Vertical Shearing Instabilities in Radially Shearing Disks: The Dustiest Layers of the Protoplanetary Nebula

Abstract

Gravitational instability of a vertically thin, dusty sheet near the midplane of a protoplanetary disk has long been proposed as a way of forming planetesimals. Before Roche densities can be achieved, however, the dust-rich layer, sandwiched from above and below by more slowly rotating dust-poor gas, threatens to overturn and mix by the Kelvin-Helmholtz instability (KHI). Whether such a threat is real has never been demonstrated: the Richardson criterion for the KHI is derived for 2-D Cartesian shear flow and does not account for rotational forces. Here we present 3-D numerical simulations of gas-dust mixtures in a shearing box, accounting for the full suite of disk-related forces: the Coriolis and centrifugal forces, and radial tidal gravity. Dust particles are assumed small enough to be perfectly entrained in gas; the two fluids share the same velocity field but obey separate continuity equations. We find that the Richardson number Ri does not alone determine stability. The critical value of Ri below which the dust layer overturns and mixes depends on the height-integrated metallicity Z (surface density ratio of dust to gas). Nevertheless, for Z between one and five times solar, the critical Ri is nearly constant at 0.1. Keplerian radial shear stabilizes those modes that would otherwise disrupt the layer at large Ri. If Z is at least 5 times greater than the solar value of 0.01, then midplane dust densities can approach Roche densities. Such an environment might be expected to produce gas giant planets having similarly super-solar metallicities.

ApJ, in press. Connections made to baroclinic instability. Movies available at http://astro.berkeley.edu/~echiang/im/im.html

References in corpus (11)

• Rapid planetesimal formation in turbulent circumstellar discs
• Streaming Instabilities in Protoplanetary Disks
• Planetesimal Formation by Gravitational Instability
• The N2K Consortium. II. A Transiting Hot Saturn Around HD 149026 With a Large Dense Core
• Spectral Energy Distributions of T Tauri and Herbig Ae Disks: Grain Mineralogy, Parameter Dependences, and Comparison with ISO LWS Observations
• Dust sedimentation and self-sustained Kelvin-Helmholtz turbulence in protoplanetary disk mid-planes. I. Radially symmetric simulations
• Inside-Out Evacuation of Transitional Protoplanetary Disks by the Magneto-Rotational Instability
• Particle Pile-ups and Planetesimal Formation
• Non-Axisymmetric g-Mode and p-Mode Instability in a Hydrodynamic Thin Accretion Disk
• The effect of the Coriolis force on Kelvin-Helmholtz-driven mixing in protoplanetary disks
• The effects of the Tidal Force on Shear Instabilities in the Dust Layer of the Solar Nebula

Cited by in corpus (50)

• Forming Planetesimals in Solar and Extrasolar Nebulae
• Particle Clumping and Planetesimal Formation Depend Strongly on Metallicity
• Dynamics of Solids in the Midplane of Protoplanetary Disks: Implications for Planetesimal Formation
• The Effect of the Radial Pressure Gradient in Protoplanetary Disks on Planetesimal Formation
• Dusty gas with one fluid
• On linear dust-gas streaming instabilities in protoplanetary discs
• Turbulent Clustering of Protoplanetary Dust and Planetesimal Formation
• The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? III. Sedimentation driven coagulation inside the snow-line
• A thermodynamic view of dusty protoplanetary disks
• On the Feeding Zone of Planetesimal Formation by the Streaming Instability
• A fast and explicit algorithm for simulating the dynamics of small dust grains with smoothed particle hydrodynamics
• From Grains to Planetesimals: Les Houches Lecture
• Turbulence-Induced Relative Velocity of Dust Particles I: Identical Particles
• Dust settling against hydrodynamic turbulence in protoplanetary discs
• Dust and gas mixtures with multiple grain species - a one-fluid approach
• From Dust to Planetesimals: Criteria for Gravitational Instability of Small Particles in Gas
• Efficient planet formation by pebble accretion in ALMA rings
• Requirements for gravitational collapse in planetesimal formation --- the impact of scales set by Kelvin-Helmholtz and nonlinear streaming instability
• Testing the Jeans, Toomre and Bonnor-Ebert concepts for planetesimal formation: 3D streaming instability simulations of diffusion regulated formation of planetesimals
• Effect of dust radial drift on viscous evolution of gaseous disk
• MULTIGRAIN: A smoothed particle hydrodynamics algorithm for multiple small dust grains and gas
• Impacts of dust feedback on a dust ring induced by a planet in a protoplanetary disk
• Small dust grain dynamics on adaptive mesh-refinement grids. I. Methods
• Forming Planetesimals by Gravitational Instability: I. The Role of the Richardson Number in Triggering the Kelvin-Helmholtz Instability
• On the Stability of Dust-Laden Protoplanetary Vortices
• Dust Settling and Clumping in MRI Turbulent Outer Protoplanetary Disks
• Vortices as nurseries for planetesimal formation in protoplanetary discs
• Stratified and vertically-shearing streaming instabilities in protoplanetary disks
• Two key parameters controlling particle clumping caused by streaming instability in the dead-zone dust layer of a protoplanetary disk
• Secular Gravitational Instability of a Dust Layer in Shear Turbulence
• Survival of ALMA Rings in the Absence of Pressure Maxima
• Forming Planetesimals by Gravitational Instability: II. How Dust Settles to its Marginally Stable State
• Induced Turbulence and the Density Structure of the Dust Layer in a Protoplanetary Disk
• Impact of Local Pressure Enhancements on Dust Concentration inTurbulent Protoplanetary Discs
• Statistical Tests of Chondrule Sorting
• Planetesimal formation around the snow line. II. Dust or pebbles?
• Planetesimal Formation at the Boundary Between Steady Super/Sub-Keplerian Flow Created by Inhomogeneous Growth of Magnetorotational Instability
• N-Body Simulation of Planetesimal Formation through Gravitational Instability of a Dust Layer in Laminar Gas Disk
• Phurbas: An Adaptive, Lagrangian, Meshless, Magnetohydrodynamics Code. I. Algorithm
• Turbulence in particle laden midplane layers of planet forming disks
• On the settling of small grains in dusty discs: analysis and formulas
• Growing dust grains in protoplanetary discs - I. Radial drift with toy growth models
• Effects of Chemistry on Vertical Dust Motion in Early Protoplanetary Disks
• A "no-drift" runaway pile-up of pebbles in protoplanetary disks II. Characteristics of the resulting planetesimal belt
• Kelvin-Helmholtz Instabilities in Multi-Sized Dust Layers
• The Prospects for Hurricane-like Vortices in Protoplanetary Disks
• Modelling dust coagulation, dynamical drag and turbulent mixing during star and disc formation
• A Pathway for Collisional Planetesimal Growth in the Ice-Dominant Regions of Protoplanetary Disks
• Two phase mixtures in SPH - A new approach
• Dust Dynamics in Hall-effected Protoplanetary Disks. I. Background Drift Hall Instability