Hall instability of thin weakly ionized stratified Keplerian disks

The stratification-driven Hall instability in a weakly ionized polytropic plasma is investigated in the local approximation within an equilibrium Keplerian disk of a small aspect ratio ε. The leading order of the asymptotic expansions in e is applied to both equilibrium and perturbation problems. The equilibrium disk with an embedded purely toroidal magnetic field is found to be stable to radial perturbations and unstable to vertical short-wave perturbations. The marginal stability surface was found in the space of the local Hall and inverse plasma- β parameters, as well as the free parameter of the model related to the total current. To estimate the minimal values of the equilibrium magnetic field that leads to the instability, it was constructed as a sum of a current free magnetic field and the simplest approximation for magnetic field created by the distributed electric current.