Formation of the Giant Planets by Concurrent Accretion of Solids and Gas

Models were developed to simulate planet formation. Three major phases are characterized in the simulations: (1) planetesimal accretion rate, which dominates that of gas, rapidly increases owing to runaway accretion, then decreases as the planet's feeding zone is depleted; (2) occurs when both solid and gas accretion rates are small and nearly independent of time; and (3) starts when the solid and gas masses are about equal and is marked by runaway gas accretion. The models applicability to planets in our Solar System are judged using two basic "yardsticks". The results suggest that the solar nebula dissipated while Uranus and Neptune were in the second phase, during which, for a relatively long time, the masses of their gaseous envelopes were small but not negligible compared to the total masses. Background information, results and a published article are included in the report

Core-Accretion Model Predicts Few Jovian-Mass Planets Orbiting Red Dwarfs

The favored theoretical explanation for giant planet formation -- in both our solar system and others -- is the core accretion model (although it still has some serious difficulties). In this scenario, planetesimals accumulate to build up planetary cores, which then accrete nebular gas. With current opacity estimates for protoplanetary envelopes, this model predicts the formation of Jupiter-mass planets in 2--3 Myr at 5 AU around solar-mass stars, provided that the surface density of solids is enhanced over that of the minimum-mass solar nebula (by a factor of a few). Working within the core-accretion paradigm, this paper presents theoretical calculations which show that the formation of Jupiter-mass planets orbiting M dwarf stars is seriously inhibited at all radial locations (in sharp contrast to solar-type stars). Planet detection programs sensitive to companions of M dwarfs will test this prediction in the near future.Comment: 10 pages including 2 figures; accepted to ApJ Letter

Recent Simulations of the Late Stages Growth of Jupiter

Presented by Lissauer et al. (2009, Icarus 199, 338) are used to test the model of capture of Jupiter's irregular satellites within proto-Jupiter's distended and thermally-supported envelope. We find such capture highly unlikely, since the envelope shrinks too slowly for a large number of moons to be retained, and many of those that would be retained would orbit closer to the planet than do the observed Jovian irregulars. Our calculations do not address (and therefore do not exclude) the possibility that the irregular satellites were captured as a result of gas drag within a circumjovian disk. Support for this research from NASA Outer Planets Research Program is gratefully acknowledged

Protostellar disks and the primitive solar nebula

The objective is to obtain quantitative information on the turbulent transport of mass, angular momentum, and energy under the conditions that characterize the solar nebula, by direct numerical calculations. These calculations were made possible by research conducted on supercomputers (Cray XMP and Cray 2) by the Ames Computational Fluid Dynamics Branch. Techniques were developed that permitted the accurate representation of turbulent flows over the full range of important eddy sizes. So far, these techniques were applied (and verified) primarily in mundane laboratory situations, but they have a strong potential for astrophysical applications. A sequence of numerical experiments were conducted to evaluate the Reynold's stress tensor, turbulent heat transfer rate, turbulent dissipation rate, and turbulent kinetic energy spectrum, as functions of position, for conditions relevant to the solar nebula. Emphasis is placed on the variation of these properties with appropriate nondimensional quantities, so that relations can be derived that will be useful for disk modeling under a variety of hypotheses and initial conditions

The opacity of grains in protoplanetary atmospheres

We have computed the size distribution of silicate grains in the outer radiative region of the envelope of a protoplanet evolving according to the scenario of Pollack et al. (1996). Our computation includes grain growth due to Brownian motion and overtake of smaller grains by larger ones. We also include the input of new grains due to the breakup of planetesimals in the atmosphere. We follow the procedure of Podolak (2003), but have speeded it up significantly. This allows us to test the sensitivity of the code to various parameters. We have also made a more careful estimate of the resulting grain opacity. We find that the grain opacity is of the order of $10^{-2}\ \mathrm{cm^2 g^{-1}}$throughout most of the outer radiative zone as Hubickyj et al. (2005) assumed for their low opacity case, but near the outer edge of the envelope, the opacity can increase to$\sim{1} \mathrm{cm^2 g^{-1}}$. We discuss the effect of this on the evolution of the models.Comment: 28 pages, 13 Figs., to be published in Icarus (accepted Sep. 2007

Oligarchic planetesimal accretion and giant planet formation II

The equation of state calculated by Saumon and collaborators has been adopted in most core-accretion simulations of giant-planet formation performed to date. Since some minor errors have been found in their original paper, we present revised simulations of giant-planet formation that considers a corrected equation of state. We employ the same code as Fortier and collaborators in repeating our previous simulations of the formation of Jupiter. Although the general conclusions of Fortier and collaborators remain valid, we obtain significantly lower core masses and shorter formation times in all cases considered. The minor errors in the previously published equation of state have been shown to affect directly the adiabatic gradient and the specific heat, causing an overestimation of both the core masses and formation times.Comment: 4 pages, 2 figures, Accepted for publication in Astronomy and Astrophysic

New Jupiter and Saturn formation models meet observations

The wealth of observational data about Jupiter and Saturn provides strong constraints to guide our understanding of the formation of giant planets. The size of the core and the total amount of heavy elements in the envelope have been derived from internal structure studies by Saumon & Guillot (2004). The atmospheric abundance of some volatile elements has been measured {\it in situ} by the {\it Galileo} probe (Mahaffy et al. 2000, Wong et al. 2004) or by remote sensing (Briggs & Sackett 1989, Kerola et al. 1997). In this Letter, we show that, by extending the standard core accretion formation scenario of giant planets by Pollack et al. (1996) to include migration and protoplanetary disk evolution, it is possible to account for all of these constraints in a self-consistent manner.Comment: Accepted in APjL. 2 color figure

Enhancement of the Accretion of Jupiters Core by a Voluminous Low-Mass Envelope

We present calculations of the early stages of the formation of Jupiter via core nucleated accretion and gas capture. The core begins as a seed body of about 350 kilometers in radius and orbits in a swarm of planetesimals whose initial radii range from 15 meters to 100 kilometers. We follow the evolution of the swarm by accounting for growth and fragmentation, viscous and gravitational stirring, and for drag-induced migration and velocity damping. Gas capture by the core substantially enhances the cross-section of the planet for accretion of small planetesimals. The dust opacity within the atmosphere surrounding the planetary core is computed self-consistently, accounting for coagulation and sedimentation of dust particles released in the envelope as passing planetesimals are ablated. The calculation is carried out at an orbital semi-major axis of 5.2 AU and an initial solids' surface density of 10/g/cm^2 at that distance. The results give a core mass of 7 Earth masses and an envelope mass of approximately 0.1 Earth mass after 500,000 years, at which point the envelope growth rate surpasses that of the core. The same calculation without the envelope gives a core mass of only 4 Earth masses

Giant planet formation: episodic impacts vs. gradual core growth

We describe the growth of gas giant planets in the core accretion scenario. The core growth is not modeled as a gradual accretion of planetesimals but as episodic impacts of large mass ratios, i.e. we study impacts of 0.02 - 1 Earth masses onto cores of 1-15 Earth masses. Such impacts could deliver the majority of solid matter in the giant impact regime. We focus on the thermal response of the envelope to the energy delivery. Previous studies have shown that sudden shut off of core accretion can dramatically speed up gas accretion. We therefore expect that giant impacts followed by periods of very low core accretion will result in a net increase in gas accretion rate. This study aims at modelling such a sequence of events and to understand the reaction of the envelope to giant impacts in more detail. To model this scenario, we spread the impact energy deposition over a time that is long compared to the sound crossing time, but very short compared to the Kelvin-Helmholtz time. The simulations are done in spherical symmetry and assume quasi-hydrostatic equilibrium. Results confirm what could be inferred from previous studies: gas can be accreted faster onto the core for the same net core growth speed while at the same time rapid gas accretion can occur for smaller cores -- significantly smaller than the usual critical core mass. Furthermore our simulations show, that significant mass fractions of the envelope can be ejected by such an impact

Theoretical Radii of Extrasolar Giant Planets: the Cases of TrES-4, XO-3b, and HAT-P-1b

To explain their observed radii, we present theoretical radius-age trajectories for the extrasolar giant planets (EGPs) TrES-4, XO-3b, and HAT-P-1b. We factor in variations in atmospheric opacity, the presence of an inner heavy-element core, and possible heating due to orbital tidal dissipation. A small, yet non-zero, degree of core heating is needed to explain the observed radius of TrES-4, unless its atmospheric opacity is significantly larger than a value equivalent to that at 10$\times$solar metallicity with equilibrium molecular abundances. This heating rate is reasonable, and corresponds for an energy dissipation parameter ($Q_p$) of $\sim10^{3.8}$ to an eccentricity of $\sim$0.01, assuming 3$\times$solar atmospheric opacity and a heavy-element core of $M_c = 30$ $M_{\oplus}$. For XO-3b, which has an observed orbital eccentricity of 0.26, we show that tidal heating needs to be taken into account to explain its observed radius. Furthermore, we reexamine the core mass needed for HAT-P-1b in light of new measurements and find that it now generally follows the correlation between stellar metallicity and core mass suggested recently. Given various core heating rates, theoretical grids and fitting formulae for a giant planet's equilibrium radius and equilibration timescale are provided for planet masses $M_p=$ 0.5, 1.0, and 1.5 $M_J$ with $a =$ 0.02-0.06 AU, orbiting a G2V star. When the equilibration timescale is much shorter than that of tidal heating variation, the ``effective age'' of the planet is shortened, resulting in evolutionary trajectories more like those of younger EGPs. Motivated by the work of \citet{jackson08a,jackson08b}, we suggest that this effect could indeed be important in better explaining some observed transit radii.Comment: 11 pages; references added; ApJ accepted versio