Three‐dimensional Simulations of a Planet Embedded in a Protoplanetary Disk

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Abstract
The dynamical influence of Jupiter-sized planets still embedded in protostellar disks is studied by means of numerical simulations. The three-dimensional structure of the disk is fully taken into account. Assuming a disk mass of 3.5 × 10-3 M☉ within 2 and 13 AU, typical values for the vertical thickness H/r = 0.05 and viscosity of the disk α ≈ 4 × 10-3, we find for the mass accretion rate onto the planet a value of 6 × 10-5 MJ yr-1 and for the migration timescale a value of 105 yr. These results are in excellent agreement with previously obtained results from two-dimensional calculations of infinitesimally thin disks. We argue that this agreement is to be expected if the vertical height of the disk is similar 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 display small deviations from two-dimensional results.