Oscillations and instabilities of fast and differentially rotating relativistic stars

Details Oscillations and instabilities of fast and differentially rotating relativistic stars Oscillations and instabilities of fast and differentially rotating relativistic stars

2009-11-14

arxiv.org/abs/0911.2764v2

Phys.Rev.D81:084019,2010

Astronomy and Astrophysics

Astrophysics

Solar and Stellar Astrophysics

16 pages, 11 figures; paper accepted for publication in Phys. Rev. D (81.084019)

Scientific paper

10.1103/PhysRevD.81.084019

We study non-axisymmetric oscillations of rapidly and differentially rotating relativistic stars in the Cowling approximation. Our equilibrium models are sequences of relativistic polytropes, where the differential rotation is described by the relativistic $j$-constant law. We show that a small degree of differential rotation raises the critical rotation value for which the quadrupolar f-mode becomes prone to the CFS instability, while the critical value of $T/|W|$ at the mass-shedding limit is raised even more. For softer equations of state these effects are even more pronounced. When increasing differential rotation further to a high degree, the neutral point of the CFS instability first reaches a local maximum and is lowered afterwards. For stars with a rather high compactness we find that for a high degree of differential rotation the absolute value of the critical $T/|W|$ is below the corresponding value for rigid rotation. We conclude that the parameter space where the CFS instability is able to drive the neutron star unstable is increased for a small degree of differential rotation and for a large degree at least in stars with a higher compactness.

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