We present a numerical study of rapid, so called type III migration for Jupiter-sized planets embedded in a protoplanetary disc. We limit ourselves to the case of outward migration, and study in detail its evolution and physics, concentrating on the
structure of the co-rotation and circumplanetary regions, and processes for stopping migration. We also consider the dependence of the migration behaviour on several key parameters. We perform this study using global, two-dimensional hydrodynamical simulations with adaptive mesh refinement. We find that the outward directed type III migration can be started if the initial conditions support $Z > 1$, that corresponds to initial value $M_rmn{Delta} ga 1.5$. Unlike the inward directed migration, in the outward migration the migration rate increases due to the growing of the volume of the co-orbital region. We find the migration to be strongly dependent on the rate of the mass accumulation in the circumplanetary disc, leading to two possible regimes of migration, fast and slow. The structure of the co-orbital region and the stopping mechanism differ between these two regimes.
Observations of extrasolar planets reveal that planets can be found in close binary systems, where the semi-major axis of the binary orbit is less than 20 AU. The existence of these planets challenges planet formation theory, because the strong gravi
tational perturbations due to the companion increase encounter velocities between planetesimals and make it difficult for them to grow through accreting collisions. We study planetesimal encounter velocities in binary systems, where the planetesimals are embedded in a circumprimary gas disc that is allowed to evolve under influence of the gravitational perturbations of the companion star. We find that the encounter velocities between planetesimals of different size strongly depend on the gas disc eccentricity. In all cases studied, inclusion of the full gas dynamics increases the encounter velocity compared to the case of a static, circular gas disc. Full numerical parameter exploration is still impossible, but we derive analytical formulae to estimate encounter velocities between bodies of different sizes given the gas disc eccentricity. The gas dynamical evolution of a protoplanetary disc in a binary system tends to make planetesimal accretion even more difficult than in a static, axisymmetric gas disc.
We study the interaction of a low-mass planet with a protoplanetary disk with a realistic treatment of the energy balance by doing radiation-hydrodynamical simulations. We look at accretion and migration rates and compare them to isothermal studies.
We used a three-dimensional version of the hydrodynamical method RODEO, together with radiative transport in the flux-limited diffusion approach. The accretion rate, as well as the torque on the planet, depend critically on the ability of the disk to cool efficiently. For densities appropriate to 5 AU in the solar nebula, the accretion rate drops by more than an order of magnitude compared to isothermal models, while at the same time the torque on the planet is positive, indicating outward migration. It is necessary to lower the density by a factor of 2 to recover inward migration and more than 2 orders of magnitude to recover the usual Type I migration. The torque appears to be proportional to the radial entropy gradient in the unperturbed disk. These findings are critical for the survival of protoplanets, and they should ultimately find their way into population synthesis models.
We present a numerical study of rapid, so called type III migration for Jupitersized planets embedded in a protoplanetary disc. We limit ourselves to the case of inward migration, and study in detail its evolution and physics, concentrating on the st
ructure of the corotation and circumplanetary regions, and processes for stopping migration. We also consider the dependence of the migration behaviour on several key parameters. We perform this study using the results of global, two-dimensional hydrodynamical simulations with adaptive mesh refinement. The initial conditions are chosen to satisfy the condition for rapid inward migration. We find that type III migration can be divided into two regimes, fast and slow. The structure of the coorbital region, mass accumulation rate, and migration behaviour differ between these two regimes. All our simulations show a transition from the fast to the slow regime, ending type III migration well before reaching the star. The stopping radius is found to be larger for more massive planets and less massive discs. A sharp density drop is also found to be an efficient stopping mechanism. In the fast migration limit the migration rate and induced eccentricity are lower for less massive discs, but almost do not depend on planet mass. Eccentricity is damped on the migration time scale.
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 planets vicinity, the dependenc
e 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.
