TUMBLING INSTABILITY IN SLOWLY ROTATING GALAXIES

We show that even modest amounts of rotation in a very wide class of stellar systems induces a tumbling instability. A weak bar-like perturbation is reinforced by the tipping of precessing orbital planes. As the amplitude of this tumbling bar grows, the orbital planes become trapped into libration. This picture is derived from the linear normal mode analysis, and we present a number of numerical experiments which agree with the predictions of linear theory and demonstrate the tipping and trapping of orbital planes. These experiments were performed for the three extremes of systems with predominantly radial orbits, predominantly circular orbits, and an isotropic velocity distribution. The introduction of a modest amount of rotational streaming destabilizes all these systems. The combination of trapped, librating orbits gives rise to a 'boxy' appearance on projection. Both the systems with predominantly radial orbits, and the isotropic systems have rotation curves verv similar to those observed in elliptical galaxies. The systems with predominantly circular orbits, however, produce 'solid body' rotation curves, as seen in 'boxy' bulges of disc galaxies. The observed correlation between 'boxy' bulges and early-type disc galaxies is compatible with this interpretation since a strong disc component may destroy the trapping of the orbital planes by the bar.