Filament Formation due to Diffusive Instabilities in Dusty Protoplanetary Disks

Abstract

We report the finding of a new, local diffusion instability in a protoplanetary disk which can operate in a dust fluid, subject to mass diffusion, shear viscosity, and dust–gas drag, provided the diffusivity, viscosity, or both, decrease sufficiently rapidly with increasing dust surface mass density. We devise a vertically averaged, axisymmetric hydrodynamic model to describe a dense, midplane dust layer in a protoplanetary disk. The gas is modeled as a passive component, imposing an effective, diffusion-dependent pressure, mass diffusivity, and viscosity onto the otherwise collisionless dust fluid, via turbulence excited by the gas alone, or dust and gas in combination. In particular, we argue that such conditions are met when the dust–gas mixture generates small-scale turbulence through the streaming instability, as supported by recent measurements of dust mass diffusion slopes in simulations. We hypothesize that the newly discovered instability may be the origin of filamentary features, almost ubiquitously found in simulations of the streaming instability. In addition, our model allows for growing oscillatory modes, which operate in a similar fashion as the axisymmetric viscous overstability in dense planetary rings. However, it remains speculative if the required conditions for such modes can be met in protoplanetary disks.

Keywords

• Protoplanetary disks
• Planet formation
• Circumstellar dust
• Hydrodynamics
• Astrophysical dust processes
• Astrophysical fluid dynamics