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 30AU and 100AU in a minimum mass solar nebula ( MMSN ) disk model , which consists of a far-UV-ionized surface layer and low-ionization disk interior .
These simulations serve as a follow up to ( 46 ) , 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 \beta _ { 0 } , the ratio of gas to magnetic pressure at the disk mid-plane ) of \beta _ { 0 } = 10 ^ { 4 } and \beta _ { 0 } = 10 ^ { 5 } , we find accretion rates \dot { M } \sim 10 ^ { -8 } – 10 ^ { -7 } M _ { \sun } / { yr } .
These accretion rates agree with observational constraints , suggesting a vertical magnetic field strength of \sim 60 –200 \mu G and 10–30 \mu G 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 .