Impact of local pressure enhancements on dust concentration in turbulent protoplanetary discs

¹ Institute of Astronomy and Astrophysics, Academia Sinica, Taipei 10617, Taiwan
e-mail: mlehmann@asiaa.sinica.edu.tw
² Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan

Received: 6 October 2021
Accepted: 7 December 2021

Abstract

The standard core accretion model for planetesimal formation in protoplanetary discs (PPDs) is subject to a number of challenges. One is related to the vertical settling of dust to the disc mid-plane against turbulent stirring. This is particularly relevant in the presence of the vertical shear instability (VSI), a purely hydrodynamic instability applicable to the outer parts of PPDs, which drives moderate turbulence characterized by large-scale vertical motions. We investigate the evolution of dust and gas in the vicinity of local pressure enhancements (pressure bumps) in a PPD with turbulence sustained by the VSI. Our goal is to determine the morphology of dust concentrations and if dust can concentrate sufficiently to reach conditions that can trigger the streaming instability (SI). We performed a suite of global 2D axisymmetric and 3D simulations of dust and gas for a range of values for Σ_d∕Σ_g (ratio of dust-to-gas surface mass densities or metallicity), particle Stokes numbers, τ, and pressure bump amplitude, A. Dust feedback onto the gas is included. For the first time, we use global 3D simulations to demonstrate the collection of dust in long-lived vortices induced by the VSI. These vortices, which undergo a slow radial inward drift, are the dusty analogs of large long-lived vortices found in previous dust-free simulations of the VSI. Without a pressure bump and for solar metallicity Z ≈ 0.01 and Stokes numbers τ ~ 10⁻², we find that such vortices can reach dust-to-gas density ratios slightly below unity in the discs’ mid-plane, while for Z ≳ 0.05, long-lived vortices are largely absent. In the presence of a pressure bump, for Z ≈ 0.01 and τ ~ 10⁻², a dusty vortex forms that reaches dust-to-gas ratios of a few times unity, such that the SI is expected to develop, before it eventually shears out into a turbulent dust ring. At intermediate metallicities, Z ~ 0.03, this occurs for τ ~ 5 × 10⁻³, but with a weaker and more short-lived vortex, while for larger τ, only a turbulent dust ring forms. For Z ≳ 0.03, we find that the dust ring becomes increasingly axisymmetric for increasing τ and dust-to-gas ratios reach order unity for τ ≳ 5 × 10⁻³. Furthermore, the vertical mass flow profile of the disc is strongly affected by dust for Z ≳ 0.03, such that gas is transported inward near the mid-plane and outward at larger heights, which is the reversed situation compared to simulations with zero or small amounts of dust. We find viscous α-values to drop moderately as ~10⁻³–10⁻⁴ for metallicities increasing as Z = 0–0.05. Our results suggest that the VSI can play an active role in the formation of planetesimals through the formation of vortices for plausible values of metallicity and particle size. Also, it may provide a natural explanation for the presence or absence of asymmetries of observed dust rings in PPDs, depending on the background metallicity.