## Linear, isentropic oscillations of the compressible MacLaurin spheroids
Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Heverlee, Belgium
Smeyers' procedure (1986) for the determination of linear, isentropic oscillations of the incompressible MacLaurin spheroids is extended to the compressible MacLaurin spheroids. It is shown that the solutions can be constructed by a direct integration of a finite set of differential equations written in spherical coordinates. Oblate spheroidal coordinates are used with regard to the boundary conditions that must be satisfied at the surface of the MacLaurin spheroid. For compressible MacLaurin spheroids with eccentricities Next, four axisymmetric modes are determined that stem from the first radial overtone, the second-harmonic - and -mode, and the fourth-harmonic Kelvin mode in the non-rotating equilibrium sphere with uniform mass density. The -mode becomes dynamically stable at the eccentricity and again dynamically unstable at .
* Research Assistant, Belgian National Fund for Scientific Research ## Contents- 1. Introduction
- 2. Equilibrium configurations
- 3. Governing equations and boundary conditions
- 4. Separation of the angular variables
- 5. Transformation of the equations
- 6. Solution of the equations
- 7. Modes for
- 8. Modes for .
- References
© European Southern Observatory (ESO) 1997 Online publication: July 8, 1998 |