On the growth and orbital evolution of giant planets in layered protoplanetary disks

Abstract

<i>Aims. <i/>We present the results of hydrodynamic simulations of the growth and orbital evolution of giant planets embedded in a protoplanetary disk with a dead-zone. The aim is to examine to what extent the presence of a dead-zone affects the rates of mass accretion and migration for giant planets.<i>Methods. <i/>We performed 3D numerical simulations using a grid-based hydrodynamics code. In these simulations of laminar, non-magnetised disks, the dead-zone is treated as a region where the vertical profile of the viscosity depends on the distance from the equatorial plane. We consider dead-zones with vertical sizes, <i>H<i/><sub>DZ<sub/>, ranging from <i>0<i/> to <i>H<i/><sub>DZ<sub/> = 2.3 <i>H<i/>, where <i>H<i/> is the disk scale-height. For all models, the vertically integrated viscous stress, and the related mass flux through the disk, have the same value (equivalent to 10<sup>-8<sup/> yr<sup>-1<sup/>), such that the simulations test the dependence of planetary mass accretion and migration on the vertical distribution of the viscous stress (and mass flux). For each model, an embedded 30 planet on a fixed circular orbit is allowed to accrete gas from the disk. Once the planet mass becomes equal to that of Saturn or Jupiter, we allow the planet orbit to evolve due to gravitational interaction with the disk.<i>Results. <i/>We find that the time scale over which a protoplanet grows to become a giant planet is essentially independent of the dead-zone size, and depends only on the total rate at which the disk viscously supplies material to the planet. For Saturn-mass planets, the migration rate depends only weakly on the size of the dead-zone for <i>H<i/><sub>DZ<sub/> <i>≤<i/> 1.5 <i>H<i/>, but becomes noticeably slower when <i>H<i/><sub>DZ<sub/> = 2.3 <i>H<i/>. This effect is apparently due to the desaturation of corotation torques which originate from residual material in the partial-gap region. For Jupiter-mass planets, there is a clear tendency for the migration to proceed more slowly as the size of the dead-zone increases, with migration rates differing by approximately 40% for models with <i>H<i/><sub>DZ<sub/> = 0 and <i>H<i/><sub>DZ<sub/> = 2.3 <i>H<i/>.<i>Conclusions. <i/>Our results indicate that for disks models in which the mass accretion rate has a well defined value, the accretion and migration rates for Saturn- and Jovian-mass planets are relatively insensitive to the presence and size of a dead-zone.