The effects of the Tidal Force on Shear Instabilities in the Dust Layer of the Solar Nebula

Abstract

The linear analysis of the instability due to vertical shear in the dust layer of the solar nebula is performed. The following assumptions are adopted throughout this paper: (1) The self-gravity of the dust layer is neglected. (2) One fluid model is adopted, where the dust aggregates have the same velocity with the gas due to strong coupling by the drag force. (3) The gas is incompressible. The calculations with both the Coriolis and the tidal forces show that the tidal force has a stabilizing effect. The tidal force causes the radial shear in the disk. This radial shear changes the wave number of the mode which is at first unstable, and the mode is eventually stabilized. Thus the behavior of the mode is divided into two stages: (1) the first growth of the unstable mode which is similar to the results without the tidal force, and (2) the subsequent stabilization due to an increase of the wave number by the radial shear. If the midplane dust/gas density ratio is smaller than 2, the stabilization occurs before the unstable mode grows largely. On the other hand, the mode grows faster by one hundred orders of magnitude, if this ratio is larger than 20. Because the critical density of the gravitational instability is a few hundreds times as large as the gas density, the hydrodynamic instability investigated in this paper grows largely before the onset of the gravitational instability. It is expected that the hydrodynamic instability develops turbulence in the dust layer and the dust aggregates are stirred up to prevent from settling further. The formation of planetesimals through the gravitational instabilities is difficult to occur as long as the dust/gas surface density ratio is equal to that for the solar abundance.

37 pages, 21 figures and 1 table. Accepted for publication in Icarus

References in corpus (4)

• Planetesimal Formation by Gravitational Instability
• Size-selective concentration of chondrules and other small particles in protoplanetary nebula turbulence
• Vortices in Protoplanetary Disks
• The Formation and Role of Vortices in Protoplanetary Disks

Cited by in corpus (23)

• Streaming Instabilities in Protoplanetary Disks
• Forming Planetesimals in Solar and Extrasolar Nebulae
• Protoplanetary Disk Turbulence Driven by the Streaming Instability: Linear Evolution and Numerical Methods
• Dust sedimentation and self-sustained Kelvin-Helmholtz turbulence in protoplanetary disk mid-planes. I. Radially symmetric simulations
• Particle Pile-ups and Planetesimal Formation
• Vertical Shearing Instabilities in Radially Shearing Disks: The Dustiest Layers of the Protoplanetary Nebula
• The effect of the Coriolis force on Kelvin-Helmholtz-driven mixing in protoplanetary disks
• Dust Size Growth and Settling in a Protoplanetary Disk
• Dust Settling in Magnetorotationally-Driven Turbulent Discs I: Numerical Methods and Evidence for a Vigorous Streaming Instability
• Three-Dimensional Simulations of Kelvin-Helmholtz Instability in Settled Dust Layers in Protoplanetary Disks
• Forming Planetesimals by Gravitational Instability: I. The Role of the Richardson Number in Triggering the Kelvin-Helmholtz Instability
• $N$-body Simulation of Planetesimal Formation Through Gravitational Instability of a Dust Layer
• Secular Gravitational Instability of a Dust Layer in Shear Turbulence
• Induced Turbulence and the Density Structure of the Dust Layer in a Protoplanetary Disk
• Rapid Growth of Dust Particles in the Vicinity of Local Gas Density Enhancements in a Solar Nebula
• Radiatively heated, protoplanetary discs with dead zones. I. Dust settling and thermal structure of discs around M stars
• Dust Concentration at the Boundary Between Steady Super/Sub-Keplerian Flow Created by Inhomogeneous Growth of MRI
• 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
• N-Body Simulation of Planetesimal Formation through Gravitational Instability and Coagulation. II. Accretion Model
• Dynamics of Porous Dust Aggregates and Gravitational Instability of Their Disk
• Planetesimal growth in turbulent discs before the onset of gravitational instability
• Kelvin-Helmholtz Instabilities in Multi-Sized Dust Layers