Impact of Local Pressure Enhancements on Dust Concentration inTurbulent Protoplanetary Discs

Abstract

The standard core accretion model for planetesimal formation in protoplanetary discs (PPDs) is known to bear a number of challenges. One is the vertical settling of dust to the disc mid-plane against turbulent stirring. This is particularly relevant in 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 perform 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 demonstrate in global 3D simulations the collection of dust in long-lived vortices induced by the VSI. These vortices, which undergo 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 Reynolds stresses or 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.

The saturation of the VSI in protoplanetary disks via parametric instability

“…Follow up numerical simulations have investigated the non-linear development of the instability, and added relevant physics such as radiative transfer, dust, and non-ideal magnetohydrodynamics (MHD) (e.g. Stoll & Kley 2014;Flock et al 2017;Lin 2019;Flock et al 2020;Cui & Bai 2020;Schäfer et al 2020;Lehmann & Lin 2021). One important feature of both the VSI's linear theory and non-linear saturation in global models is the importance of remarkably coherent wave patterns.…”