On the Oscillations and Stability of Rotating Stellar Models. I. Mathematical Techniques
Abstract
In this paper the secondorder virial equations are employed to analyze, in a first approximation, the stability of nonuniformly rotating, centrally condensed stellar models. The characteristic frequencies for the lowest seven modes (having a plane of symmetry) are calculated under the assumptions that the angular velocity at equilibrium depends only on the distance from the axis of rotation, that the dis placement is a linear function of the positional coordinate T, and that the perturbations are adiabatic. It is not assumed that the rotational effects are small in any part of the star. In the limit of zero rotation, six frequencies correspond to the lowest radial acoustic mode and the Kelvin modes belonging to the sec ondorder spherical harmonics. The seventh mode vanishes when rotation is absent. The acoustic mode, which is now coupled with the axisymmetric Kelvin mode, may become dynami cally unstable when the adiabatic exponent falls below a certain critical value. Also, there is one non axisymmetric Kelvin mode which becomes overstable, for sufficiently large values of the total angular momentum, at a point corresponding to the instability and possible fission of the classic Maclaurin spheroid. A procedure is outlined by which the various integral quantities, which are required by the stability analysis, can be conveniently calculated
 Publication:

The Astrophysical Journal
 Pub Date:
 November 1968
 DOI:
 10.1086/149784
 Bibcode:
 1968ApJ...154..613T