Models of particle layers in the midplane of the solar nebula

In the absence of global turbulence, solid particles in the solar nebula tend to settle into a thin layer in the central plane. Shear between this layer and pressure-supported gas produces localized turbulence in the midplane; the thickness of the particle layer is determined by balance between settling and turbulent diffusion. A numerical model is described, which allows computation of the vertical structure of a layer of particles of arbitrary size, with self-consistent distributions of particle density, turbulent velocity, and radial fluxes of particles and gas. Effects of varying particle size and the abundances of solids and gas are evaluated. If the surface density of solids is increased by an order of magnitude over nominal solar abundance, the peak density within a layer of small particles can approach the critical value needed for gravitational instability. However, depletion of the nebular gas is much less effective for raising the density of such a layer to the critical value, due to decreased coupling of particles to the gas as the density of the gas decreases. The variation of radial particle flux with surface density of the particle layer is not consistent with secular instability of the layer driven by gas drag.     

Ice lines, planetesimal composition and solid surface density in the solar nebula

To date, there is no core accretion simulation that can successfully account for the formation of Uranus or Neptune within the observed 2–3 Myr lifetimes of protoplanetary disks. Since solid accretion rate is directly proportional to the available planetesimal surface density, one way to speed up planet formation is to take a full accounting of all the planetesimal-forming solids present in the solar nebula. By combining a viscously evolving protostellar disk with a kinetic model of ice formation, which includes not just water but methane, ammonia, CO and 54 minor ices, we calculate the solid surface density of a possible giant planet-forming solar nebula as a function of heliocentric distance and time. Our results can be used to provide the starting planetesimal surface density and evolving solar nebula conditions for core accretion simulations, or to predict the composition of planetesimals as a function of radius. We find three effects that favor giant planet formation by the core accretion mechanism: (1) a decretion flow that brings mass from the inner solar nebula to the giant planet-forming region, (2) the fact that the ammonia and water ice lines should coincide, according to recent lab results from Collings et al. [Collings, M.P., Anderson, M.A., Chen, R., Dever, J.W., Viti, S., Williams, D.A., McCoustra, M.R.S., 2004. Mon. Not. R. Astron. Soc. 354, 1133–1140], and (3) the presence of a substantial amount of methane ice in the trans-saturnian region. Our results show higher solid surface densities than assumed in the core accretion models of Pollack et al. [Pollack, J.B., Hubickyj, O., Bodenheimer, P., Lissauer, J.J., Podolak, M., Greenzweig, Y., 1996. Icarus 124, 62–85] by a factor of 3–4 throughout the trans-saturnian region. We also discuss the location of ice lines and their movement through the solar nebula, and provide new constraints on the possible initial disk configurations from gravitational stability arguments.     

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.     

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.     

Impact angle influence in high velocity dust collisions during planetesimal formation

We have examined the influence of impact angle in collisions between small dust aggregates and larger dust targets through laboratory experiments. Targets consisted of μm-sized quartz dust and had a porosity of about 67%; the projectiles, between 1 and 5 mm in diameter, were slightly more compact (64% porosity). The collision velocity was centered at 20 m/s and impact angles range from 0° to 45°. At a given impact angle, the target gained mass for projectiles smaller than a threshold size, which decreases with increasing angle from about 3 mm to 1 mm. The fact that growth is possible up to the largest angles studied supports the idea of planetesimal formation by sweep-up of small dust aggregates.     

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.     

The effects of the tidal force on shear instabilities in the dust layer of the solar nebula

The linear analysis of the instability due to vertical shear in the dust layer of the solar nebula is performed. The following assumptions are adopted throughout this paper: (1) The self-gravity of the dust layer is neglected. (2) One fluid model is adopted, where the dust aggregates have the same velocity with the gas due to strong coupling by the drag force. (3) The gas is incompressible. The calculations with both the Coriolis and the tidal forces show that the tidal force has a stabilizing effect. The tidal force causes the radial shear in the disk. This radial shear changes the wave number of the mode which is at first unstable, and the mode is eventually stabilized. Thus the behavior of the mode is divided into two stages: (1) the first growth of the unstable mode which is similar to the results without the tidal force, and (2) the subsequent stabilization due to an increase of the wave number by the radial shear. If the midplane dust/gas density ratio is smaller than 2, the stabilization occurs before the unstable mode grows largely. On the other hand, the mode grows faster by one hundred orders of magnitude, if this ratio is larger than 20. Because the critical density of the gravitational instability is a few hundreds times as large as the gas density, the hydrodynamic instability investigated in this paper grows largely before the onset of the gravitational instability. It is expected that the hydrodynamic instability develops turbulence in the dust layer and the dust aggregates are stirred up to prevent from settling further. The formation of planetesimals through the gravitational instabilities is difficult to occur as long as the dust/gas surface density ratio is equal to that for the solar abundance. On the other hand, the shear instability is suppressed and the planetesimal formation through the gravitational instability may occur, if dust/gas surface density ratio is hundreds times as large as that for the solar abundance.     

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.     

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.     

Conditions for collisional growth of a grain aggregate

Collisional growth of grain aggregates is a critical process in the early stage of planet formation. A collision between grain aggregates is numerically simulated by means of a smoothed particle hydrodynamic code, treating a grain aggregate as a continuum media. A model for mechanical response of a grain aggregate is developed based on published experimental data. Free parameters of the model are the bulk modulus, compressive, shear, and tensile strengths of a grain aggregate, and impact velocity. I have determined three conditions for the growth of an aggregate within the mechanical response model. (1) Compressive strength is the smallest among the three components of strengths. (2) Impact velocity is as low as 4% of the sound speed of an aggregate. (3) Effective restoration of the strengths is necessary due to reconnection between grains followed by compaction of an aggregate. Possibilities of these conditions in the solar nebula are discussed.     

Blowing in the wind: III. Accretion of dust rims by chondrule-sized particles in a turbulent protoplanetary nebula

The fabric of primitive meteorites is dominated by small but macroscopic particles—chondrules, refractory mineral inclusions (CAIs), metal grains, and their like. One interesting aspect of these particles is that they are often surrounded by well-attached rims of fine-grained dust which appear to have been “accreted” onto solid mineral cores. The rim thickness varies from one meteorite to another, but there seems to be a proportionality between the thickness of the rim and the size of the core. We make use of recently derived analytical expressions for absolute and relative velocities of chondrule-and-CAI-sized particles in a weakly turbulent nebula (Cuzzi and Hogan, 2003, paper I of this series) to assess the acquisition of fine-grained accretionary dust rims by particles in the chondrule-to-CAI size range. We compare these predictions with meteoritic observations, and show how the existence of fairly compact dust rims on chondrules and similar size objects can be easily understood within the turbulent nebula context. We estimate the time needed to accrete such rims to be in the 10²-10³ year range. More observations of the form of the correlation between rim and core diameter in dust-rimmed chondrules are needed in order to strongly constrain the environment and history of these objects.     

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.     

Impacts into weak dust targets under microgravity and the formation of planetesimals

We carried out 16 collision experiments in the drop tower in Bremen, Germany. Dust projectiles and solid projectiles of several mm in size impacted a dust target 5 cm in depth and width at velocities between 3.5 and 21.5 m/s. For solid impactors we found significant mass loss on the front (impact) side of the target. Mass loss depended on the impact velocity and projectile type (solid sphere or dust) and was up to 35 times the projectile mass for targets of the lowest tensile strength. Typical fragment velocities on the front side of the target ranged from 3 to 12 cm/s. The ejecta velocity was independent of the impact velocity but it increased with projectile mass. On the back side of the target (opposite to the impact side) mass was ejected from the target above a certain threshold impact velocity. Ejection velocity on the back side increased with impact velocity and is larger for solid projectiles than for dust projectiles. In one case a slightly stronger target gained mass in a slow dust-dust collision. We verified that collisions of dust projectiles with compact, very strong dust targets lead to a more massive target accreting part of the projectile. Applied to planetesimal formation, the experiments suggest that the maximum possible ejecta velocity from a body of several cm in size after a collision is small. Ejecta were slow enough that they were reaccreted by means of gas flow if large pores were part of the body's morphology. While very weak bodies cannot grow in the primary collision at the given velocities, this can lead to growth by secondary collisions. Slight compression, which could result from preceding collisions, might lead to immediate growth of a body in slow collisions by adding projectile mass.     

On the mean oxygen isotope composition of the Solar System

Since the first discovery of extraordinary oxygen isotope compositions in carbonaceous meteorites by Clayton et al. [Clayton, R.N., Grossman, L., Mayeda, T.K., 1973. Science 182, 485-488], numerous studies have been done to explain the unusual mass-independent isotope fractionation, but the problem is still unresolved to this day. Clayton's latest interpretation [Clayton, R.N., 2002. Nature 415, 860-861] sheds new light on the problem, and possible hypotheses now seem to be fairly well defined. A key issue is to resolve whether the oxygen isotopes in the Solar System represented by the Sun (solar oxygen) are the same as oxygen isotopes in planetary objects such as bulk meteorites, Mars, Earth, and Moon, or whether the solar oxygen is more similar to the lightest oxygen isotopes observed in CAIs (Calcium Aluminum-rich Inclusions) in primitive meteorites. Here, we examined the problem using oxygen isotope analytical data of about 400 bulk meteorite samples of various classes or types (data compiled by K. Lodders). We used in our discussion exclusively the parameter , a direct measure of the degree of mass-independent isotope fractionation of oxygen isotopes. When is arranged according to a characteristic size of their host planetary object, it shows a systematic trend: (1) values scatter around zero; (2) the scatter from the mean () decreases with increasing representative size of the respective host planetary object. This systematic trend is easily understood on the basis of a hierarchical scenario of planetary formation, that is, larger planetary objects have formed by progressive accretion of planetesimals by random sampling over a wide spectrum of proto-solar materials. If this progressive random sampling of planetesimals were the essential process of planetary formation, the isotopic composition of planetary oxygen should approach that of the solar oxygen. To test this random sampling hypothesis, we applied a multiscale, multistep bootstrap statistical method [Shimodaira, H., 2004. Ann. Statist. 32, 2616-2641] to the meteorite oxygen isotope data, and deduced a σ-N relation, where σ is the standard deviation of , and N is the representative size of a host planetary object. If we assign 200 and 500 km as a representative sizes of the chondrite and achondrite parent bodies, the observed σ of agree well with the values predicted by the σ-N relation. A common mean value of for all planetary objects also agrees with the progressive random sampling process. Therefore, we conclude that the solar oxygen is the same as planetary oxygen, but differs from CAI oxygen. The conclusion implies that a massive enrichment in ¹⁷O and ¹⁸O resulting from CO self-shielding, a current influential interpretation of CAI-O, did not occur.     

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.     

A gas-poor planetesimal capture model for the formation of giant planet satellite systems

Assuming that an unknown mechanism (e.g., gas turbulence) removes most of the subnebula gas disk in a timescale shorter than that for satellite formation, we develop a model for the formation of regular (and possibly at least some of the irregular) satellites around giant planets in a gas-poor environment. In this model, which follows along the lines of the work of Safronov et al. [1986. Satellites. Univ. of Arizona Press, Tucson, pp. 89-116], heliocentric planetesimals collide within the planet's Hill sphere and generate a circumplanetary disk of prograde and retrograde satellitesimals extending as far out as ∼RH/2. At first, the net angular momentum of this proto-satellite swarm is small, and collisions among satellitesimals leads to loss of mass from the outer disk, and delivers mass to the inner disk (where regular satellites form) in a timescale ?¹⁰⁵ years. This mass loss may be offset by continued collisional capture of sufficiently small <1 km interlopers resulting from the disruption of planetesimals in the feeding zone of the giant planet. As the planet's feeding zone is cleared in a timescale ?¹⁰⁵ years, enough angular momentum may be delivered to the proto-satellite swarm to account for the angular momentum of the regular satellites of Jupiter and Saturn. This feeding timescale is also roughly consistent with the independent constraint that the Galilean satellites formed in a timescale of ¹⁰⁵-¹⁰⁶ years, which may be long enough to accommodate Callisto's partially differentiated state [Anderson et al., 1998. Science 280, 1573; Anderson et al., 2001. Icarus 153, 157-161]. In turn, this formation timescale can be used to provide plausible constraints on the surface density of solids in the satellitesimal disk (excluding satellite embryos for satellitesimals of size ∼1 km), which yields a total disk mass smaller than the mass of the regular satellites, and means that the satellites must form in several ∼10 collisional cycles. However, much more work will need to be conducted concerning the collisional evolution both of the circumplanetary satellitesimals and of the heliocentric planetesimals following giant planet formation before one can assess the significance of this agreement. Furthermore, for enough mass to be delivered to form the regular satellites in the required timescale one may need to rely on (unproven) mechanisms to replenish the feeding zone of the giant planet. We compare this model to the solids-enhanced minimum mass (SEMM) model of Mosqueira and Estrada [2003a. Icarus 163, 198-231; 2003b. Icarus 163, 232-255], and discuss its main consequences for Cassini observations of the saturnian satellite system.     

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.     

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.     

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.     

Evaporation of nebular fines during chondrule formation

Studies of matrix in primitive chondrites provide our only detailed information about the fine fraction (diameter <2 μm) of solids in the solar nebula. A minor fraction of the fines, the presolar grains, offers information about the kinds of materials present in the molecular cloud that spawned the Solar System. Although some researchers have argued that chondritic matrix is relatively unaltered presolar matter, meteoritic chondrules bear witness to multiple high-temperature events each of which would have evaporated those fines that were inside the high-temperature fluid. Because heat is mainly transferred into the interior of chondrules by conduction, the surface temperatures of chondrules were probably at or above 2000 K. In contrast, the evaporation of mafic silicates in a canonical solar nebula occurs at around 1300 K and FeO-rich, amorphous, fine matrix evaporates at still lower temperatures, perhaps near 1200 K. Thus, during chondrule formation, the temperature of the placental bath was probably >700 K higher than the evaporation temperatures of nebular fines. The scale of chondrule forming events is not known. The currently popular shock models have typical scales of about ¹⁰⁵ km. The scale of nebular lightning is less well defined, but is certainly much smaller, perhaps in the range 1 to 1000 m. In both cases the temperature pulses were long enough to evaporate submicrometer nebular fines. This interpretation disagrees with common views that meteoritic matrix is largely presolar in character and CI-chondrite-like in composition. It is inevitable that presolar grains (both those recognized by their anomalous isotopic compositions and those having solar-like compositions) that were within the hot fluid would also have evaporated. Chondrule formation appears to have continued down to the temperatures at which planetesimals formed, possibly around 250 K. At temperatures >600 K, the main form of C is gaseous CO. Although the conversion of CO to CH₄ at lower temperatures is kinetically inhibited, radiation associated with chondrule formation would have accelerated the conversion. There is now evidence that an appreciable fraction of the nanodiamonds previously held to be presolar were actually formed in the solar nebula. Industrial condensation of diamonds from mixtures of CH₄ and H₂ implies that high nebular CH₄/CO ratios favored nanodiamond formation. A large fraction of chondritic insoluble organic matter may have formed in related processes. At low nebular temperatures appreciable water should have been incorporated into the smoke that condensed following dust (and some chondrule) evaporation. If chondrule formation continued down to temperatures as low as 250 K this process could account for the water concentration observed in primitive chondrites such as LL3.0 and CO3.0 chondrites. Higher H₂O contents in CM and CI chondrites may reflect asteroidal redistribution. In some chondrite groups (e.g., CR) the Mg/Si ratio of matrix material is appreciably (30%) lower than that of chondrules but the bulk Mg/Si ratio is roughly similar to the CI or solar ratio. This has been interpreted as a kind of closed-system behavior sometimes called “complementarity.” This leads to the conclusion that nebular fines were efficiently agglomerated. Its importance, however is obscured by the observation that bulk Mg/Si ratios in ordinary and enstatite chondrites are much lower than those in carbonaceous chondrites, and thus that complementarity did not hold throughout the solar nebula.