Physics
Scientific paper
Aug 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000rmns.proge...1a&link_type=abstract
Presented at the KITP Miniprogram: R-Modes in Neutron Stars, Aug 3, 2000, Kavli Institute for Theoretical Physics, University of
Physics
Scientific paper
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 oflow-frequency rotational modes is highly sensitive to the stellar equation of state.If the starand its perturbations obey the same one-parameter equation of state(when there is no stratification in the star) there exist no pure r-modes atall - no modeswhose limit, for a star with zero angular velocity, is an axial-parityperturbation. Rotating stars of this kind similarly have no pureg-modes, no modes whose spherical limit is a perturbation with polarparity and vanishing perturbed pressure and density.In spherical stars of this kind, the r-modes and g-modes form adegenerate zero-frequency subspace. Our results show that rotation splits thedegeneracy to zeroth order in the star's angular velocityand the resulting modes are generically hybrids with both axial and polar parts.Non-stratified Newtonian stars retain a vestigial set of purelyaxial modes (those with l=m); however, for corresponding relativisticstars we show that these modes must also be replaced by axial-led hybrids.On the other hand, if the star is stratified (ifthe perturbed star obeys an equation of state that differs from that ofthe unperturbed star) the r-modes alone span the degenerate zero-frequencysubspace of the spherical star. In Newtonian stars, this degeneracy issplit only by the higher order rotational corrections. However, whenrelativistic effects are included the degeneracy is again broken at zerothorder.Finally, I discuss results for the first post-Newtonian corrections to theNewtonian r-modes for both stratified and non-stratified stars.
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