Tidal Interaction between a Planet and a Three-dimensional Gas Disk

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Tidal interaction with the solar nebula is effective for orbital evolution of planetary embryos in planet formation process. In most of studies of disk-planet interaction, the gas disk was assumed infinitesimally thin. We studied the tidal interaction between a planet and a three-dimensional isothermal gas disk, and evaluated the evolution rates of the orbital elements (i.e., semimajor axis, eccentricity, and inclination) by linear calculation. In our three-dimensional calculation, the excited density wave is expanded in Fourier series for the φ -axis of the cylindrical coordinates and it is further expanded with Hermite polynomials for z-axis. Our result shows that the semimajor a, the eccentricity e, and the inclination i decrease due to the tidal interaction as well as the results of 2D calculation. For earth-mass planets at 1AU in the minimum mass nebula, the damping time-scales of a, e, and i are obtained as 1x105, 4x102, and 6x102 years, respectively. These damping time-scales are inversely proportional to the planet mass and the disk surface density. This damping due to tidal interaction is more effective than that due to frictional gas drag for planetary embryos lager than 1024g.

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