On Necessary and Sufficient Global Stability Criteria for Axisymmetric Perturbations of the Stellar Dynamic Disk

摘要

Necessary and sufficient global stability criteria are obtained which govern the stellar‐dynamic stability to axisymmetric perturbations for disk models of galaxies. They are more complicated and difficult to apply than Toomre's criterion because they are global and allow general orbits of disk equilibria. If local and epicyclic assumptions are added, they then reduce to Toomre's criterion. But unlike the latter, in these new criteria, stability is determined by some average velocity dispersion rather than its local values, thus local variations in Toomre'sQparameter appears possible