Dust settling in magnetorotationally driven turbulent discs - I. Numerical methods and evidence for a vigorous streaming instability

Abstract

In this paper, we have used the RIEMANN 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.

Can dust coagulation trigger streaming instability?

“…Youdin & Johansen (2007) and Johansen et al (2007) confirmed that this instability is able to produce very dense dust clumps and leads to rapid planetesimal formation. This result was later confirmed by high resolution numerical simulations (Johansen et al 2011), as well as by other authors using different methods and codes (Balsara et al 2009;Tilley et al 2010;Bai & Stone 2010a;Jacquet et al 2011;Kowalik et al 2013).…”

Inclination-induced polarization of scattered millimetre radiation from protoplanetary discs: the case of HL Tau

“…It is conceivable that there are two populations of dust grains, with one responsible for polarization, the other for β. The two populations do not have to be located co-spatially in the disk; for example, large grains responsible for the bulk of the unpolarized continuum (and thus β) may have set-tled close to the midplane, whereas smaller grains that dominate the polarized millimeter radiation may remain floating higher up above the midplane (e.g., Dullemond & Dominik 2004;Tanaka et al 2005;Balsara et al 2009 ). If this speculation turns out correct, polarized emission in millimeter would provide a powerful probe of not only grain growth, but also the expected vertical stratification of grain sizes, especially in conjunction with observations of optical/IR polarization, which probe even smaller, micron-sized, grains that are higher up still above the disk midplane.…”

Linear growth of streaming instability in pressure bumps

“…Hence, streaming instability may be responsible for the Initial Mass Function of planetesimals in discs (Simon et al 2016;Schäfer et al 2017). The robustness of the streaming instability has been tested against several numerical schemes (Balsara et al 2009;Miniati 2010;Tilley et al 2010;Bai & Stone 2010a;Johansen et al 2012Johansen et al , 2014, towards the aim of simulating its E-mail: mailto:guillaume.laibe@ens-lyon.fr effect in a global disc (Lyra & Kuchner 2013;Kowalik et al 2013;Yang & Johansen 2014). Other physical processes such as vortices (Raettig et al 2015), photo-evaporation (Carrera et al 2017), presence of small grains (Laibe & Price 2014), grain growth (Drażkowska & Dullemond 2014) or snow lines (Schoonenberg & Ormel 2017) may reinforce the ability of streaming instability to concentrate dust.…”