Max Planck Institute for Astronomy - Annual Report 2007

max( p )/< g >
1000
100
10
1
0.1
0
100 200 300
Time t [ 1 / ]
=3.0 (BC)
=1.0 (BB)
=0.2 (BA)
400 500
Fig. II.3.2: Development of maximum particle density in units
of average gas density. Shown are results for three models with
varying dust-to-gas ratio e.
With increased computing effort and 20 million particles,
two cases were calculated even three-dimensionally,
whereby he limited himself to a cube-like volume in the
disk. In the case of small particles and a limited dust-togas
ratio (as in Fig. II.3.1) one can clearly see how the
dust filaments are drawn out longitudinally (Fig. II.3.4).
An exact time analysis of simulations indicates that
the condensations involve a dynamic, collective phenomenon,
rather than a permanent increase in den-
Fig. II.3.3: Cumulative distribution of particle density for all
six models with varying coupling strength (t) and dust-to-gas
ratio (e).
P (< p )
10
10 –1
10 –2
10 –3
10 –4
10
0.1
–5
s =0.1, =0.2
s =0.1, =1.0
s =0.1, =3.0
s =0.1, =0.2
s =0.1, =1.0
s =0.1, =3.0
1 10 100 1000
p /< p >
II.3 Rapid Formation of Planetesimals in Turbulent Disks 31
sity. Accordingly, rather than large boulders, loose “sand
heaps” develop in the disk which dissolve again later. Yet
this phenomenon can have something to do with the fact
that self-gravity of the condensations is not considered
in the models. The theoreticians pursued this additional
phenomenon in a second work in which they additionally
considered the effect of magnet fields. The magnetorotational
turbulence (MRI turbulence) appearing here
additionally strengthens the turbulences and supports the
formation of planetisimals.
Magnet Fields support the Formation of Planetesimals
The MRI turbulence results from an interplay of sheer
flows and magnetic fields which could be imagined
as follows: In the protoplanetary disks the gas that is
nearer to the star flows faster than at greater distances.
Experiments and analytical investigations have shown
that the sheer flows, which otherwise grow rapidly
unstable, do not so easily become turbulent in disks, because
the disk rotates around the star with a high speed:
The rotation’s high angular momentum stabilizes the
sheer flow.
Near the young star, the gas is probably ionized and the
charged particles couple to the magnetic field lines. Like
rubber bands, these pull through the disk and attempt to
prevent the sheering, with the effect that the inner region
Fig. II.3.4: Three-dimensional development of particle density in
the same case shown in two dimensions in Fig. II.3.1.