共查询到20条相似文献，搜索用时 62 毫秒
1.
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
2.
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
3.
《天文和天体物理学研究(英文版)》2016,(9)
We study drag-driven instability in a protoplanetary disc consisting of a layer of single-sized dust particles which are coupled to the magnetized gas aerodynamically and the particle-to-gas feedback is included. We find a dispersion relation for axisymmetric linear disturbances and growth rate of the unstable modes are calculated numerically. While the secular gravitational instability in the absence of particle-togas feedback predicts the dust layer is unstable, magnetic fields significantly amplify the instability if the Toomre parameter for the gas component is fixed. We also show that even a weak magnetic field is able to amplify the instability more or less irrespective of the dust-gas coupling. 相似文献
4.
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
5.
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6.
The gravitational instability in the dust layer of a protoplanetary disk with nonuniform dust density distributions in the direction vertical to the midplane is investigated. The linear analysis of the gravitational instability is performed. The following assumptions are used: (1) One fluid model is adopted, that is, difference of velocities between dust and gas are neglected. (2) The gas is incompressible. (3) Models are axisymmetric with respect to the rotation axis of the disk. Numerical results show that the critical density at the midplane is higher than the one for the uniform dust density distribution by Sekiya (1983, Prog. Theor. Phys. 69, 1116-1130). For the Gaussian dust density distribution, the critical density is 1.3 times higher, although we do not consider this dust density distribution to be realistic because of the shear instability in the dust layer. For the dust density distribution with a constant Richardson number, which is considered to be realized due to the shear instability, the critical density is 2.85 times higher and is independent of the value of the Richardson number. Further, if a constant Richardson number could decrease to the order of 0.001, the gravitational instability would be realized even for the dust to gas surface density ratio with the solar abundance. Our results give a new restriction on planetesimal formation by the gravitational instability. 相似文献
7.
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. 相似文献
8.
We have developed a two-dimensional model of a flared protoplanetary disk (PPD) incorporating a self-consistent treatment
of gas and dust temperature, and a detailed treatment of the gas-phase chemistry as well as the freeze-out and desorption
of material from dust grains. The results show that, in the inner 10 AU of the disk, the gas-phase abundances are dominated
by material evaporated from dust grains. The surface layer of the disk shows many of the characteristics of photon-dominated
regions.
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.
11.
S.J. Weidenschilling 《Icarus》1980,44(1):172-189
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. 相似文献
12.
《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
13.
We study the rate of radial diffusion of planetesimals due to mutual gravitational encounters under Hill’s approximations in the three-body problem. Planetesimals orbiting a central star radially migrate inward and outward as a result of mutual gravitational encounters and transfer angular momentum. We calculate the viscosity in a disk of equal-sized planetesimals due to their mutual gravitational encounters using three-body orbital integrations, and obtain a semianalytic expression that reproduces the numerical results. We find that the viscosity is independent of the velocity dispersion of planetesimals when the velocity dispersion is so small that Kepler shear dominates planetesimals’ relative velocities. On the other hand, in high-velocity cases where random velocities dominate the relative velocities, the viscosity is a decreasing function of the velocity dispersion, and is found to agree with previous estimates under the two-body approximation neglecting the solar gravity. We also calculate the rate of radial diffusion of planetesimals due to gravitational scattering by a massive protoplanet. Using these results, we discuss a condition for formation of nonuniform radial surface density distribution of planetesimals by gravitational perturbation of an embedded protoplanet. 相似文献
14.
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
15.
Conventional planet formation models via coagulation of planetesimals require timescales in the range of several 10 or even 100 Myr in the outer regions of a protoplanetary disk. But according to observational data, the lifetime of a protoplanetary disk is limited to about 6 Myr. Therefore the existence of Uranus and Neptune poses a problem. Planet formation via gravitational instability may be a solution for this discrepancy. We present a parameter study of the possibility of gravitationally triggered disk instability. Using a restricted N‐body model which allows for a survey of an extended parameter space, we show that a passing dwarf star with a mass between 0.1 and 1 M⊙ can probably induce gravitational instabilities in the pre‐planetary solar disk for prograde passages with minimum separations below 80‐170 AU. Inclined and retrograde encounters lead to similar results but require slightly closer passages. Such encounter distances are quite likely in young moderately massive star clusters. The induced gravitational instabilities may lead to enhanced planetesimal formation in the outer regions of the protoplanetary disk, and could therefore be relevant for the formation of Uranus and Neptune. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
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
17.
18.
《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
19.
The linear analysis of the instability due to vertical shear in the dust layer of the solar nebula is performed. The following assumptions are adopted throughout this paper: (1) The self-gravity of the dust layer is neglected. (2) One fluid model is adopted, where the dust aggregates have the same velocity with the gas due to strong coupling by the drag force. (3) The gas is incompressible. The calculations with both the Coriolis and the tidal forces show that the tidal force has a stabilizing effect. The tidal force causes the radial shear in the disk. This radial shear changes the wave number of the mode which is at first unstable, and the mode is eventually stabilized. Thus the behavior of the mode is divided into two stages: (1) the first growth of the unstable mode which is similar to the results without the tidal force, and (2) the subsequent stabilization due to an increase of the wave number by the radial shear. If the midplane dust/gas density ratio is smaller than 2, the stabilization occurs before the unstable mode grows largely. On the other hand, the mode grows faster by one hundred orders of magnitude, if this ratio is larger than 20. Because the critical density of the gravitational instability is a few hundreds times as large as the gas density, the hydrodynamic instability investigated in this paper grows largely before the onset of the gravitational instability. It is expected that the hydrodynamic instability develops turbulence in the dust layer and the dust aggregates are stirred up to prevent from settling further. The formation of planetesimals through the gravitational instabilities is difficult to occur as long as the dust/gas surface density ratio is equal to that for the solar abundance. On the other hand, the shear instability is suppressed and the planetesimal formation through the gravitational instability may occur, if dust/gas surface density ratio is hundreds times as large as that for the solar abundance. 相似文献
20.
J. A. WOOD 《Meteoritics & planetary science》1996,31(5):641-645
Abstract— A widely held view of nebular evolution is that during the ～0.5 Ma while interstellar material was collapsing onto the disk, the latter grew in mass to the point of gravitational instability. It responded to this by losing axial symmetry, growing spiral arms that had the capacity to tidally redistribute disk mass (inward) and angular momentum (outward) and prevent further increase in the disk/protosun mass ratio. The spiral arms (density waves) rotated differently than the substance of the nebula, and in some parts of the disk, nebular material may have encountered the arms at supersonic velocities. The disk gas, and solid particles entrained in it, would have been heated to some degree when they passed through shock fronts at the leading edges of the spiral arms. The present paper proposes this was the energetic nebular setting or environment that has long been sought, in which the material now in the planets and chondritic meteorites was thermally processed. 相似文献