Adiabatic pulsations and convective instability of uniformly rotating gaseous masses

Third-order virial equations are used to investigate the oscillations and the stability of the sequence of uniformly rotating compressible Maclaurin spheroids, referred to in an inertial frame. It is seen that in the case of the oscillations belonging to the third harmonics, the frequency spectrum of the Maclaurin sequence referred to in an inertial frame is distinct from the spectrum of the Maclaurin sequence considered stationary in a rotating frame of reference. Considering the Maclaurin sequence in an inertial frame, the neutral point and the point of onset of dynamical instability (corresponding to the third harmonic deformations) are isolated. They occur for the values of the eccentricitye=0.73113 and 0.96696, respectively. The neutral point is the analogue of the first point of bifurcation along the Dedekind sequence of ellipsoids and is distinct from the neutral point (e=0.89926) along the Maclaurin sequence considered stationary in a rotating frame; this latter point is the analogue of the first point of bifurcation along the Jacobian sequence. Both the Maclaurin sequences in an inertial frame and in a rotating frame become, however, dynamically unstable for the same eccentricitye=0.96696.