Instabilities in rotating relativistic stars driven by viscosity |
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| Authors: | Motoyuki Saijo Eric Gourgoulhon |
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| Institution: | (1) School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK;(2) Laboratoire de l’Univers et de ses Théories, UMR 8102 du CNRS, Observatoire de Paris, 92195 Meudon Cedex, France |
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| Abstract: | We investigate the instability driven by viscosity in rotating relativistic stars by means of an iterative approach. We focus
on polytropic rotating equilibrium stars and impose an m=2 perturbation in the lapse. We vary both the stiffness of the equation of state and the compactness of the star to study
these factors on the critical value T/W for the instability. For a rigidly rotating star, the criterion T/W, where T is the rotational kinetic energy and W the gravitational binding energy, mainly depends on the compactness of the star and takes values around 0.13–0.16, which
slightly differ from that of Newtonian incompressible stars (∼0.14). For differentially rotating stars, the critical value
of T/W is found to span the range 0.17–0.25. The value is significantly larger than in the rigidly rotating case with the same compactness
of the star. Finally we discuss the possibility of detecting gravitational waves from viscosity-driven instabilities using
ground-based interferometers.
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| Keywords: | Instabilities Stars: rotation Relativity Gravitational waves |
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