Biology
Scientific paper
Dec 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010agufm.p31a1521d&link_type=abstract
American Geophysical Union, Fall Meeting 2010, abstract #P31A-1521
Biology
[5205] Planetary Sciences: Astrobiology / Formation Of Stars And Planets, [6296] Planetary Sciences: Solar System Objects / Extra-Solar Planets
Scientific paper
Most of the mass of a gaseous giant planet is acquired from the proto-planetary disk, in which the planet forms, during a phase of envelope collapse. Rapid contraction of the envelope begins when the mass of the envelope is of the same order of the solid core mass. During this phase, a giant planet accretes gas at a rate that is limited by whatever amount the disk can supply. This is a phase of hydrodynamical accretion, regulated by tidal interactions between the planet and the disk. The assumption of spherical symmetry that can be used to describe earlier stages of growth, when the solid core accumulates and the gaseous envelope is very tenuous, is no longer applicable. This phase of growth is best described by hydrodynamical calculations of a planet interacting with a disk. We have performed 3D high-resolution calculations of planets accreting gas at the limiting rate provided by a proto-planetary disk and derived a formula for the accretion rate of gas onto the planet. This formula may apply from the onset of rapid envelope contraction to the end of gas accretion, when the disk eventually dissipates. The mass accretion rate depends primarily on the planet-to-star mass ratio and on the unperturbed local mass and orbital frequency of the disk. We have considered cases with planet-to-star mass ratios up to 0.01. Tidal effects, such as density gap formation, tend to reduce the mass flux towards the planet. These effects increase in strength as turbulent viscosity and pressure scale-height of the disk decrease. Therefore, the accretion rate of a gas giant implicitly depends on disk viscosity and sound speed. These two quantities, however, are not well constrained by observations and are likely to vary over the disk lifetime. We have concentrated on disk models with a relative thickness H/r=0.05 and a viscosity characterized by α =0.004. We have integrated numerically the gas accretion rate formula over time to check whether there is a correlation between the final planet mass and the stellar mass. Since the solution requires the local unperturbed disk mass, we have used a simple approach whereby the evolution of the disk surface density is taken from available analytical solutions. In our integration procedure, the final mass of the planet depends on a number of parameters: 1) the planet mass at the onset of envelope collapse, 2) the time when envelope collapse begins, 3) the planet orbital radius, 4) the disk mass, 5) the accretion rate of the star, and 6) the disk dissipation (i.e., photo-evaporation) timescale. The values of these six parameters are constrained within chosen limits. We have performed hundred of thousands of integrations in each of which the six parameters are randomly selected from the parameter space. The procedure gives a distribution of planet masses for a given stellar mass. Although some or most of the six parameters may depend on the stellar mass, we have only assumed that the disk mass is proportional to the stellar mass, as observations suggest. We find that the planet mass at which distributions peak tend to increase with stellar mass. However, the impact of interdependencies among parameters and of dependencies on the stellar mass remains to be explored.
D'Angelo Gennaro
Lissauer Jack . J.
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