Radial and vertical angular momentum transport in protostellar discs

Angular momentum in protostellar discs can be transported either radially, through turbulence induced by the magnetorotational instability (MRI), or vertically, through the torque exerted by a large-scale magnetic field. We present a model of steady-state discs where these two mechanisms operate at the same radius and derive approximate criteria for their occurrence in an ambipolar diffusion dominated disc. We obtain "weak field" solutions-which we associate with the MRI channel modes in a stratified disc-and transform them into accretion solutions with predominantly radial angular-momentum transport by implementing a turbulent-stress prescription based on published results of numerical simulations. We also analyze "intermediate field strength" solutions in which both radial and vertical transport operate at the same radial location. Our results suggest, however, that this overlap is unlikely to occur in real discs.