A new criterion for Bar-Forming Instability in Rapidly Rotating Gaseous and Stellar Systems. I. Axisymmetric Form

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  • 15 February 1995
Abstract
We analyze previous results on the stability of uniformly and differentially rotating, self-gravitating, gaseous and stellar, axisymmetric systems to derive a new stability criterion for the appearance of toroidal, m=2 Intermediate or I-modes and bar modes. We demonstrate that the bar modes in stellar systems and the m=2 I-modes in gaseous systems have many common physical characteristics and only one substantial difference: because of the anisotropy of the stress tensor, dynamical instability sets in at lower rotation in stellar systems. This difference is reflected also in the new stability criterion `alpha' which is formulated first for uniformly rotating systems and is based on the angular momentum content of a system. `Alpha' can be extended to and calculated for a variety of differentially rotating, gaseous and stellar, axisymmetric disk and spheroidal models whose equilibrium structures and stability characteristics are known. We also estimate `alpha' for gaseous toroidal models and for stellar disk systems embedded in an inert or responsive `halo.' We find that the new stability criterion holds equally well for all these previously published axisymmetric models.

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