Non-Radial Oscillations of Slowly Rotating Polytropes
Abstract
The linearized equations for non-radial adiabatic oscillations of slowly rotating polytropes are studied for both stable and marginally stable states. For oscillations in the stable state, the eigenfrequencies are a continuous function of the parameter = (~ - F)/(m~)2, which measures the ratio of buoyant to gyroscopic forces; here T = 1 + 1/n, where n is the polytropic index, ~y is the ratio of the specific heats, w the non-dimensional angular velocity, and m determines the azimuthal dependence. The structures of these oscillations, which could be called gravitational gyroscopic waves, are determined from two coupled first-order partial differential equations. In the marginally stable state one finds the solutions to be oscillatory, thus indicating overstability; the parameter yi takes on discrete negative values which indicate the stabilizing influence of rotation
- Publication:
-
The Astrophysical Journal
- Pub Date:
- April 1968
- DOI:
- 10.1086/149543
- Bibcode:
- 1968ApJ...152..255D