Turbulence in outer protoplanetary disks: MRI or VSI?

Abstract: The outer protoplanetary disks (PPDs) can be subject to the magnetorotational instability (MRI) and the vertical shear instability (VSI). While both processes can drive turbulence in the disk, existing numerical simulations have studied them separately. In this paper, we conduct global 3D non-ideal magnetohydrodynamic (MHD) simulations for outer PPDs with ambipolar diffusion and instantaneous cooling, and hence conductive to both instabilities. Given the range of ambipolar Els\"{a}sser numbers ($Am$) explored, it is found that the VSI turbulence dominates over the MRI when ambipolar diffusion is strong ($Am=0.1$); the VSI and MRI can co-exist for $Am=1$; and the VSI is overwhelmed by the MRI when ambipolar diffusion is weak ($Am=10$). Angular momentum transport process is primarily driven by MHD winds, while viscous accretion due to MRI and/or VSI turbulence makes a moderate contribution in most cases. Spontaneous magnetic flux concentration and formation of annular substructures remain robust in strong ambipolar diffusion dominated disks ($Am\leq1$) with the presence of the VSI. Ambipolar diffusion is the major contributor to the magnetic flux concentration phenomenon rather than advection.