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 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.