Two-fluid instability of dust and gas in the dust layer of a protoplanetary disk (original) (raw)
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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.
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.
Secular Gravitational Instability of a Dust Layer in Shear Turbulence
The Astrophysical Journal, 2012
We perform a linear stability analysis of a dust layer in a turbulent gas disk. Youdin (2011) investigated the secular gravitational instability of a dust layer using hydrodynamic equations with a turbulent diffusion term. We obtain essentially the same result independently of Youdin (2011). In the present analysis, we restrict the area of interest to small dust particles, while investigating the secular gravitational instability in a more rigorous manner. We discuss the time evolution of the dust surface density distribution using a stochastic model and derive the advection-diffusion equation. The validity of the analysis by Youdin is confirmed in the strong drag limit. We demonstrate quantitatively that the finite thickness of a dust layer weakens the secular gravitational instability and that the density-dependent diffusion coefficient changes the growth rate. We apply the obtained results to the turbulence driven by the shear instability and find that the secular gravitational instability is faster than the radial drift when the gas density is three times as large as that in the minimum-mass disk model. If the dust particles are larger than chondrules, the secular gravitational instability grows within the lifetime of a protoplanetary disk.
The instability in protoplanetary disks due to gas-dust friction and self-gravity of gas and dust is investigated by linear analysis. For conditions typical of protoplanetaly disks, the instability grows, even in gravitationally stable disks, on a timescale of order 10 4−5 yr at a radius of order 100AU. If we ignore the dynamical feedback from dust grains in the gas equation of motion, the instability reduces to the so-called "secular gravitational instability", that was investigated previously as the instability of dust in a fixed background gas flow. In this work, we solve the equation of motion for both gas and dust consistently and find that long-wavelength perturbations are stable, in contrast to the secular gravitational instability in the simplified treatment. The instability is expected to form ring structures in protoplanetary disks. The width of the ring formed at a radius of 100 AU is a few tens of AU. Therefore, the instability is a candidate for the formation mechanism of observed ring-like structures in disks. Another aspect of the instability is the accumulation of dust grains, hence the instability may play an important role in the formation of planetesimals, rocky protoplanets, and cores of gas giants located at radii ∼100 AU. If these objects survive the dispersal of the gaseous component of the disk, they may be the origin of debris disks.
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.
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...
2015
We investigate the dynamics of dust grains with various sizes in protoplanetary disk winds driven by magnetorotational turbulence, by simulating the time evolution of the dust grain distribution in the vertical direction. Small dust grains, which are well coupled to the gas, are dragged upward with the up-flowing gas, while large grains remain near the midplane of a disk. Intermediate-size grains float near the sonic point of the disk wind located at several scale heights from the midplane, where the grains are loosely coupled to the background gas. For the minimum mass solar nebula at 1 AU, dust grains with size of 25 -45 µm float around 4 scale heights from the midplane. Considering the dependence on the distance from the central star, smaller-size grains remain only in an outer region of the disk, while larger-size grains are distributed in a broader region. We also discuss the implication of our result to the observation of dusty material around young stellar objects.