Dust Settling in Magnetorotationally-Driven Turbulent Discs I: Numerical Methods and Evidence for a Vigorous Streaming Instability

摘要

(Abridged) In this paper we have used the RIEMANN code for computationalastrophysics to study the interaction of a realistic distribution of dustgrains with gas in a vertically stratified protostellar accretion disc. Thedisc was modeled to have the density and temperature of a minimum mass solarnebula, and was driven to a fully-developed turbulence via themagnetorotational instability (MRI). We find that the inclusion of standarddust to gas ratios does not have any significant effect on the MRI even whenthe dust sediments to the midplane of the accretion disc. The densitydistribution of the dust reaches a Gaussian profile, and the scale heights forthe dust that we derive are shown to be proportional to the reciprocal of thesquare root of the dust radius. The largest dust shows a strong tendency tosettle to the midplane of the accretion disc, and tends to organize itself intoelongated clumps of high density. The dynamics of these clumps is shown to beconsistent with a streaming instability. The streaming instability is seen tobe very vigorous and persistent once it forms. Each stream of high density dustdisplays a reduced RMS velocity dispersion, and the densest clumpings of largedust are shown to form where the streams intersect. We have also shown that themean free path and collision time for the dust that participates in thestreaming instability is reduced by almost two orders of magnitude relative tothe average mean free paths and collision times. We show that some of the largedust in our 10 au simulations should have a propensity for grain coalescence.