were formed by the agglomeration of unaltered, ice-coated, interstellar grains. Laboratory experiments showed that amorphous water ice traps H2, D2, and Ne below 20 K and does not release them completely until the ice is heated to 150 K. Gas/ice ratios as high as 0.63 are obtainable. Thus, if the ice-coated interstellar grains were not heated above approximately 110 K, prior to their agglomeration into cometary nuclei, the inward propagating heat waves should release from the comets a continuous flux of molecular hydrogen. This flux would exceed that of water molecules at approximately 3 AU preperihelion and approximately 4 AU postperihelion.     

Carbon dioxide segregation in 1:4 and 1:9 CO2:H2O ices

The mid-infrared spectra of mixed vapor deposited ices of CO₂ and H₂O were studied as a function of both deposition temperature and warming from 15 to 100 K. The spectra of ices deposited at 15 K show marked changes on warming beginning at 60 K. These changes are consistent with CO₂ segregating within the ice matrix into pure CO₂ domains. Ices deposited at 60 and 70 K show a greater degree of segregation, as high as 90% for 1:4 CO₂:H₂O ice mixtures deposited at 70 K. As the ice is warmed above 80 K, preferential sublimation of the segregated CO₂ is observed. The kinetics of the segregation process is also examined. The segregation of the CO₂ as the ice is warmed corresponds to temperatures at which the structure of the water ice matrix changes from the high density amorphous phase to the low density amorphous phase. We show how these microstructural changes in the ice have a profound effect on the photochemistry induced by ultraviolet irradiation. These experimental results provide a framework in which observations of CO₂ on the icy bodies of the outer Solar System can be considered.     

On the existence of small comets and their interactions with planets

Arguments are presented for a substantial, unexplored population of comets with radii less than 1 km. Known examples confirm this population and extrapolation of any plausible size-distribution function indicates large numbers. However, their accurate numbers, orbital characteristics, and physical properties are unknown. Thus, even though the small comets may be the most frequent cometary bodies impacting the planets, a quantitative evaluation is not currently possible. We advocate an optimized, dedicated search program to characterize this population.     

Activity of comets at large heliocentric distances pre-perihelion

We present observational data for two long-period and three dynamically new comets observed at heliocentric distances between 5.8 to 14.0 AU. All of the comets exhibited activity beyond the distance at which water ice sublimation can be significant. We have conducted experiments on gas-laden amorphous ice samples and show that considerable gas emission occurs when the ice is heated below the temperature of the amorphous-crystalline ice phase transition (T∼137 K). We propose that annealing of amorphous water ice is the driver of activity in comets as they first enter the inner Solar System. Experimental data show that large grains can be ejected at low velocity during annealing and that the rate of brightening of the comet should decrease as the heliocentric distance decreases. These results are consistent with both historical observations of distant comet activity and with the data presented here. If observations of the onset of activity in a dynamically new comet are ever made, the distance at which this occurs would be a sensitive indicator of the temperature at which the comet had formed or represents the maximum temperature that it has experienced. New surveys such as Pan STARRS, may be able to detect these comets while they are still inactive.     

Embedded star clusters and the formation of the Oort cloud: II. The effect of the primordial solar nebula

This paper deals with Oort cloud formation while the Sun was in an embedded cluster and surrounded by its primordial nebula. This work is a continuation of Brasser et al. [Brasser, R., Duncan, M., Levison, H., 2006. Icarus 184, 59-82], building on the model presented therein, and adding the aerodynamic drag and gravitational potential of the primordial solar nebula. Results are presented of numerical simulations of comets subject to the gravitational influence of the Sun, Jupiter, Saturn, star cluster and primordial solar nebula; some of the simulations included the gravitational influence of Uranus and Neptune as well. The primordial solar nebula was approximated by the minimum-mass Hayashi model [Hayashi, C., Nakozawa, K., Nakagawa, Y., 1985. In: Black, D.C., Matthews, M.S. (Eds.). Protostars and Planets II. Univ. of Arizona Press, Tucson, AZ] whose inner and outer radii have been truncated at various distances from the Sun. A comet size of 1.7 km was used for most of our simulations. In all of our simulations, the density of the primordial solar nebula decayed exponentially with an e-folding time of 2 Myr. It turns out that when the primordial solar nebula extends much beyond Saturn or Neptune, virtually no material will end up in the Oort cloud (OC) during this phase. Instead, the majority of the material will be on circular orbits inside of Jupiter if the inner edge of the disk is well inside Jupiter's orbit. If the disk's inner edge is beyond Jupiter's orbit, most comets end up on orbits in exterior mean-motion resonances with Saturn when Uranus and Neptune are not present. In those cases where the outer edge of the disk is close to Saturn or Neptune, the fraction of material that ends up in the subsequently formed OC is much less than that found in Brasser et al. [Brasser, R., Duncan, M., Levison, H., 2006. Icarus 184, 59-82] for the same cluster densities. This implies that for comets of roughly 2 km in size, the presence of the primordial solar nebula hinders OC formation. A byproduct of some of our simulations are endresults with a substantial fraction of the comets in the Uranus-Neptune scattered disk. A subsequent followup of this material is planned for the near future. In order to determine the effect of the size of the comets on OC formation efficiency, a set of runs with the same initial conditions but different cometary radii have been performed as well, from which it is determined that the threshold comet size to begin producing significant Oort clouds is roughly 20 km. This implies that the presence of the primordial solar nebula acts as a size-sorting mechanism, with large bodies unaffected by the gas drag and ending up in the OC while small bodies remain trapped in the planetary region, in the models studied.     

Do explosive ice ejections occur on Jupiter’s and Saturn’s satellites?

The possibility of an explosive mechanical instability of ice (the Bridgman effect) in the thick icy shells of Jupiter’s and Saturn’s satellites is discussed in principle. The Bridgman effect is an explosive instability of dielectric solid bodies, which disintegrate into microscopic fragments under a quasistatic uniaxial loading in open compression systems at high pressures. The explosive instabilities of ice recently discovered in laboratory experiments with the Bridgman effect are also expected to occur in the extensive deep layers of the shells of icy planetary satellites (for example, in the case of episodical formation of major cracks in their lithospheres due to tidal forces, nonsynchronous rotation of the satellites, or extremely powerful impacts). The depths of occurrence of mechanically unstable ice in the thick crusts of Ganymede, Europa, and Titan, taken as examples, are crudely estimated using a pure-ice model without a possible ammonia admixture. The estimated thickness of the explosive-instability zone in the icy crust of Ganymede (under the assumption that the crust is ～75 km thick) ranges from ～7 to ～27 km at depths from ～40 to ～67 km, depending on the scaling parameter E = 0.2–1. This parameter relates the experimentally determined thicknesses of the ice samples in which the Bridgman effect occurs under laboratory conditions to the expected thicknesses of the explosively unstable layers in the envelopes of the icy satellites. Explosive effects are possible not throughout the entire thickness of the unstableice layer but only within some part of it, several centimeters to several tens of meters in thickness. According to the estimated location of the unstable layer in the crust of Europa (for an assumed crust thickness of ～30 km), such a layer can exist only at scaling factors E < 0.6 at depths ranging from ～21 to ～28 km. For Titan, if its crust is ～100 km thick, the thickness of the unstable layer is similarly estimated to range from ～15 to ～55 km at depths from ～37 to ～92 km for a scaling parameter E lying within the range 0.2–1. At E 0.2, which is quite possible, explosive instabilities of ice could also be expected on the Earth, in the icy shells of Antarctica and Greenland at depths from ～1 to ～1.5 km.     

On the dectectability of icy grains in the comae of comets

Evaporation of icy grains over the distance scale of the visible cometary coma sets very specific limits on their temperature. Unless the grains are very pure water ice, the maximum size of an icy grain halo will be limited to a few hundred kilometers at heliocentric distances ?2.5 AU. It is unlikely that the 1.5- or 2-μm ice band could be detected in the scattering by icy grains. Detection of the 3?μm ice band might be possible in comets which display a coma at large heliocentric distances.     

Numerical simulations of the differentiation of accreting planetesimals with 26Al and 60Fe as the heat sources

Abstract— Numerical simulations have been performed for the differentiation of planetesimals undergoing linear accretion growth with ²⁶Al and ⁶⁰Fe as the heat sources. Planetesimal accretion was started at chosen times up to 3 Ma after Ca‐Al‐rich inclusions (CAIs) were formed, and was continued for periods of 0.001–1 Ma. The planetesimals were initially porous, unconsolidated bodies at 250 K, but became sintered at around 700 K, ending up as compact bodies whose final radii were 20, 50, 100, or 270 km. With further heating, the planetesimals underwent melting and igneous differentiation. Two approaches to core segregation were tried. In the first, labelled A, the core grew gradually before silicate began to melt, and in the second, labelled B, the core segregated once the silicate had become 40% molten. In A, when the silicate had become 20% molten, the basaltic melt fraction began migrating upward to the surface, carrying ²⁶Al with it. The ⁶⁰Fe partitioned between core and mantle. The results show that the rate and timing of core and crust formation depend mainly on the time after CAIs when planetesimal accretion started. They imply significant melting where accretion was complete before 2 Ma, and a little melting in the deep interiors of planetesimals that accreted as late as 3 Ma. The latest melting would have occurred at <10 Ma. The effect on core and crust formation of the planetesimal's final size, the duration of accretion, and the choice of (⁶⁰Fe/⁵⁶Fe)_initial were also found to be important, particularly where accretion was late. The results are consistent with the isotopic ages of differentiated meteorites, and they suggest that the accretion of chondritic parent bodies began more than 2 or 3 Ma after CAIs.     

From icy planetesimals to outer planets and comets

Numerical simulations of planet growth in the outer solar system shows thatgrwoth of Uranus and Neptune occurs in reasonably short time, well below the actual age of the system, without the need for ad hoc assumptions about excess mass or artificially low relative velocities among the icy planetesimals. Low velocities, which speed accretion, are a natural consequence of the non-power-law size distribution of planetesimals, just as in our earlier simulations of terrestial planet growth. Initial planetesimals of size ～ 100 km, predicted by formal expressions for gravitational instability in a thin disk of solid material, failed to produce sufficient debris in the size range 1 to 10 km to account for population of the Oort cloud with comet-sized bodies. However, our model of nonhomologous settling of grains to the midplane of the solar system shows that gravitational clumping did not wait until all solid material had settled to the midplane, as had been assumed in earlier models. Rather, the clumping occurred in successive portions of the material that reached the midplane, producing “initial” planetesimals probably of comet-like sizes. Models of subsequent collisional evolution show that such an initial size distribution, similar to known comets, would have been required in order to have an adequate comet-like size distribution available to feed the Oort cloud as the other planets reach full size. Comets are probably unaltered remnants of the initial population of planetesimals in the outer solar system, not fragments of larger bodies.