The magnetorotational instability across the dead zone of protoplanetary disks

We examine the linear stability of a flow threaded by a weak, vertical magnetic field in a disk with a Keplerian rotation profile and a vertical stratification of the ionization degree as that predicted for vast portions of protoplanetary disks. A quasi-global analysis is carried out, in which the form of the perturbations in the vertical direction is determined. Considering the ohmic magnetic diffusivity of the gas, the conditions leading to the magnetorotational instability are analyzed as a function of the diffusivity at the disk surfaces, its vertical profile, and the strength of the unperturbed magnetic field. For typical conditions believed to prevail in protoplanetary disks at radial distances between 0.1 and 10 AU, where the so-called dead zone is proposed to exist, we find that generally the instability is damped. This implies that, if the MRI is considered the only possible source of turbulence in protoplanetary disks, no viscous angular momentum transport occurs at those radii.