Two-fluid Instability of Dust and Gas in the Dust Layer of a Protoplanetary Disk

TL;DR

This study investigates a two-fluid instability in protoplanetary dust layers, revealing that initial dust density gradients and vertical shear can induce turbulence that disperses dust, impacting planet formation processes.

Contribution

It introduces a new understanding of dust-gas instabilities driven by vertical shear and density gradients, extending previous models of streaming instability.

Findings

Instability develops rapidly even with small gas friction times.

Vertical shear and dust-gas relative motion drive the instability.

Dust density decreases due to turbulent diffusion.

Abstract

Instabilities of the dust layer in a protoplanetary disk are investigated. It is known that the streaming instability develops and dust density concentration occurs in a situation where the initial dust density is uniform. This work considers the effect of initial dust density gradient vertical to the midplane. Dust and gas are treated as different fluids. Pressure of dust fluid is assumed to be zero. The gas friction time is assumed to be constant. Axisymmetric two-dimensional numerical simulation was performed using the spectral method. We found that an instability develops with a growth rate on the order of the Keplerian angular velocity even if the gas friction time multiplied by the Keplerian angular velocity is as small as 0.001. This instability is powered by two sources: (1) the vertical shear of the azimuthal velocity, and (2) the relative motion of dust and gas coupled with the dust density fluctuation due to advection. This instability diffuses dust by turbulent advection and the maximum dust density decreases. This means that the dust concentration by the streaming instability which is seen in the case of a uniform initial dust density becomes ineffective as dust density gradient increases by the dust settling toward the midplane.