Orbital Eccentricity Growth of Giant Planets

The average orbital eccentricity of known extra-solar planets, most of which are gas giants, is between 0.2 and 0.3. Orbital eccentricity of giant planets may be excited through dynamical scattering due to the presence of other planetary bodies or through secular perturbations induced by a distant binary companion. However, these processes are likely to produce either very low or very high eccentric orbits. Therefore, other processes may be responsible for more typical eccentricities observed in extra-solar planets. It has been suggested that orbital eccentricity growth of Jupiter-mass planets may also occur through tidal interactions with the circumstellar disk from which the planet has formed. Yet, it is unclear to what extent and under what conditions this growth can be sustained. In order to gain some deeper insight into this process, high-resolution hydrodynamical simulations were carried out of a giant planet interacting with a viscous circumstellar disk. This study involved a range of planet masses from 1 to 3 Jupiter masses (MJ) and a range of initial orbital eccentricities from 0 to 0.4. Various disk conditions were also examined. It was found that gravitational interactions between a circumstellar disk and a planet lead to growth of the planet's orbital eccentricity. For a 2 MJ and a 3 MJ planet embedded in a disk with viscosity ≈ 1015 cm2 s-1, the orbital eccentricity increases from 0 to 0.1 within about 2500 orbits. Under the same disk conditions, the orbital eccentricity of a 1 MJ planet grows from 0 to 0.02 within about 3000 orbits. For a case of a 1 MJ planet with an initial eccentricity of 0.01, the orbital eccentricity grows to 0.09 over 4000 orbital periods. Disk viscosity plays an important role in orbital eccentricity growth, with larger growth rates obtained for lower viscosity levels. Orbital (i.e., radial) migration of giant planets is directed towards the star but the migration rate is also affected by orbital eccentricity. When a planet's orbit becomes eccentric, radial migration slows considerably. If a planet's orbital eccentricity becomes sufficiently large (~ 0.2), migration can reverse and therefore be directed outwards, i.e., away from the star.