The role of sticky interstellar organic material in the formation of asteroids

Abstract— Collision experiments and measurements of viscoelastic properties were performed involving an interstellar organic material analogue to investigate the growth of organic grains in the protosolar nebula. The organic material was found to be stickiest at a radius of between 2.3 and 3.0 AU, with a maximum sticking velocity of 5 m s^?1 for millimeter‐size organic grains. This stickiness is considered to have resulted in the very rapid coagulation of organic grain aggregates and subsequent formation of planetesimals in the early stage of the turbulent accretion disk. The planetesimals formed in this region appear to be represent achondrite parent bodies. In contrast, the formation of planetesimals at <2.1 and >3.0 AU begins with the establishment of a passive disk because silicate and ice grains are not as sticky as organic grains.     

Conditions for collisional growth of a grain aggregate

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

Shattering and coagulation of dust grains in interstellar turbulence

We investigate shattering and coagulation of dust grains in turbulent interstellar medium (ISM). The typical velocity of dust grain as a function of grain size has been calculated for various ISM phases based on a theory of grain dynamics in compressible magnetohydrodynamic turbulence. In this paper, we develop a scheme of grain shattering and coagulation and apply it to turbulent ISM by using the grain velocities predicted by the above turbulence theory. Since large grains tend to acquire large velocity dispersions as shown by earlier studies, large grains tend to be shattered. Large shattering effects are indeed seen in warm ionized medium within a few Myr for grains with radius   a ≳ 10⁻⁶  cm. We also show that shattering in warm neutral medium can limit the largest grain size in ISM  ( a ∼ 2 × 10⁻⁵ cm)  . On the other hand, coagulation tends to modify small grains since it only occurs when the grain velocity is small enough. Coagulation significantly modifies the grain size distribution in dense clouds (DC), where a large fraction of the grains with   a < 10⁻⁶ cm  coagulate in 10 Myr. In fact, the correlation among   R_V   , the carbon bump strength and the ultraviolet slope in the observed Milky Way extinction curves can be explained by the coagulation in DC. It is possible that the grain size distribution in the Milky Way is determined by a combination of all the above effects of shattering and coagulation. Considering that shattering and coagulation in turbulence are effective if dust-to-gas ratio is typically more than ∼1/10 of the Galactic value, the regulation mechanism of grain size distribution should be different between metal-poor and metal-rich environments.     

Observed Weak Electron Beam Discharge Driven Grain Acceleration/Accretion with Implications for Planet Formation

Work presented here addresses the issue of grain accretion, an essential yet poorly understood process in planetary system formation, linking the dynamically modeled steps of temperature-dependent condensation of gases after proto-sun gravitational collapse to coalescence of kilometer-size planetesimals into planets. The mechanism for grain accretion has proven difficult to model dynamically. Here, we attempt to test the thesis that the accretion process is electrostatically-driven by non-uniform charging of grains in a low discharge/weak field environment equivalent to periodic conditions in protoplanetary nebulae during solar discharge events such as flares. We simulate in the laboratory the behavior of grains in relationship to surfaces in such an environment. The nature of the observed disaggregation, repulsion, and acceleration of grains away from initial surfaces, and their reaggregation as coatings on surrounding oppositely charged surfaces, provide an empirical experimental basis for an electrostatically-driven model for grain behavior and accretion. Similar weak discharge processes in the protoplanetary disk solar nebula could give rise to increased grain acceleration and collisional compression induced surface coating, necessary conditions for increased accretion. The frequency, timing, and level of energetic output of the proto-sun would influence the effectiveness of such processes in developing stable aggregates, and the nature of the solar system that would result.     

Dust coagulation in star formation with different metallicities

Dust grains coagulate into larger aggregates in dense gas. This changes their size distribution and possibly affects the thermal evolution of star-forming clouds. We here investigate dust coagulation in collapsing pre-stellar cores with different metallicities by considering the thermal motions of grains. We show that coagulation does occur even at low metallicity  ∼10⁻⁶ Z_⊙  . However, we also find (i) that the H₂ formation rate on dust grains is reduced only after the majority of H₂ is formed and (ii) that the dust opacity is modified only after the core becomes optically thick. Therefore, we conclude that the effects of dust coagulation can safely be neglected in discussing the temperature evolution of the pre-stellar cores for any metallicity as long as the grain motions are thermal.     

Temperature distribution in the solar nebula at successive stages of its evolution

We have constructed a model of the solar nebula that allows for the temperature and pressure distributions at various stages of its evolution to be calculated. The mass flux from the accretion envelope to the disk and from the disk to the Sun, the turbulent viscosity parameter α, the opacity of the disk material, and the initial angular momentum of the protosun are the input model parameters that are varied. We also take into account the changes in the luminosity and radius of the young Sun. The input model parameters are based mostly on data obtained from observations of young solar-type stars with disks. To correct the input parameters, we use the mass and chemical composition of Jupiter, as well as models of its internal structure and formation that allow constraints to be imposed on the temperature and surface density of the protoplanetary disk in Jupiter’s formation zone. Given the derived constraints on the input parameters, we have calculated models of the solar nebula at successive stages of its evolution: the formation inside the accretion envelope, the evolution around the young Sun going through the T Tauri stage, and the formation and compaction of a thin dust layer (subdisk) in the disk midplane. We have found the following evolutionary trend: an increase in the temperature of the disk at the stage of its formation, cooling at the T Tauri stage, and the subsequent internal heating of the dust subdisk by turbulence dissipation that causes a temperature rise in the formation zone of the terrestrial planets at the high subdisk density and the opacity in this zone. We have obtained the probable ranges of temperatures in the disk midplane, i.e., the temperatures of the protoplanetary material in the formation region of the terrestrial planets at the initial stage of their formation.     

Hydrodynamic Aspects of Modeling of the Mass Transfer and Coagulation Processes in Turbulent Accretion Disks

This paper considers, in the context of modeling the evolution of a protoplanetary cloud, the hydrodynamic aspects of the theory of concurrent processes of mass transfer and coagulation in a two-phase medium in the presence of shear turbulence in a differentially rotating gas–dust disk and of polydisperse solid particles suspended in a carrying flow of solid particles. The defining relations are derived for diffuse fluxes of particles of different sizes in the equations of turbulent diffusion in the gravitational field, which describe the convective transfer, turbulent mixing, and sedimentation of disperse dust grains onto the central plane of the disk, as well as their coagulation growth. A semiempirical method is developed for calculating the coefficients of turbulent viscosity and turbulent diffusion for particles of different kinds. This method takes into account the inverse effects of dust transfer on the turbulence evolution in the disk and the inertial differences between disperse solid particles. To solve rigorously the problem of the mutual influence of the turbulent mixing and coagulation kinetics in forming the gas–dust subdisk, the possible mechanisms of gravitational, turbulent, and electric coagulation in a protoplanetary disk are explored and the parametric method of moments for solving the Smoluchowski integro-differential coagulation equation for the particles' size distribution function is considered. This method takes into account the fact that this distribution belongs to a definite parametric class of distributions.     

Condensation and aggregation of solar corundum and corundum‐hibonite grains

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.     

Accretion disks around Jupiter and Saturn at the stage of regular satellite formation

Modern models of the formation of the regular satellites of giant planets, constructed with consideration for their structure and composition suggest that this process lasted for a considerable period of time (0.1–1 Myr) and developed in gas-dust circumplanetary disks at the final stage of giant planet formation. The parameters of protosatellite disks (e.g., the radial distribution of surface density and temperature) serve as important initial conditions for such models. Therefore, the development of protosatellite disk models that take into account currently known cosmochemical and physical restrictions remains a pressing problem. It is this problem that is solved in the paper. New models of the accretion disks of Jupiter and Saturn were constructed with consideration for the disk heating by viscous dissipation of turbulent motions, by accretion of material from the surrounding region of the solar nebula, and by radiation from the central planets. The influence of a set of input model parameters (the total rate of mass infall onto the disk, the turbulent viscosity and opacity of disk material, and the centrifugal radius of the disk) on thermal conditions in the accretion disks was studied. The dependence of opacity on temperature and the abundance and size of solid particles present in the disk was taken into account. Those constructed models that satisfy the existing constraints limit the probable values of input parameters (primarily rates of mass infall onto the disks of Jupiter and Saturn at the stage of regular satellite formation and, to a lesser extent, the disk opacities). Constraints on the location of the regions of formation of the major satellites of Jupiter and Saturn are suggested based on the constructed models and simple analytical estimates concerning the formation of satellites in the accretion disks. It is shown that Callisto and Titan could hardly be formed at significantly greater distances from their planets.     

Accretion of the gaseous envelope of Jupiter around a 5-10 Earth-mass core

New numerical simulations of the formation and evolution of Jupiter are presented. The formation model assumes that first a solid core of several M_⊕ accretes from the planetesimals in the protoplanetary disk, and then the core captures a massive gaseous envelope from the protoplanetary disk. Earlier studies of the core accretion-gas capture model [Pollack, J.B., Hubickyj, O., Bodenheimer, P., Lissauer, J.J., Podolak, M., Greenzweig, Y., 1996. Icarus 124, 62-85] demonstrated that it was possible for Jupiter to accrete with a solid core of 10-30 M_⊕ in a total formation time comparable to the observed lifetime of protoplanetary disks. Recent interior models of Jupiter and Saturn that agree with all observational constraints suggest that Jupiter's core mass is 0-11 M_⊕ and Saturn's is 9-22 M_⊕ [Saumon, G., Guillot, T., 2004. Astrophys. J. 609, 1170-1180]. We have computed simulations of the growth of Jupiter using various values for the opacity produced by grains in the protoplanet's atmosphere and for the initial planetesimal surface density, σinit,Z, in the protoplanetary disk. We also explore the implications of halting the solid accretion at selected core mass values during the protoplanet's growth. Halting planetesimal accretion at low core mass simulates the presence of a competing embryo, and decreasing the atmospheric opacity due to grains emulates the settling and coagulation of grains within the protoplanet's atmosphere. We examine the effects of adjusting these parameters to determine whether or not gas runaway can occur for small mass cores on a reasonable timescale. We compute four series of simulations with the latest version of our code, which contains updated equation of state and opacity tables as well as other improvements. Each series consists of a run without a cutoff in planetesimal accretion, plus up to three runs with a cutoff at a particular core mass. The first series of runs is computed with an atmospheric opacity due to grains (hereafter referred to as ‘grain opacity’) that is 2% of the interstellar value and . Cutoff runs are computed for core masses of 10, 5, and 3 M_⊕. The second series of Jupiter models is computed with the grain opacity at the full interstellar value and . Cutoff runs are computed for core masses of 10 and 5 M_⊕. The third series of runs is computed with the grain opacity at 2% of the interstellar value and . One cutoff run is computed with a core mass of 5 M_⊕. The final series consists of one run, without a cutoff, which is computed with a temperature dependent grain opacity (i.e., 2% of the interstellar value for ramping up to the full interstellar value for ) and . Our results demonstrate that reducing grain opacities results in formation times less than half of those for models computed with full interstellar grain opacity values. The reduction of opacity due to grains in the upper portion of the envelope with has the largest effect on the lowering of the formation time. If the accretion of planetesimals is not cut off prior to the accretion of gas, then decreasing the surface density of planetesimals lowers the final core mass of the protoplanet, but increases the formation timescale considerably. Finally, a core mass cutoff results in a reduction of the time needed for a protoplanet to evolve to the stage of runaway gas accretion, provided the cutoff mass is sufficiently large. The overall results indicate that, with reasonable parameters, it is possible that Jupiter formed at 5 AU via the core accretion process in 1 Myr with a core of 10 M_⊕ or in 5 Myr with a core of 5 M_⊕.     

Models of the protosatellite disk of Saturn: Conditions for Titan’s formation

Models of the protosatellite accretion disk of Saturn are developed that satisfy cosmochemical constraints on the volatile abundances in the atmospheres of Saturn and Titan with due regard for the data obtained with the Cassini orbiter and the Huygens probe, which landed on Titan in January 2005. All basic sources of heating of the disk and protosatellite bodies are taken into account in the models, namely, dissipation of turbulence in the disk, accretion of gaseous and solid material onto the disk from the feeding zone of Saturn in the solar nebula, and heating by the radiation of young Saturn and thermal radiation of the surrounding region of the solar nebula. Two-dimensional (axisymmetric) temperature, pressure, and density distributions are calculated for the protosatellite disk. The distributions satisfy the cosmochemical constraints on the disk temperature, according to which the temperature at the stage of the satellite formation ranged from 60–65 K to 90–100 K at pressures from 10^?7 to ?10^?4 bar in the zone of Titan’s formation (according to estimates, r = 20–35R _Sat). Variations of the basic input parameters (the accretion rate onto the protosatellite disk of Saturn from the feeding zone of the planet ?; the parameter α characterizing turbulent viscosity of the disk; and the mass concentration ratio in the solid/gas system) satisfying the aforementioned temperature constraint are found. The spectrum of models satisfying the cosmochemical constraints covers a considerable range of consistent parameters. A model with a rather small flux of ? = 10^?8 M _Sat/ yr and a tenfold depletion of Saturn’s disk in gas due to gas scattering from the solar nebula is at one side of this range. A model with a much higher flux of ? = 10^?6 M _Sat/yr and a hundredfold decrease in opacity of the disk matter owing to decreased concentration of dust particles and/or their agglomeration into large aggregates and sweeping up by planetesimals is at the other side of the range.     

Induced velocities of grains embedded in a turbulent gas

A theory is presented for the dynamics of dust particles in an incompressible turbulent fluid. Grain-gas coupling occurs through friction forces that are proportional to the mean grain velocity relative to the gas. This test particle theory is applied to the case of a Kolmogoroff spectrum in a protostellar cloud. The mean turbulence induced grain velocity and the mean turbulent relative velocity of two grains are calculated. Whereas the former should determine the dust scale height, grain-grain collisions are influenced by the latter. For a resonable strength of the turbulence, the mean induced relative velocity of two particles turns out to be at least as large as the corresponding terminal velocity difference during gravitational settling.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

Dust to planetesimals: Settling and coagulation in the solar nebula

The behavior of solid particles in a low-mass solar nebula during settling to the central plane and the formation of planetesimals is examined. Gravitational instability in a dust layer and collisional accretion are considered as possible mechanisms of planetesimal formation. Non-Keplerian rotation of the nebula results in shear between the gas and a dust layer. This shear produces turbulence within the layer which inhibits gravitational instability, unless the mean particle size exceeds a critical value, ～1 cm at 1 AU. The size requirement is less stringent at larger heliocentric distances, suggesting a possible difference in planetesimal formation mechanisms between the inner and outer nebula. Coagulation of grains during settling is expected in the solar nebula environment. Van der Waals forces appear adequate to produce centimeter-sized aggregates. Growth is primarily due to sweepup of small particles by larger ones due to size-dependent settling velocities. A numerical model for computing simultaneous coagulation and settling is described. Relative velocities are determined by gas drag and the non-Keplerian rotation of the nebula. The settling is very nonhomologous. Most of the solid matter reaches the central plane as centimeter-sized aggregates in a few times 10³ revolutions, but some remains suspended in the form of fine dust. Drag-induced relative velocities result in collisions. The growth of bodies in the central plane is initially rapid. After sizes reach ～10³ cm, relative velocities decrease and the growth rate declines. Gas drag rapidly damps the out-of-plane motions of these intermediate-sized bodies. They settle into a thin layer which is subject to gravitational instability. Kilometer-sized planetesimals are formed by this composite process.     

The contribution of small grains to the opacity of protoplanetary atmospheres

I compute the opacity of grains in a protoplanetary atmosphere. The grain size distribution at different levels in the atmosphere is calculated using a simple microphysical model of grain growth via collisions and destruction via vaporization at high temperatures. The Rosseland mean opacity of the resulting distribution is then computed. For most cases examined, the grain opacity is significantly lower than earlier estimates.     

Dust in the disk winds from young stars as a source of the circumstellar extinction

We consider the problem of dust grain survival in the disk winds from T Tauri and Herbig Ae stars. For our analysis, we have chosen a disk wind model in which the gas component of the wind is heated through ambipolar diffusion to a temperature of ～10⁴ K. We show that the heating of dust grains through their collisions with gas atoms is inefficient compared to their heating by stellar radiation and, hence, the grains survive even in the hot wind component. As a result, the disk wind can be opaque to the ultraviolet and optical stellar radiation and is capable of absorbing an appreciable fraction of it. Calculations show that the fraction of the wind-absorbed radiation for T Tauri stars can be from 20 to 40% of the total stellar luminosity at an accretion rate ? _a = 10^?8-10^?6 M _⊙yr^?1. This means that the disk winds from T Tauri stars can play the same role as the puffed-up inner rim in current accretion disk models. In Herbig Ae stars, the inner layers of the disk wind (r ≤ 0.5 AU) are dust-free, since the dust in this region sublimates under the effect of stellar radiation. Therefore, the fraction of the radiation absorbed by the disk wind in this case is considerably smaller and can be comparable to the effect from the puffed-up inner rim only at an accretion rate of the order of or higher than 10^?6 M _⊙yr^?1. Since the disk wind is structurally inhomogeneous, its optical depth toward the observer can be variable, which should be reflected in the photometric activity of young stars. For the same reason, moving shadows from gas and dust streams with a spiral-like shape can be observed in high-angular-resolution circumstellar disk images.     

The formation of comets in wind-driven shells around protostars

It is shown that the dense, turbulent, decelerating shells produced by protostellar flows around young stars are a probable site for rapid grain growth by coalescing collisions. The growth of grains occurs in a thin dust layer at the leading edge of the gas shell until a critical grain size on the order of 1−10 μm is reached. Grains larger than this decouple from the turbulence and eventually reach sizes of ≈100 μm. These large grains form a thin dust shell with low-velocity dispersion, in which ultimately local gravitational instability takes place. This causes the accumulation of comet-sized aggregations of dust, assuming that the dust velocity dispersion is on the order of 10⁻² m sec⁻¹. It is proposed that the mechanism could lead to a high space density of comets in molecular clouds. The efficient formation of “giant” grains, and even comet nuclei, in the regions around young stars has important implications both for cometary astronomy and for understanding the dynamical and chemical evolution of molecular clouds and the interstellar medium.     

Radiative heating of interstellar grains falling toward the solar nebula: 1-D diffusion calculations

As the dense molecular cloud that was the precursor of our Solar System was collapsing to form a protosun and the surrounding solar-nebula accretion disk, infalling interstellar grains were heated much more effectively by radiation from the forming protosun than by radiation from the disk's accretion shock. Accordingly, we have estimated the temperatures experienced by these infalling grains using radiative diffusion calculations whose sole energy source is radiation from the protosun. Although the calculations are 1-dimensional, they make use of 2-D, cylindrically symmetric models of the density structure of a collapsing, rotating cloud. The temperature calculations also utilize recent models for the composition and radiative properties of interstellar grains (Pollack et al. 1994. Astrophys. J. 421, 615-639), thereby allowing us to estimate which grain species might have survived, intact, to the disk accretion shock and what accretion rates and molecular-cloud rotation rates aid that survival. Not surprisingly, we find that the large uncertainties in the free parameter values allow a wide range of grain-survival results: (1) For physically plausible high accretion rates or low rotation rates (which produce small accretion disks), all of the infalling grain species, even the refractory silicates and iron, will vaporize in the protosun's radiation field before reaching the disk accretion shock. (2) For equally plausible low accretion rates or high rotation rates (which produce large accretion disks), all non-ice species, even volatile organics, will survive intact to the disk accretion shock. These grain-survival conclusions are subject to several limitations which need to be addressed by future, more sophisticated radiative-transfer models. Nevertheless, our results can serve as useful inputs to models of the processing that interstellar grains undergo at the solar nebula's accretion shock, and thus help address the broader question of interstellar inheritance in the solar nebula and present Solar System. These results may also help constrain the size of the accretion disk: for example, if we require that the calculations produce partial survival of organic grains into the solar nebula, we infer that some material entered the disk intact at distances comparable to or greater than a few AU. Intriguingly, this is comparable to the heliocentric distance that separates the C-rich outer parts of the current Solar System from the C-poor inner regions.     

Fundamentals of the mechanics of heterogeneous media in the circumsolar protoplanetary cloud: The effects of solid particles on disk turbulence

We formulate a complete system of equations of two-phase multicomponent mechanics including the relative motion of the phases, coagulation processes, phase transitions, chemical reactions, and radiation in terms of the problem of reconstructing the evolution of the protoplanetary gas-dust cloud that surrounded the proto-Sun at an early stage of its existence. These equations are intended for schematized formulations and numerical solutions of special model problems on mutually consistent modeling of the structure, dynamics, thermal regime, and chemical composition of the circumsolar disk at various stages of its evolution, in particular, the developed turbulent motions of a coagulating gas suspension that lead to the formation of a dust subdisk, its gravitational instability, and the subsequent formation and growth of planetesimals. To phenomenologically describe the turbulent flows of disk material, we perform a Favre probability-theoretical averaging of the stochastic equations of heterogeneous mechanics and derive defining relations for the turbulent flows of interphase diffusion and heat as well as for the “relative” and Reynolds stress tensors needed to close the equations of mean motion. Particular attention is given to studying the influence of the inertial effects of dust particles on the properties of turbulence in the disk, in particular, on the additional generation of turbulent energy by large particles near the equatorial plane of the proto-Sun. We develop a semiempirical method of modeling the coefficient of turbulent viscosity in a two-phase disk medium by taking into account the inverse effects of the transfer of a dispersed phase (or heat) on the growth of turbulence to model the vertically nonuniform thermohydrodynamic structure of the subdisk and its atmosphere. We analyze the possible “regime of limiting saturation” of the subdisk atmosphere by fine dust particles that is responsible for the intensification of various coagulation mechanisms in a turbulized medium. For steady motion when solid particles settle to the midplane of the disk under gravity, we analyze the parametric method of moments for solving the Smoluchowski integro-differential coagulation equation for the particle size distribution function. This method is based on the fact that the sought-for distribution function a priori belongs to a certain parametric class of distributions.