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.

Abstract. We study the evolution of embedded protoplanets in a protostellar disk using very high resolution nestedgrid computations. This method allows us to perform global simulations of planets orbiting in disks and, at the same time, to resolve in detail the dynamics of the flow inside the Roche lobe of the planet. The primary interest of this work lies in the analysis of the gravitational torque balance acting on the planet. For this purpose we study planets of different masses, ranging from one Earth-mass up to one Jupiter-mass, assuming typical parameters of the protostellar disk. The high resolution supplied by the nested-grid technique permits an evaluation of the torques, resulting from short and very short range disk-planet interactions, more reliable than the one previously estimated with the aid of numerical methods. Likewise, the mass flow onto the planet is computed in a more accurate fashion. The obtained migration time scales are in the range from few times 10 4 years, for intermediate mass planets, to 10 6 years, for very low and high mass planets. These are longer than earlier assessments due to the action of circumplanetary material. Typical growth time scales depend strongly on the planetary mass. Below 64 Earth-masses, we find this time scale to increase as the 2/3-power of the planet's mass; otherwise it rises as the 4/3-power. In the case of Jupiter-size planets, the growth time scale is several times ten thousand years.

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Intermediate between the prestellar and Class 0 protostellar phases, the first core is a quasi-equilibrium hydrostatic object with a short lifetime and an extremely low luminosity. Recent MHD simulations suggest that the first core can even drive a molecular outflow before the formation of the second core (i.e., protostar). Using the Submillimeter Array and the Spitzer Space Telescope, we present high angular resolution observations towards the embedded dense core IRS2E in L1448. We find that source L1448 IRS2E is not visible in the sensitive Spitzer infrared images (at wavelengths from 3.6 to 70 µm), and has weak (sub-) millimeter dust continuum emission. Consequently, this source has an extremely low bolometric luminosity (< 0.1 L ⊙ ). Infrared and (sub-) millimeter observations clearly show an outflow emanating from this source; L1448 IRS2E represents thus far the lowest luminosity source known to be driving a molecular outflow. Comparisons with prestellar cores and Class 0 protostars suggest that L1448 IRS2E is more evolved than prestellar cores but less evolved than Class 0 protostars, i.e., at a stage intermediate between prestellar cores and Class 0 protostars. All these results are consistent with the theoretical predictions of the radiative/magneto hydrodynamical simulations, making L1448 IRS2E the most promising candidate of the first hydrostatic core revealed so far.