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A New Criterion for Bar-Forming Instability in Rapidly Rotating Gaseous and Stellar Systems. I. Axisymmetric Form
Astrophysics · Submitted 7 Nov 1994
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that the new stability criterion holds equally well for all these previously published axisymmetric models.
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The abstract, sentence by sentence
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 (I) and bar modes. In the process, 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. The new stability parameter "alpha" is formulated first for uniformly rotating systems and is based on the angular momentum content rather than on the energy content of a system. For stability of stellar systems "alpha" = 0.254-0.258, while it is in the range of 0.341-0.354 for gaseous systems. For uniform rotation, one can write "alpha" as a function of the total (rotational) kinetic and gravitational energies, and of a parameter which is characteristic of the topology/connectedness and the geometric shape 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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 (I) and bar modes. | contribution 0.99 | 0.88 | 0.22 | asserted 0.99 |
| s1 | In the process, 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. | result 0.89 | 0.87 | 0.35 | asserted 1.00 |
| s2 | This difference is reflected also in the new stability criterion. | interpretation 0.89 | 0.63 | 0.09 | asserted 1.00 |
| s3 | The new stability parameter "alpha" is formulated first for uniformly rotating systems and is based on the angular momentum content rather than on the energy content of a system. | contribution 0.70 | 0.93 | 0.20 | asserted 1.00 |
| s4 | For stability of stellar systems "alpha" = 0.254-0.258, while it is in the range of 0.341-0.354 for gaseous systems. | result 1.00 | 0.83 | 0.25 | asserted 1.00 |
| s5 | For uniform rotation, one can write "alpha" as a function of the total (rotational) kinetic and gravitational energies, and of a parameter which is characteristic of the topology/connectedness and the geometric shape of a system. | method 0.79 | 0.84 | 0.07 | asserted 0.68 |
| s6 | "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. | method 0.67 | 0.84 | 0.08 | asserted 0.80 |
| s7 | We also estimate "alpha" for gaseous toroidal models and for stellar disk systems embedded in an inert or responsive "halo". | contribution 0.72 | 0.94 | 0.05 | asserted 0.91 |
| s8 | We find that the new stability criterion holds equally well for all these previously published axisymmetric models. | result 0.98 | 0.92 | 0.55 | asserted 1.00 |
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Original 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 (I) and bar modes. In the process, 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. The new stability parameter "alpha" is formulated first for uniformly rotating systems and is based on the angular momentum content rather than on the energy content of a system. For stability of stellar systems "alpha" = 0.254-0.258, while it is in the range of 0.341-0.354 for gaseous systems. For uniform rotation, one can write "alpha" as a function of the total (rotational) kinetic and gravitational energies, and of a parameter which is characteristic of the topology/connectedness and the geometric shape 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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This paper has been removed by arXiv admin because it was an erroneous duplicate of astro-ph/9411031.
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