Thermomagnetic and magnetorotational instabilities of thin Keplerian discs in poloidal magnetic fields

Stability of thin hot Keplerian discs is investigated asymptotically in small disc's aspect ratio, ε. The study is carried out in the local approximation for short vertical waves in the disc-thickness scale. Besides the radial rotation shear and the vertical magnetic field, the background configuration is characterized by a vertically near-constant temperature profile with a small vertical gradient. The temperature-gradient term in Ohm's law, which characterizes the thermomagnetic transport is found to be of the order of ε. The effect of the thermomagnetic transport slightly modifies the conventional magnetorotational instability (MRI), while a new thermomagnetic instability (TMI) emerges in regions of the wavenumber space where MRI is absent. Explicit solutions are obtained for a wide range of values of plasma beta, β, and thermomagnetic transport coefficient, λ. In particular, it is shown for λ ≪ 1 that the MRI dominates in weak magnetic fields, β ≫ 1, while the TMI is exhibited in strong magnetic fields, β ∼ 1, also with the growth rate of the order of inverse rotation period.