On the stability of an accretion disc containing a toroidal magnetic field: The effect of resistivity

We extend a previous study of the global stability of a stratified differentially rotating disc containing a toroidal magnetic field to include the effect of a non-zero resistivity eta. We consider the situation when the disc is stable to convection in the absence of the magnetic field. The most robust buoyancy driven unstable modes, which occur when the field is strong enough, have low azimuthal mode number m. They grow exponentially, apparently belonging to a discrete spectrum. They exist for the dimensionless ratio eta/(H-2 Omega) smaller than similar to 10(-2), where Omega is the angular velocity and H is the disc semithickness. In contrast the magnetorotational modes develop arbitrarily small radial scale and show transient amplification as expected from a shearing sheet analysis. The most robust modes of this type are local in all directions. Because of their more global character, the buoyancy driven modes may be important for the generation of large-scale fields and outflows.