Evolution of Planetary Systems in Resonance
Wilhelm Kley, Jochen Peitz & Geoffrey Bryden
Astronomy & Astrophysics, 414, 735-747 (2004)
We study the time evolution of two protoplanets
still embedded in a protoplanetary disk.
The results of two different numerical approaches are presented and compared.
In the first approach, the motion of the disk material is computed with
viscous hydrodynamical simulations, and the planetary motion is
determined by N-body calculations including exactly the gravitational
forces exerted by the disk material.
In the second approach, only the N-body integration is performed
but with additional dissipative forces included such as to mimic
the effect of the disk torques acting on the disk.
This type of modeling is much faster than the full hydrodynamical
simulations, and gives comparative results provided that parameters
are adjusted properly.
Resonant capture of the planets is seen in both approaches, where
the order of the resonance depends on the properties of the disk
and the planets.
Resonant capture leads to a rise in the eccentricity and to an
alignment of the spatial orientation of orbits.
The numerical results are compared with the
observed planetary systems in mean motion resonance
(GJ 876, HD 82943, and 55 Cnc).
We find that the forcing together of two planets by their parent disk
produces resonant configurations similar to those observed,
but that eccentricity damping greater than that obtained
in our hydrodynamic simulations is required to match the
GJ 876 observations.
Reprint, January 2004
pdf-file (ca. 1.1 MB)