A&A 443, 1067-1085 (2005)
On the orbital evolution of low mass protoplanets in
turbulent, magnetised disksR. P. Nelson
Queen Mary, University of London, Mile End Rd, London E1 4NS, UK
(Received 23 December 2004 / Accepted 11 August 2005)
We present the results of MHD simulations of low mass protoplanets
interacting with turbulent, magnetised protostellar disks. We calculate the
orbital evolution of "planetesimals" and protoplanets with masses
in the range
. The disk models are cylindrical
models with toroidal net-flux magnetic
fields, having aspect ratio H/r=0.07 and
effective viscous stress parameter
A significant result is that the
"planetesimals", and protoplanets of
all masses considered, undergo stochastic migration due to gravitational
interaction with turbulent density fluctuations in the disk.
For simulation run times currently feasible
(covering between 100-150 planet orbits),
the stochastic migration dominates over type I migration for many models.
Fourier analysis of the torques experienced by protoplanets
indicates that the torque fluctuations contain components with significant
power whose time scales of variation are similar to the simulation run
times. These long term torque fluctuations in part explain the
dominance of stochastic torques in the models, and
may provide a powerful means of counteracting the effects of
type I migration acting on some planets in turbulent disks.
The effect of superposing type I migration torques appropriate for laminar
disks on the stochastic torques was examined. This analysis predicts
that a greater degree of inward migration should occur than
was observed in the MHD simulations.
This may be a first hint that type I
torques are modified in a turbulent disk, but the results are not
conclusive on this matter.
The turbulence is found
to be a significant source of eccentricity driving, with the
"planetesimals" attaining eccentricities in the range
during the simulations. The eccentricity evolution of the protoplanets
shows strong dependence on the protoplanet mass. Protoplanets with
attained eccentricities in the range
. Those with
This trend is in basic agreement with a model in which eccentricity growth
arises because of turbulent forcing, and eccentricity damping occurs through
interaction with disk material at coorbital Lindblad resonances.
These results are significant for the theory of planet formation.
Stochastic migration may provide a means
of preventing at least some planetary cores from migrating into the
central star due to type I migration before they become gas giants.
The growth of planetary cores may be enhanced by preventing
isolation during planetesimal accretion. The excitation of
eccentricity by the turbulence, however, may act to reduce
the growth rates of planetary cores during the runaway and
oligarchic growth stages, and may cause collisions between planetesimals
to be destructive rather than accumulative.
accretion, accretion disks --
magnetohydrodynamics (MHD) --
methods: numerical --
planetary systems: formation --
planetary systems: protoplanetary disks
© ESO 2005