Substructures induced by dust drag in protoplanetary disks

¹ Max-Planck-Institut für Astronomie, 69117 Heidelberg, Germany
² Fakultät für Physik und Astronomie, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
³ Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, 24118 Kiel, Germany

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 11 March 2026
Accepted: 20 April 2026

Abstract

Dust substructures observed in protoplanetary disks are commonly attributed to embedded planets; however, intrinsic gas-dust interactions can also generate complex morphologies. We performed two-dimensional, axisymmetric simulations of gas and dust that include dust back-reaction and parameterized turbulence to investigate how the streaming instability (SI) and vertical shear instability (VSI) shape dust distributions. With moderate viscosity and sufficiently high metallicity, we identify a characteristic shuttlecock-shaped dust substructure composed of a dense, vertically settled “head” and a vertically extended “tail”. This morphology arises from nonlinear SI driven by marginally coupled grains and the associated modification of gas flows. The dust scale height in the tail exceeds predictions based on the simple diffusion-settling balance, indicating strong self-generated turbulence. With lower viscosity, VSI becomes more vigorous, disrupts midplane structures, and increases vertical stirring; nevertheless, for dust grains with Stokes numbers around 0.01, SI can still attain dust-to-gas ratios of up to 20-50, potentially approaching the Hill density for gravitational binding. Our results demonstrate that intrinsic gas-dust interactions can generate prominent dust substructures even in disks with finite viscosity and, under favorable conditions, concentrate dust to levels relevant for planetesimal formation.