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.     

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.     

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.     

A shock-wave heating model for chondrule formation II. Minimum size of chondrule precursors

Chondrule formation due to the shock wave heating of dust particles with a wide variety of shock properties are examined. We numerically simulate the steady postshock region in a framework of one-dimensional hydrodynamics, taking into account many of the physical and chemical processes that determine the properties of the region, especially nonequilibrium chemical reactions of gas species. We mainly focus on the dust particle shrinkage due to the evaporation in the postshock hot gas and the precursor size conditions for chondrule formation. We find that the small precursors whose radii are smaller than a critical value, , cannot form chondrules because they evaporate away completely in the postshock region. The minimum value of is about 10 μm, though it depends on the shock speed and the preshock gas density. Furthermore, we demonstrate the chondrule size distributions which are formed through the shock-wave heating. These results indicate that the shock-wave heating model can be regarded as a strong candidate for the mechanism of chondrule formation.     

A Shock-Wave Heating Model for Chondrule Formation: Effects of Evaporation and Gas Flows on Silicate Particles

A shock-wave heating model is one of the possible models for chondrule formation. We examine, within the framework of a shock-wave heating model, the effects of evaporation on the heating of chondrule precursor particles and the stability of their molten state in the postshock flow. We numerically simulate the heating process in the flow taking into account evaporation. We find that the melting criterion and the minimum radius criterion do not change significantly. However, if the latent heat cooling due to the evaporation dominates the radiative cooling from the precursor particle, the peak temperature of the precursor particle is suppressed by a few hundred Kelvins. We also find that the total gas pressure (ram plus static) acting on the precursor particle exceeds the vapor pressure of the molten precursor particle. Therefore, it is possible to form chondrules in the shock-wave heating model if the precursor temperature increases up to the melting point.     

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.     

Free collisions in a microgravity many-particle experiment – II: The collision dynamics of dust-coated chondrules

The formation of planetesimals in the early Solar System is hardly understood, and in particular the growth of dust aggregates above millimeter sizes has recently turned out to be a difficult task in our understanding (Zsom, A., Ormel, C.W., Güttler, C., Blum, J., Dullemond, C.P. [2010]. Astron. Astrophys., 513, A57). Laboratory experiments have shown that dust aggregates of these sizes stick to one another only at unreasonably low velocities. However, in the protoplanetary disk, millimeter-sized particles are known to have been ubiquitous. One can find relics of them in the form of solid chondrules as the main constituent of chondrites. Most of these chondrules were found to feature a fine-grained rim, which is hypothesized to have formed from accreting dust grains in the solar nebula. To study the influence of these dust-coated chondrules on the formation of chondrites and possibly planetesimals, we conducted collision experiments between millimeter-sized, dust-coated chondrule analogs at velocities of a few cm s^?1. For 2 and 3 mm diameter chondrule analogs covered by dusty rims of a volume filling factor of 0.18 and 0.35–0.58, we found sticking velocities of a few cm s^?1. This velocity is higher than the sticking velocity of dust aggregates of the same size. We therefore conclude that chondrules may be an important step towards a deeper understanding of the collisional growth of larger bodies. Moreover, we analyzed the collision behavior in an ensemble of dust aggregates and non-coated chondrule analogs. While neither the dust aggregates nor the solid chondrule analogs show sticking in collisions among their species, we found an enhanced sicking efficiency in collisions between the two constituents, which leads us to the conjecture that chondrules might act as “catalyzers” for the growth of larger bodies in the young Solar System.     

Maximal size of chondrules in shock wave heating model: Stripping of liquid surface in a hypersonic rarefied gas flow

Abstract— We examined partially molten dust particles that have a solid core and a surrounding liquid mantle, and estimated the maximal size of chondrules in a framework of the shock wave heating model for chondrule formation. First, we examined the dynamics of the liquid mantle by analytically solving the hydrodynamics equations for a core‐mantle structure via a linear approximation. We obtained the deformation, internal flow, pressure distribution in the liquid mantle, and the force acting on the solid core. Using these results, we estimated conditions in which liquid mantle is stripped off from the solid core. We found that when the particle radius is larger than about 1–2 mm, the stripping is expected to take place before the entire dust particle melts. So chondrules larger than about 1–2 mm are not likely to be formed by the shock wave heating mechanism. Also, we found that the stripping of the liquid mantle is more likely to occur than the fission of totally molten particles. Therefore, the maximal size of chondrules may be determined by the stripping of the liquid mantle from the partially molten dust particles in the shock waves. This maximal size is consistent with the sizes of natural chondrules.     

Chondrules born in plasma? Simulation of gas–grain interaction using plasma arcs with applications to chondrule and cosmic spherule formation

We are investigating chondrule formation by nebular shock waves, using hot plasma as an analog of the heated gas produced by a shock wave as it passes through the protoplanetary environment. Precursor material (mainly silicates, plus metal, and sulfide) was dropped through the plasma in a basic experimental set‐up designed to simulate gas–grain collisions in an unconstrained spatial environment (i.e., no interaction with furnace walls during formation). These experiments were undertaken in air (at atmospheric pressure), to act as a “proof‐of‐principle”—could chondrules, or chondrule‐analog objects (CAO), be formed by gas–grain interaction initiated by shock fronts? Our results showed that if accelerating material through a fixed plasma field is a valid simulation of a supersonic shock wave traveling through a cloud of gas and dust, then CAO certainly could be formed by this process. Melting of and mixing between starting materials occurred, indicating temperatures of at least 1266 °C (the olivine‐feldspar eutectic). The production of CAO with mixed mineralogy from monomineralic starting materials also shows that collisions between particles are an important mechanism within the chondrule formation process, such that dust aggregates are not necessarily required as chondrule precursors. Not surprisingly, there were significant differences between the synthetic CAO and natural chondrules, presumably mainly because of the oxidizing conditions of the experiment. Results also show similarity to features of micrometeorites like cosmic spherules, particularly the dendritic pattern of iron oxide crystallites produced on micrometeorites by oxidation during atmospheric entry and the formation of vesicles by evaporation of sulfides.     

Blowing in the wind: I. Velocities of chondrule-sized particles in a turbulent protoplanetary nebula

Small but macroscopic particles—chondrules, higher temperature mineral inclusions, metal grains, and their like—dominate the fabric of primitive meteorites. The properties of these constituents, and their relationship to the fine dust grains which surround them, suggest that they led an extended existence in a gaseous protoplanetary nebula prior to their incorporation into their parent primitive bodies. In this paper we explore in some detail the velocities acquired by such particles in a turbulent nebula. We treat velocities in inertial space (relevant to diffusion), velocities relative to the gas and entrained microscopic dust (relevant to accretion of dust rims), and velocities relative to each other (relevant to collisions). We extend previous work by presenting explicit, closed-form solutions for the magnitude and size dependence of these velocities in this important particle size regime, and we compare these expressions with new numerical calculations. The magnitude and size dependence of these velocities have immediate applications to chondrule and CAI rimming by fine dust and to their diffusion in the nebula, which we explore separately.     

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.     

An unusual compound object in Yamato 793408 (H3.2‐an): The missing link between compound chondrules and macrochondrules?

We found a large (~2 mm) compound object in the primitive Yamato 793408 (H3.2‐an) chondrite. It consists mostly of microcrystalline material, similar to chondrule mesostasis, that hosts an intact barred olivine (BO) chondrule. The object contains euhedral pyroxene and large individual olivine grains. Some olivine cores are indicative of refractory forsterites with very low Fe‐ and high Ca, Al‐concentrations, although no ¹⁶O enrichment. The entire object is most likely a new and unique type, as no similar compound object has been described so far. We propose that it represents an intermediate stage between compound chondrules and macrochondrules, and formed from the collision between chondrules at low velocities (below 1 m s^?1) at high temperatures (around 1550 °C). The macrochondrule also trapped and preserved a smaller BO chondrule. This object appears to be the first direct evidence for a genetic link between compound chondrules and macrochondrules. In accordance with previous suggestions and studies, compound chondrules and macrochondrules likely formed by the same mechanism of chondrule collisions, and each represents different formation conditions, such as ambient temperature and collision speed.     

Macrochondrules in chondrites—Formation by melting of mega‐sized dust aggregates and/or by rapid collisions at high temperatures?

Abstract– Seventy‐four macrochondrules with sizes >3 mm were studied. Considering the extraordinary size of the chondrules (occasionally achieving a mass of 1000 times (and more) the mass of a normal‐sized chondrule), the conditions in the formation process must have been somewhat different compared with the conditions for the formation of the common chondrules. Macrochondrules are typically rich in olivine and texturally similar to specific chondrule types (barred, radial, porphyritic, and cryptocrystalline) of normal‐sized chondrules. However, our studies show that most of the macrochondrules are fine‐grained or have elongated crystals (mostly BO, RP, and C), which lead to the assumption that they were once totally molten and cooled quite rapidly. Porphyritic chondrules belong to the least abundant types of macrochondrules. This distribution of chondrule types is highly unusual and just a reverse of the distribution of chondrule types among the typical‐sized chondrules in most chondrite groups except for the CH and CB chondrites. New chondrule subtypes (like radial‐olivine [RO] or multi‐radial [MR] chondrules) are defined to better describe the textures of certain large chondrules. Macrochondrules may have formed due to melting of huge precursor dust aggregates or due to rapid collisions of superheated melt droplets, which led to the growth of large molten spherules in regions with high dust densities and high electrostatic attraction.     

Motion of iron sulfide inclusions inside a shock‐melted chondrule

Abstract— We calculated the trajectories of molten spheres of iron sulfide inclusions inside a melted chondrule during the nebular shock wave heating. Our calculations included the effects of high‐velocity internal flow in the melted chondrule and apparent gravitational force caused by the drag force of nebular gas flow. The calculated results show that large iron sulfide inclusions, which have radii 0.23 times larger than those of the parent chondrules, must reach the surface of the melted chondrule within a short period of time (<<1 s). This effect will provide us with very important information about chondrule formation by nebular shock wave heating.     

Growth of planetesimals by impacts at ∼25 m/s

We study central collisions between millimeter-sized dust projectiles and centimeter-sized dust targets in impact experiments. Target and projectile are dust aggregates consisting of micrometer-sized SiO₂ particles. Collision velocities range up to 25 m/s. The general outcome of a collision strongly depends on the impact velocity. For collisions below 13 m/s rebound and a small degree of fragmentation occur. However, at higher collision velocities up to 25 m/s approximately 50% of the mass of the projectile rigidly sticks to the target after the collision. Thus, net growth of a body is possible in high speed collisions. This supports the idea that planetesimal formation via collisional growth is a viable mechanism at higher impact velocities. Within our set of parameters the experiments even suggest that higher impact velocities might be preferable for growth in collisions between dusty bodies. For the highest impact velocities most of the ejecta is within small dust aggregates about 500 μm in size. In detail the size distribution of ejected dust aggregates is flat for very small particles smaller than 500 μm and follows a power law for larger ejected dust aggregates with a power of −5.6±0.2. There is a sharp upper cut-off at about 1 mm in size with only a few particles being slightly larger. The ejection angle is smaller than 3° with respect to the target surface. These fast ejecta move with 40±10% of the impact velocity.     

High-resolution simulations of clump–clump collisions using SPH with particle splitting

We investigate, by means of numerical simulations, the phenomenology of star formation triggered by low-velocity collisions between low-mass molecular clumps. The simulations are performed using a smoothed particle hydrodynamics code which satisfies the Jeans condition by invoking on-the-fly particle splitting.
Clumps are modelled as stable truncated (non-singular) isothermal, i.e. Bonnor–Ebert, spheres. Collisions are characterized by M ₀ (clump mass), b (offset parameter, i.e. ratio of impact parameter to clump radius) and     (Mach number, i.e. ratio of collision velocity to effective post-shock sound speed). The gas subscribes to a barotropic equation of state, which is intended to capture (i) the scaling of pre-collision internal velocity dispersion with clump mass, (ii) post-shock radiative cooling and (iii) adiabatic heating in optically thick protostellar fragments.
The efficiency of star formation is found to vary between 10 and 30 per cent in the different collisions studied and it appears to increase with decreasing M ₀, and/or decreasing b , and/or increasing     . For   b < 0.5  collisions produce shock-compressed layers which fragment into filaments. Protostellar objects then condense out of the filaments and accrete from them. The resulting accretion rates are high,     , for the first     . The densities in the filaments,     , are sufficient that they could be mapped in NH₃ or CS line radiation, in nearby star formation regions.     

Planetary growth with collisional fragmentation and gas drag

As planetary embryos grow, gravitational stirring of planetesimals by embryos strongly enhances random velocities of planetesimals and makes collisions between planetesimals destructive. The resulting fragments are ground down by successive collisions. Eventually the smallest fragments are removed by the inward drift due to gas drag. Therefore, the collisional disruption depletes the planetesimal disk and inhibits embryo growth. We provide analytical formulae for the final masses of planetary embryos, taking into account planetesimal depletion due to collisional disruption. Furthermore, we perform the statistical simulations for embryo growth (which excellently reproduce results of direct N-body simulations if disruption is neglected). These analytical formulae are consistent with the outcome of our statistical simulations. Our results indicate that the final embryo mass at several AU in the minimum-mass solar nebula can reach about ∼0.1 Earth mass within 10⁷ years. This brings another difficulty in formation of gas giant planets, which requires cores with ∼10 Earth masses for gas accretion. However, if the nebular disk is 10 times more massive than the minimum-mass solar nebula and the initial planetesimal size is larger than 100 km, as suggested by some models of planetesimal formation, the final embryo mass reaches about 10 Earth masses at 3-4 AU. The enhancement of embryos’ collisional cross sections by their atmosphere could further increase their final mass to form gas giant planets at 5-10 AU in the Solar System.     

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.     

Fragmentation model dependence of collision cascades

Mass depletion of bodies through successive collisional disruptions (i.e., collision cascade) is one of the most important processes in the studies of the asteroids belt, the Edgeworth-Kuiper belt, debris disks, and planetary formation. The collisional disruption is divided into two types, i.e., catastrophic disruption and cratering. Although some studies of the collision cascades neglected the effect of cratering, it is unclear which type of disruption makes a dominant contribution to the collision cascades. In the present study, we construct a simple outcome model describing both catastrophic disruption and cratering, which has some parameters characterizing the total ejecta mass, the mass of the largest fragment, and the power-law exponent of the size distribution of fragments. Using this simple outcome model with parameters, we examine the model dependence of the mass depletion time in collision cascades for neglect of coalescence of colliding bodies due to high collisional velocities. We find the cratering collisions are much more effective in collision cascades than collisions with catastrophic disruption in a wide region of the model parameters. It is also found that the mass depletion time in collision cascades is mainly governed by the total ejecta mass and almost insensitive to the mass of the largest fragment and the power-law exponent of fragments for a realistic parameter region. The total ejecta mass is usually determined by the ratio of the impact energy divided by the target mass (i.e. Q-value) to its threshold value for catastrophic disruption, as well as in our simple model. We derive a mass depletion time in collision cascades, which is determined by of the high-mass end of collision cascades. The mass depletion time derived with our model would be applicable to debris disks and planetary formation.     

The origin of chondrules and chondrites: Debris from low‐velocity impacts between molten planetesimals?

Abstract– We investigate the hypothesis that many chondrules are frozen droplets of spray from impact plumes launched when thin‐shelled, largely molten planetesimals collided at low speed during accretion. This scenario, here dubbed “splashing,” stems from evidence that such planetesimals, intensely heated by ²⁶Al, were abundant in the protoplanetary disk when chondrules were being formed approximately 2 Myr after calcium‐aluminum‐rich inclusions (CAIs), and that chondrites, far from sampling the earliest planetesimals, are made from material that accreted later, when ²⁶Al could no longer induce melting. We show how “splashing” is reconcilable with many features of chondrules, including their ages, chemistry, peak temperatures, abundances, sizes, cooling rates, indented shapes, “relict” grains, igneous rims, and metal blebs, and is also reconcilable with features that challenge the conventional view that chondrules are flash‐melted dust‐clumps, particularly the high concentrations of Na and FeO in chondrules, but also including chondrule diversity, large phenocrysts, macrochondrules, scarcity of dust‐clumps, and heating. We speculate that type I (FeO‐poor) chondrules come from planetesimals that accreted early in the reduced, partially condensed, hot inner nebula, and that type II (FeO‐rich) chondrules come from planetesimals that accreted in a later, or more distal, cool nebular setting where incorporation of water‐ice with high Δ¹⁷O aided oxidation during heating. We propose that multiple collisions and repeated re‐accretion of chondrules and other debris within restricted annular zones gave each chondrite group its distinctive properties, and led to so‐called “complementarity” and metal depletion in chondrites. We suggest that differentiated meteorites are numerically rare compared with chondrites because their initially plentiful molten parent bodies were mostly destroyed during chondrule formation.