Resistive double-diffusive instability in the dead zones of protostellar discs

We outline a novel linear instability that may arise in the dead zones of protostellar discs, and possibly the fluid interiors of planets and protoplanets. In essence it is an axisymmetric buoyancy instability, but one that would not be present in a purely hydrodynamical gas. The necessary ingredients for growth include a negative radial entropy gradient ( of any magnitude), weak magnetic fields and efficient resistive diffusion ( in comparison with thermal diffusion). The character of the instability is local, axisymmetric and double-diffusive, and it attacks lengths much shorter than the resistive scale. Like the axisymmetric convective instability, it draws its energy from the negative radial entropy gradient, but by utilizing the diffusing magnetic field, it can negate the stabilizing influence of rotation. Its non-linear saturated state, while not transporting appreciable angular momentum, could drive radial and vertical mixing, which may influence the temperature structure of the disc, dust dynamics and, potentially, planet formation.