Turbulence in the Outer Regions of Protoplanetary Disks. Ii. Strong Accretion Driven by a Vertical Magnetic Field

We carry out a series of local, vertically stratified shearing box simulations of protoplanetary disks that include ambipolar diffusion and a net vertical magnetic field. The ambipolar diffusion profiles we employ correspond to 30 AU and 100 AU in a minimum mass solar nebula (MMSN) disk model, which consists of a far-ultraviolet-ionized surface layer and low-ionization disk interior. These simulations serve as a follow-up to Simon et al., in which we found that without a net vertical field, the turbulent stresses that result from the magnetorotational instability (MRI) are too weak to account for observed accretion rates. The simulations in this work show a very strong dependence of the accretion stresses on the strength of the background vertical field; as the field strength increases, the stress amplitude increases. For a net vertical field strength (quantified by β 0 , the ratio of gas to magnetic pressure at the disk mid-plane) of β 0 = 10 4 and β 0 = 10 5 , we find accretion rates –10 −7 M ☉ yr −1 . These accretion rates agree with observational constraints, suggesting a vertical magnetic field strength of ∼60–200 μG and 10–30 μG at 30 AU and 100 AU, respectively, in a MMSN disk. Furthermore, the stress has a non-negligible component due to a magnetic wind. For sufficiently strong vertical field strengths, MRI turbulence is quenched, and the flow becomes largely laminar, with accretion proceeding through large-scale correlations in the radial and toroidal field components as well as through the magnetic wind. In all simulations, the presence of a low-ionization region near the disk mid-plane, which we call the ambipolar damping zone, results in reduced stresses there.