3.1 Quasi-Normal Modes of OscillationRotating Stars in Relativity2.5 Properties of Equilibrium Models

3 Oscillations and Stability

The study of oscillations of relativistic stars has the potential of yielding important information about both the bulk properties and the composition of the interior of the star, i.e. about the equation of state of matter at very high densities, in about the same way that helioseismology is providing us with information about the interior of the Sun. In a neutron star-accretion disk system, the star-disk interaction can drive oscillations, and one of the possible explanations for kHz quasi-periodic oscillations recently discovered in several X-ray sources is neutron star pulsations [74] (For an early proposal that such oscillations may be observable, see [75].).

Neutron star pulsations may be a detectable source of gravitational radiation. The pulsations can be excited after a core collapse or during the final stages of a neutron star binary system coalescence. Rapidly rotating neutron stars are unstable to the emission of detectable gravitational waves for a short time after their formation. The identification of gravitational waves produced by a neutron star can lead to the determination of its mass and radius and several such determinations can help reconstruct the equation of state of matter at very high energy densities [76].

The oscillations of relativistic stars are actually a non-linear phenomenon; their numerical computation would require a full 3-D relativistic hydrodynamics code, which is not yet available. However, apart from the initial oscillations following core collapse, the oscillations of an equilibrium star are of small magnitude compared to its radius; it will suffice to approximate them as linear perturbations. Such perturbations can be described in two equivalent ways. In the Lagrangian approach, one studies the changes in a given fluid element as it oscillates about its equilibrium position. In the Eulerian approach, one studies the change in fluid variables at a fixed point in space. Both approaches have their strengths and weaknesses.

In the Newtonian limit, the Lagrangian approach has been used to develop variational principles [77, 78Jump To The Next Citation Point In The Article], but the Eulerian approach proved to be more suitable for numerical computations of mode frequencies and eigenfunctions [79Jump To The Next Citation Point In The Article, 80Jump To The Next Citation Point In The Article, 81Jump To The Next Citation Point In The Article, 82Jump To The Next Citation Point In The Article, 83Jump To The Next Citation Point In The Article]. Clement [84] used the Lagrangian approach to obtain axisymmetric normal modes of rotating stars, while nonaxisymmetric solutions were obtained in the Lagrangian approach by Imamura et al. [85Jump To The Next Citation Point In The Article] and in the Eulerian approach by Managan [80Jump To The Next Citation Point In The Article] and Ipser and Lindblom [81Jump To The Next Citation Point In The Article].





3.1 Quasi-Normal Modes of OscillationRotating Stars in Relativity2.5 Properties of Equilibrium Models

image Rotating Stars in Relativity
Nikolaos Stergioulas
http://www.livingreviews.org/lrr-1998-8
© Max-Planck-Gesellschaft. ISSN 1433-8351
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