Schedule Aug 3, 2000
R-Modes in Relativistic Stars
Nils Andersson (Univ Southampton, Math)
In this talk I describe recent progress into the study of r-modes and rotational ``hybrid'' modes of relativistic stars. It is shown that - as in Newtonian gravity - the spectrum of low-frequency rotational modes is highly sensitive to the stellar equation of state. If the star and its perturbations obey the same one-parameter equation of state (when there is no stratification in the star) there exist no pure r-modes at all - no modes whose limit, for a star with zero angular velocity, is an axial-parity perturbation. Rotating stars of this kind similarly have no pure g-modes, no modes whose spherical limit is a perturbation with polar parity and vanishing perturbed pressure and density. In spherical stars of this kind, the r-modes and g-modes form a degenerate zero-frequency subspace. Our results show that rotation splits the degeneracy to zeroth order in the star's angular velocity and the resulting modes are generically hybrids with both axial and polar parts. Non-stratified Newtonian stars retain a vestigial set of purely axial modes (those with l=m); however, for corresponding relativistic stars we show that these modes must also be replaced by axial-led hybrids. On the other hand, if the star is stratified (if the perturbed star obeys an equation of state that differs from that of the unperturbed star) the r-modes alone span the degenerate zero-frequency subspace of the spherical star. In Newtonian stars, this degeneracy is split only by the higher order rotational corrections. However, when relativistic effects are included the degeneracy is again broken at zeroth order. Finally, I discuss results for the first post-Newtonian corrections to the Newtonian r-modes for both stratified and non-stratified stars.

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