Nebular shock waves generated by planetesimals passing through Jovian resonances: Possible sites for chondrule formation

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.     

Chondrule formation by the ablation of small planetesimals

Abstract— Numerous models have been proposed to explain the formation of chondrules, but none can be reconciled with the highly diverse properties of these objects. Here the formation of chondrules by the surface melting and ablation of small planetesimals in nebula shock waves is investigated using a numerical model. It is shown that bodies between ～1 mm and 500 m in diameter would have produced molten droplets by ablation during gas drag in nebula shocks stronger than ～2.0 Mach. The properties of chondrules produced by ablation are estimated by comparison with meteorite fusion crusts and through consideration of the environment within the bow shock envelope of ablating planetesimals. It is suggested that most ablation chondrules will have broadly chondritic compositions with depletions in siderophile and chalcophile elements and relatively high volatile contents and textures that are mainly porphyritic. The formation of chondrules by ablation of planetesimals in shock waves was probably most important at a late stage in nebula history and occurred at the same time as chondrules formed by the melting of dust particles. The high abundance of dust particles relative to larger bodies at all stages of accretion implies that only a proportion of chondrules may have been formed by ablation and that genetic groups of chondrules with very different origins may coexist in meteorites.     

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 Nebular Shock Wave Model for Chondrule Formation: Shock Processing in a Particle-Gas Suspension

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.     

Evaluating planetesimal bow shocks as sites for chondrule formation

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.     

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.     

The planetesimal bow shock model for chondrule formation: A more quantitative assessment of the standard (fixed Jupiter) case

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.     

Shock waves propagation in the turbulent interplanetary plasma

Effect of turbulence on interplanetary shock waves propagation is considered. It is shown that background turbulence results in the additional shock wave deceleration which may be comparable with the deceleration due to plasma sweeping. The turbulent deceleration is connected with the energy losses due to the strong turbulence amplification behind the moving shock front.     

On the MHD Simple Waves in Fully Relativistic Electron-Positron Plasmas with Radiation

The one dimensional propagation of simple waves in the system of electron-positron and photon gas at relativistic temperatures is considered. The presence of the transverse (across the wave propagation direction) velocity will change the dependencies of the phase velocity and magnetosound velocity upon temperature essentially. It is shown that at the presence of transverse velocity, the decrease of these characteristic velocities of simple wave takes place, while the time of shock wave formation becomes shorter. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

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.     

MHD shock interactions in coronal structures

We consider the magnetohydrodynamic (MHD) interactions of solar coronal fast shock waves of flare and/or nonflare origin with the boundaries of coronal streamers and coronal holes. Boundaries are treated as MHD tangential discontinuities (TD). Different parameters of the observed corona are used in the investigation. The general case of the oblique interaction is studied.It is shown that a solar fast shock wave must be refracted usually as a fast shock wave inside the coronal streamer. For the special case of the velocity shear across TD, a slow shock wave is generated. On the contrary, the shock wave refracted inside the coronal hole is indeed a slow shock wave.The significance of different effects due to the interaction of fast and slow shock waves on the coronal magnetic field is noticed, especially at the time of a coronal mass ejection (CME). It is also shown, that an oblique fast MHD coronal shock wave may trigger an instability at the boundary of a streamer considered as a TD. It might have a relation with the observed process of abrupt disappearance of the streamer's boundary in the solar corona.On leave from the Academy of Sciences, Central Astronomical Observatory Pulkovo, 196140, St. Petersburg, Russia.     

Numerical simulation of slow shocks in the solar wind

The evolutionary state of slow forward shock waves is examined with the use of two MHD numerical codes. Our study is intended to be exploratory rather than a detailed parametric one. The first code is one-dimensional (with three components of velocity and magnetic field) which is used to follow a slow shock that propagates into a positive gradient of density versus distance. It is found that the slow shock evolves into an extraneous (intermediate) shock wave. The second code has a spherical, one-dimensional, planar geometry (with two velocity and magnetic field components) which is used to follow a spiral interplanetary magnetic field. It is found that a slow shock type perturbation can generate a forward slow shock; a fast forward shock is generated in the front of the slow shock; a contact discontinuity is formed behind the slow shock, and a compound nonlinear MHD wave is formed behind the contact discontinuity with a fast reverse shock formed further behind. Thus, we demonstrate that the evolution of a slow shock into (solely) a fast shock, as suggested by Whang (1987), is much more complicated.     

Whistler mode propagation through weakly ionized magnetoplasma

The VLF wave generation by ?erenkov process from weakly ionized plasma has been considered. The effect of collisions on ?erenkov power spectrum and on propagation of VLF waves in whistler mode has been studied. The radiated power is shown to depend on the collisional parameter. The presence of collisions is found to modify the refractive index surfaces. It is shown that the focussing of VLF waves is less probable in the presence of collisions.     

Thermal waves in stars

Conclusions In this paper I have set forth in detail the theory of thermal waves in inhomogeneous media; it has, I believe, independent theoretical interest. I wish also to point out the fact that the mechanism of separation of an envelope in a nova explosion has hitherto remained obscure, since it strongly depends on the nature of the energy source of the explosion. Thus, if this energy is liberated by thermonuclear reactions, it is more probable that the time of development of the phenomenon reaches hundreds or even thousands of seconds. In such a case, the ejection of an envelope of the star is the result of the total effect of an infinite series of acoustic and weak shock waves that, added together, give a powerful pressure wave [6]. But if the energy of the explosion is gravitational in nature, its liberation may be virtually instantaneous, and the mechanism that transports the energy to infinity could be either a shock wave or a thermal wave. Moreover, if the explosion is due to a rearrangement of only the outer shell of the star, a thermal wave is more probable. And although the velocities of the thermal waves themselves are high, the rate of expansion of the matter of the shell will be appreciably less, since the time (of the order of a few seconds) is too short for interaction between radiation and matter. This distribution of velocities of the matter behind the thermal front can be obtained by a numerical solution of the equations of gas dynamics with allowance for the effects of radiative thermal conductivity; I hope to find such a solution in the future.Astronomical Observatory, L'vov University. Translated from Astrofizika, Vol. 9, No. 2, pp. 307–317, April–June, 1973.     

Wave reflections in the solar atmosphere

The small phase-lag between velocities observed at different chromospheric levels is interpreted as being due to acoustic waves reflected by the very hot atmospheric layers of the chromosphere-corona transition zone. We consider first an isothermal slab, then a realistic solar atmospheric model and calculate weighting functions for velocities in Ca ii lines. It is shown that taking into account these functions and integrating over horizontal wave numbers leads to a good agreement with previous observations (Mein, 1977) in the case of 8498 and 8542 Ca ii lines. For the K line, the less good agreement shows that magnetoacoustic waves become important in the upper chromospheric layers.     

Experimental Investigation of Shock Wave Attenuation in Basalt

Shock compression experiments on Kinosaki basalt were carried out in the interest of studying collisional phenomena in the solar nebula. Shock waves of 7 and 31 GPa were generated using a thin flyer plate, and a shock wave of 16 GPa was generated using a thick cylindrical projectile. By employing in-material manganin and carbon pressure gauges, the shock wave attenuation was examined and the propagation velocities of the shock wave and rarefaction wave were measured.The attenuation mechanism consists of two effects: the rarefaction wave and geometrical expansion. The rarefaction effect includes the reflected wave and the edge wave. The efficiency of these mechanisms depends on the geometry of the projectile, initially induced pressure, and materials of the target and projectile.As a result of the experiments, a cylindrical impactor created an isobaric region of size almost equal to the projectile radius. The shock wave in the far field was attenuated similarly with the power of −1.7 to −1.8 of the propagation distance under our experimental conditions. The shock wave generated using a thin flyer plate was attenuated by the rarefaction wave generated on the back surface of the flyer plate and by geometrical expansion effects. The shock wave generated using a thick projectile was attenuated by edge-wave and by geometrical expansion effects.According to elastic theory, the rigidity of basalt at 7 and 31 GPa was calculated as 35±7 and 0±3 GPa, respectively, using the measured rarefaction wave velocities. The decayed shock pressure was related to the ejection velocity of the impact fragments, which were obtained in previous disruption experiments. The attenuation rates in previous experiments were consistent with ours. The previous impact scaling parameter called “nondimensional impact stress (PI)” has been improved.     

The effect of multiple particle sizes on cooling rates of chondrules produced in large‐scale shocks in the solar nebula

Chondrules represent one of the best probes of the physical conditions and processes acting in the early solar nebula. Proposed chondrule formation models are assessed based on their ability to match the meteoritic evidence, especially experimental constraints on their thermal histories. The model most consistent with chondrule thermal histories is passage through shock waves in the solar nebula. Existing models of heating by shocks generally yield a good first‐order approximation to inferred chondrule cooling rates. However, they predict prolonged heating in the preshock region, which would cause volatile loss and isotopic fractionation, which are not observed. These models have typically included particles of a single (large) size, i.e., chondrule precursors, or at most, large particles accompanied by micron‐sized grains. The size distribution of solids present during chondrule formation controls the opacity of the affected region, and significantly affects the thermal histories of chondrules. Micron‐sized grains evaporate too quickly to prevent excessive heating of chondrule precursors. However, isolated grains in chondrule‐forming regions would rapidly coagulate into fractal aggregates. Preshock heating by infrared radiation from the shock front would cause these aggregates to melt and collapse into intermediate‐sized (tens of microns) particles. We show that inclusion of such particles yields chondrule cooling rates consistent with petrologic and isotopic constraints.     

Chondrule formation by repeated evaporative melting and condensation in collisional debris clouds around planetesimals

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.