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Dust Settling in Magnetorotationally-Driven Turbulent Discs II: The Pervasiveness of the Streaming Instability and its Consequences

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 MRI-driven turbulence. This establishes a steady state scale height 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 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 in the outer disc. We characterize the scale heights of dust whose size ranges from a few microns to a few centimeters. We find that for spherical grains, a power-law relationship develops for the scale height 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 favorable 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.