Numerical experiments on the oscillations of a rotating, axisymmetric galaxy

Modes of oscillation in six rotating, axisymmetric N-body systems are studied in a sequence of self-consistent, three-dimensional numerical experiments. The experimental systems are realizations of theoretical models of galaxies which are stellar-dynamical counterparts of uniformly rotating polytropes of index equal to 0.5. The ratio of the rotational kinetic energy to the gravitational potential energy ranges from 0.13 to 0.20. The systems oscillate axisymmetrically; the oscillations are interpreted as superpositions of a mode of radial pulsation and a Kelvin-like mode of oscillation. The experimental frequencies of these modes agree very well with theoretical predictions. When these modes are suppressed, the states of the experimental systems are very steady. The systems are dynamically unstable with respect to a toroidal mode when the ratio of the rotational kinetic energy to the gravitational potential energy exceeds a value lying between 0.16 and 0.17.