Max Planck Institute for Astronomy - Annual Report 2005

not only causes a diffusion of the smallest dust particles,
it also creates relative velocities between rock-sized bodies
that are not coupled to the gas any longer. On the one
hand more collisions will occur, on the other hand a local
concentration of the rocks will develop. So for instance,
boulders up to several meters across can be captured this
way in vortices. Such vortices can form in the so-called
magnetorotational turbulence (MRI turbulence).
MRI turbulence is an interplay of shear flows and
magnetic fields that can be visualized more or less the
following way. Shear flows can cause turbulence. This is
known, e.g., from fast sports cars where the circumfluent
air can become turbulent. The skill of car designers is to
shape the car in such a way that the turbulence is minimized
since the developing vortices increase the drag.
Spoilers and streamlining help to shift the occurrence of
turbulence as far behind the sports car as possible.
Such a shear flow also occurs in gaseous disks surrounding
young stars. Close to the star the gas flows faster
than further out. Experiments and analytical studies
have shown that the flow in disks does not easily become
turbulent since the circumstellar disk rotates very fast.
The related angular momentum stabilizes the shear flow,
acting like a spoiler on a sports car.
Now the effect of the magnetic fields is added. The gas
surrounding the young star is probably is ionized, and the
charge carriers couple to the magnetic field lines. These
lines pass through the disk like elastic bands, trying to
prevent the shear. So the inner region of the disk is slowed
down and the outer part is sped up. However, this
destabilizes the flow in the disk to such an extent that it
becomes turbulent, forming vortices. The magnetic fields
thus act like a forest of antennas screwed onto one’s
sports car: the drag is increased enormously as the flow
around the car becomes turbulent – despite all spoilers.
Theorists at MPIA simulated numerically the phenomenon
of MRI turbulence in the disks around young
stars. Two million particles represented rocks moving in
a gas. Friction could be varied by a parameter. Then the
MRI turbulence of the gas was included in the simulation
in order to study the effect of this phenomenon on the
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II. 4. Plantesimal Formation by Gravitational Instability 27
motion of macroscopic bodies. Since a complete threedimensional
treatment of the entire disk is far beyond the
computing power of present-day computers the simulation
had to be limited to a volume within the disk. Values
for a radial density gradient and a pressure gradient were
each varied over a range expected for protoplanetary
disks. The sizes of the rocks was assumed to be ten centimeters
as well as one and ten meters.
The simulations performed with various parameters
showed surprising results. The MRI turbulence produces
vortices in the gas that have a slightly higher density
and a marginally higher pressure than their environment.
These condensations survive in the disks for some orbital
periods, corresponding to some ten or – in the outer regions
of the disk – even hundred years. Then they disperse,
but might form again somewhere else.
The vortices rotate in different directions and can be
distinguished, as in the earth’s atmosphere, into cyclones
and anticyclones according to their sense of rotation.
Interestingly the solid bodies move towards the anticyclones,
remaining captured there. Cyclones, on the other
hand, disperse the particles. This effect even increases
with the size of the particles, reaching a maximum for
meter-sized bodies: Here the local concentration of the
bodies is a hundred times higher than on average while
the effect is much lower for the small grains and for
larger objects (Fig. II.4.1 and Fig. II.4.2). The motion of
the particles towards the anticyclone regions is caused
by the pressure gradient existing there. These accumulations
of large bodies survive for a while even when
the gas vortices that had created them already have
dispersed.
A second interesting result was that the MRI turbulence
slows down the drift of the rocks towards the central
star mentioned above. Compared to a laminar disk
this velocity is reduced by up to 40 percent (Fig. II.4.3).
Fig. II.4.2: Like Fig. II.4.1, but for particles 10 cm (lower curve)
and 10 m across. Clearly evident is the higher-than-average
concentration of the large boulders.
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