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1.
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. 相似文献
2.
We consider gravitational instability of the dust layer in the midplane of a protoplanetary disk with turbulence and shear stresses between the gas in the disk and that in the dust layer. We solve a linearized system of hydrodynamic equations for perturbations of dust (monodisperse) and gas phases in the incompressible gas approximation. We take into account the gas drag of solid particles (dust aggregates), turbulent diffusion and the velocity dispersion of particles, and the perturbation of the azimuthal velocity of gas in the layer upon the transfer of angular momentum from solid particles to it and from this gas to the surrounding gas in the disk. We obtain and solve the dispersion equation for the layer with the ratio of surface densities of the dust phase and gas being well above unity. The following parameters of gravitational instability in the dust layer are calculated: the critical surface density of solid matter and the Stokes number of particles corresponding to the onset of instability, the wavelength range in which instability occurs, and the rate of its growth as a function of the perturbation wavelength in the circumsolar disk at radial distances of 1 and 10 AU. We show that at 10 AU, the maximum instability growth rate increases due to the transfer of angular momentum of gas in the layer to gas outside it, a new maximum emerges at a longer wavelength, a long-wavelength instability “tail” forms, and the critical surface density initiating instability decreases relative to that determined without the transfer of angular momentum to gas outside the layer. None of these effects are observed at 1 AU, since instability in this region probably develops faster than the transfer of angular momentum to the surrounding gаs of a protoplanetary disk occurs. 相似文献
3.
Gravitational instability of the dust layer formed after the aggregates of dust particles settle toward the midplane of a protoplanetary disk under turbulence is considered. A linearized system of hydrodynamic equations for perturbations of dust (monodisperse) and gas phases in the incompressible gas approximation is solved. Turbulent diffusion and the velocity dispersion of solid particles and the perturbation of gas azimuthal velocity in the layer upon the transfer of angular momentum from the dust phase due to gas drag are taken into account. Such an interaction of the particles and the gas establishes upper and lower bounds on the perturbation wavelength that renders the instability possible. The dispersion equation for the layer in the case when the ratio of surface densities of the dust phase and the gas in the layer is well above unity is obtained and solved. An approximate gravitational instability criterion, which takes the size-dependent stopping time of a particle (aggregate) in the gas into account, is derived. The following parameters of the layer instability are calculated: the wavelength range of its subsistence and the dependence of the perturbation growth rate on the perturbation wavelength in the circumsolar disk at a radial distance of 1 and 10 AU. It is demonstrated that at a distance of 1 AU, the gas–dust disk should be enriched with solids by a factor of 5–10 relative to the initial abundance as well as the particle aggregates should grow to the sizes higher than about 0.3 m in order for the instability to emerge in the layer in the available turbulence models. Such high disk enrichment and aggregate growth is not needed at a distance of 10 AU. The conditions under which this gravitational instability in the layer may be examined with no allowance made for the transfer of angular momentum from the gas in the layer to the gas in a protoplanetary disk outside the layer are discussed. 相似文献
4.
An heuristic way of modeling the turbulent exchange coefficients for Keplerian accretion disks surrounding solar-type stars is considered. The formulas for these coefficients, taking into account the inverse effects of dust transfer and potential temperature on the maintenance of shear turbulence, generalize to protoplanetary gas–dust clouds the expression for the turbulent viscosity coefficient in so-called a-disks which was obtained in a classic work by Shakura and Syunyaev (1973). The defining relationships are derived for turbulent diffusion and heat flows, which describe, for the two-phase mixture rotating differentially at an angular velocity O(r, z), the dust and heat transfer in the direction perpendicular to the central plane of the disk. The regime of limiting saturation by small dust particles of the layer of “cosmic fluid” located slightly above (or below) the dust subdisk is analyzed. 相似文献
5.
The evolutionary hydrodynamic model for the formation and growth of loose dust aggregates in the aerodisperse medium of a laminar disk, which was originally comprised of the gas and solid (sub)micrometer particles, is considered as applied to the problem of the formation of planetesimals in the Solar protoplanetary cloud. The model takes into account the fractal properties of dust clusters. It is shown that the clusters partly merge in the process of cluster-cluster coagulation, giving rise to the formation of large fractal aggregates that are the basic structure-forming elements of loose protoplanetesimals arising as a result of physicochemical and hydrodynamic processes similar to the processes of growth of the fractal clusters. Earlier, the modeling was conventionally performed in an “ordinary” continuous medium without considering the multifractional structure of the dust component of the protoplanetary cloud and the fractal nature of the dust clusters being formed during its evolution. Instead, we propose to consider a complex of loose dust aggregates as a special type of continuous medium, namely, the fractal medium for which there exist points and regions that are not filled with its particles. We suggest performing the hydrodynamic modeling of this medium, which has a noninteger mass dimensionality, in a fractional integral model (its differential form) that takes the fractality into account using fractional integrals whose order is determined by a fractal dimensionality of the disk medium. 相似文献
6.
Studying the origin and evolution of the Solar system is among the fundamental problems of modern natural science. This problem is interdisciplinary and requires the development of mathematical models for the physical structure and evolution of a gas–dust accretion disk from the initial stages of its formation to the formation of a planetary system. One of the key problems is the formation and growth of bodies in a protoplanetary disk, the basis for which is a study of the collisional processes of the solidbody component. We have performed a parametric analysis of the cluster–cluster collision processes occurring in a protoplanetary disk within the model of permeable particles being developed by us. The outcome of such collisions is shown to be affected significantly by the topological properties of colliding dust clusters with a fractal internal structure. The results of our parametric analysis show that for sufficiently “dense” fractal dust clusters, at low relative collision velocities, there exists a range in which the colliding clusters bounce. At the same time, for “porous” fractal clusters the bounce is impossible for any sets of collision parameters. As the relative collision velocities increase, the cluster coalescence processes begin to dominate due to a rearrangement of the fractal structure in the contact zone. However, as the kinetic energy of collisions increases further, a critical threshold is reached beyond which the collision energy exceeds the particle binding energy in clusters and the fractal dust cluster destruction processes are switched on during collisions. Thus, our parametric analysis imposes quite definite constraints on the dynamics and chronology of the evolution processes during the formation of primordial solid bodies and planetesimals. The proposed approach and the results obtained are fairly realistic and open prospects for more comprehensive model studies of the initial evolutionary phase of a protoplanetary disk. 相似文献
7.
The sequence of evolution of the protoplanetary gas-and-dust disk around the parent star includes, according to modern concepts, its compression in the central plane and decay into separate dust condensations (clusters) due to the occurrence of various types of instabilities. The interaction of dust clusters of a fractal structure during their collisions is considered as a key mechanism for the formation and growth of primary solids, which serve as the basis for the subsequent formation of planetesimals and embryos of planets. Among the mechanisms contributing to the formation of planetesimals, an important place belongs, along with gravitational instability, hydrodynamic instabilities, in particular, the socalled streaming instability of the two-phase gas-dust layer due to its ability to concentrate dispersed particles in dense clots. In contrast to a number of existing models of streaming instability, in which dust particles are considered structurally compact and monodisperse, this paper proposes a more realistic model of polydisperse particles of fractal nature, forming dust clusters as a result of coagulation. The instability of the dust layer in the central plane of the protoplanetary disk under linear axisymmetric perturbations of its parameters is considered. A preliminary conclusion can be drawn that the proposed model of dust fractal aggregates of different scales increases the efficiency of linear growth of hydrodynamic instabilities, including the streaming instabilities associated with the difference between the velocities of the dust and gas phases.
相似文献8.
Most main sequence stars are binaries or higher multiplicity Systems and it appears that at birth most stars have circumstellar
disks. It is commonly accepted that planetary systems arise from the material of these disks; consequently, binary and multiple
systems may have a main role in planet formation. In this paper, we study the stage of planetary formation during which the
particulate material is still dispersed as centimetre-to-metre sized primordial aggregates. We investigate the response of
the particles, in a protoplanetary disk with radius RD = 100 AU around a solar-like star, to the gravitational field of bound perturbing companions in a moderately wide (300–1600
AU) orbit. For this purpose, we have carried out a series of simulations of coplanar hierarchical configurations using a direct
integration code that models gravitational and viscous forces. The massive protoplanetary disk is around one of the components
of the binary. The evolution in time of the dust sub-disk depends mainly on the nature (prograde or retrograde) of the relative
revolution of the stellar companion, and on the temperature and mass of the circumstellar disk. Our results show that for
binary companions near the limit of tidal truncation of the disk, the perturbation leads to an enhanced accretion rate onto
the primary, decreasing the lifetime of the particles in the protoplanetary disk with respect to the case of a single star.
As a consequence of an enhanced accretion rate the mass of the disk decreases faster, which leads to a longer resultant lifetime
for particles in the disk. On the other hand, binary companions may induce tidal arms in the dust phase of protoplanetary
disks. Spiral perturbations with m = 1 may increase in a factor 10 or more the dust surface density in the neighbourhood of
the arm, facilitating the growth of the particles. Moreover, in a massive disk (0.01M⊙) the survival time of particles is
significantly shorter than in a less massive nebula (0.001M⊙) and the temperature of the disk severely influences the spiral-in
time of particles. The rapid evolution of the dust component found in post T Tauri stars can be explained as a result of their
binary nature. Binarity may also influence the evolution of circumpulsar disks.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
J.E. Chambers 《Icarus》2010,208(2):505-19170
The formation of 1-1000 km diameter planetesimals from dust grains in a protoplanetary disk is a key step in planet formation. Conventional models for planetesimal formation involve pairwise sticking of dust grains, or the sedimentation of dust grains to a thin layer at the disk midplane followed by gravitational instability. Each of these mechanisms is likely to be frustrated if the disk is turbulent. Particles with stopping times comparable to the turnover time of the smallest eddies in a turbulent disk can become concentrated into dense clumps that may be the precursors of planetesimals. Such particles are roughly millimeter-sized for a typical protoplanetary disk. To survive to become planetesimals, clumps need to form in regions of low vorticity to avoid rotational breakup. In addition, clumps must have sufficient self gravity to avoid break up due to the ram pressure of the surrounding gas. Given these constraints, the rate of planetesimal formation can be estimated using a cascade model for the distribution of particle concentration and vorticity within eddies of various sizes in a turbulent disk. We estimate planetesimal formation rates and planetesimal diameters as a function of distance from a star for a range of protoplanetary disk parameters. For material with a solar composition, the dust-to-gas ratio is too low to allow efficient planetesimal formation, and most solid material will remain in small particles. Enhancement of the dust-to-gas ratio by 1-2 orders of magnitude, either vertically or radially, allows most solid material to be converted into planetesimals within the typical lifetime of a disk. Such dust-to-gas ratios may occur near the disk midplane as a result of vertical settling of short-lived clumps prior to clump breakup. Planetesimal formation rates are sensitive to the assumed size and rotational speed of the largest eddies in the disk, and formation rates increase substantially if the largest eddies rotate more slowly than the disk itself. Planetesimal formation becomes more efficient with increasing distance from the star unless the disk surface density profile has a slope of −1.5 or steeper as a function of distance. Planetesimal formation rates typically increase by an order-of-magnitude or more moving outward across the snow line for a solid surface density increase of a factor of 2. In all cases considered, the modal planetesimal size increases with roughly the square root of distance from the star. Typical modal diameters are 100 km and 400 km in the regions corresponding to the asteroid belt and Kuiper belt in the Solar System, respectively. 相似文献
10.
《Planetary and Space Science》2007,55(5):536-546
We describe a model designed to track simultaneously the evolution of gas and solids in protoplanetary disks from an early stage, when all solids are in the dust form, to the stage when most solids are in the form of a planetesimal swarm. The model is computationally efficient and allows for a global, comprehensive approach to the evolution of solid particles due to gas–solid coupling, coagulation, sedimentation, and evaporation/condensation. We have used it to calculate the co-evolution of gas and solids starting from a comprehensive domain of initial conditions. Then based on the core accretion-gas capture scenario, we have estimated the planet-bearing capability of the environment defined by the final planetesimal swarm and the still evolving gaseous component of the disk. We describe how the disk's capability of formation of giant planets depends on the initial mass and size of a protoplanetary disk, its thermal structure, mass of the central star and properties of the material forming solid grains. 相似文献
11.
We consider the formation of cometlike and larger bodies in the trans-Neptunian region of the protoplanetary gas–dust disk. Once the particles have reached 1–10 cm in size through mutual collisions, they compact and concentrate toward the midplane of the disk to form a dust subdisk there. We show that after the subdisk has reached a critical density, its inner, equatorial layer that, in contrast to the two subsurface layers, contains no shear turbulence can be gravitationally unstable. The layer breaks up into 1012-cm clumps whose small fragments (109 cm) can rapidly contract to form bodies 10 km in size. We consider the sunward drift of dust particles at a velocity that decreases with decreasing radial distance as the mechanism of radial contraction and compaction of the layer that contributes to its gravitational instability and the formation of larger (100 km) planetesimals. Given all of the above processes, it takes 106 yr for planetesimals to form, which is an order of magnitude shorter than the lifetime of the gas–dust protoplanetary disk. We discuss peculiarities of the structure of planetesimals. 相似文献
12.
Radial contraction of the dust layer in the midplane of a gas–dust protoplanetary disk that consists of large dust aggregates is modeled. Sizes of aggregates vary from centimeters to meters assuming the monodispersion of the layer. The highly nonlinear continuity equation for the solid phase of the dust layer is solved numerically. The purpose of the study is to identify the conditions under which the solid matter is accumulated in the layer, which contributes to the formation of planetesimals as a result of gravitational instability of the dust phase of the layer. We consider the collective interaction of the layer with the surrounding gas of the protoplanetary disk: shear stresses act on the gas in the dust layer that has a higher orbital velocity than the gas outside the layer, this leads to a loss of angular momentum and a radial drift of the layer. The stress magnitude is determined by the turbulent viscosity, which is represented as the sum of the α-viscosity associated with global turbulence in the disk and the viscosity associated with turbulence that is localized in a thin equatorial region comprising the dust layer and is caused by the Kelvin–Helmholtz instability. The evaporation of water ice and the continuity of the mass flux of the nonvolatile component on the ice line is also taken into account. It is shown that the accumulation of solid matter on either side of the ice line and in other regions of the disk is determined primarily by the ratio of the radii of dust aggregates on either side of the ice line. If after the ice evaporation the sizes (or density) of dust aggregates decrease by an order of magnitude or more, the density of the solid phase of the layer’s matter in the annular zone adjacent to the ice line from the inside increases sharply. If, however, the sizes of the aggregates on the inner side of the ice line are only a few times smaller than behind the ice line, then in the same zone there is a deficit of mass at the place of the modern asteroid belt. We have obtained constraints on the parameters at which the layer compaction is possible: the global turbulence viscosity parameter (α < 10?5), the initial radial distribution of the surface density of the dust layer, and the distribution of the gas surface density in the disk. Restrictions on the surface density depend on the size of dust aggregates. It is shown that the timescale of radial contraction of a dust layer consisting of meter-sized bodies is two orders of magnitude and that of decimeter ones, an order of magnitude greater than the timescale of the radial drift of individual particles if there is no dust layer. 相似文献
13.
《天文和天体物理学研究(英文版)》2010,(12)
More than a decade of dedicated experimental work on the collisional physics of protoplanetary dust has brought us to a point at which the growth of dust aggregates can-for the first time-be self-consistently and reliably modeled. In this article, the emergent collision model for protoplanetery dust aggregates, as well as the numerical model for the evolution of dust aggregates in protoplanetary disks, is reviewed. It turns out that, after a brief period of rapid collisional growth of fluffy dust aggregates to sizes of a few centimeters, the protoplanetary dust particles are subject to bouncing collisions, in which their porosity is considerably decreased. The model results also show that low-velocity fragmentation can reduce the final mass of the dust aggregates but that it does not trigger a new growth mode as discussed previously. According to the current stage of our model, the direct formation of kilometer-sized planetesimals by collisional sticking seems unlikely, implying that collective effects, such as the streaming instability and the gravitational instability in dust-enhanced regions of the protoplanetary disk, are the best candidates for the processes leading to planetesimals. 相似文献
14.
We analyze the conditions for the formation and time evolution of peripheral comet structures of solar-type planetary systems. In the Solar system, these include the Kuiper belt, the Oort cloud, the comet spear, and the Galactic comet ring that marks the Galactic orbit of the Sun. We consider the role of the viscosity of a protoplanetary gas–dust disk, major planets, field stars, globular clusters, giant molecular clouds, and the Galactic gravitational field in the formation of these peripheral structures marked by comets and asteroids. We give a list of the closest past and future passages of neighboring stars through the solar Oort cloud that perturb the motion of its comets and, thus, contribute to the enhancement of its cometary activity, on the one hand, and to the replenishment of the solar comet spear with new members, on the other hand. 相似文献
15.
16.
17.
V. V. Akimkin Y. N. Pavlyuchenkov A. I. Vasyunin D. S. Wiebe M. S. Kirsanova T. Henning 《Astrophysics and Space Science》2011,335(1):33-38
We study details of the UV radiation transfer in a protoplanetary disk, paying attention to the influence of dust growth and
sedimentation on the disk density and temperature. Also, we show how the dust evolution affects photoreaction rates of key
molecules, like CN and CS. 相似文献
18.
19.
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. 相似文献
20.
F.J. Ciesla 《Icarus》2009,200(2):655-671
Large-scale radial transport of solids appears to be a fundamental consequence of protoplanetary disk evolution based on the presence of high temperature minerals in comets and the outer regions of protoplanetary disks around other stars. Further, inward transport of solids from the outer regions of the solar nebula has been postulated to be the manner in which short-lived radionuclides were introduced to the terrestrial planet region and the cause of the variations in oxygen isotope ratios in the primitive materials. Here, both outward and inward transport of solids are investigated in the context of a two-dimensional, viscously evolving protoplanetary disk. The dynamics of solids are investigated to determine how they depend on particle size and the particular stage of protoplanetary disk evolution, corresponding to different rates of mass transport. It is found that the outward flows that arise around the disk midplane of a protoplanetary disk aid in the outward transport of solids up to the size of CAIs s and can increase the crystallinity fraction of silicate dust at 10 AU around a solar mass star to as much as ∼40% in the case of rapidly evolving disks, decreasing as the accretion rate onto the star slows. High velocity, inward flows along the disk surface aid in the rapid transport of solids from the outer disk to the inner disk, particularly for small dust. Despite the diffusion that occurs throughout the disk, the large-scale, meridonal flows associated with mass transport prevent complete homogenization of the disk, allowing compositional gradients to develop that vary in intensity for a timescale of one million of years. The variations in the rates and the preferred direction of radial transport with height above the disk midplane thus have important implications for the dynamics and chemical evolution of primitive materials. 相似文献