Meta-stability in galactic discs

A major discrepancy between Toomre's theory of bar instabilities and recent N-body experiments is resolved. Toomre's prediction that bars ought to be inhibited by a low-mass but dense central bulge is shown to be correct for small amplitude perturbations but it is also demonstrated that such a model is merely meta-stable and will form a bar when subject to a large enough initial perturbation. Density fluctuations arising from tens of thousands of randomly distributed particles in N-body experiments are generally substantial enough to alter the predicted small amplitude behaviour drastically. The different behaviour at finite amplitude is largely attributable to saturation at inner Lindblad resonances.