A method for integrating the equations that govern linear isentropic oscillations of an incompressible MacLaurin spheroid embedded in a spheroidal halo

Details A method for integrating the equations that govern linear isentropic oscillations of an incompressible MacLaurin spheroid embedded in a spheroidal halo A method for integrating the equations that govern linear isentropic oscillations of an incompressible MacLaurin spheroid embedded in a spheroidal halo

May 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986a%26a...160..385s&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 160, no. 2, May 1986, p. 385-391.

Astronomy and Astrophysics

Astrophysics

3

Astrophysics, Galactic Structure, Harmonic Oscillation, Oblate Spheroids, Eigenvalues, Halos, Kinematics, Linear Systems, Numerical Integration, Stellar Rotation, Vibration Mode

Scientific paper

A method is presented for the solution of the eigenvalue problem that governs linear isentropic oscillations of an incompressible MacLaurin spheroid embedded in a spheroidal halo by direct and analytical integration of a finite system of differential equations. The method is based on a combined use of spherical coordinates in the main body of the MacLaurin spheroid, where the equations are integrated from the center, and of oblatespheroidal coordinates at the surface, where the boundary conditions are imposed. It can be applied even for the derivation of higher-harmonic oscillations. The validity of the method is verified by determining the timedependent second-harmonic modes and by comparing the results with those derived by Chandrasekhar (1969) and Durisen (1978) with the tensor virial equation method. The second-harmonic modes that are commouly called toroidal modes appear to be purely poloidal modes. Furthermore, the connection is made with the modes found in the limiting case of the non-rotating, selfgravitating equilibrium sphere with the same uniform density in the absence of a halo.

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