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1.
Abstract— We present a model for the thermal processing of particles in shock waves typical of the solar nebula. This shock model improves on existing models in that the dissociation and recombination of H2 and the evaporation of particles are accounted for in their effects on the mass, momentum and energy fluxes. Also, besides thermal exchange with the gas and gas‐drag heating, particles can be heated by absorbing the thermal radiation emitted by other particles. The flow of radiation is calculated using the equations of radiative transfer in a slab geometry. We compute the thermal histories of particles as they encounter and pass through the shock. We apply this shock model to the melting and cooling of chondrules in the solar nebula. We constrain the combinations of shock speed and gas density needed for chondrules to reach melting temperatures, and show that these are consistent with shock waves generated by gravitational instabilities in the protoplanetary disk. After their melting, cooling rates of chondrules in the range 10–1000 K h?1 are naturally reproduced by the shock model. Chondrules are kept warm by the reservoir of hot shocked gas, which cools only as fast as the dust grains and chondrules themselves can radiate away the gas's energy. We predict a positive correlation between the concentration of chondrules in a region and the cooling rates of chondrules in that region. This correlation is supported by the unusually high frequency of (rapidly cooled) barred chondrules among compound chondrules, which must have collided preferentially in regions of high chondrule density. We discuss these and other compelling consistencies between the meteoritic record and the shock wave model of chondrule formation.  相似文献   

2.
Abstract— We investigate the possible formation of chondrules by planetesimal bow shocks. The formation of such shocks is modeled using a piecewise parabolic method (PPM) code under a variety of conditions. The results of this modeling are used as a guide to study chondrule formation in a one‐dimensional, finite shock wave. This model considers a mixture of chondrule‐sized particles and micron‐sized dust and models the kinetic vaporization of the solids. We found that only planetesimals with a radius of ?1000 km and moving at least ?8 km/s with respect to the nebular gas can generate shocks that would allow chondrule‐sized particles to have peak temperatures and cooling rates that are generally consistent with what has been inferred for chondrules. Planetesimals with smaller radii tend to produce lower peak temperatures and cooling rates that are too high. However, the peak temperatures of chondrules are only matched for low values of chondrule wavelength‐averaged emissivity. Very slow cooling (<?100s of K/hr) can only be achieved if the nebular opacity is low, which may result after a significant amount of material has been accreted into objects that are chondrule‐sized or larger, or if chondrules formed in regions of the nebula with small dust concentrations. Large shock waves of approximately the same scale as those formed by gravitational instabilities or tidal interactions between the nebula and a young Jupiter do not require this to match the inferred thermal histories of chondrules.  相似文献   

3.
We present numerical simulations of the thermal and dynamical histories of solid particles (chondrules and their precursors—treated as 1-mm silicate spheres) during passage of an adiabatic shock wave through a particle-gas suspension in a minimum-mass solar nebula. The steady-state equations of energy, momentum, and mass conservation are derived and integrated for both solids and gas under a variety of shock conditions and particle number densities using the free-molecular-flow approximation. These simulations allow us to investigate both the heating and cooling of particles in a shock wave and to compare the time and distance scales associated with their processing to those expected for natural chondrules. The interactions with the particles cause the gas to achieve higher temperatures and pressures both upstream and downstream of the shock than would be reached otherwise. The cooling rates of the particles are found to be nonlinear but agree approximately with the cooling rates inferred for chondrules by laboratory simulations. The initial concentration of solids upstream of the shock controls the cooling rates and the distances over which they are processed: Lower concentrations cool more slowly and over longer distances. These simulations are consistent with the hypothesis that large-scale shocks, e.g., those due to density waves or gravitational instabilities, were the dominant mechanism for chondrule formation in the nebula.  相似文献   

4.
The importance of experiments: Constraints on chondrule formation models   总被引：1，自引：0，他引：1  
Abstract— We review a number of constraints that have been placed on the formation of chondrules and show how these can be used to test chondrule formation models. Four models in particular are examined: the “X‐wind” model (sudden exposure to sunlight <0.1 AU from the proto‐Sun, with subsequent launching in a magnetocentrifugal outflow); solar nebula lightning; nebular shocks driven by eccentric planetesimals; and nebular shocks driven by diskwide gravitational instabilities. We show that constraints on the thermal histories of chondrules during their melting and crystallization are the most powerful constraints and provide the least ambiguous tests of the chondrule formation models. Such constraints strongly favor melting of chondrules in nebular shocks. Shocks driven by gravitational instabilities are somewhat favored over planetesimal bow shocks.  相似文献   

5.
Meteoritical and astrophysical models of planet formation make contradictory predictions for dust concentration factors in chondrule-forming regions of the solar nebula. Meteoritical and cosmochemical models strongly suggest that chondrules, a key component of the meteoritical record, formed in regions with solids-to-gas mass ratios orders above the solar nebula average. However, models of dust grain dynamics in protoplanetary disks struggle to surpass concentration factors of a few except during very short-lived stages in a dust grain's life. Worse, those models do not predict significant concentration factors for dust grains the size of chondrule precursors. We briefly develop the difficulty in concentrating dust particles in the context of nebular chondrule formation and show that the disagreement is sufficiently stark that cosmochemists should explore ideas that might revise the concentration factor requirements downward.  相似文献   

6.
Abstract— The Mg‐isotopic compositions in five barred olivine (BO) chondrules, one coarse‐grained rim of a BO chondrule, a relic spinel in a BO chondrule, one skeletal olivine chondrule similar to BO chondrules in mineralogy and composition, and two non‐BO chondrules from the Allende meteorite have been measured by thermal ionization mass spectrometry. The Mg isotopes are not fractionated and are within terrestrial standard values (±2.0%o per amu) in seven of the eight analyzed ferromagnesian chondrules. A clump of relic spinel grain and its host BO chondrule R‐11 give well‐resolvable Mg fractionations that show an enrichment of the heavier isotopes, up to +2.5%‰ per amu. The Mg‐isotopic compositions of coarse‐grained rim are identical to those of the host chondrule with BO texture. The results imply that ferromagnesian and refractory precursor components of the Allende chondrule may have been formed from isotopically heterogeneous reservoirs. In the nebula region where Allende chondrules formed, recycling of chondrules and multiple high‐temperature heating did not significantly alter the chemical and isotopic memory of earlier generations. Chemical and isotopic characteristics of refractory precursors of carbonaceous chondrite chondrules and CAIs are more closely related than previously thought. One of the refractory chondrule precursors of CV Allende is enriched in the heavier Mg isotopes and different from those of more common ferromagnesian chondrule precursors. The most probable scenario at the location where chondrule R‐11 formed is as follows. Before chondrule formation, several high‐temperature events occurred and then RPMs, refractory oxides, and silicates condensed from the nebular gas in which Mg isotopes were fractionated. Then, this CAI was transported into the chondrule formation region and mixed with more common, ferromagnesian precursors with normal Mg isotopes, and formed the BO chondrule. Because Mg isotope heterogeneity among silicates and spinel are found in some CAIs (Esat and Taylor, 1984), we cannot rule out the possibility that Mg isotopes of a melted portion of the refractory precursor (i.e., outer portion of CAI) are normal or enriched in the light isotope. Magnesium isotopes in the R‐11 host are also enriched in the heavier isotopes, +2.5%o per amu, which suggests that effects of isotopic heterogeneity among silicates and spinel, if they existed, are not considered to be large. It is possible that CAI precursor silicates partially dissolved during the chondrule forming event, contributing Mg to the melt and producing a uniform Mg‐isotopic signature but enriched in the heavier Mg isotopes, +2.5%‰ per amu. Most Mg isotopes in more common ferromagnesian chondrules represent normal chondritic material. Chemical and Mg‐isotopic signatures formed during nebular fractionations were not destroyed during thermal processes that formed the chondrule, and these were partly preserved in relic phases. Recycling of Allende chondrules and multiple heating at high temperature did not significantly alter the chemical and Mg‐isotopic memory of earlier generations.  相似文献   

7.
Abstract– Here, we show that several geochemical indicators point to number densities during chondrule formation that were far higher than can be accounted for by known nebula processes. The number densities implied by compound chondrules and nonspherical chondrules are shown to be significantly higher than estimated in previous studies. At the implied chondrule number densities, if a chondrule formation region survived a formation event it would have been gravitationally bound and would have collapsed quite rapidly to form an asteroidal‐sized body. The diversity of chondrule compositions and textures in a chondrite group could have formed in a single event in subvolumes of a formation region that were chemically isolated from one another because of slow diffusion in the gas. Within these subvolumes, equilibration between chondrules with different compositions would have been fairly rapid, although small isotopic mass fractionations in elements like Fe, Si, Mg, and O may persist. This could explain the existence of the small isotopic mass fractionations in these elements that have been observed in chondrules. However, the evidence for recycling of chondrules requires that there was more than one chondrule formation event prior to formation of a parent asteroid. Finally, we argue that OC and CO chondrule Mg‐Al systematics are both consistent with single ages or narrow ranges of ages, and that the CO, and possibly the OC, ages date parent body alteration. This would resolve the conundrum of needing to preserve in a turbulent nebula physically and chemically distinct CO and OC chondrule populations for 1–2 Myr.  相似文献   

8.
Abstract— Detailed numerical models have shown that solar nebula shock waves would be able to thermally process chondrules in a way that is consistent with experimental constraints. However, it has recently been argued that the high relative velocities that would be generated between chondrules of different sizes immediately behind the shock front would lead to energetic collisions that would destroy the chondrules as they were processed rather than preserving them for incorporation into meteorite parent bodies. Here the outcome of these collisions is quantitatively explored using a simple analytic expression for the viscous dissipation of collisional energy in a liquid layer. It is shown that molten chondrules can survive collisions at velocities as high as a few hundred meters per second. It is also shown that the thermal evolution of chondrules in a given shock wave varies with chondrule size, which may allow chondrules of different textures to form in a given shock wave. While experiments are needed to further constrain the parameters used in this work, these calculations show that the expected outcomes from collisions behind shock waves are consistent with what is observed in meteorites.  相似文献   

9.
Abstract— The primordial asteroid belt contained at least several hundred and possibly as many as 10,000 bodies with diameters of 1000 km or larger. Following the formation of Jupiter, nebular gas drag combined with passage of such bodies through Jovian resonances produced high eccentricities (e = 0.3‐0.5), low inclinations (i < 0.5°), and, therefore, high velocities (3–10 km/s) for “resonant” bodies relative to both nebular gas and non‐resonant planetesimals. These high velocities would have produced shock waves in the nebular gas through two mechanisms. First, bow shocks would be produced by supersonic motion of resonant bodies relative to the nebula. Second, high‐velocity collisions of resonant bodies with non‐resonant bodies would have generated impact vapor plume shocks near the collision sites. Both types of shocks would be sufficient to melt chondrule precursors in the nebula, and both are consistent with isotopic evidence for a time delay of ?1‐1.5 Myr between the formation of CAIs and most chondrules. Here, initial simulations are first reported of impact shock wave generation in the nebula and of the local nebular volumes that would be processed by these shocks as a function of impactor size and relative velocity. Second, the approximate maximum chondrule mass production is estimated for both bow shocks and impact‐generated shocks assuming a simplified planetesimal population and a rate of inward migration into resonances consistent with previous simulations. Based on these initial first‐order calculations, impact‐generated shocks can explain only a small fraction of the minimum likely mass of chondrules in the primordial asteroid belt (?1024‐1025g). However, bow shocks are potentially a more efficient source of chondrule production and can explain up to 10–100 times the estimated minimum chondrule mass.  相似文献   

10.
We report trace element analyses by laser ablation inductively coupled plasma mass spectrometry (LA‐ICP‐MS) of metal grains from nine different CR chondrites, distinguishing grains from chondrule interior (“interior grains”), chondrule surficial shells (“margin grains”), and the matrix (“isolated grains”). Save for a few anomalous grains, Ni‐normalized trace element patterns are similar for all three petrographic settings, with largely unfractionated refractory siderophile elements and depleted volatile Au, Cu, Ag, S. All three types of grains are interpreted to derive from a common precursor approximated by the least‐melted, fine‐grained objects in CR chondrites. This also excludes recondensation of metal vapor as the origin of the bulk of margin grains. The metal precursors were presumably formed by incomplete condensation, with evidence for high‐temperature isolation of refractory platinum‐group‐element (PGE)‐rich condensates before mixing with lower temperature PGE‐depleted condensates. The rounded shape of the Ni‐rich, interior grains shows that they were molten and that they equilibrated with silicates upon slow cooling (1–100 K h?1), largely by oxidation/evaporation of Fe, hence their high Pd content, for example. We propose that Ni‐poorer, amoeboid margin grains, often included in the pyroxene‐rich periphery common to type I chondrules, result from less intense processing of a rim accreted onto the chondrule subsequent to the melting event recorded by the interior grains. This means either that there were two separate heating events, which formed olivine/interior grains and pyroxene/margin grains, respectively, between which dust was accreted around the chondrule, or that there was a single high‐temperature event, of which the chondrule margin records a late “quenching phase,” in which case dust accreted onto chondrules while they were molten. In the latter case, high dust concentrations in the chondrule‐forming region (at least three orders of magnitude above minimum mass solar nebula models) are indicated.  相似文献   

11.
Abstract— Forty‐three corundum grains (1–11 μm in size) and 5 corundum‐hibonite grains with corundum overgrown by hibonite (4–7 μm in size), were found in the matrix of the mineralogically pristine, ungrouped carbonaceous chondrite Acfer 094 by using cathodoluminescence imaging. Some of the corundum and corundum‐hibonite grains occur as aggregates of 2 to 6 grains having similar sizes. The oxygen isotopic compositions of some of the corundum‐bearing grains suggest their solar nebula origin. 26Al‐26Mg systematics of one corundum grain showed the canonical initial 26Al/27Al ratio, also suggesting a solar nebula origin. Quantitative evaluation of condensation and accretion processes made based on the homogeneous nucleation of corundum, diffusion‐controlled hibonite formation, collisions of grains in the nebula, and critical velocity for sticking, indicates that, in contrast to the hibonite‐bearing aggregates of corundum grains, the hibonite‐free corundum aggregates could not have formed in the slowly cooling nebular region with solar composition. We suggest instead that such aggregates formed near the protosun, either in a region that stayed above the condensation temperature of hibonite for a long time or in a chemically fractionated, Ca‐depleted region, and were subsequently physically removed from this hot region, e.g., by disk wind.  相似文献   

12.
Abstract— We examine the size sorting of chondrules and metal grains within the context of the jet flow model for chondrule/CAI formation. In this model, chondrules, CAIs, AOAs, metal grains, and related components of meteorites are assumed to have formed in the outflow region of the innermost regions of the solar nebula and then were ejected, via the agency of a bipolar jet flow, to outer regions of the nebula. We wish to see if size sorting of chondrules and metal grains is a natural consequence of this model. To assist in this task, we used a multiprocessor system to undertake Monte Carlo simulations of the early solar nebula. The paths of a statistically significant number of chondrules and metal grains were analyzed as they were ejected from the outflow and travelled over or into the solar nebula. For statistical reasons, only distances ≤3 AU from the Sun were examined. Our results suggest that size sorting can occur provided that the solar nebula jet flow had a relatively constant flow rate as function of time. A constant flow rate outflow produces size sorting, but it also produces a sharp size distribution of particles across the nebula and a metal‐rich Fe/Si ratio. When the other extreme of a fully random flow rate was examined, it was found that size sorting was removed, and the initial material injected into the flow was simply spread over most of the the solar nebula. These results indicate that the outflow can act as a size and density classifier. By simply varying the flow rate, the outflow can produce different types of proto‐meteorites from the same chondrule and metal grain feed stock. As a consequence of these investigations, we observed that the number of particles that impact into the nebula drops off moderately rapidly as a function of distance r from the Sun. We also derive a corrected form of the Epstein stopping time.  相似文献   

13.
Abstract— In this paper, we review the mineralogy and chemistry of calcium‐aluminum‐rich inclusions (CAIs), chondrules, FeNi‐metal, and fine‐grained materials of the CR chondrite clan, including CR, CH, and the metal‐rich CB chondrites Queen Alexandra Range 94411, Hammadah al Hamra 237, Bencubbin, Gujba, and Weatherford. The members of the CR chondrite clan are among the most pristine early solar system materials, which largely escaped thermal processing in an asteroidal setting (Bencubbin, Weatherford, and Gujba may be exceptions) and provide important constraints on the solar nebula models. These constraints include (1) multiplicity of CAI formation; (2) formation of CAIs and chondrules in spatially separated nebular regions; (3) formation of CAIs in gaseous reservoir(s) having 16O‐rich isotopic compositions; chondrules appear to have formed in the presence of 16O‐poor nebular gas; (4) isolation of CAIs and chondrules from nebular gas at various ambient temperatures; (5) heterogeneous distribution of 26Al in the solar nebula; and (6) absence of matrix material in the regions of CAI and chondrule formation.  相似文献   

14.
Abstract— The degree of isotopic spatial heterogeneity in the solar nebula has long been a puzzle, with different isotopic systems implying either large‐scale initial spatial homogeneity (e.g., 26Al chronometry) or a significant amount of preserved heterogeneity (e.g., ratios of the three stable oxygen isotopes, 16O, 17O, and 18O). We show here that in a marginally gravitationally unstable (MGU) solar nebula, the efficiency of large‐scale mixing and transport is sufficient to spatially homogenize an initially highly spatially heterogeneous nebula to dispersions of ?10% about the mean value of 26Al/27Al on time scales of thousands of years. A similar dispersion would be expected for 17O/16O and 18O/16O ratios produced by ultraviolet photolysis of self‐shielded molecular CO gas at the surface of the outer solar nebula. In addition to preserving a chronological interpretation of initial 26Al/27Al ratios and the self‐shielding explanation for the oxygen isotope ratios, these solar nebula models offer a self‐consistent environment for achieving large‐scale mixing and transport of thermally annealed dust grains, shock‐wave processing of chondrules and refractory inclusions, and giant planet formation.  相似文献   

15.
Abstract– We have developed new sample preparation and analytical techniques tailored for entire aerogel tracks of Wild 2 sample analyses both on “carrot” and “bulbous” tracks. We have successfully ultramicrotomed an entire track along its axis while preserving its original shape. This innovation allowed us to examine the distribution of fragments along the entire track from the entrance hole all the way to the terminal particle. The crystalline silicates we measured have Mg‐rich compositions and O isotopic compositions in the range of meteoritic materials, implying that they originated in the inner solar system. The terminal particle of the carrot track is a 16O‐rich forsteritic grain that may have formed in a similar environment as Ca‐, Al‐rich inclusions and amoeboid olivine aggregates in primitive carbonaceous chondrites. The track also contains submicron‐sized diamond grains likely formed in the solar system. Complex aromatic hydrocarbons distributed along aerogel tracks and in terminal particles. These organics are likely cometary but affected by shock heating.  相似文献   

16.
Abstract– A synthesis of previous work leads to a model of chondrule formation that involves periodic melting of dispersed dust in debris clouds that were generated by collisions between chondritic planetesimals. I suggest that chondrules formed by the passage of nebular shock waves through these dust clumps, which temporarily surrounded disrupted planetesimals. Type I chondrules formed by more intense evaporative heating of fewer particles in tenuous clumps, or at the edges of dense clumps, and type II chondrules formed by less intense evaporative heating of more particles deeper within dense clumps. Chondrules reaccreted by self‐gravity into the planetesimals, mixing with less heated dust and rock. This process of disruption, melting, and reaccretion could have repeated many times. In this way, chondrite components of various origins and thermal histories could remain preserved in planetesimals as a distinctive mix of materials for extended periods of time, while still allowing for a repetitive melting process that converted some of the planetesimal debris into chondrules. I also suggest that during chondrule formation, the inner solar nebula gas was evolving by the gradual incorporation and heating of icy bodies depleted in 16O, causing a general increase in gaseous Δ17O with time in most places, especially close to the “snow line.” In this model, early formed type I chondrules in C chondrites with lower Δ17O values were produced inside the snow line, and later formed type I and type II chondrules in C and O chondrites with higher Δ17O values were created nearer the snow line after it had moved closer to the young Sun.  相似文献   

17.
Abstract— We have measured O‐isotopic ratios in a variety of olivine grains in the CO3 chondrite Allan Hills (ALH) A77307 using secondary ion mass spectrometry in order to study the chondrule formation process and the origin of isolated olivine grains in unequilibrated chondrites. Oxygen‐isotopic ratios of olivines in this chondrite are variable from δ17O = ?15.5 to +4.5% and δ18O = ?11.5 to +3.9%, with Δ17O varying from ?10.4 to +3.5%. Forsteritic olivines, Fa<1, are enriched in 16O relative to the bulk chondrite, whereas more FeO‐rich olivines are more depleted in 16O. Most ratios lie close to the carbonaceous chondrite anhydrous minerals (CCAM) line with negative values of Δ17O, although one grain of composition Fa4 has a mean Δ17O of +1.6%. Marked O‐isotopic heterogeneity within one FeO‐rich chondrule is the result of incorporation of relic, 16O‐rich, Mg‐rich grains into a more 16O‐depleted host. Isolated olivine grains, including isolated forsterites, have similar O‐isotopic ratios to olivine in chondrules of corresponding chemical composition. This is consistent with derivation of isolated olivine from chondrules, as well as the possibility that isolated grains are chondrule precursors. The high 16O in forsteritic olivine is similar to that observed in forsterite in CV and CI chondrites and the ordinary chondrite Julesburg and suggests nebula‐wide processes for the origin of forsterite that appears to be a primitive nebular component.  相似文献   

18.
The dynamics of grain motion through gas are examined in terms of the injection of isotopically anomalous (compared to solar abundances) material into the early solar nebula. Calculations indicate that the injected grains cannot penetrate to the center of any of a range of reasonable configurations, suggesting the formation of an edge region enriched in injected material. Furthermore, the dynamical behavior of grains in turbulent flows indicates that pockets of grains can have some resistance to turbulent diffusion. The constraints developed here are used to delineate a set of consistent, injected-grain models for the origin of the isotopic anomalies in meteorite inclusions.Invited contribution to the Proceedings of a Workshop onThermodynamics and Kinetics of Dust Formation in the Space Medium held at the Lunar and Planetary Institute, Houston, 6–8 September, 1978.  相似文献   

19.
Abstract– Enstatite chondrites (ECs) were subjected to noble gas analyses using stepped crushing and pyrolysis extraction methods. ECs can be classified into subsolar gas‐carrying and subsolar gas‐free ECs based on the 36Ar/84Kr/132Xe ratios. For subsolar gas‐free ECs, elemental ratios, and Xe isotopic compositions indicate that Q gas is the dominant trapped component, the Q gas concentration can be correlated with the petrologic type, reasonably explained by gas release from a common EC parental material during subsequent heating. Atmospheric Xe with sub‐Q elemental ratios is found in Antarctic E3s at 600–800 °C and through crushing. The 132Xe released in these fractions accounts for 30–60% of the bulk concentrations. Hence, the sub‐Q signature is generally due to contamination of elementally fractionated atmosphere. Subsolar gas is mainly released (up to 78% of the bulk 36Ar) at 1300–1600 °C and through crushing, suggesting that enstatite and friable phases are the host phases. Subsolar gas is isotopically identical to solar gas, but elementally fractionated. These observations are consistent with a previous study, which suggested that subsolar gas could be fractionated solar wind having been implanted into chondrule precursors ( Okazaki et al. 2001 ). Unlike subsolar gas‐free ECs, the primordial gas concentrations of subsolar gas‐carrying ECs are not simply correlated with the petrologic type. It is inferred that subsolar gas‐rich chondrules were heterogeneously distributed in the solar nebula and accreted to form subsolar gas‐carrying ECs. Subsequent metamorphic and impact‐shock heating events have affected noble gas compositions to various degrees.  相似文献   

20.
Abstract– One transient heating mechanism that can potentially explain the formation of most meteoritic chondrules 1–3 Myr after CAIs is shock waves produced by planetary embryos perturbed into eccentric orbits via resonances with Jupiter following its formation. The mechanism includes both bow shocks upstream of resonant bodies and impact vapor plume shocks produced by high‐velocity collisions of the embryos with small nonresonant planetesimals. Here, we investigate the efficiency of both shock processes using an improved planetesimal accretion and orbital evolution code together with previous simulations of vapor plume expansion in the nebula. Only the standard version of the model (with Jupiter assumed to have its present semimajor axis and eccentricity) is considered. After several hundred thousand years of integration time, about 4–5% of remaining embryos have eccentricities greater than about 0.33 and shock velocities at 3 AU exceeding 6 km s?1, currently considered to be a minimum for melting submillimeter‐sized silicate precursors in bow shocks. Most embryos perturbed into highly eccentric orbits are relatively large—half as large as the Moon or larger. Bodies of this size could yield chondrule‐cooling rates during bow shock passage compatible with furnace experiment results. The cumulative area of the midplane that would be traversed by highly eccentric embryos and their associated bow shocks over a period of 1–2 Myr is <1% of the total area. However, future simulations that consider a radially migrating Jupiter and alternate initial distributions of the planetesimal swarm may yield higher efficiencies.  相似文献   

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