Turbulent Transport of Dust Particles in Protostellar Disks: The Effect of Upstream Diffusion

We study the long-term radial transport of micron to millimeter-size grains in protostellar disks (PSDs) based on diffusion and viscosity coefficients measured from 3D global stratified-disk simulations with a Lagrangian hydrodynamic method. While gas drag tends to transport dust species radially inwards, stochastic diffusion can spread a considerable fraction of dust radially outwards (upstream) depending on the nature of turbulence. In gravitationally unstable disks, we measure a high radial diffusion coefficient D_r ∼ H²Ω with little dependence on altitude. This leads to strong and vertically homogeneous upstream diffusion in early PSDs. In the solar nebula, the robust upstream diffusion of micron to millimeter-size grains not only efficiently transports highly refractory micron-size grains (such as those identified in the samples of comet 81P/Wild 2) from their regions of formation inside the snow line out to the Kuiper Belt, but can also spread millimeter-size calcium–aluminum-rich inclusions formed close to the Sun to distances where they can be assimilated into chondritic meteorites. In disks dominated by magnetorotational instability, the upstream diffusion effect is generally milder, with a separating feature due to diffusion being stronger in the surface layer than in the midplane. This variation becomes much more pronounced if we additionally consider a quiescent midplane with lower turbulence and larger characteristic dust size due to nonideal MHD effects. This segregation scenario helps to account for the dichotomy of the spatial distribution of two dust populations as observed in scattered light and Atacama Large Millimeter/submillimeter Array images.