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1.
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
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.
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
5.
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
6.
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
7.
S.J. Weidenschilling 《Icarus》2006,181(2):572-586
In the absence of global turbulence, solid particles in the solar nebula tend to settle into a thin layer in the central plane. Shear between this layer and pressure-supported gas produces localized turbulence in the midplane; the thickness of the particle layer is determined by balance between settling and turbulent diffusion. A numerical model is described, which allows computation of the vertical structure of a layer of particles of arbitrary size, with self-consistent distributions of particle density, turbulent velocity, and radial fluxes of particles and gas. Effects of varying particle size and the abundances of solids and gas are evaluated. If the surface density of solids is increased by an order of magnitude over nominal solar abundance, the peak density within a layer of small particles can approach the critical value needed for gravitational instability. However, depletion of the nebular gas is much less effective for raising the density of such a layer to the critical value, due to decreased coupling of particles to the gas as the density of the gas decreases. The variation of radial particle flux with surface density of the particle layer is not consistent with secular instability of the layer driven by gas drag. 相似文献
8.
We numerically model the evolution of dust in a protoplanetary disk using a two-phase (gas+dust) Smoothed Particle Hydrodynamics
(SPH) code, which is non-self-gravitating and locally isothermal. The code follows the three dimensional distribution of dust
in a protoplanetary disk as it interacts with the gas via aerodynamic drag. In this work, we present the evolution of a disk
comprising 1% dust by mass in the presence of an embedded planet for two different disk configurations: a small, minimum mass
solar nebular (MMSN) disk and a larger, more massive Classical T Tauri star (CTTS) disk. We then vary the grain size and planetary
mass to see how they effect the resulting disk structure.
We find that gap formation is much more rapid and striking in the dust layer than in the gaseous disk and that a system with
a given stellar, disk and planetary mass will have a different appearance depending on the grain size and that such differences
will be detectable in the millimetre domain with ALMA. For low mass planets in our MMSN models, a gap can open in the dust
disk while not in the gas disk. We also note that dust accumulates at the external edge of the planetary gap and speculate
that the presence of a planet in the disk may facilitate the growth of planetesimals in this high density region. 相似文献
9.
S.J Weidenschilling 《Icarus》2003,165(2):438-442
For standard cosmic abundances of heavy elements, a layer of small particles in the central plane of the solar nebula cannot attain the critical density for gravitational instability. Youdin and Shu (2002, Astrophys. J. 580, 494-505) suggest that the local surface density of solids can be enhanced by radial migration of particles due to gas drag. However, they consider only motions of individual particles. Collective motion due to turbulent stress on the particle layer acts to inhibit such enhancement and may prevent gravitational instability. 相似文献
10.
《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
11.
Stuart J. WEIDENSCHILLING 《Meteoritics & planetary science》2010,45(2):276-288
Abstract– In the absence of global turbulence, solid particles in the solar nebula tend to settle toward the midplane, forming a layer with enhanced solids/gas ratio. Shear relative to the surrounding pressure‐supported gas generates turbulence within the layer, inhibiting further settling and preventing gravitational instability. Turbulence and size‐dependent drift velocities cause collisions between particles. Relative velocities between small grains and meter‐sized bodies are typically about 50 m s?1 for isolated particles; however, in a dense particle layer, collective effects alter the motion of the gas near the midplane. Here, we develop a numerical model for the coupled motions of gas and particles of arbitrary size, based on the assumption that turbulent viscosity transfers momentum on the scale of the Ekman length. The vertical distribution of particles is determined by a balance between settling and turbulent diffusion. Self‐consistent distributions of density, turbulent velocities, and radial fluxes of gas and particles of different sizes are determined. Collective effects generate turbulence that increases relative velocities between small particles, but reduce velocities between small grains and bodies of decimeter size or larger by bringing the layer’s motion closer to Keplerian. This effect may alleviate the “meter‐size barrier” to collisional growth of planetesimals. 相似文献
12.
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13.
Augusto Carballido 《Icarus》2011,211(1):876-884
Numerical magnetohydrodynamic (MHD) simulations of a turbulent solar nebula are used to study the growth of dust mantles swept up by chondrules. A small neighborhood of the solar nebula is represented by an orbiting patch of gas at a radius of 3 AU, and includes vertical stratification of the gas density. The differential rotation of the nebular gas is replaced by a shear flow. Turbulence is driven by destabilization of the flow as a result of the magnetorotational instability (MRI), whereby magnetic field lines anchored to the gas are continuously stretched by the shearing motion. A passive contaminant mimics small dust grains that are aerodynamically well coupled to the gas, and chondrules are modeled by Lagrangian particles that interact with the gas through drag. Whenever a chondrule enters a region permeated by dust, its radius grows at a rate that depends on the local dust density and the relative velocity between itself and the dust. The local dust abundance decreases accordingly. Compaction and fragmentation of dust aggregates are not included. Different chondrule volume densities ρc lead to varying depletion and rimmed-chondrule size growth times. Most of the dust sweep-up occurs within ～1 gas scale-height of the nebula midplane. Chondrules can reach their asymptotic radius in 10–800 years, although short growth times due to very high ρc may not be altogether realistic. If the sticking efficiency Q of dust to chondrules depends on their relative speed δv, such that Q < 10?2 whenever δv > vstick ≈ 34 cm/s (with vstick a critical sticking velocity), then longer growth times result due to the prevalence of high MRI-turbulent relative velocities. The vertical variation of nebula turbulent intensity results in a moderate dependence of mean rimmed-chondrule size with nebula height, and in a ～20% dispersion in radius values at every height bin. The technique used here could be combined with Monte Carlo (MC) methods that include the physics of dust compaction, in a self-consistent MHD-MC model of dust rim growth around chondrules in the solar nebula. 相似文献
14.
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
15.
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
16.
Sang Min Lee 《New Astronomy》2009,14(1):44-50
Under influence of external gravity generated by Galactic all components excluding ISM, a magnetized gas disk may experience both Parker and convective instabilities. Growth rate of the convective instability increases with decreasing perturbation wavelength, and the convective motion makes sheet-like structures all over before the Parker instability forms structures of any meaningful size in the disk. Yet the Parker instability is thought to be an ideal route to form large-scale condensations in the Galaxy. In search of a means to curb convective activities in the Galactic ISM disk, the external gravity is replaced by self-gravity as a driving force of the Parker instability and the gravitational instability is invoked to reinforce the Parker instability. Perturbation of interchange mode is known to trigger convective instability in such disk and the one of undular mode to activate the Parker instability, while the gravitational instability can be triggered by both modes. Therefore, the resulting Jeans instability would help the Parker instability to overcome disrupting behavior of the convection. Dynamical properties of the disk can be characterized by ratio α of magnetic to gas pressure, adiabatic exponent γ, scale height H of the ISM, and disk thickness za. A linear stability analysis has been done to the disk, and the maximum growth rate of the Parker–Jeans instability is compared with that of the convective instability. The latter may or may not be higher than the former, depending on the disk parameters. The Parker–Jeans instability has chances to override the convective instability, when the disk is thicker than a certain value. In the disk thinner than the critical one, the Jeans instability can always suppress the convection. Since the growth rate of the convective instability is proportional to local gravitational acceleration, thereby in the general Galactic gravity, the convective instability works actively only in upper regions, we expect chaotic features to appear in regions of low density far from Galactic mid-plane. 相似文献
17.
G. A. Gontcharov 《Astronomy Letters》2013,39(8):550-560
The joint use of accurate near- and mid-infrared photometry from the 2MASS and WISE catalogues has allowed the variations of the extinction law and the dust grain size distribution in high Galactic latitudes (|b| > 50°) at distances up to 3 kpc from the Galactic midplane to be analyzed. The modified method of extrapolation of the extinction law applied to clump giants has turned out to be efficient for separating the spatial variations of the sample composition, metallicity, reddening, and properties of the medium. The detected spatial variations of the coefficientsE(H ? W1)/E(H ? Ks), E(H ? W2)/E(H ? Ks), and E(H ? W3)/E(H ? Ks) are similar for all high latitudes and depend only on the distance from the Galactic midplane. The ratio of short-wavelength extinction to long-wavelength one everywhere outside the Galactic disk has been found to be smaller than that in the disk and, accordingly, the mean dust grain size is larger, while the grain size distribution in the range 0.5–11 µm is shifted toward coarse dust. Specifically, the mean grain size initially increases sharply with distance from the Galactic midplane, then decreases gradually, approaching a value typical of the disk at |Z| ≈ 2.4 kpc, and, further out, stabilizes or may increase again. The coefficients under consideration change with coordinate Z with a period of about 1312 ± 40 pc, coinciding every 656 ± 20 pc to the south and the north and showing a significant anticorrelation between their values in the southern and northern hemispheres at intermediate Z. Thus, there exists a unified large-scale periodic structure of the interstellar medium at high latitudes within at least 5 kpc. The same periodic variations have also been found for the extinction coefficient R V within 600 pc of the Galactic midplane through the reduction of different photometric data for stars of different classes. 相似文献
18.
Hideko Nomura 《Astrophysics and Space Science》2004,292(1-4):435-438
We have constructed self-consistent temperature and density profiles of irradiated active protoplanetary disks, using a two-dimensional radiative transfer calculation. By means of these profiles we have studied the stabilization of the convective instability by radiative heating and the magnetorotational instability (MRI) via ohmic dissipation, taking into account the effect of dust particle growth. Simple chemistry such as ionization by cosmic rays and recombination on dust grains are used to calculate the ionization degree of gas in the disks. Our results show that the dust growth stabilizes the convective instability due to the 2D effect of radiative transfer, while it enhances the MRI through the decrease in the recombination of ions on the dust grains. In addition, the influences of the dust settling toward the midplane of the disks on the instabilities are discussed. 相似文献
19.
We discuss certain dynamical processes during the final stage of the sinking of the dust layer. We supposed that turbulance gave rise to a state of slow sinking (quasi-equilibrium) and evaluated the critical thickness at the onset of gravitational instability in the radial direction. We gave a precise numerical relation between 3 length-scales: , the first being the mean height of the dust particles at the onset of radial instability, the second being that value of the half-thickness and of the height at which the self-gravity of the dust layer is equal to the solar z-component, and the last being the longest wavelength at the onset of ring instability. We also calculated the time required for the formation of rings and found it to be far shorter than the sinking time. 相似文献
20.
The stability of a galactic disk in the gravitational field of a massive body is studied. The mutual friction of the gaseous and dust components is taken into account. Criteria for dynamical and secular instability are found. Asymptotic expressions are obtained for the growth rates in the case of a low density of dust. The cosmogonic significance of these results is discussed. 相似文献