Simulations of Giant Planet Migration in Gas Disks

The Paper

Authors: Graeme Lufkin and Tom Quinn

Abstract: We present the results of a suite of giant planet migration simulations using Smoothed Particle Hydrodynamics (SPH). These simulations take a disk model with an embedded planet and evolve the system for several dynamical times, measuring the rates of migration and accretion. The simulations are global, three-dimensional, include the self-gravify of the disk, have free boundary conditions, and do not prescribe a model for accretion onto the planet. These are the first simulations to include these features simultaneously. The suite covers variation in the initial planet and disk masses and numerical parameters. The disk mass varied from 0.005 to 0.09 Solar masses, and initial planet mass from 0.25 to 2 Jupiter masses. During the first few hundred years, most of the systems exhibited a constant rate of inward migration. A 1 Jupiter mass planet initially on a circular orbit at 5.2 AU in a 0.01 Solar mass disk moved inward at 10^-3 AU/yr. The dependence of migration rate on disk mass was linear, as predicted by the theory of type I migration. We found no dependence on planet mass, contrary to linear theory. This is because the disk response to the planet is non-linear. The process of accretion is a more complicated function of disk and planet mass, and can depend sensitively on numerical parameters.

You can get my typeset copy here (1.1M) or in gzipped Postscript (2.1M).

Note: This paper was originally a chapter in my thesis. It has been significantly edited; see the original for even more detail.

Figures

All figures are included in the paper, and are available here in independent high-resolution bitmap form as PNGs.

Figure 1, migration rate as a function of planet mass, in our standard disk
Figure 2, migration rate as a function of planet mass, in a disk similar to Nelson & Benz 2003
Figure 3, accretion rate as a function of planet mass, in our standard disk
Figure 4, accretion rate as a function of planet mass, in a disk similar to Nelson & Benz 2003
Figure 5, migration rate as a function of disk mass, in our standard disk
Figure 6, migration rate as a function of disk mass, similar to Nelson & Benz 2003
Figure 7, accretion rate as a function of disk mass, in our standard disk
Figure 8, accretion rate as a function of disk mass, similar to Nelson & Benz 2003
Figure 9, migration rate as a function of simulation resolution
Figure 10, accretion rate as a function of simulation resolution
Figure 11, accretion rate as a function of the softening length of the gas particles
Figure 12, accretion rate as a function of the softening length of planet particle
Figure 13, zero velocity curves in the restricted 3-body problem
Figure 14, particles that will soon become trapped as part of the planet
Figure 15, semi-major axis and mass of a planet as it forms a gap in the disk
Figure 16, successive surface density profiles as a planet forms a gap in the disk
Figure 17, a simulation snapshot of a planet in a gap

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