Planet Migration in a Proto-planetary DiskHui Zhang 1,3 ， Chien-Chang Yen 1,2 and Chi Yuan 1

1 Institute of Astronomy and Astrophysics, Academia Sinica2 Department of Mathematics, Fu Jen Catholic University

3 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.

Advantages of Cartesian Frame

•No inner boundary with which we can’t deal perfectly

•Avoid an artificial hole in the center

•More efficient: resolution, computation time

•Uniform resolution all over domain

•Could deal with high q(q=Mp/Ms) case

Migration curves•Type I,II,III migration

•Migration in high surface density disk

•Migration in self-gravitation disk

High resolution disk evolution

High surface density disk evolution

Planet experienced Torque•Torques from innerdisk are positive•Torques from outerdisk are negative•Torques from planet’s Roche lobe•During Type I,III migration , most torque comes from the planet’s 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 disk’s surface density it will migrate inward faster and closer to the central star.

•Effects of self gravitation:Enhance eccentricity; Decrease migration rate ;The higher surface density the greater self gravitation effects.