The equilibrium and the stability of the Jeans spheroids with toroidal magnetic fields

Abstract

We examine the effect of a toroidal magnetic field on the equilibrium and stability of homogeneous masses distorted by the tidal effects of a secondary (of mass M' at a distance R). It is shown that if the toroidal magnetic field is assumed to be axisymmetric about the direction of the line joining the centres of mass of the primary and the secondary, then the equilibrium configuration is a prolate spheroid. Also determined are the characteristic frequencies of the various modes of oscillations belonging to the second harmonics. It is found that the magnetic field shifts these frequencies to higher values than the ones which prevail in the absence of a magnetic field.