Secular Gravitational Instability of a Dust Layer in Shear Turbulence

TL;DR

This paper performs a linear stability analysis of dust layers in turbulent gas disks, confirming previous results and exploring the effects of finite dust layer thickness and density-dependent diffusion on gravitational instability growth rates.

Contribution

It provides a more rigorous analysis of secular gravitational instability focusing on small dust particles and confirms the validity of previous hydrodynamic models in the strong drag limit.

Findings

Finite dust layer thickness weakens gravitational instability.

Density-dependent diffusion alters growth rates.

Instability can grow faster than radial drift in certain conditions.

Abstract

We perform a linear stability analysis of a dust layer in a turbulent gas disk. Youdin (2011) investigated the secular gravitational instability of a dust layer using hydrodynamic equations with a turbulent diffusion term. We obtain essentially the same result independently of Youdin (2011). In the present analysis, we restrict the area of interest to small dust particles, while investigating the secular gravitational instability in a more rigorous manner. We discuss the time evolution of the dust surface density distribution using a stochastic model and derive the advection-diffusion equation. The validity of the analysis by Youdin (2011) is confirmed in the strong drag limit. We demonstrate quantitatively that the finite thickness of a dust layer weakens the secular gravitational instability and that the density-dependent diffusion coefficient changes the growth rate. We apply the obtained results to the turbulence driven by the shear instability and find that the secular gravitational instability is faster than the radial drift when the gas density is three times as large as that in the minimum-mass disk model. If the dust particles are larger than chondrules, the secular gravitational instability grows within the lifetime of a protoplanetary disk.