Max Planck Institute for Astronomy - Annual Report 2005

28 II. Highlights
azimuthal direction relative to box center [c s / � 0 ]
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Fig. II.4.3: Looking from above the disc we see the integrated
column density of the gas (left) and particles (right) in a
corotating box. While the gas density within the vortices is
varying only slightly compared to the average value of the
surroundings, considerable density concentrations occur for the
particles. c 0 / Ω 0 � 1 AU.
However, only global simulations of the entire disk
could show how these processes would affect the formation
scenario of planetesimals. It nevertheless seems
plausible that the concentration of bodies in the anticyclones
favors further gravitational accumulation.
It is not clear yet whether the reduced drift speed
suffices to prevent the bodies from premature vaporization.
Anyway, MRI turbulence appears to benefit the
formation of planetesimals. A simple estimate shows the
concentration in the clumps to be high enough for the
individual rocks to feel their mutual gravity. Gravity may
be strong enough now to prevent the dispersion of the
clump. This could result in a collapse of the dust clump,
finally forming a kilometer-sized planetesimal. The numerical
experiment for this is in preparation.
Kelvin-Helmholtz Turbulence
It has been known for a long time that MRI turbulence
is prevented in too weakly ionized disks since the magnetic
fields do not couple to neutral gas. But now a second
form of instability occurs that must have a considerable
effect on the protoplanetary disk and the formation of
planetesimals: the Kelvin-Helmholtz instability (KH
instability for short). It develops in a dusty gas disk in
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radial direction relative to box center [cs / �0 ]
the following way: At first the dust sinks towards the
mid-plane of the disk (sedimentation) which otherwise
would have been prevented by MRI turbulence. In a
protoplanetary disk temperature and density decrease
with increasing distance from the central star. Therefore
a radial pressure gradient exists, causing the gas to rotate
more slowly than it would on a pure Keplerian orbit. The
dust on the other hand does not react to the pressure gradient
but only feels the gravity. It therefore revolves on
Keplerian orbits. When the dust/gas ratio in the central
plane of the disk gets high enough, the dust will drag
the gas particles along, forcing them also to adopt the
velocity of a Keplerian orbit. Consequently the gas is
moving faster in the central plane than above and below.
Therefore a vertical velocity shear occurs, resulting in the
occurrence of a KH instability.
The turbulent gas motion setting in can cause the dust
to be whirled out of the central plane, thus preventing
a gravitational accumulation of dust to planetesimals.
More than twenty years ago, this process already had
been considered an obstacle to the growth of dust grains
to planetesimals. Correspondingly, there were many
different suggestions to solve this problem. In a numerical
simulation dust and gas have to be treated as two
independent systems that are able to interact and move
against one another – a demanding non-linear problem.
Again simulations were performed with particles of
three different sizes: one centimeter, ten centimeters and
one meter. Figure II.4.4 shows a result for centimetersized
grains. In an initially Gaussian density distribution
in the z-direction (top) vortices form in the mid-plane as
the dust density increases, which even can break up the
original dust disk at many places (bottom). The larger the
particles the faster the process sets in since the larger par-
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