Resonant excitation of motion perpendicular to galactic planes

Resonant coupling between oscillations perpendicular to the equatorial plan of a galaxy and periodic changes in the force towards the Galactic Centre can cause stars to move far from the plane. The variation of the force to the Galactic Centre may be caused by a non-axisymmetric potential, but instability is possible even in the axisymmetric case. I discuss the circumstances under which these instabilities occur in highly flattened potentials and in nearly spherical systems. This work clarifies the restrictions one may place on the shapes of elliptical galaxies from observations of their nuclear discs. However, it appears that the most important instability is one experienced by stars that orbit at large radii in the disc of a galaxy which has a rotating central bar. Any barred galaxy will have an annulus of such stars. Complete analysis of the importance of this annulus requires that the theory of this paper be extended to include the disc's self-gravity. But the mechanism discussed here may help us understand (i) warps and corrugations in the gaseous discs of galaxies, (ii) the kinematics of stars in the solar neighbourhood, and (iii) the sharp edges possessed by many stellar discs.