A Self-Consistent Reduced Model for Dusty Magnetorotationally Unstable Discs

TL;DR

This paper develops a simplified model to study how dust grain settling interacts with MRI turbulence in protoplanetary disks, revealing conditions for dust distribution and stability of the system.

Contribution

It introduces a coupled differential equation model combining turbulence and dust diffusion, providing new insights into dust behavior near dead zones in disks.

Findings

Dust settling can suppress MRI turbulence near the midplane.

High-altitude dust concentrations are possible under certain conditions.

Equilibrium solutions of the model are linearly stable.

Abstract

The interaction between settling of dust grains and magnetorotational instability (MRI) turbulence in protoplanetary disks is analyzed. We use a reduced system of coupled ordinary differential equations to represent the interaction between the diffusion of grains and the inhibition of the MRI. The coupled equations are styled on a Landau equation for the turbulence and a Fokker-Planck equation for the diffusion. The turbulence-grain interaction is probably most relevant near the outer edge of the disk's quiescent, or "dead" zone. Settling is most pronounced near the midplane, where a high dust concentration can self-consistently suppress the MRI. Under certain conditions, however, grains can reach high altitudes, a result of some observational interest. Finally, we show that the equilibrium solutions are linearly stable.