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Numerical simulations of the type III migration:I. Disc model and convergence tests
We investigate the fast (type III) migration regime of high-mass protoplanets
orbiting in protoplanetary disks. This type of migration is dominated by
corotational torques. We study the details of flow structure in the planet's
vicinity, the dependence of migration rate on the adopted disc model, and the
numerical convergence of models (independence of certain numerical parameters
such as gravitational softening). We use two-dimensional hydrodynamical
simulations with adaptive mesh refinement,based on the FLASH code with improved
time-stepping scheme. We perform global disk simulations with sufficient
resolution close to the planet, which is allowed to freely move throughout the
grid. We employ a new type of equation of state in which the gas temperature
depends on both the distance to the star and planet, and a simplified
correction for self-gravity of the circumplanetary gas. We find that the
migration rate in the type III migration regime depends strongly on the gas
dynamics inside the Hill sphere (Roche lobe of the planet) which, in turn, is
sensitive to the aspect ratio of the circumplanetary disc. Furthermore,
corrections due to the gas self-gravity are necessary to reduce numerical
artifacts that act against rapid planet migration. Reliable numerical studies
of Type III migration thus require consideration of both the thermal andthe
self-gravity corrections, as well as a sufficient spatial resolution and the
calculation of disk-planet attraction both inside and outside the Hill sphere.
With this proviso, we find Type III migration to be a robust mode of migration,
astrophysically promising because of a speed much faster than in the previously
studied modes of migration.Comment: 17 pages, 15 figures, submitted to MNRAS. Comments welcom