Blowing in the wind. II. Creation and redistribution of refractory inclusions in a turbulent protoplanetary nebula

Ca-Al rich refractory mineral inclusions (CAIs) found at 1-6% mass fraction in primitive chondrites appear to be 1-3 million years older than the dominant (chondrule) components which were accreted into the same parent bodies. A prevalent concern is that it is difficult to retain CAIs for this long against gas-drag-induced radial drift into the Sun. We reassess the situation in terms of a hot inner (turbulent) nebula context for CAI formation, using analytical models of nebula evolution and particle diffusion. We show that outward radial diffusion in a weakly turbulent nebula can overcome inward drift, and prevent significant numbers of CAI-size particles from being lost into the Sun for times on the order of 10⁶ years. CAIs can form early, when the inner nebula was hot, and persist in sufficient abundance to be incorporated into primitive planetesimals at a much later time. Small (?0.1 mm diameter) CAIs persist for longer times than large (?5 mm diameter) ones. To obtain a quantitative match to the observed volume fractions of CAIs in chondrites, another process must be allowed for: a substantial enhancement of the inner hot nebula in silicate-forming material, which we suggest was caused by rapid inward drift of meter-sized objects. This early in nebula history, the drifting rubble would have a carbon content probably an order of magnitude larger than even the most primitive (CI) carbonaceous chondrites. Abundant carbon in the evaporating material would help keep the nebula oxygen fugacity low, plausibly solar, as inferred for the formation environment of CAIs. The associated production of a larger than canonical amount of CO₂ might also play a role in mass-independent fractionation of oxygen isotopes, leaving the gas rich in ¹⁶O as inferred from CAIs and other high temperature condensates.     

The evolution of the water distribution in a viscous protoplanetary disk

Astronomical observations have shown that protoplanetary disks are dynamic objects through which mass is transported and accreted by the central star. This transport causes the disks to decrease in mass and cool over time, and such evolution is expected to have occurred in our own solar nebula. Age dating of meteorite constituents shows that their creation, evolution, and accumulation occupied several Myr, and over this time disk properties would evolve significantly. Moreover, on this timescale, solid particles decouple from the gas in the disk and their evolution follows a different path. It is in this context that we must understand how our own solar nebula evolved and what effects this evolution had on the primitive materials contained within it. Here we present a model which tracks how the distribution of water changes in an evolving disk as the water-bearing species experience condensation, accretion, transport, collisional destruction, and vaporization. Because solids are transported in a disk at different rates depending on their sizes, the motions will lead to water being concentrated in some regions of a disk and depleted in others. These enhancements and depletions are consistent with the conditions needed to explain some aspects of the chemistry of chondritic meteorites and formation of giant planets. The levels of concentration and depletion, as well as their locations, depend strongly on the combined effects of the gaseous disk evolution, the formation of rapidly migrating rubble, and the growth of immobile planetesimals. Understanding how these processes operate simultaneously is critical to developing our models for meteorite parent body formation in the Solar System and giant planet formation throughout the galaxy. We present examples of evolution under a range of plausible assumptions and demonstrate how the chemical evolution of the inner region of a protoplanetary disk is intimately connected to the physical processes which occur in the outer regions.     

The origin of non-porphyritic pyroxene chondrules in UOCs: Liquid solar nebula condensates?

A total of 56 non-porphyritic pyroxene and pyroxene/olivine micro-objects from different unequilibrated ordinary chondrites were selected for detailed studies to test the existing formation models. Our studies imply that the non-porphyritic objects represent quickly quenched liquids with each object reflecting a very complex and unique evolutionary history. Bulk major element analyses, obtained with EMPA and ASEM, as well as bulk lithophile trace element analyses, determined by LA-ICP-MS, resulted in unfractionated (solar-like) ratios of CaO/Al₂O₃, Yb/Ce as well as Sc/Yb in many of the studied objects and mostly unfractionated refractory lithophile trace element (RLTE) abundance patterns. These features support an origin by direct condensation from a gas of solar nebula composition. Full equilibrium condensation calculations show that it is theoretically possible that pyroxene-dominated non-porphyritic chondrules with flat REE patterns could have been formed as droplet liquid condensates directly from a nebular gas strongly depleted in olivine. Thus, it is possible to have enstatite as the stable liquidus phase in a 800 × Cl dust-enriched nebular gas at a ptot of 10⁻³ atm, if about 72% of the original Mg is removed (as forsterite?) from the system. Condensation of liquids from vapor (primary liquid condensation) could be considered as a possible formation process of the pyroxene-dominated non-porphyritic objects. This process can produce a large spectrum of chemical compositions, which always have unfractionated RLTE abundances. Late stage and subsolidus metasomatic events appear to have furthered the compositional diversity of chondrules and related objects by addition of moderately volatile and volatile elements to these objects by exchange reactions with the chondritic reservoir (e.g., V, Cr, Mn, FeO as well as K and Na). The strong fractionation displayed by the volatile lithophile elements could be indicative of a variable efficiency of metasomatic processes occurring during and/or after chondrule formation. Histories of individual objects differ in detail from each other and clearly indicate individual formation and subsequent processing.     

Experiments on the photophoretic motion of chondrules and dust aggregates—Indications for the transport of matter in protoplanetary disks

In a set of 16 drop tower experiments the motion of sub-millimeter to millimeter-sized particles under microgravity was observed. Illumination by a halogen lamp induced acceleration of the particles due to photophoresis. Photophoresis on dust-free chondrules, on chondrules, glass spheres and metal spheres covered with SiC dust and on pure SiC dust aggregates was studied. This is the first time that photophoretic motion of millimeter-sized particles has been studied experimentally. The absolute values for the photophoretic force are consistent with theoretical expectations for spherical particles. The strength of the photophoretic force varies for chondrules, dust covered particles and pure dust from low to strong, respectively. The measurements support the idea that photophoresis in the early Solar System can be efficient to transport solid particles outward.     

Compound chondrule formation in the shock-wave heating model: Three-dimensional hydrodynamics simulation of the disruption of a partially-molten dust particle

We carried out three-dimensional hydrodynamics simulations of the disruption of a partially-molten dust particle exposed to high-speed gas flow to examine the compound chondrule formation due to mutual collisions between the fragments (fragment-collision model; [Miura, H., Yasuda, S., Nakamoto, T., 2008a. Icarus194, 811-821]).In the shock-wave heating model, which is one of the most plausible models for chondrule formation, the gas friction heats and melts the surface of the cm-sized dust particle (parent particle) and then the strong gas ram pressure causes the disruption of the molten surface layer. The hydrodynamics simulation shows details of the disruptive motion of the molten surface, production of many fragments and their trajectories parting from the parent particle, and mutual collisions among them. In our simulation, we identified 32 isolated fragments extracted from the parent particle. The size distribution of the fragments was similar to that obtained from the aerodynamic experiment in which a liquid layer was attached to a solid core and it was exposed to a gas flow. We detected 12 collisions between the fragments, which may result in the compound chondrule formation. We also analyzed the paths of all the fragments in detail and found the importance of the shadow effect in which a fragment extracted later blocks the gas flow toward a fragment extracted earlier. We examined the collision velocity and impact parameter of each collision and found that 11 collisions should result in coalescence. It means that the ratio of coalescent bodies to single bodies formed in this disruption of a parent particle is R_coa=11/(32-11)=0.52. We concluded that compound chondrule formation can occur just after the disruption of a cm-sized molten dust particle in shock-wave heating.     

A liquid-supported condensation of major minerals in the solar nebula: Evidence from glasses in the Kaba (CV3) chondrite

Glasses, in the Kaba CV3 chondrite, occur as mesostasis in chondrules and aggregates and as inclusions in olivines, both confined or open and connected to the mesostasis. The inclusions in olivine and the glassy mesostasis of aggregates seem to have formed contemporaneously. The confined glass inclusions and open inclusions in olivine were formed during olivine growth and the mesostasis glass during olivine aggregation. All glasses have high trace element contents (10-20×CI) with unfractionated CI-normalized abundances of refractory trace elements. In contrast, V, Mn, Li, and Cr are depleted in all glasses with respect to the refractory trace elements, as is Rb in the glass inclusions in olivine but not in the mesostasis glass. This abundance pattern indicates vapor fractionation and a common condensation origin for both glasses. Glasses of confined glass inclusions in olivine have a SiAlCa-rich composition with a chondritic Ca/Al ratio. Glasses of open glass inclusions and mesostasis are poor in Ca and enriched in alkalis. However, Ca contents of olivines indicate crystallization from a Ca-rich melt of a composition similar to that of the glass inclusions. In addition, trace element abundances indicate that these glasses (liquids) probably had an original composition similar to that of the inclusion glass. They apparently lost Ca in exchange for alkalis in a metasomatic exchange reaction, presumably with the vapor. There is now growing evidence that liquids can indeed condense from a solar nebula gas, provided the gas/dust ratio is sufficiently low. In these regions with enhanced oxygen fugacity as compared to that of a nebula of solar composition, liquids (the glass precursor) probably played an important role in growing crystals from the vapor by liquid-phase epitaxy. The glasses appear to be the remnants of this thin liquid layer interface that supported the growth of olivine from the vapor following the Vapor-Liquid-Solid process. This liquid will have a refractory composition and will have trace element contents which are in equilibrium with the vapor, and, therefore, will not change much during the time of olivine growth. The composition of the liquid seems to be unconstrained by the phases it is in contact with. Samples of this liquid will be retained as glass inclusions in olivine. The glassy mesostasis could also be a sample of this liquid that got trapped in inter-crystal spaces. The mesostasis glass subsequently behaved as an open system and its Ca was exchanged—presumably with the vapor—for the alkali elements Na, K, and Rb. In contrast, glass inclusions in olivine were protected by the host, could not react, and thus preserved the original composition of this liquid.     

The distributions and ages of refractory objects in the solar nebula

Refractory objects such as Calcium, Aluminum-rich Inclusions, Amoeboid Olivine Aggregates, and crystalline silicates, are found in primitive bodies throughout our Solar System. It is believed that these objects formed in the hot, inner solar nebula and were redistributed during the mass and angular momentum transport that took place during its early evolution. The ages of these objects thus offer possible clues about the timing and duration of this transport. Here we study how the dynamics of these refractory objects in the evolving solar nebula affected the age distribution of the grains that were available to be incorporated into planetesimals throughout the Solar System. It is found that while the high temperatures and conditions needed to form these refractory objects may have persisted for millions of years, it is those objects that formed in the first 10⁵ years that dominate (make up over 90%) those that survive throughout most of the nebula. This is due to two effects: (1) the largest numbers of refractory grains are formed at this time period, as the disk is rapidly drained of mass during subsequent evolution and (2) the initially rapid spreading of the disk due to angular momentum transport helps preserve this early generation of grains as opposed to later generations. This implies that most refractory objects found in meteorites and comets formed in the first 10⁵ years after the nebula formed. As these objects contained live ²⁶Al, this constrains the time when short-lived radionuclides were introduced to the Solar System to no later than 10⁵ years after the nebula formed. Further, this implies that the t=0 as defined by meteoritic materials represents at most, the instant when the solar nebula finished accreting significant amounts of materials from its parent molecular cloud.     

Origin of three-dimensional shapes of chondrules: I. Hydrodynamics simulations of rotating droplet exposed to high-velocity rarefied gas flow

The origin of three-dimensional shapes of chondrules is an important information to identify their formation mechanism in the early solar nebula. The measurement of their shapes by using X-ray computed topography suggested that they are usually close to perfect spheres, however, some of them have rugby-ball-like (prolate) shapes [Tsuchiyama, A., Shigeyoshi, R., Kawabata, T., Nakano, T., Uesugi, K., Shirono, S., 2003. Lunar Planet. Sci. 34, 1271-1272]. We considered that the prolate shapes reflect the deformations of chondrule precursor dust particles when they are heated and melted in the high velocity gas flow. In order to reveal the origin of chondrule shapes, we carried out the three-dimensional hydrodynamics simulations of a rotating molten chondrule exposed to the gas flow in the framework of the shock-wave heating model for chondrule formation. We adopted the gas ram pressure acting on the chondrule surface of in a typical shock wave. Considering that the chondrule precursor dust particle has an irregular shape before melting, the ram pressure causes a net torque to rotate the particle. The estimated angular velocity is for the precursor radius of r₀=1 mm, though it has a different value depending on the irregularity of the shape. In addition, the rotation axis is likely to be perpendicular to the direction of the gas flow. Our calculations showed that the rotating molten chondrule elongates along the rotation axis, in contrast, shrinks perpendicularly to it. It is a prolate shape. The reason why the molten chondrule is deformed to a prolate shape was clearly discussed. Our study gives a complementary constraint for chondrule formation mechanisms, comparing with conventional chemical analyses and dynamic crystallization experiments that have mainly constrained the thermal evolutions of chondrules.     

Breakup of liquids by high velocity flow and size distribution of chondrules

As a new approach to understanding the chondrule formation process, we carried out aerodynamic experiments in which a liquid layer was attached to solid cores, and the breakup of this layer occurred by means of the interaction with a high-velocity gas flow. The size distribution of the dispersed droplets was investigated and compared with the size distributions of chondrules. Both distributions had an exponential form. Using the experimental results, the hydrodynamic pressure to produce the chondrule size distributions was estimated to be ∼ 10⁴ Pa.     

Fragment-collision model for compound chondrule formation: Estimation of collision probability

We propose a new scenario for compound chondrule formation named as “fragment-collision model,” in the framework of the shock-wave heating model. A molten cm-sized dust particle (parent) is disrupted in the high-velocity gas flow. The extracted fragments (ejectors) are scattered behind the parent and the mutual collisions between them will occur. We modeled the disruption event by analytic considerations in order to estimate the probability of the mutual collisions assuming that all ejectors have the same radius. In the typical case, the molten thin () layer of the parent surface will be stripped by the gas flow. The stripped layer is divided into about 200 molten ejectors (assuming that the radius of ejectors is 300 μm) and then they are blown away by the gas flow in a short period of time (). The stripped layer is leaving from the parent with the velocity of depending on the viscosity, and we assumed that the extracted ejectors have a random velocity Δv of the same order of magnitude. Using above values, we can estimate the number density of ejectors behind the parent as . These ejectors occupy ∼9% of the space behind the parent in volume. Considering that the collision rate (number of collisions per unit time experienced by an ejector) is given by Rcoll=σcollneΔv, where σcoll is the cross-section of collision [e.g., Gooding, J.K., Keil, K., 1981. Meteoritics 16, 17-43], we obtain by substituting above values. Since most collisions occur within the short duration () before the ejectors are blown away, we obtain the collision probability of Pcoll∼0.36, which is the probability of collisions experienced by an ejector in one disruption event. The estimated collision probability is about one order of magnitude larger than the observed fraction of compound chondrules. In addition, the model predictions are qualitatively consistent with other observational data (oxygen isotopic composition, textural types, and size ratios of constituents). Based on these results, we concluded that this new model can be one of the strongest candidates for the compound chondrule formation. It should be noted that all collisions do not necessarily lead to the compound chondrule formation. The formation efficiency and the future works which should be investigated in the forthcoming paper are also discussed.     

Shock-wave heating model for chondrule formation: Hydrodynamic simulation of molten droplets exposed to gas flows

Millimeter-sized, spherical silicate grains abundant in chondritic meteorites, which are called as chondrules, are considered to be a strong evidence of the melting event of the dust particles in the protoplanetary disk. One of the most plausible scenarios is that the chondrule precursor dust particles are heated and melt in the high-velocity gas flow (shock-wave heating model). We developed the non-linear, time-dependent, and three-dimensional hydrodynamic simulation code for analyzing the dynamics of molten droplets exposed to the gas flow. We confirmed that our simulation results showed a good agreement in a linear regime with the linear solution analytically derived by Sekyia et al. [Sekyia, M., Uesugi, M., Nakamoto, T., 2003. Prog. Theor. Phys. 109, 717-728]. We found that the non-linear terms in the hydrodynamical equations neglected by Sekiya et al. [Sekiya, M., Uesugi, M., Nakamoto, T., 2003. Prog. Theor. Phys. 109, 717-728] can cause the cavitation by producing negative pressure in the droplets. We discussed that the fragmentation through the cavitation is a new mechanism to determine the upper limit of chondrule sizes. We also succeeded to reproduce the fragmentation of droplets when the gas ram pressure is stronger than the effect of the surface tension. Finally, we compared the deformation of droplets in the shock-wave heating with the measured data of chondrules and suggested the importance of other effects to deform droplets, for example, the rotation of droplets. We believe that our new code is a very powerful tool to investigate the hydrodynamics of molten droplets in the framework of the shock-wave heating model and has many potentials to be applied to various problems.     

The primary liquid condensation model and the origin of barred olivine chondrules

Barred olivine (BO) chondrules are some of the most striking objects in chondrites. Their ubiquitous presence and peculiar texture caught the attention of researchers and, as a consequence, considerable effort has been expensed on unraveling their origin(s). Here we report on a detailed study of two types of chondrules: the Classic and the Multiple-Plate Type of BO chondrules from the Essebi (CM2), Bishunpur (LL3.1), Acfer 214 (CH3) and DAG 055 (C3-UNGR) chondrites, and discuss the petrographic and chemical data of their major mineral phases and glasses. Glasses occur as mesostasis or as glass inclusions, the latter either enclosed inside the olivine bars (plates) or still connected to the mesostasis. The chemical composition of all glasses, characterized by being Si-Al-Ca-rich and free of alkali elements, is similar to those of the constituents (the building blocks, such as chondrules, aggregates, inclusions, mineral fragments, etc.) of CR and CV3 chondrites. They all have high trace element contents (∼10×CI) with unfractionated CI-normalized abundances of refractory trace elements and depletions in moderately volatile and volatile elements with respect to the refractory trace elements. The presence of alkali elements (Na + K + Rb) is coupled with a low Ca content and is only observed in those glasses that have behaved as open systems. This result supports the previous finding that Ca was replaced by alkalis (e.g., Na-Ca exchange), presumably through a vapor-solid reaction. The glasses apparently are the quenched liquid from which the olivine plates crystallized. However, they do not show any chemical fractionation that could have resulted from the crystallization of the olivines, but rather have a constant chemical compositions throughout the formation of the chondrule. In a previous contribution we were able to demonstrate the role of these liquids in supporting crystal growth directly from the vapor. Here we extend application of the primary liquid condensation model to formulate a new model for the origin of BO chondrules. The primary liquid condensation model is based on the ability of dust-enriched solar-nebula gas to directly condense into a liquid, provided the gas/dust ratio is sufficiently low. Thus, we propose that chondrules can be formed by condensation of a liquid droplet directly from the solar nebula. The extensive variability in chemical composition of BO chondrules, which ranges from alkali-poor to alkali-rich, can be explained by elemental exchange reactions with the cooling nebula. We calculate the chemical composition of the initial liquid droplet from which BO chondrules could have formed and speculate about the physical and chemical conditions that prevail in the specific regions of the solar nebula that can promote creation of these objects.     

Size distributions of chondrules and dispersed droplets caused by liquid breakup: An application to shock wave conditions in the solar nebula

We present the results of an aerodynamic liquid dispersion experiment using initially molten silicate samples. We investigate the threshold of breakup and the size distribution of dispersed droplets. The breakup threshold is consistent with the previous experiments using water and a mixture of water and glycerol. Also, we confirm the previous results that the size distributions of dispersed droplets are represented by an exponential form and that the characteristic size of dispersed droplets is related to the dynamic pressure of high-velocity gas flow. The size distribution has a similar form to that of chondrules, though the experiment is not exactly corresponding to the shock heating models for chondrule formation that consider solid precursors which are molten by the shocks. The experimental results indicate that, if liquid chondrule-precursors were dispersed by high-velocity flow, the dynamic pressure of the flow is ∼10 kPa. A chondrule formation condition in a shock-wave heating model suggests that this pressure can be realized at the regions within ∼1 AU in the minimum solar-nebula mass models. However, if the nebula had a larger mass and gravitational instabilities occurred, this pressure may be realized in the spiral arms at 2-3 AU and chondrules may be formed in asteroid belt.     

UV photolysis, organic molecules in young disks, and the origin of meteoritic amino acids

The origin of complex organic molecules such as amino acids and their precursors found in meteorites and comets is unknown. Previous studies have accounted for the complex organic inventory of the Solar System by aqueous chemistry on warm meteoritic parent bodies, or by accretion of organics formed in the interstellar medium. This paper proposes a third possibility: that complex organics were created in situ by ultraviolet light from nearby O/B stars irradiating ices already in the Sun’s protoplanetary disk. If the Sun was born in a dense cluster near UV-bright stars, the flux hitting the disk from external stars could be many orders of magnitude higher than that from the Sun alone. Such photolysis of ices in the laboratory can rapidly produce amino acid precursors and other complex organic molecules. I present a simple model coupling grain growth and UV exposure in a young circumstellar disk. It is shown that the production may be sufficient to create the Solar System’s entire complex organic inventory within 10⁶ yr. Subsequent aqueous alteration on meteoritic parent bodies is not ruled out.     

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

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

Origin of the differences in refractory-lithophile-element abundances among chondrite groups

Chondrite groups can be distinguished on the basis of their abundances of refractory lithophile elements (RLE). These abundances are, in part, functions of the mass fraction of Ca-Al-rich inclusions (CAIs) within the chondrites. Carbonaceous chondrites contain the most CAIs and the highest RLE abundances; they also contain modally abundant fine-grained matrix material that consists largely of modified nebular dust. The amount of dust varied throughout the solar nebula: enstatite and ordinary chondrites formed in low-dust regions in the inner part of the nebula, R chondrites formed in higher-dust zones at somewhat greater heliocentric distances, and carbonaceous chondrites formed in even dustier regions farther from the Sun. The amount of ambient dust peaked in the region where CV and CK chondrites accreted; these chondrites have abundant matrix, the highest modal abundances of CAIs, and the highest bulk RLE contents. Substantial amounts of nebular dust occurred in highly porous multi-millimeter-to-centimeter-size dustballs that were on the order of 100 times more massive than CAIs. Radial drift processes in the nebula affected these dustballs to approximately the same extent as the CAIs; both types of objects were aerodynamically concentrated in the same nebular regions. These regions maintained approximately the same relative amounts of dust through the periods of chondrule formation and chondrite accretion.     

Planetesimal formation by turbulent concentration

The formation of 1-1000 km diameter planetesimals from dust grains in a protoplanetary disk is a key step in planet formation. Conventional models for planetesimal formation involve pairwise sticking of dust grains, or the sedimentation of dust grains to a thin layer at the disk midplane followed by gravitational instability. Each of these mechanisms is likely to be frustrated if the disk is turbulent. Particles with stopping times comparable to the turnover time of the smallest eddies in a turbulent disk can become concentrated into dense clumps that may be the precursors of planetesimals. Such particles are roughly millimeter-sized for a typical protoplanetary disk. To survive to become planetesimals, clumps need to form in regions of low vorticity to avoid rotational breakup. In addition, clumps must have sufficient self gravity to avoid break up due to the ram pressure of the surrounding gas. Given these constraints, the rate of planetesimal formation can be estimated using a cascade model for the distribution of particle concentration and vorticity within eddies of various sizes in a turbulent disk. We estimate planetesimal formation rates and planetesimal diameters as a function of distance from a star for a range of protoplanetary disk parameters. For material with a solar composition, the dust-to-gas ratio is too low to allow efficient planetesimal formation, and most solid material will remain in small particles. Enhancement of the dust-to-gas ratio by 1-2 orders of magnitude, either vertically or radially, allows most solid material to be converted into planetesimals within the typical lifetime of a disk. Such dust-to-gas ratios may occur near the disk midplane as a result of vertical settling of short-lived clumps prior to clump breakup. Planetesimal formation rates are sensitive to the assumed size and rotational speed of the largest eddies in the disk, and formation rates increase substantially if the largest eddies rotate more slowly than the disk itself. Planetesimal formation becomes more efficient with increasing distance from the star unless the disk surface density profile has a slope of −1.5 or steeper as a function of distance. Planetesimal formation rates typically increase by an order-of-magnitude or more moving outward across the snow line for a solid surface density increase of a factor of 2. In all cases considered, the modal planetesimal size increases with roughly the square root of distance from the star. Typical modal diameters are 100 km and 400 km in the regions corresponding to the asteroid belt and Kuiper belt in the Solar System, respectively.     

Crystallization of cosmic dust from highly supersaturated silicate vapor in a rapidly cooled environment

Growth conditions and the resultant morphology of cosmic forsterite and enstatite particles condensed from the vapor were investigated experimentally as a function of growth temperature and supersaturation using flash-heating by CO₂ laser irradiation. Forsterite particles grew dominantly, followed by a few pyroxenes. No silica minerals were observed. The forsterite morphology changed systematically depending on the temperature (T) and the vapor supersaturation (σ). As the temperature decreased and the vapor supersaturation increased, the forsterite morphology changed from a bulky type (T=1000-1450 °C, σ<97) to a platy type (T=700-1000 °C, σ=97-161), then to a columnar needle shape (T=500-820 °C, σ=131-230), and finally to a droplet type (T<500 °C, σ>230). Very thin polygonal growth steps, which suggest vapor-solid (VS) growth, were detected on the surface of the faceted bulky and platy forsterite particles. Transmission electron microscopic (TEM) observation showed that the tip of the columnar and needle-shaped forsterite was covered with an amorphous layer. This amorphous coverage illustrates that a liquid phase can be condensed from the vapor, even under the stable conditions where crystalline forsterite is stable. This amorphous layer plays a role in the vapor-liquid-solid (VLS) mechanism of the forsterite particles. The difference in the growth mechanism as a function of vapor supersaturation and temperature can be explained by metastable liquid condensation. The experimentally synthesized coexisting patterns of VS-grown and VLS-grown olivine particles resemble the pattern of matrix olivine or chondrule rims in primitive meteorites. Forsterite can crystallize more easily than either pyroxene or silica minerals, which is consistent with the dominance of forsterite in cometary dust particles, as suggested by its infrared spectrum.     

Accretion among preplanetary bodies: The many faces of runaway growth

When preplanetary bodies reach proportions of ∼1 km or larger in size, their accretion rate is enhanced due to gravitational focusing (GF). We have developed a new numerical model to calculate the collisional evolution of the gravitationally-enhanced growth stage. The numerical model is novel as it attempts to preserve the individual particle nature of the bodies (like N-body codes); yet it is statistical in nature since it must incorporate the very large number of planetesimals. We validate our approach against existing N-body and statistical codes. Using the numerical model, we explore the characteristics of the runaway growth and the oligarchic growth accretion phases starting from an initial population of single planetesimal radius R₀. In models where the initial random velocity dispersion (as derived from their eccentricity) starts out below the escape speed of the planetesimal bodies, the system experiences runaway growth. We associate the initial runaway growth phase with increasing GF-factors for the largest body. We find that during the runaway growth phase the size distribution remains continuous but evolves into a power-law at the high-mass end, consistent with previous studies. Furthermore, we find that the largest body accretes from all mass bins; a simple two-component approximation is inapplicable during this stage. However, with growth the runaway body stirs up the random motions of the planetesimal population from which it is accreting. Ultimately, this feedback stops the fast growth and the system passes into oligarchy, where competitor bodies from neighboring zones catch up in terms of mass. We identify the peak of GF with the transition between the runaway growth and oligarchy accretion stages. Compared to previous estimates, we find that the system leaves the runaway growth phase at a somewhat larger radius, especially at the outer disk. Furthermore, we assess the relevance of small, single-size fragments on the growth process. In classical models, where the initial velocity dispersion of bodies is small, these do not play a critical role during the runaway growth; however, in models that are characterized by large initial relative velocities due to external stirring of their random motions, a situation can emerge where fragments dominate the accretion, which could lead to a very fast growth.