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We present a series of simulations of turbulent stratified protostellar discs with the goal of characterizing the settling of dust throughout a minimum-mass solar nebula. We compare the evolution of both compact spherical grains, as well as highly fractal grains. Our simulations use a shearing-box formulation to study the evolution of dust grains locally within the disc, and collectively our simulations span the entire extent of a typical accretion disc. The dust is stirred by gas that undergoes magnetorotational instability-driven turbulence. The turbulence tends to lift the dust above the disc's mid-plane, while gravity tends to draw it back to the mid-plane. This establishes a steady state scaleheight for the dust that is different for dust of different sizes. This sedimentation of dust is an important first step in planet formation and we predict that the Atacama Large Millimeter Array (ALMA) should be able to observationally verify its existence. When significant sedimentation occurs, the dust will participate in a streaming instability that significantly enhances the dust density. We show that the streaming instability is pervasive at many of the outer radial stations in a disc. We characterize the scaleheights of dust whose size ranges from a few micrometres all the way up to a few centimetres. We find that for spherical grains, a power-law relationship develops for the scaleheight with grain size, with a slope that is slightly steeper than −1/2. The sedimentation is strongest in the outer disc and increases for large grains. The results presented here show that direct measurements of grain settling can be made by ALMA and we present favourable conditions for observability. The streaming instability should also be directly observable and we provide conditions for directly observing it. We calculate collision rates and growth rates for the dust grains in our simulations of various sizes colliding with other grains, and find that these rates are significantly enhanced through the density enhancement arising from the streaming instability. [ABSTRACT FROM AUTHOR]

In this paper, we have used theriemann code for computational astrophysics to study the interaction of a realistic distribution of dust grains with gas at specific radial locations in a vertically stratified protostellar accretion disc. The disc was modelled to have the density and temperature of a minimum mass solar nebula, and shearing box simulations at radii of 0.3 and 10 au are reported here. The disc was driven to a fully developed turbulence via the magnetorotational instability (MRI). The simulations span three gas scaleheights about the disc's midplane. We find that the inclusion of standard dust-to-gas ratios does not have any significant effect on the MRI even when the dust sediments to the midplane of the accretion disc. The density distribution of the dust of all sizes reached a Gaussian profile within two scaleheights of the disc's midplane. The vertical scaleheights of these Gaussian profiles are shown to be proportional to the reciprocal of the square root of the dust radius when large spherical dust grains are considered. This result is consistent with theoretical expectation. The largest two families of dust in one of our simulations show a strong tendency to settle to the midplane of the accretion disc. The large dust tends to organize itself into elongated clumps of high density. The dynamics of these clumps is shown to be consistent with a streaming instability. The streaming instability is seen to be very vigorous and persistent once it forms. Each stream of high-density dust displays a reduced rms velocity dispersion. The velocity directions within the streams are also aligned relative to the mean shear, providing further evidence that we are witnessing a streaming instability. The densest clumpings of large dust are shown to form where the streams intersect. We have also shown that the mean free path and collision time for dust that participates in the streaming instability are reduced by almost two orders of magnitude relative to the average mean free paths and collision times. The rms velocities between the grains also need to fall below a minimum threshold in order for the grains to stick and we show that a small amount of the large dust in our 10 au simulation should have a propensity for grain coalescence. The results of our simulations are likely to be useful for those who model spectral energy distributions of protostellar discs and also for those who model dust coagulation and growth. [ABSTRACT FROM AUTHOR]