ALBERT

Description: 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.

Description: 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.

Description: 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.

Description: New numerical simulations of the formation of the giant planets are presented, in which for the first time both the gas and planetesimal accretion rates are calculated in a self-consistent, interactive fashion. The simulations combine three elements: 1) three-body accretion cross-sections of solids onto an isolated planetary embryo, 2) a stellar evolution code for the planet's gaseous envelope, and 3) a planetesimal dissolution code within the envelope, used to evaluate the planet's effective capture radius and the energy deposition profile of accreted material. Major assumptions include: The planet is embedded in a disk of gas and small planetesimals with locally uniform initial surface mass density, and planetesimals are not allowed to migrate into or out of the planet's feeding zone. All simulations are characterized by three major phases. During the first phase, the planet's mass consists primarily of solid material. The planetesimal accretion rate, which dominates that of gas, rapidly increases owing to runaway accretion, then decreases as the planet's feeding zone is depleted. During the second phase, both solid and gas accretion rates are small and nearly independent of time. The third phase, marked by runaway gas accretion, starts when the solid and gas masses are about equal. It is engendered by a strong positive feedback on the gas accretion rates, driven by the rapid contraction of the gaseous envelope and the rapid expansion of the outer boundary, which depends on the planet's total mass. The overall evolutionary time scale is generally determined by the length of the second phase. The actual rates at which the giant planets accreted small planetesimals is probably intermediate between the constant rates assumed in most previous studies and the highly variable rates that we have used. Within the context, of the adopted model of planetesimal accretion, the joint constraints of the time scale for dissipation of the solar nebula and the current high-Z masses of the giant planets lead to estimates of the initial surface density (sigma(sub init)) of planetesimals in the outer region of the solar nebula. The results show sigma(sub init) approx. = 10 g/sq cm near Jupiter's orbit and that sigma(sub init) proportional to alpha(sup -2), where alpha is the distance from the Sun. These values are a factor of 3 - 4 times as high as that of the "minimum mass" solar nebula at Jupiter's distance and a factor of 2 - 3 times as high it Saturn's distance. Our estimates for the formation time of Jupiter and Saturn are 1 - 10 million years while those for Uranus fall in the range of 2 - 16 million years. These estimates follow from the properties of our Solar System and do not necessarily apply to giant planets in other planetary systems.

Description: This project investigates the origin of giant planets, both in the Solar System and around other stars. It is assumed that the planets form by the core accretion process: small solid particles in a disk surrounding a young star gradually coagulate into objects of a few kilometers in size, known as planetesimals, which then accumulate into solid protoplanetary cores. Once the cores have become large enough, they are able to attract gas from the surrounding disk to form the deep gaseous envelope of the giant planet. Our code simulates giant planet growth in a spherical approximation, and it has been quite successful in addressing a number of basic planetary properties. Further improvements to the code have been made to achieve a more realistic understanding of planetary formation. The computations of the models were based on an earlier version of our code and were stopped at the onset of runaway gas accretion. Now, improved boundary conditions have been incorporated into the code to allow for hydrodynamic inflow of gas and to handle the late stages of evolution when the planet evolves at constant mass. These changes were made to the version of the code that uses a constant accretion rate and to the version that uses a self-consistent method for calculating both the solid and gas accretion rates. The equation of state has been updated to incorporate the detailed tables of Saumon, Chabrier, and Van Horn. The opacities were updated to include the results of Alexander and Ferguson. The outer boundary conditions were modified. During the accretion phase when the planet's radius is between the accretion radius and the tidal radius, we set the outer boundary at a 'modified' accretion radius, which is the point where thermal energy is enough to bring gas to the edge of the Hill sphere.

Description: New theoretical models of stars pulsating in the first overtone have been constructed to simulate RR Lyr variables of Bailey type c. Despite the use of different opacities, these new models agree very well with earlier models built by Christy and Stellingwerf. Quantitative comparisons using empirical light curves and velocity curves of metal-poor type c variables confirm the validity of the models. Masses of 0.55-0.65 solar mass and luminosities of 40-50 solar luminosities derived here for the type c variables, are consistent with previous results obtained for type ab variables. A Christy echo of the kind normally associated with fundamental-mode pulsators was detected in the interior velocity structure of one first-overtone model that happens to have a large velocity amplitude.