Astronomy and Astrophysics – Astrophysics
Scientific paper
Feb 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982a%26a...106..240w&link_type=abstract
Astronomy and Astrophysics, vol. 106, no. 2, Feb. 1982, p. 240-244.
Astronomy and Astrophysics
Astrophysics
16
Axisymmetric Flow, Dynamic Stability, Flow Stability, Hydrodynamics, Stellar Motions, Stellar Oscillations, Stellar Systems, Ellipsoids, Inhomogeneity, Virial Theorem
Scientific paper
In this paper the investigation of axisymmetric stellar systems with respect to the point of bifurcation and dynamical stability is pursued. Using the first variation of the second order virial equations a characteristic equation for the frequency of linear perturbations is developed, and it can be shown that a neutral mode of oscillation occurs at the point of bifurcation, which itself lies in a region of dynamical stability. Thus, as far as the co-existence of triaxial and axisymmetric shapes is concerned, there is a close analogy between hydrodynamical and stellar systems. Due to the anisotropy of the velocity distribution, however, a condition for dynamical stability different from the classical one is found. Finally, the general results are applied to a class of inhomogeneous ellipsoidal models.
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