Spontaneous concentrations of solids through two-way drag forces between gas and sedimenting particles (original) (raw)
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Particle Trapping and Streaming Instability in Vortices in Protoplanetary Disks
The Astrophysical Journal, 2015
We analyse the concentration of solid particles in vortices created and sustained by radial buoyancy in protoplanetary disks, i.e. baroclinic vortex growth. Besides the gas drag acting on particles we also allow for back-reaction from dust onto the gas. This becomes important when the local dustto-gas ratio approaches unity. In our 2D, local, shearing sheet simulations we see high concentrations of grains inside the vortices for a broad range of Stokes numbers, St. An initial dust-to-gas ratio of 1:100 can easily be reversed to 100:1 for St = 1. The increased dust-to-gas ratio triggers the streaming instability, thus counter-intuitively limiting the maximal achievable overdensities. We find that particle trapping inside vortices opens the possibility for gravity-assisted planetesimal formation even for small particles (St = 0.01) and low initial dust-to-gas ratios (1:10 4 ).
Two-fluid Instability of Dust and Gas in the Dust Layer of a Protoplanetary Disk. ArXiv e-prints
Instabilities of the dust layer in a protoplanetary disk are investigated. It is known that the streaming instability develops and dust density concentration occurs in a situation where the initial dust density is uniform. This work considers the effect of initial dust density gradient vertical to the midplane. Dust and gas are treated as different fluids. Pressure of dust fluid is assumed to be zero. The gas friction time is assumed to be constant. Axisymmetric two-dimensional numerical simulation was performed using the spectral method. We found that an instability develops with a growth rate on the order of the Keplerian angular velocity even if the gas friction time multiplied by the Keplerian angular velocity is as small as 0.001. This instability is powered by two sources: (1) the vertical shear of the azimuthal velocity, and (2) the relative motion of dust and gas coupled with the dust density fluctuation due to advection. This instability diffuses dust by turbulent advection and the maximum dust density decreases. This means that the dust concentration by the streaming instability which is seen in the case of a uniform initial dust density becomes ineffective as dust density gradient increases by the dust settling toward the midplane.
The Astrophysical Journal
Our previous linear analysis presents a new instability driven by dust coagulation in protoplanetary disks. The coagulation instability has the potential to concentrate dust grains into rings and assist dust coagulation and planetesimal formation. In this series of papers, we perform numerical simulations and investigate the nonlinear outcome of coagulation instability. In this paper (Paper I), we first conduct local simulations to demonstrate the existence of coagulation instability. Linear growth observed in the simulations is in good agreement with the previous linear analysis. We next conduct radially global simulations to demonstrate that coagulation instability develops during the inside-out disk evolution owing to dust growth. To isolate the various effects on dust concentration and growth, we neglect the effects of back-reaction to a gas disk and dust fragmentation in Paper I. This simplified simulation shows that neither back-reaction nor fragmentation is a prerequisite for...
Turbulent diffusion of large solids in a protoplanetary disc
Monthly Notices of the Royal Astronomical Society, 2011
We study the turbulent diffusion of solids in a protoplanetary disc, in order to discriminate between two existing analytical models of the turbulent diffusion process. These two models predict the same radial turbulent diffusion coefficient D p,x for small particles (τ s 1), but differ in the value of D p,x for large particles (τ s 1, where τ s is the dimensionless particle stopping time, closely related to particle radius). The model given by Youdin & Lithwick (YL) takes into account orbital oscillations of the solids, while the other model given by Cuzzi, Dobrovolskis & Champney (CDC) does not. The CDC model predicts D p,x ∼ τ −1 s for τ s 1, but the YL model gives D p,x ∼ τ −2 s. To investigate, we perform 3D, magnetohydrodynamic (MHD) numerical simulations. Turbulence in the disc is generated by the magnetorotational instability. The ATHENA code is used to solve the equations of ideal MHD in the shearing-box approximation, which allows us to model a local region of the disc with the relevant orbital dynamics. Solids are represented by Lagrangian particles that interact with the gas through drag, and are also subject to orbital forces. The aerodynamic coupling of particles to the gas is parametrized by τ s. In one set of simulations, particle displacements along the radial direction are measured in a shearing box without vertical stratification of the gas density. In another simulation, the vertical component of stellar gravity is included, with a Gaussian gas density vertical profile, but the particle motion is restricted to fixed planes of constant height z. In both cases, the radial diffusion coefficient as a function of stopping time τ s is in very good agreement with the YL model. To study particle vertical diffusion, we use the unstratified shearing box, in which we allow the effects of vertical gravity and turbulence on the particles to balance out, resulting in particle layers whose scaleheight varies approximately as τ −1/2 s. Based on this result and YL, we calculate a vertical diffusion coefficient D p,z that, in the limit τ s 1, varies as τ −2 s , similarly to radial diffusivity.
Two-fluid instability of dust and gas in the dust layer of a protoplanetary disk
Instabilities of the dust layer in a protoplanetary disk are investigated. It is known that the streaming instability develops and dust density concentration occurs in a situation where the initial dust density is uniform. This work considers the effect of initial dust density gradient vertical to the midplane. Dust and gas are treated as different fluids. Pressure of dust fluid is assumed to be zero. The gas friction time is assumed to be constant. Axisymmetric two-dimensional numerical simulation was performed using the spectral method. We found that an instability develops with a growth rate on the order of the Keplerian angular velocity even if the gas friction time multiplied by the Keplerian angular velocity is as small as 0.001. This instability is powered by two sources: (1) the vertical shear of the azimuthal velocity, and (2) the relative motion of dust and gas coupled with the dust density fluctuation due to advection. This instability diffuses dust by turbulent advection and the maximum dust density decreases. This means that the dust concentration by the streaming instability which is seen in the case of a uniform initial dust density becomes ineffective as dust density gradient increases by the dust settling toward the midplane.
On linear dust-gas streaming instabilities in protoplanetary discs
Monthly Notices of the Royal Astronomical Society, 2011
We revisit, via a very simplified set of equations, a linear streaming instability (technically an overstability), which is present in, and potentially important for, dusty protoplanetary discs. The goal is a better understanding of the physical origin of such instabilities, which are notoriously subtle. Rotational dynamics seem to be essential to this type of instability, which cannot be captured by one-dimensional Cartesian models. Dust 'pile-ups' in moving pressure maxima are an important triggering mechanism of the instability, and drag feedback of dust upon the gas allows these maxima to be strengthened. Coriolis forces and the background drift counteract the effects of the pressure force.
Streaming Instability in Turbulent Protoplanetary Disks
The Astrophysical Journal, 2020
The streaming instability for solid particles in protoplanetary disks is reexamined assuming the familiar alpha (α) model for isotropic turbulence. Turbulence always reduces the growth rates of the streaming instability relative to values calculated for globally laminar disks. While for small values of the turbulence parameter, α < 10 −5 , the wavelengths of the fastest-growing disturbances are small fractions of the local gas vertical scale height H, we find that for moderate values of the turbulence parameter, i.e., α ∼ 10 −5 − 10 −3 , the lengthscales of maximally growing disturbances shift toward larger scales, approaching H. At these moderate turbulent intensities and for particle to gas mass density ratios < 0.5, the vertical scales of the most unstable modes begin to exceed the corresponding radial scales so that the instability appears in the form of vertically oriented sheets. We find that for hydrodynamical turbulent instability models reported in the literature, leading to α = 4 × 10 −5 − 10 −4 , the streaming instability is present in principle for a narrow range of Stokes numbers, ∼ 0.01 < τ s < 0.05 (τ s is the ratio of the particle gas drag stopping time to the local orbit time). However, with these levels of α and canonical solids-togas abundances, we find that the streaming instability stalls and saturates as growing modes approach = 1 from smaller values, resulting in only modest particle overdensities of factors of 4-20 at best. Our results are consistent with, and place in context, published numerical studies of streaming instabilities.
PARTICLE CLUMPING AND PLANETESIMAL FORMATION DEPEND STRONGLY ON METALLICITY
2009
We present three-dimensional numerical simulations of particle clumping and planetesimal formation in protoplanetary disks with varying amounts of solid material. As centimeter-size pebbles settle to the midplane, turbulence develops through vertical shearing and streaming instabilities. We find that when the pebbleto-gas column density ratio is 0.01, corresponding roughly to solar metallicity, clumping is weak, so the pebble density rarely exceeds the gas density. Doubling the column density ratio leads to a dramatic increase in clumping, with characteristic particle densities more than ten times the gas density and maximum densities reaching several thousand times the gas density. This is consistent with unstratified simulations of the streaming instability that show strong clumping in particle dominated flows. The clumps readily contract gravitationally into interacting planetesimals of order 100 km in radius. Our results suggest that the correlation between host star metallicity and exoplanets may reflect the early stages of planet formation. We further speculate that initially low metallicity disks can be particle enriched during the gas dispersal phase, leading to a late burst of planetesimal formation.