From: LARRY KLAES (ljk4_at_msn.com)
Date: Thu Sep 01 2005 - 13:36:39 UTC
Paper: astro-ph/0508659
Date: Tue, 30 Aug 2005 20:28:18 GMT (56kb)
Title: Planetesimal Formation without Thresholds. I: Dissipative
Gravitational
Instabilities and Particle Stirring by Turbulence
Authors: Andrew N. Youdin (Princeton University)
Comments: 10 pages, 4 figures, submitted to ApJ
\\
We analyze the gravitational collapse of solids subject to gas drag in a
protoplanetary disk. We also study the stirring of solids by turbulent
fluctuations to determine the velocity dispersion and thickness of the
midplane
particle layer. The usual thresholds for determining gravitational
instability
in disks, Toomre's criterion and/or the Roche density, do not apply.
Dissipation of angular momentum allows instability at longer wavelengths,
lower
densities, and higher velocity dispersions than without drag. Small solids
will
slowly leak into axisymmetric rings since initial collapse occurs over many
orbits. Growth is fastest when particle stopping times are comparable to
orbital times. Our analysis of particle stirring by turbulence is consistent
with previous results for tightly coupled particles, but is generalized to
loose coupling where epicyclic motions contribute to random velocities. A
companion paper applies these results to turbulent protoplanetary disks.
\\ ( http://arXiv.org/abs/astro-ph/0508659 , 56kb)
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\\
Paper: astro-ph/0508662
Date: Tue, 30 Aug 2005 20:15:31 GMT (57kb)
Title: Planetesimal Formation without Thresholds. II: Gravitational
Instability
of Solids in Turbulent Protoplanetary Disks
Authors: Andrew N. Youdin (Princeton University)
Comments: 9 pages, 8 figures, submitted to ApJ
\\
We show that small solids in low mass, turbulent protoplanetary disks
collect
into self-gravitating rings. Growth is faster than disk lifetimes and radial
drift times for moderately strong turbulence, characterized by dimensionless
diffusivities, $\alpha_g < 10^{-6} -- 10^{-3}$ when particles are mm-sized.
This range reflects a strong dependance on disk models. Growth is faster for
higher particle surface densities. Lower gas densities and larger solids
also
give faster growth, as long as aerodynamic coupling is tight. In simple
power
law models, growth is slowest around ~0.3 AU, where drag coupling is
strongest
for mm-sized solids. Growth is much faster close to the star where orbital
times are short, with implications for in situ formation of short period
extrasolar planets. Growth times also decrease toward the outer disk where
lower gas densities allow greater particle settling. Beyond roughly Kuiper
Belt
distances however, solids are sufficiently decoupled from gas that
dissipative
gravitational instabilities are less effective. Turbulence not only slows
growth, but also increases radial wavelengths. The initial solid mass in an
unstable ring can be ~0.01 M_Earth or greater, huge compared to km-sized
planetesimals. Nonlinear fragmentation, which has not been studied in
detail,
will lower the final planetesimal mass. We consider applications to the
asteroid belt and discuss the alternate hypothesis of collisional
agglomeration.
\\ ( http://arXiv.org/abs/astro-ph/0508662 , 57kb)
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