Stability of rotating, charged fluids: Generalization of the Høiland conditions in Newtonian nonconductive case

We study the conditions for stability of electrically charged, nonconductive perfect fluid tori with respect to linear perturbations. To this end, we employ Lagrangian perturbation formalism, and we assume a system where the fluid orbits a central body. Gravitational field of the latter is described in the Newtonian framework. We first formulate the criteria valid for a general, nonaxisymmetric situation, and then we concentrate on the axisymmetric model in more detail. In the latter case, we generalize the H{}iland criterion of stability to a nonvanishing electric charge and classify special examples. Toroidal structures with constant angular momentum distribution are found to be linearly stable. Subsequently, like in the uncharged case, rotating charged fluids are found to be unstable with respect to nonaxisymmetric perturbations.