A model of the thermal processing of particles in solar nebula shocks: Application to the cooling rates of chondrules

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.     

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.     

The dual role of shear in large‐scale dynamos

The role of shear in alleviating catastrophic quenching by shedding small‐scale magnetic helicity through fluxes along contours of constant shear is discussed. The level of quenching of the dynamo effect depends on the quenched value of the turbulent magnetic diffusivity. Earlier estimates that might have suffered from the force‐free degeneracy of Beltrami fields are now confirmed for shear flows where this degeneracy is lifted. For a dynamo that is saturated near equipartition field strength those estimates result in a 5‐fold decrease of the magnetic diffusivity as the magnetic Reynolds number based on the wavenumber of the energy‐carrying eddies is increased from 2 to 600. Finally, the role of shear in driving turbulence and large‐scale fields by the magneto‐rotational instability is emphasized. New simulations are presented and the 3π /4 phase shift between poloidal and toroidal fields is confirmed. It is suggested that this phase shift might be a useful diagnostic tool in identifying mean‐field dynamo action in simulations and to distinguish this from other scenarios invoking magnetic buoyancy as a means to explain migration away from the midplane. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The role of Fischer‐Tropsch catalysis in solar nebula chemistry

Abstract— Fischer‐Tropsch catalysis, the iron/nickel catalyzed conversion of CO and H₂ to hydrocarbons, would have been the only thermally‐driven pathway available in the solar nebula to convert CO into other forms of carbon. A major issue in meteoritics is to determine the origin of meteoritic organics: are they mainly formed from CO in the solar nebula via a process such as Fischer‐Tropsch, or are they derived from interstellar organics? In order to determine the role that Fischer‐Tropsch catalysis may have played in the organic chemical evolution of the solar nebula, we have developed a kinetic model for this process. Our model results agree well with experimental data from several existing laboratory studies. In contrast, empirical rate equations, which have been derived from experimental rate data for a limited temperature (T) and pressure (P) range, are inconsistent with experimental rate data for higher T and lower P. We have applied our model to pressure and temperature profiles for the solar nebula, during the epoch in which meteorite parent bodies condensed and agglomerated. We find that, under nebular conditions, the conversion rate of CO to CH₄ does not simply increase with temperature as the empirically‐derived equations suggest. Instead, our model results show that this process would have been most efficient in a fairly narrow region that coincides with the present position of the asteroid belt. Our results support the hypothesis that Fischer‐Tropsch catalysis may have played a role in solar nebula chemistry by converting CO into less volatile materials that can be much more readily processed in the nebula and in parent bodies.     

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.     

Evidence in CO3.0 chondrules for a drift in the O isotopic composition of the solar nebula

Abstract— Several recent studies have shown that materials such as magnetite that formed in asteroids tend to have higher Δ¹⁷O (=δ¹⁷O ? 0.52 × δ¹⁸O) values than those recorded in unaltered chondrules. Other recent studies have shown that, in sets of chondrules from carbonaceous chondrites, Δ¹⁷O tends to increase as the FeO contents of the silicates increase. We report a comparison of the O isotopic composition of olivine phenocrysts in low‐FeO (≤Fa₁) type I and high‐FeO (≥Fa₁₅) type II porphyritic chondrules in the highly primitive CO3.0 chondrite Yamato‐81020. In agreement with a similar study of chondrules in CO3.0 ALH A77307 by Jones et al. (2000), Δ¹⁷O tends to increase with increasing FeO. We find that Δ¹⁷O values are resolved (but only marginally) between the two sets of olivine phenocrysts. In two of the high‐FeO chondrules, the difference between Δ¹⁷O of the late‐formed, high‐FeO phenocryst olivine and those in the low‐FeO cores of relict grains is well‐resolved (although one of the relicts is interpreted to be a partly melted amoeboid olivine inclusion by Yurimoto and Wasson [2002]). It appears that, during much of the chondrule‐forming period, there was a small upward drift in the Δ¹⁷O of nebular solids and that relict cores preserve the record of a different (and earlier) nebular environment.     

The cooling of flare produced plasmas in the solar corona

Solar flare X-rays, at energies less than 10 keV, are emitted by hot plasmas located in the corona. Three plasma cooling models are examined in detail. The cooling of the electrons by Coulomb collisions with ions at a lower temperature would require the observed material to occupy very large volumes. Cooling could take place by conduction or by radiation and observations are proposed which would allow the dominant cooling mechanism to be established.On leave during a portion of this work as University Research Fellow in Astronomy, University of Leicester, England.     

Suppression of the large‐scale Lorentz force by turbulence

The components of the total stress tensor (Reynolds stress plus Maxwell stress) are computed within the quasilinear approximation for a driven turbulence influenced by a large‐scale magnetic background field. The conducting fluid has an arbitrary magnetic Prandtl number and the turbulence without the background field is assumed as homogeneous and isotropic with a free Strouhal number St. The total large‐scale magnetic tension is always reduced by the turbulence with the possibility of a ‘catastrophic quenching’ for large magnetic Reynolds number Rm so that even its sign is reversed. The total magnetic pressure is enhanced by turbulence in the high‐conductivity limit but it is reduced in the low‐conductivity limit. Also in this case the sign of the total pressure may reverse but only for special turbulences with sufficiently large St > 1. The turbulence‐induced terms of the stress tensor are suppressed by strong magnetic fields. For the tension term this quenching grows with the square of the Hartmann number of the magnetic field. For microscopic (i.e. small) diffusivity values the magnetic tension term becomes thus highly quenched even for field amplitudes much smaller than their equipartition value. In the opposite case of large‐eddy simulations the magnetic quenching is only mild but then also the turbulence‐induced Maxwell tensor components for weak fields remain rather small (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effects of self-gravity on the solar nebula

We study the distribution and transport of angular momentum in a self-gravitating accretion disk formed during the collapse of a rotating gas cloud. Using the surface density for the low-viscosity models and minimum-mass models presented by Cassen and Summers, Poisson's equation is solved explicitly to determine the effects of self-gravitation of the protostellar disk. Analytic expressions for the angular momentum of the central star and other relevant quantities of interest during the formation stage are presented.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.On leave from the City College of the City University of New York, U.S.A.     

The effects of nebula surface density profile and giant‐planet eccentricities on planetary accretion in the inner solar system

Abstract— We describe results of 32 N‐body planetary accretion simulations that investigate the dependence of terrestrial‐planet formation on nebula surface density profile σ and evolution of the eccentricities of Jupiter and Saturn e_j,s. Two surface density profiles are examined: a decaying profile with σ ∝ 1/a, where a is orbital semi‐major axis, and a peaked profile in which σ increases for a < 2 AU and decreases for a > 2 AU. The peaked profiles are generated by models of coagulation in an initially hot nebula. Models with initial e_j,s = 0.05 (the current value) and 0.1 are considered. Simulations using the decaying profile with e_j,s = 0.1 produce systems most like the observed planets in terms of mass‐weighted mean a and the absence of a planet in the asteroid belt. Simulations with doubled σ produce planets roughly twice as massive as the nominal case. Most initial embryos are removed in each simulation via ejection from the solar system or collision with the Sun. The asteroid belt is almost entirely cleared on a timescale of 10–100 Ma that depends sensitively on e_j,s. Most initial mass with a < 2 AU survives, with the degree of mass loss increasing with a. Mass loss from the terrestrial region occurs on a timescale that is long compared to the mass loss time for the asteroid belt. Substantial radial mixing of material occurs in all simulations, but is greater in simulations with initital e_j,s = 0.05. The degree of mixing is equivalent to a feeding zone of half width 1.5 and 0.9 AU for an Earth mass planet at 1 AU for the cases e_j,s = 0.05 and 0.1, respectively. In simulations with e_j,s = 0.05, roughly one‐third and 5–10% of the mass contained in final terrestrial planets originated in the region a > 2.5 AU for the decaying and peaked profiles, respectively. In the case e_j,s = 0.1, the median mass accreted from a > 2.5 AU is zero for both profiles.     

Dynamics of high‐temperature materials delivered by jets to the outer solar nebula

Abstract— The presence of high‐temperature materials in the Stardust collection that are isotopically similar to those seen in chondritic meteorites argues for the outward transport of materials from the hot, inner region of the solar nebula to the region where comets formed. A number of mechanisms have been proposed to be responsible for this transport, with a number of models being developed to show that such outward transport is possible. However, these models have not examined in detail how these grains are transported after they have been delivered to the comet formation region or how they may be distributed in the cometary nuclei that form. Here, the dynamical evolution of crystalline silicates injected onto the surface of the solar nebula as proposed by jet models for radial transport is considered. It is generally found that crystalline grains should be heterogeneously distributed within the population of comets and within individual cometary nuclei. In order to achieve a homogeneous distribution of such grains, turbulence must be effective at mixing the crystalline silicates with native, amorphous grains on fine scales. However, this turbulent mixing would serve to dilute the crystalline silicates as it would redistribute them over large radial distances. These results suggest that it is difficult to infer the bulk properties of Wild 2 from the Stardust samples, and that the abundance of crystalline grains in these samples cannot alone be used to rule out or in favor of any of the different radial transport models that have been proposed.     

The origin of the angular momentum distribution in the solar nebula

Supersonic non-central collision and coalescence of interstellar matter clouds is suggested as a physical process that could lead to the formation of a solar nebula with an appropriate distribution of the spinangular momentum.     

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 distribution of mass in the planetary system and solar nebula

A model solar nebula is constructed by adding the solar complement of light elements to each planet, using recent models of planetary compositions. Uncertainties in this approach are estimated. The computed surface density varies approximately asr ^–3/2. Mercury, Mars and the asteroid belt are anomalously low in mass, but processes exist which would preferentially remove matter from these regions. Planetary masses and compositions are generally consistent with a monotonic density distribution in the primordial solar nebula.     

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 lack of potassium‐isotopic fractionation in Bishunpur chondrules

Abstract— In a search for evidence of evaporation during chondrule formation, the mesostases of 11 Bishunpur chondrules and melt inclusions in olivine phenocrysts in 7 of them have been analyzed for their alkali element abundances and K‐isotopic compositions. Except for six points, all areas of the chondrules that were analyzed had δ⁴¹K compositions that were normal within error (typically ±3%, 2s?). The six “anomalous” points are probably all artifacts. Experiments have shown that free evaporation of K leads to large ⁴¹K enrichments in the evaporation residues, consistent with Rayleigh fractionation. Under Rayleigh conditions, a 3% enrichment in δ⁴¹K is produced by ～12% loss of K. The range of L‐chondrite‐normalized K/Al ratios (a measure of the K‐elemental fractionation) in the areas analyzed vary by almost three orders of magnitude. If all chondrules started out with L‐chondrite‐like K abundances and the K loss occurred via Rayleigh fractionation, the most K‐depleted chondrules would have had compositions of up to δ⁴¹K ? 200%. Clearly, K fractionation did not occur by evaporation under Rayleigh conditions. Yet experiments and modeling indicate that K should have been lost during chondrule formation under currently accepted formation conditions (peak temperature, cooling rate, etc.). Invoking precursors with variable alkali abundances to produce the range of K/Al fractionation in chondrules does not explain the K‐isotopic data because any K that was present should still have experienced sufficient loss during melting for there to have been a measurable isotopic fractionation. If K loss and isotopic fractionation was inevitable during chondrule formation, the absence of K‐isotopic fractionation in Bishunpur chondrules requires that they exchanged K with an isotopically normal reservoir during or after formation. There is evidence for alkali exchange between chondrules and rim‐matrix in all unequilibrated ordinary chondrites. However, melt inclusions can have alkali abundances that are much lower than the mesostases of the host chondrules, which suggests that they at least remained closed since formation. If it is correct that some or all melt inclusions remained closed since formation, the absence of K‐isotopic fractionation in them requires that the K‐isotopic exchange took place during chondrule formation, which would probably require gas‐chondrule exchange. Potassium evaporated from fine‐grained dust and chondrules during chondrule formation may have produced sufficient K‐vapor pressure for gas‐chondrule isotopic exchange to be complete on the timescales of chondrule formation. Alternatively, our understanding of chondrule formation conditions based on synthesis experiments needs some reevaluation.     

The effect of photoionization on the cooling rates of enriched, astrophysical plasmas

Radiative cooling is central to a wide range of astrophysical problems. Despite its importance, cooling rates are generally computed using very restrictive assumptions, such as collisional ionization equilibrium and solar relative abundances. We simultaneously relax both assumptions and investigate the effects of photoionization of heavy elements by the metagalactic ultraviolet (UV)/X-ray background and of variations in relative abundances on the cooling rates of optically thin gas in ionization equilibrium. We find that photoionization by the metagalactic background radiation reduces the net cooling rates by up to an order of magnitude for gas densities and temperatures typical of the shock-heated intergalactic medium and proto-galaxies  (10⁴ K ≲ T ≲ 10⁶ K, ρ/〈ρ〉≲ 100)  . In addition, photoionization changes the relative contributions of different elements to the cooling rates. We conclude that photoionization by both the ionizing background and heavy elements needs to be taken into account in order for the cooling rates to be correct to an order of magnitude. Moreover, if the rates need to be known to better than a factor of a few, then departures of the relative abundances from solar need to be taken into account. We propose a method to compute cooling rates on an element-by-element basis by interpolating pre-computed tables that take photoionization into account. We provide such tables for a popular model of the evolving UV/X-ray background radiation, computed using the photoionization package cloudy .     

Statistical technique to study the connection between large‐scale structures in the ISM and low‐mass star formation

Applying a color index selection the Point Source Catalog of the Two Micron All Sky Survey (2MASS PSC) has been searched for Classical T Tauri (CTT) stars in the 2nd and 3rd Galactic quadrant based on their apparent K_S excess. The selection resulted in 3872 reliable CTT candidates. The obtained CTT sample is extended enough for statistical examination of the inhomogeneities in their distribution due to correlation with structures in the ISM, like infrared loops. A correlation was observed between the presence of dust loops and the CTT density. The latter shows an excess on loops with respect to that expected from random fluctuation in a homogeneous distribution matching with the observed overall distribution. Monte Carlo simulations were used to show the significance of the excess. The results imply that the formation of a fraction of CTTs was triggered during the loop formation. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The iodine‐xenon system in clasts and chondrules from ordinary chondrites: Implications for early solar system chronology

Abstract— We have studied the I‐Xe system in chondrules and clasts from ordinary chondrites. Cristobalite‐bearing clasts from Parnallee (LL3.6) closed to Xe loss 1–4 Ma after Bjurböle. Feline (a feldspar‐ and nepheline‐rich clast also from Parnallee) closed at 7.04 ± 0.15 Ma. Two out of three chondrules from Parnallee that yielded well‐defined initial I ratios gave ages identical to Bjurböle's within error. A clast from Barwell (L6) has a well‐defined initial I ratio corresponding to closure 3.62 ± 0.60 Ma before Bjurböle. Partial disturbance and complete obliteration of the I‐Xe system by shock are revealed in clasts from Julesburg (L3.6) and Quenggouk (H4), respectively. Partial disturbance by shock is capable of generating anomalously high initial I ratios. In some cases, these could be misinterpreted, yielding erroneous ages. A macrochondrule from Isoulane‐n‐Amahar contains concentrations of I similar to “ordinary” chondrules but, unlike most ordinary chondrules, contains no radiogenic ¹²⁹Xe. This requires resetting 50 Ma or more later than most chondrules. The earliest chondrule ages in the I‐Xe, Mn‐Cr, and Al‐Mg systems are in reasonable agreement. This, and the frequent lack of evidence for metamorphism capable of resetting the I‐Xe chronometer, leads us to conclude that (at least) the earliest chondrule I‐Xe ages represent formation. If so, chondrule formation took place at a time when sizeable parent bodies were present in the solar system.     

The effects of disk building on the distributions of refractory materials in the solar nebula

Abstract– Refractory materials, such as calcium‐aluminum‐rich inclusions (CAIs) and crystalline silicates, are widely found in chondritic meteorites as well as comets, taken as evidence for large‐scale mixing in the solar nebula. Most models for mixing in the solar nebula begin with a well‐formed protoplanetary disk. Here, we relax this assumption by modeling the formation and evolution of the solar nebula during and after the period when it accreted material from its parent molecular cloud. We consider how disk building impacts the long‐term evolution of the disk and the implications for grain transport and mixing within it. Our model shows that materials that formed before infall was complete could be preserved in primitive bodies, especially those that accreted in the outer disk. This potentially explains the discovery of refractory objects with low initial ²⁶Al/²⁷Al ratios in comets. Our model also shows that the highest fraction of refractory materials in meteorites formed around the time that infall stopped. Thus, we suggest that the calcium‐aluminum‐rich inclusions in chondrites would be dominated by the population that formed during the transition from class I to class II stage of young stellar objects. This helps us to understand the meaning of t = 0 in solar system chronology. Moreover, our model offers a possible explanation for the existence of isotopic variations observed among refractory materials—that the anomalous materials formed before the collapse of the parent molecular cloud was complete.