Vibrational stability of differentially rotating stars

The formal solution, in linear, nonadiabatic theory, has been obtained of the problem of the vibrational stability of a system possesing arbitrary, but steady, inviscid flows in its unperturbed (nonoscillating) state. The unperturbed system may have any geometry, but no large-scale magnetic fields are assumed. A special case is a (steadily) rotating star, where the rotation may be uniform or differential, slow or fast. This formulation may ultimately provide a new approach to the problem of the interaction (in linear theory) between stellar convection and pulsations. The formal solution is expressed in terms of certain integrals over the volume of the system. These integrals involve the nonadiabatic eigenfunctions for the oscillating system, but they may be approximated by suitable trial functions. This solution is surprisingly simple, bears considerable resemblance to previously derived formal solutions, and has a straightforward physical interpretation. (AIP)