The effects of the Tidal Force on Shear Instabilities in the Dust Layer of the Solar Nebula
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 v...
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Zusammenfassung: | 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. |
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DOI: | 10.48550/arxiv.astro-ph/0305596 |