Max Planck Institute for Astronomy - Annual Report 2005

26 II. Highlights
II.4 Planetesimal Formation by Gravitational Instability
According to current views planet formation in protoplanetary
disks takes place in several stages. At first dust
particles collide and stick together, growing eventually
to the size of planetesimals. Planetesimals then accumulate
gravitationally and finally reach the sizes of planets.
Many individual steps in the sequence of processes that
leads to the formation of planets are not yet understood.
Among other things the role of various kinds of turbulence
has not been possible to model satisfactorily so
far because of insufficient computing power. Theorists at
the Institute have now studied numerically the influence
of magnetorotational and Kelvin-Helmholtz turbulence.
One surprising result has been that turbulence does not
impede the gravitational formation of planetesimals – as
it was expected – but can even stimulate it.
During the first stages of planet formation small dust
particles collide and stick to each other (coagulate).
The necessary relative velocities are provided to the
particles by Brownian motion. The speed decreases with
increasing particle mass, however, and therefore can
only play a role during the earliest stage of growth. In
the further course of events the ever growing particles
sink are sinking towards the mid-plane of the developing
protoplanetary disk under the influence of the protostar‘s
gravity. As the sedimentation speed increases with growing
particle mass, here too relative velocities between the
dust grains occur, resulting in more collisions and further
growth. This way, the grains may achieve diameters of
several centimeters when they arrive at the mid-plane of
the disk.
In the mid-plane the dust density is relatively high so
that the particles will now collide more frequently and
can grow to planetesimals of several kilometers size. But
at the same time there are several mechanisms counter-
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acting this growth. Microscopic particles can only coagulate
if they collide with speeds that are not too high.
The same is true for collisions of small dust particles and
meter-sized rocks. Above a certain velocity the dusty bodies
just rebound from one another. It is even worse for
collisions between macroscopic bodies. Two rocks will
never stick together, no matter what their velocities are
during collision. Above a critical relative speed the bodies
will even destroy one another. Where this threshold
lies is still debated – probably at some ten meters per
second. In addition, meter-sized bodies will lose angular
momentum because of their friction with the gas of the
disk and thus will drift on spiral orbits towards the central
star. Estimates show that within about one hundred
years a rock this size can come close enough to the star
to vaporize. In order to avoid this fate it has to grow
within this short period of time by at least one order of
magnitude, corresponding to an increase of mass of three
orders of magnitudes. According to current theoretical
models, however, the growth during this phase requires
at least 1000 years.
Magnetorotational Turbulence Concentrates Rocks
The second problem (the high drift rates of the rocks)
relates to disks with a laminar flow of gas and dust.
However, it has already been suspected for some time
that turbulence may play a major role here. Turbulence
Fig. II.4.1: Number of particles within one grid cell as a function
of time for meter-sized rocks. The particle density reaches a
value up to eighty times higher than the average density. Time
is given in units of orbits.
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