Statistics – Computation
Scientific paper
Jun 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003phdt..........d&link_type=abstract
Ph.D. Thesis, University of Tuebingen (186 pages)
Statistics
Computation
4
Accretion Disks, Hydrodynamics, Planetary Systems
Scientific paper
The aim of this thesis is the study the dynamical interactions occurring between a forming planet and its surrounding protostellar environment. This task is accomplished by means of both 2D and 3D numerical simulations.
The first part of this work concerned global simulations in 3D. These were intended to investigate large-scale effects caused by a Jupiter-size body still in the process of accreting matter from its surroundings. Simulations show that, despite a density gap forms along the orbital path, Jupiter-mass protoplanets still accrete at a rate on the order of 0.01 Earth's masses per year when they are embedded in a minimum-mass Solar nebula. In the same conditions, the migration time scale due to gravitational torques by the disk is around 100000 years.
The second part of the work was dedicated to perform 2D calculations, by employing a nested-grid technique. This method allows to carry out global simulations of planets orbiting in disks and, at the same time, to resolve in great detail the dynamics of the flow inside the Roche lobe of both massive and low-mass planets. Regardless of the planet mass, the high resolution supplied by the nested-grid technique permits an evaluation of the torques, resulting from short and very short range gravitational 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. Resulting migration time scales are in the range from 20000 years, for intermediate-mass planets, to 1000000 years, for very low-mass as well as high-mass planets. Circumplanetary disks form inside of the Roche lobe of Jupiter-size secondaries.
In order to evaluate the consequences of the flat geometry on the local flow structure around planets, 3D nested-grid simulations were carried out to investigate a range of planetary masses spanning from 1.5 Earth's masses to one Jupiter's mass. Outcomes show that migration rates are relatively constant when perturbing masses lie above approximately a 0.1 of the Jupiter's mass, as prescribed by Type II migration regime. In a range between 7 and 15 Earth's masses, it is found a dependency of the migration speed on the planetary mass that yields time scales considerably longer than those predicted by linear analytical theories. Type I migration regime is well reproduced outside of such mass interval. The growth time scale is minimum around 20 Earth-masses, but it rapidly increases for both smaller and larger mass values. With respect to accretion and migration rates, significant differences between 2D and 3D calculations are found in particular for objects with masses smaller than 10 Earth-masses.
The final part of this work was dedicated to the simulation of non-local isothermal (i.e., radiative) models, by restricting to 2D computations. Different temperature regimes are examined, according to the magnitude of the fluid's kinematic viscosity. The gap structure was found to depend on the viscosity regime, and only cold environments offer the right conditions for a wide and deep gap to be carved in. The temperature profile inside of proto-Jovian disks falls off as the inverse of the distance from the planet. As for migration and accretion, estimates are generally on the same order of magnitude as those acquired with the aid of local isothermal models. Since the gap is generally filled in the high-viscosity case, Type I migration regime might extend to larger planetary masses, thereby causing a reduction of migration rates.
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