Planetesimal and Protoplanet Dynamics in a Turbulent Protoplanetary Disk: Ideal Stratified Disks

Abstract: Due to the gravitational influence of density fluctuations driven by magneto-rotational instability in the gas disk, planetesimals and protoplanets undergo diffusive radial migration as well as changes in other orbital properties. The magnitude of the effect on particle orbits can have important consequences for planet formation scenarios. We use the local-shearing-box approximation to simulate an ideal, isothermal, magnetized gas disk with vertical density stratification and simultaneously evolve numerous massless particles moving under the gravitational field of the gas and the host star. We measure the evolution of the particle orbital properties, including mean radius, eccentricity, inclination, and velocity dispersion, and its dependence on the disk properties and the particle initial conditions. Although the results converge with resolution for fixed box dimensions, we find the response of the particles to the gravity of the turbulent gas correlates with the horizontal box size, up to 16 disk scale heights. This correlation indicates that caution should be exercised when interpreting local-shearing-box models involving gravitational physics of magneto-rotational turbulence. Based on heuristic arguments, nevertheless, the criterion L_h / R ~ O(1), where L_h is the horizontal box size and R is the distance to the host star, is proposed to possibly circumvent this conundrum. If this criterion holds, we can still conclude that magneto-rotational turbulence seems likely to be ineffective at driving either diffusive migration or collisional erosion under most circumstances.