Taku Takeuchi, Shigeru Ida
We estimate minimum dust abundances required for secular gravitational
instability (SGI) to operate at the midplane dust layer of protoplanetary
disks. For SGI to be a viable process, the growth time of the instability
T_grow must be shorter than the radial drift time of the dust T_drift. The
growth time depends on the turbulent diffusion parameter alpha, because the
modes with short wavelengths are stabilized by turbulent diffusion. Assuming
that turbulence is excited via the Kelvin-Helmholtz or streaming instabilities
in the dust layer, and that its strength is controlled by the energy supply
rate from dust accretion, we estimate the diffusion parameter and the growth
time of the instability. The condition T_grow < T_drift requires that the dust
abundance must be greater than a critical abundance Z_min, which is a function
of the Toomre parameter Q_g and aspect ratio h_g / r of the gas disk. For a
wide range of parameter space, the required dust abundance is less than 0.1. A
slight increase in dust abundance opens a possible route for the dust to
directly collapse to planetesimals.
View original:
http://arxiv.org/abs/1202.5412
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