The equilibrium and bifurcation of rotating stellar systems

Mathematics

Scientific paper

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Astrodynamics, Equilibrium Equations, Galactic Rotation, Stellar Motions, Stellar Systems, Virial Theorem, Angular Velocity, Branching (Mathematics), Dynamic Stability, Potential Flow, Tensor Analysis

Scientific paper

Moment equations of stellar dynamics up to the third order are used to obtain the conditions of equilibrium in virial tensor form for uniformly rotating stellar systems with non-isotropic velocity dispersion. The dependence of the geometrical parameters on the angular velocity is determined by the ratio P(11)/P(33) of the velocity dispersions, and the upper limit for the point of bifurcation along the axisymmetric series is described. A series of non-axisymmetric (three-axial) equilibria is defined, although, due to the presence of the ratio P(11)/P(33) in the equations of equilibrium, it is not certain that the point of bifurcation can always be reached.

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