title: Magnetorotational instability in protoplanetary discs

authors: Mark Wardle

abstract: I examine the implications of Hall and ambipolar diffusion for the extent of MHD turbulence in protoplanetary discs.   I begin by describing magnetic field evolution in partially ionised gases, contrasting the limits of ambipolar diffusion, resistive MHD and hall drift, and then consider the stability of a weak, axisymmetric magnetic field with vertical and azimuthal components to axisymmetric perturbations.

The destabilising effects of Hall and ambipolar diffusion allow the magnetorotational instability to occur for much lower ionisation levels than would otherwise be possible.   I illustrate the critical effect of magnetic field-line drift on the extent of dead zones in protoplanetary discs by applying a local stability criterion to a simple model of the minimum-mass solar nebula at 1 au, including x-ray and cosmic-ray ionisation and a population of 1 micron grains.  Hall drift increases or decreases the MRI-active column density by an order of magnitude or more, depending on whether the vertical component of B is parallel or antiparallel to the rotation axis, respectively.   Although numerical simulations of MRI-driven turbulence suggest that the consequences for the saturated state are less significant than suggested by linear analysis, close inspection reveals that the simulations have yet to probe the Hall-dominated regime.  Existing estimates of the depth of magnetically active layers in protoplanetary discs may prove to be wildly inaccurate.