Dynamical Evolution and Growth of Protoplanets Embedded in a Turbulent Gas Disk

Abstract

Simulations were performed to determine the effect of turbulence on protoplanets as they accrete inside of a planetary gas disk at the stage of planet formation that involves interactions between relatively large, similar sized bodies. The effect of turbulence was implemented into an existing N-Body code using a parameterization of magnetohydrodynamic (MHD) turbulence performed by Laughlin et. al. (2004). The investigation focussed on the effect of turbulent perturbations on planetary dynamics and accretion at various locations in the disk, particularly at large semimajor axis. At these distances, protoplanet collisions are generally less frequent due to the large induced eccentricities from close encounters and due to the trapping of protoplanets in mutual resonances. It is, however, essential that large protoplanets develop at these distances since some must eventually grow large enough to accrete the massive gas envelopes indicative of the giant planets.

The interaction between a protoplanet and the surrounding gas disk creates a torque imbalance acting on the protoplanet, which is generally believed to result in the rapid inward spiraling of the protoplanet. In order to create a fixed region in the disk within which protoplanets may interact without migrating into the central star, two scenarios were considered that would inhibit the inward migration of the protoplanets. The first scenario involved a gas disk that had been truncated at the inner edge, referred to as a planet trap, and the second involved the existence of a stationary giant planet within a gap in the disk, referred to as a planet barrier. Each scenario was tested using different density profiles of the gas disk, different numbers and masses of initial protoplanets, various rates of gas disk decay and also four different levels of turbulence intensities.

The results demonstrated that the addition of turbulence to the gas disk promotes planet mixing and results in an increased number of collisions between planets, even at large heliocentric distances. A turbulent disk has the tendency to create a final system where the planets are, on average, larger than those produced in a non-turbulent disk.