Rossby wave instability in magnetized protoplanetary discs – I. Azimuthal or vertical B-fields

Rossby wave instability (RWI) is considered the underlying mechanism to crescent-shaped azimuthal asymmetries, discovered in (sub-)millimeter dust continuum of many protoplanetary discs. Previous works on linear theory were conducted in the hydrodynamic limit. Nevertheless, protoplanetary discs are likely magnetized and weakly ionized. We examine the influence of magnetic fields and non-ideal magnetohydrodynamic (MHD) effects – namely, Ohmic resistivity, Hall drift, and ambipolar diffusion – on the RWI unstable modes. We perform radially global linear analyses, employing constant azimuthal (B_φ) or vertical (Bz) background magnetic fields. It is found that, in the ideal MHD regime, magnetism can either enhance or diminish RWI growth. Strong non-ideal MHD effects cause RWI growth rates to recover hydrodynamic results. The sign of Hall Elsässer number slightly complicates the results. Vertical wavenumbers can diminish growth rates.