We model the growth of Jupiter via core nucleated accretion, applying constraints from hydrodynamical processes that result from the disk-planet interaction. We compute the planet's internal structure using a well tested planetary formation code that is based upon a Henyey-type stellar evolution code. The planet's interactions with the protoplanetary disk are calculated using 3-D hydrodynamic simulations. Previous models of Jupiter's growth have taken the radius of the planet to be approximately one Hill sphere radius, R H . However, 3-D hydrodynamic simulations show that only gas within ∼ 0.25 R H remains bound to the planet, with the more distant gas eventually participating in the shear flow of the protoplanetary disk. Therefore in our new simulations, the planet's outer boundary is placed at the location where gas has the thermal energy to reach the portion of the flow not bound to the planet. We find that the smaller radius increases the time required for planetary growth by ∼ 5%. Thermal pressure limits the rate at which a planet less than a few dozen times as massive as Earth can accumulate gas from the protoplanetary disk, whereas hydrodynamics regulates the growth rate for more massive planets. Within a moderately viscous disk, the accretion rate peaks when the planet's mass is about equal to the mass of Saturn. In a less viscous disk hydrodynamical limits to accretion are smaller, and the accretion rate peaks at lower mass. Observations suggest that the typical lifetime of massive disks around young stellar objects is ∼ 3 Myr. To account for the dissipation of such disks, we perform some of our simulations of Jupiter's growth within a disk whose surface gas density decreases on this timescale. In all of the cases that we simulate, the planet's effective radiating temperature rises to well above 1000 K soon after hydrodynamic limits begin to control the rate of gas accretion and the planet's distended envelope begins to contract. According to our simulations, proto-Jupiter's distended and thermally-supported envelope was too small to capture the planet's current retinue of irregular satellites as advocated by Pollack et al. [Pollack, J.B., Burns, J.A., Tauber, M.E., 1979. Icarus 37, 587-611].

We perform numerical simulations of a disc-planet system using various grid-based and smoothed particle hydrodynamics (SPH) codes. The tests are run for a simple setup where Jupiter and Neptune mass planets on a circular orbit open a gap in a protoplanetary disc during a few hundred orbital periods. We compare the surface density contours, potential vorticity and smoothed radial profiles at several times. The disc mass and gravitational torque time evolution are analyzed with high temporal resolution. There is overall consistency between the codes. The density profiles agree within about 5% for the Eulerian simulations while the SPH results predict the correct shape of the gap although have less resolution in the low density regions and weaker planetary wakes. The disc masses after 200 orbital periods agree within 10%. The spread is larger in the tidal torques acting on the planet which agree within a factor 2 at the end of the simulation. In the Neptune case the dispersion in the torques is greater than for Jupiter, possibly owing to the contribution from the not completely cleared region close to the planet.Comment: 32 pages, accepted for publication in MNRA

We analyze the gas accretion flow through a planet-produced gap in a protoplanetary disk. We adopt the alpha disk model and ignore effects of planetary migration. We develop a semi-analytic, one-dimensional model that accounts for the effects of the planet as a mass sink and also carry out two-dimensional hydrodynamical simulations of a planet embedded in a disk. The predictions of the mass flow rate through the gap based on the semi-analytic model generally agree with the hydrodynamical simulations at the 25% level. Through these models, we are able to explore steady state disk structures and over large spatial ranges. The presence of an accreting ∼ 1M J planet significantly lowers the density of the disk within a region of several times the planet's orbital radius. The mass flow rate across the gap (and onto the central star) is typically 10% to 25% of the mass accretion rate outside the orbit of the planet, for planet-to-star mass ratios that range from 5 × 10 −5 to 1 × 10 −3 . Subject headings: accretion, accretion discs -hydrodynamics -planets and satellites: generalThis 2-column preprint was prepared with the AAS L A T E X macros v5.0, modified by Gennaro D'Angelo.

We investigate the evolution of protoplanets with different masses embedded in an accretion disk, via global fully three-dimensional hydrodynamical simulations. We consider a range of planetary masses extending from one and a half Earth's masses up to one Jupiter's mass, and we take into account physically realistic gravitational potentials of forming planets. In order to calculate accurately the gravitational torques exerted by disk material and to investigate the accretion process onto the planet, the flow dynamics has to be thoroughly resolved on long as well as short length scales. We achieve this strict resolution requirement by applying a nested-grid refinement technique which allows to greatly enhance the local resolution. Our results from altogether 51 simulations show that for large planetary masses, approximately above a tenth of the Jupiter's mass, migration rates are relatively constant, as expected in type II migration regime and in good agreement with previous two-dimensional calculations. In a range between seven and fifteen Earth's masses, we find a dependency of the migration speed on the planetary mass that yields time scales considerably longer than those predicted by linear analytical theories. This property may be important in determining the overall orbital evolution of protoplanets. The growth time scale is minimum around twenty Earth-masses, but it rapidly increases for both smaller and larger mass values. Significant differences between two-and three-dimensional calculations are found in particular for objects with masses smaller than ten Earth-masses. We also derive an analytical approximation for the numerically computed mass growth rates.

The increase of computational resources has recently allowed high resolution, three dimensional calculations of planets embedded in gaseous protoplanetary disks. They provide estimates of the planet migration timescale that can be compared to analytical predictions. While these predictions can result in extremely short migration timescales for cores of a few Earth masses, recent numerical calculations have given an unexpected outcome: the torque acting on planets with masses between 5 M ⊕ and 20 M ⊕ is considerably smaller than the analytic, linear estimate. These findings motivated the present work, which investigates existence and origin of this discrepancy or "offset", as we shall call it, by means 1 Also at IA-UNAM, Ciudad Universitaria, Apartado Postal 70-264, Mexico DF 04510, Mexico 2 Send offprint requests to fmasset@cea.fr 3 NASA Postdoctoral Fellow.-2of two and three dimensional numerical calculations. We show that the offset is indeed physical and arises from the coorbital corotation torque, since (i) it scales with the disk vortensity gradient, (ii) its asymptotic value depends on the disk viscosity, (iii) it is associated to an excess of the horseshoe zone width. We show that the offset corresponds to the onset of non-linearities of the flow around the planet, which alter the streamline topology as the planet mass increases: at low mass the flow non-linearities are confined to the planet's Bondi sphere whereas at larger mass the streamlines display a classical picture reminiscent of the restricted three body problem, with a prograde circumplanetary disk inside a "Roche lobe". This behavior is of particular importance for the sub-critical solid cores (M 15 M ⊕ ) in thin (H/r 0.06) protoplanetary disks. Their migration could be significantly slowed down, or reversed, in disks with shallow surface density profiles.