Nonlinear Pulsations and Stability of Slowly Rotating Stars
Abstract
This paper deals with finiteamplitude oscillations of slowly rotating, slightly distorted stars. Lagrangian variables and the scalar virial theorem are employed to describe, in a first approximation, nonlinear adiabatic motions which, in the limit of zero rotation, are purely radial. The linear approximation predicts that the critical adiabatic exponent at which dynamical instability sets in, L, is reduced from by rotation; the present nonlinear theory shows that, for L stability depends crucially on the initial amount of kinetic energy available to maintain the pulsations. Actually, for L < , oscillatory motions exist only when the amplitudes remain less than a certain critical value; for larger initial velocities, a rotating star expands from its equilibrium state. In contrast to the usual linear prediction, such an expanding motion eventually becomes `uniform in time. Finally, irrespective of initial velocities, all nonlinear pulsations are stable when > 2, and monotonically increase with time when __ W L.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 1970
 DOI:
 10.1086/150490
 Bibcode:
 1970ApJ...160.1031T