arXiv subjects

Willy Kley

Publications and source records attributed to Willy Kley.

25 records · Page 2Linked to original sources

arXiv1999

On the migration of a system of protoplanets

The evolution of a system consisting of a protoplanetary disc with two embedded Jupiter sized planets is studied numerically. The disc is assumed to be flat and non-self gravitating, which is modeled by the planar (two-dimensional) Navier-Stokes equations. The mutual gravitational interaction of the planets and the star, and the gravitational torques of the disc acting on the planets and the central star are included. The planets have an initial mass of one Jupiter mass $M_{Jup}$ each and the radial distances from the star are one and two semi-major axis of Jupiter, respectively. During the evolution both planets increase their mass due to accretion of gas from the disc; after about 2500 orbital periods of the inner planet it has reached a mass of 2.3 and the outer planet of 3.2~$M_{Jup}$. The net gravitational torques exerted by the disc on the planets result in an inward migration of the outer planet on time-scales comparable to the viscous evolution time of the disc, while the semi-major axis of the inner planet remains constant. When the distance of close approach eventually becomes smaller than their mutual Hill radius the eccentricities increase strongly and the system may turn unstable. The implications for the origin of the solar system and the extrasolar planets are discussed.

astro-ph↗

arXiv1999

The Migration and Growth of Protoplanets in Protostellar Discs

We investigate the gravitational interaction of a Jovian mass protoplanet with a gaseous disc with aspect ratio and kinematic viscosity expected for the protoplanetary disc from which it formed. Different disc surface density distributions have been investigated. We focus on the tidal interaction with the disc with the consequent gap formation and orbital migration of the protoplanet. Nonlinear hydrodynamic simulations are employed using three independent numerical codes. A principal result is that the direction of the orbital migration is always inwards and such that the protoplanet reaches the central star in a near circular orbit after a characteristic viscous time scale of approximately 10,000 initial orbital periods. This was found to be independent of whether the protoplanet was allowed to accrete mass or not. Inward migration is helped through the disappearance of the inner disc, and therefore the positive torque it would exert, because of accretion onto the central star.Our results indicate that a realistic upper limit for the masses of closely orbiting giant planets is approximately 5 Jupiter masses, because of the reduced accretion rates obtained for planets of increasing mass. Assuming some process such as termination of the inner disc through a magnetospheric cavity stops the migration, the range of masses estimated for a number of close orbiting giant planets (Marcy, Cochran, & Mayor 1999; Marcy & Butler 1998) as well as their inward orbital migration can be accounted for by consideration of disc--protoplanet interactions during the late stages of giant planet formation. Maximally accreting protoplanets reached about four Jovian masses on reaching the neighbourhood of the central star.

astro-ph↗

arXiv1999

The tidal interaction between planets and the protoplanetary disk

The discovery of now about 20 extrasolar planets orbiting solar-type stars with properties quite different from those in our Solar System has raised many questions about the formation and evolution of planets. The tidal interaction between the planet and the surrounding disk determines the orbital properties and the mass of the planet. We have performed numerical computations of a planet embedded in a protoplanetary disk and found that for typical values of the viscosity the planet may easily grow upto ten Jupiter masses. New results on the mass evolution and the migration of the planet are presented.

astro-ph↗

arXiv1998

Relativistic dust disks and the Wilson-Mathews approach

Treating problems in full general relativity is highly complex and frequently approximate methods are employed to simplify the solution. We present comparative solutions of a infinitesimally thin relativistic, stationary, rigidly rotating disk obtained using the full equations and the approximate approach suggested by Wilson & Mathews. We find that the Wilson-Mathews method has about the same accuracy as the first post-Newtonian approximation.

gr-qc↗

arXiv1998

Mass Flow and Accretion through gaps in Accretion Discs

We study the structure and dynamics of the gap created by a protoplanet in an accretion disc. The hydrodynamic equations for a flat, two-dimensional, non-selfgravitating protostellar accretion disc with an embedded, Jupiter sized protoplanet on a circular orbit are solved. To simulate possible accretion of mass onto the protoplanet we continually remove mass from the interior of the planet's Roche lobe which is monitored. Firstly, it is shown that consistent results independent on numerical issues (such as boundary or initial conditions, artificial viscosity or resolution) can be obtained. Then, a detailed parameter study delineates the influence of the disc viscosity and pressure on the magnitude of the accretion rate. We find that, even after the formation of a gap in the disc, the planet is still able to accrete more mass from the disc. This accretion occurs from regions of the disc which are radially exterior and interior to the planet's orbital radius. The rate depends on the magnitude of the viscosity and vertical thickness of the disc. For a disc viscosity alpha=10^{-3} and vertical thickness H/r=0.05 we estimate the time scale for the accumulation of one Jupiter mass to be of order hundred thousand years. For a larger(smaller) viscosity and disc thickness this accretion rate is increasing(decreasing). For a very small viscosity (alpha < 5 10^{-4}) the mass accretion rate through the gap onto the planet is markedly reduced, and the corresponding accretion time scale becomes larger than the viscous evolution time of the disc.

astro-ph↗

arXiv1998

On the treatment of the Coriolis force in computational astrophysics

In numerical computations of astrophysical flows one frequently has to deal with situations which require the use of a corotating coordinate system. Then, in addition to the centrifugal force, the Coriolis terms have to be included in the Navier-Stokes equations. In usual numerical treatments of solving the equations of motion these non-inertial forces are included explicitly as source terms. In this letter we show that this procedure, if applied to the angular momentum equation, may lead to erroneous results. Using the specific sample calculation of a protoplanet embedded in a protostellar disk, we then demonstrate that only a conservative treatment of the Coriolis term in the angular momentum equation yields results which are identical to those obtained by computations performed in the inertial frame.

astro-ph↗

arXiv1997

On relativistic discs and rings

Sequences of infinitesimally thin, uniformly rotating, self-gravitating relativistic discs with internal two-dimensional pressure have been constructed. It is shown that in weaker relativistic configurations the sequences undergo a continuous bifurcation from a disc to a ring structure, while in stronger relativistic cases the sequences terminate at the mass-shed limit where gravitational forces are exactly balanced by centrifugal forces.

astro-ph↗