Planet Migration in a Protoplanetary Disk

1
Planet Migration in a Proto-planetary Disk Hui
Zhang 1,3,Chien-Chang Yen 1,2 and Chi Yuan 11
Institute of Astronomy and Astrophysics, Academia
Sinica2 Department of Mathematics, Fu Jen
Catholic University3 Department of Astronomy,
NanJing university
Abstract We present the results of numerical
simulations of the migration of a Jovian planet
embedded in a self-gravitating proto-planetary
disk. The Antares code we have developed is
adopted in the calculations. It is a 2-D Godunov
code based on the exact Reimann solution for
isothermal or polytropic gas, featured with
non-reflecting boundary conditions and Poisson
solver for non-periodic boundary conditions. We
use the Cartesian coordinate version of the code
to avoid the well-known problem of the inner
boundary. To carry out the calculation, however,
a softening length is assigned to the central
star. Normally the planet would migrate through
all three types of migration phases, from Type I
(embedded) to Type III (presence of horseshoe
configuration) to Type II (forming a clear gap).
Sometime Type III will re-appear after Type II
phase. We find that the rapid migration in Type I
and Type III is associated with the net negative
torque within the Roche lobe of the planet, which
accounts for more than 60\ of the total torques
the planet experiences. When the gap forms (Type
II), hence matter in the lobe is drastically
depleted, the planet will migrate slowly. We also
notice that the self-gravity of the disk will
change planet's migration rate and enhance its
eccentricity. These effects are more pronounced
after the gap is well formed. The work is in
parts supported by a grant from National Science
Council,Taiwan NSC94-2752-M-001-002-PAE.
High resolution disk evolution

• Advantages of Cartesian Frame
• No inner boundary with which we cant deal
  perfectly
• Avoid an artificial hole in the center
• More efficient resolution, computation time
• Uniform resolution all over domain
• Could deal with high q(qMp/Ms) case

• Migration curves
• Type I,II,III migration
• Migration in high surface density disk
• Migration in self-gravitation disk

High surface density disk evolution

• Planet experienced Torque
• Torques from innerdisk are positive
• Torques from outerdisk are negative
• Torques from planets Roche lobe
• During Type I,III migration , most torque comes
  from the planets Roche lobe

• Eccentricity evolution
• Self-gravitation effect
• High surface density effect
• High ratio(Mplanet/Mstar )

• Conclusion
• The high resolution simulations show that planet
  migration may experience Type III migration
  before the gap is well formed
• The rapid migration in Type I and Type III is
  associated with the net negative torque within
  the Roche lobe of the planet
• For a Jupiter mass planet, after the gap is well
  formed it will be locked in an orbit for a
  long time, while when we enhance the disks
  surface density it will migrate inward faster and
  closer to the central star.
• Effects of self gravitationEnhance eccentricity
  Decrease migration rate The higher surface
  density the greater self gravitation effects.