Simulations of Gaseous Disc-Embedded Planet Interaction

The Paper

Authors: Graeme Lufkin, Tom Quinn, James Wadsley, Joachim Stadel, Fabio Governato

Abstract: We present three-dimensional self-gravitating smoothed-particle hydrodynamics (SPH) simulations of an isothermal gaseous disc interacting with an embedded planet. Discs of varying stability are simulated with planets ranging from 10 Earth-masses to 2 Jupiter-masses. The SPH technique provides the large dynamic range needed to accurately capture the large scale behavior of the disc as well as the small scale interaction of the planet with surrounding material. Most runs used 10^5 gas particles, giving us the spatial resolution required to observe the formation of planets. We find four regions in parameter space: low-mass planets undergo Type I migration; higher-mass planets can form a gap; the gravitational instability mode of planet formation in marginally stable discs can be triggered by embedded planets; discs that are completely unstable can fragment to form many planets. The disc stability is the most important factor in determing which interaction a system will exhibit. For the stable disc cases, our migration and accretion time-scales are shorter and scale differently than previously suggested.

You can get a copy here, either the high-quality MNRAS print version (4.2M PDF) or my typesetting colorized, linked PDF (1.2M) or gzipped PostScript (1M).

Status: Accepted to MNRAS, January 2004, Vol 347 pp. 421-429.

Errata: On the second page, Section 2: Initial Conditions: Density Profile, the expression given for the density is both confusing and incorrect. The correct expression (and that used in the simulations) gives only one normalization constant, and differs by a power of r. My typeset versions of the paper (available above) have been corrected; the MNRAS version contains the original, incorrect expression.

Figures

These figures are in png format.

• Figure 1, a map of parameter space
• Figure 2, mass of a planets opening a gap
• Figure 3, orbital radius of planets opening gaps
• Figure 4, a sequence of snapshots where a planet triggers further planet formation, colorized
• Figure 5, a sequence of snapshots from an unstable disc, colorized
• Figure 6, orbital radius of clumps in unstable disc
• Figure 7, mass of clumps in unstable disc
• Figure 8, surface density of discs for migration and gap formation runs

Movies

Triggered Instability

In this scenario we take a disc that is stable by itself, and embed a planet in it. Presumably the planet formed via some process that did not siginificantly disrupt the rest of the disc. If the planet is massive enough and in the right location, the spiral waves it generates can trigger the gravitional collapse of the gas into further planets.

• A 0.1 Solar-mass disc, with a 1 Jupiter-mass planet at 12.5 AU. The planet drives spiral waves in the disc. One of these waves drives the local density high enough that the region collapses. This happens several times, creating several additional planets.
  DivX 600x600 1.9M

Unstable Discs

Here the disc is susceptible to gravitational collapse with no external perturber (the numerical noise is sufficient). Portions of the disc fragment into collapsed objects that we identify as planets.

• A 0.2 Solar-mass disc. Initially the disc extends from 1 to 25 AU. Observe the interaction between clumps: mergers, disruption, ejection. The movie spans about 450 years. The color represents the density (log-scale).
  MPEG 640x480 9.2M
  DivX 640x480 7.8M
  DivX 600x600 11M

Go here for more movies, and information regarding video codecs.

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