Induced Turbulence and the Density Structure of the Dust Layer in a Protoplanetary Disk

TL;DR

This paper estimates turbulence in a protoplanetary dust layer caused by dust accretion energy, aligning with prior research, and explores how dust-to-gas ratio variations influence turbulence strength and dust layer thickness.

Contribution

It provides a novel energetics-based estimate of turbulence strength in dust layers, connecting dust accretion dynamics with turbulence levels and dust layer structure.

Findings

Turbulence strength peaks at a dust-to-gas ratio of ~10^(-2).

Maximum viscosity parameter alpha_max is approximately 10^(-4) times the stopping time T_s.

Deviations from the standard dust-to-gas ratio weaken turbulence and thin the dust layer.

Abstract

We study the turbulence induced in the dust layer of a protoplanetary disk based on the energetics of dust accretion due to gas drag. We estimate turbulence strength from the energy supplied by dust accretion, using the radial drift velocity of the dust particles in a laminar disk. Our estimate of the turbulence strength agrees with previous analytical and numerical research on the turbulence induced by Kelvin-Helmholtz and/or streaming instabilities for particles whose stopping time is less than the Keplerian time. For such small particles, the strongest turbulence is expected to occur when the dust-to-gas ratio of the disk is ~C_eff^(1/2) (h_g / r) ~ 10^(-2), where C_eff ~ 0.2 represents the energy supply efficiency to turbulence and h_g / r ~ 5 x 10^(-2) is the aspect ratio of the gas disk. The maximum viscosity parameter is alpha_max ~ C_eff T_s (h_g / r)^2 ~ 10^(-4) T_s, where T_s (<1) is the non-dimensional stopping time of the dust particles. Modification in the dust-to-gas ratio from the standard value, 10^(-2), by any process, results in weaker turbulence and a thinner dust layer, and consequently may accelerate the growth process of the dust particles.