Dust Transport in MRI Turbulent Disks: Ideal and Non-ideal MHD with Ambipolar Diffusion

Abstract

We study dust transport in turbulent protoplanetary disks using three-dimensional global unstratified magnetohydrodynamic (MHD) simulations including Lagrangian dust particles. The turbulence is driven by the magnetorotational instability (MRI) with either ideal or non-ideal MHD that includes ambipolar diffusion (AD). In ideal MHD simulations, the surface density evolution (except for dust that drifts fastest), turbulent diffusion, and vertical scale height of dust can all be reproduced by simple one-dimensoinal and/or analytical models. However, in AD dominated simulations which simulate protoplanetary disks beyond 10s of AU, the vertical scale height of dust is larger than previously predicted. To understand this anomaly in more detail, we carry out both unstratified and stratified local shearing box simulations with Lagrangian particles, and find that turbulence in AD dominated disks has very different properties (e.g., temporal autocorrelation functions and power spectra) than turbulence in ideal MHD disks, which leads to quite different particle diffusion efficiency. For example, MRI turbulence with AD has a longer correlation time for the vertical velocity, which causes significant vertical particle diffusion and large dust scale height. In ideal MHD the Schmidt numbers ($Sc$) for radial and vertical turbulent diffusion are $Sc_{r}\sim 1$ and $Sc_{z}\gtrsim 3$, but in the AD dominated regime both $Sc_{r}$ and $Sc_{z}$ are $\lesssim 1$. Particle concentration in pressure bumps induced by MRI turbulence has also been studied. Since non-ideal MHD effects dominate most regions in protoplanetary disks, our study suggests that modeling dust transport in turbulence driven by MRI with non-ideal MHD effects is important for understanding dust transport in realistic protoplanetary disks.