Physics
Scientific paper
Oct 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002phdt.........1r&link_type=abstract
PhD thesis, K.U.Leuven
Physics
Close Binaries, Oscillations, Analytical Methods
Scientific paper
The effects of the tidal force exerted by a companion on linear, isentropic oscillations of a uniformly rotating star that is a component of a circular-orbit close binary are studied. In contrast with earlier investigations, the procedure starts from an arbitrary physical model of a spherically symmetric equilibrium star. The tidal field and the nonspherical tidally perturbed star are determined by means of the theory of dynamic tides, in which the tides are treated as forced, linear, isentropic oscillations of a nonrotating spherically symmetric star. The equations governing linear, isentropic oscillations of a tidally perturbed star are established in the domain instantaneously occupied by the star and are transformed into equations defined in the domain of the spherically symmetric star, so that usual perturbation methods can be applied. They are derived for the general case in which the star's rotation is not necessarily synchronous with the orbital motion of the companion.
In the second part, a stellar component of a close binary that is rotating synchronously with the orbital motion of its companion is considered. By the introduction of the equilibrium tide, the degeneracy of the eigenvalue problem of the linear isentropic oscillations of a spherically symmetric equilibrium star is lifted partially, so that, for a mode of a degree l, the (2l+1)-fold eigenfrequency is split up into l+1 eigenfrequencies. A main result is that the eigenfrequencies of the modes belonging to a given degree l are split up according to the same pattern. Attention is also paid to the linear combinations of eigenfunctions that have to be adopted at order zero.
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