Stability of Rotating, Charged Fluids: Generalization of the Hoiland Conditions in Newtonian Non-conductive Case

Abstract

We study the conditions for stability of electrically charged, non-conductive 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, non-axisymmetric situation, and then we concentrate on the axisymmetric model in more detail. In the latter case we generalize the Høiland criterion of stability to non-vanishing 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 non-axisymmetric perturbations.

14 pages, 3 figures

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• Electrically charged matter in rigid rotation around magnetized black hole
• Off-equatorial orbits in strong gravitational fields near compact objects
• Charged tori in spherical gravitational and dipolar magnetic fields
• Lagrangian perturbation theory for rotating magnetic stars
• Charged fluids encircling compact objects: force representations and conformal geometries