Three-dimensional simulations of a planet embedded in a protoplanetary disk

The dynamical influence of Jupiter-sized planets still embedded in protoste llar disks is studied by means of numerical simulations. The three-dimensio nal structure of the disk is fully taken into account. Assuming a disk mass of 3.5 x 10(-3) M. within 2 and 13 AU, typical values for the vertical thi ckness H/r = 0.05 and viscosity of the disk alpha approximate to 4 x 10(-3) , we find for the mass accretion rate onto the planet a value of 6 x 10(-5) M-J yr(-1) and for the migration timescale a value of 10(5) yr. These resu lts are in excellent lent agreement with previously obtained results from t wo-dimensional calculations of infinitesimally thin disks. We argue that th is agreement is to be expected if the vertical height of the disk is simila r or smaller than the size of the Roche lobe of the embedded planet. Three- dimensional models having a lower planetary mass or different H/r values di splay small deviations from two-dimensional results.