### Abstract

We investigate the viscosity driven instability in rotating relativistic stars by means of an iterative approach. We focus on polytropic rotating equilibrium stars and impose a m=2 perturbation in the lapse. We vary both the stiffness of the equation of state and the compactness of the star to study those effects on the value of the threshold. For a uniformly rotating star, the criterion T/W, where T is the rotational kinetic energy and W is the gravitational binding energy, mainly depends on the compactness of the star and takes values around 0.13-0.16, which differ slightly 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. This is significantly larger than the uniformly rotating case with the same compactness of the star. Finally we discuss a possibility of detecting gravitational waves from viscosity driven instability with ground-based interferometers.

Original language | English |
---|---|

Article number | 084006 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 74 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2006 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*74*(8), [084006]. https://doi.org/10.1103/PhysRevD.74.084006

**Viscosity driven instability in rotating relativistic stars.** / Saijo, Motoyuki; Gourgoulhon, Eric.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 74, no. 8, 084006. https://doi.org/10.1103/PhysRevD.74.084006

}

TY - JOUR

T1 - Viscosity driven instability in rotating relativistic stars

AU - Saijo, Motoyuki

AU - Gourgoulhon, Eric

PY - 2006

Y1 - 2006

N2 - We investigate the viscosity driven instability in rotating relativistic stars by means of an iterative approach. We focus on polytropic rotating equilibrium stars and impose a m=2 perturbation in the lapse. We vary both the stiffness of the equation of state and the compactness of the star to study those effects on the value of the threshold. For a uniformly rotating star, the criterion T/W, where T is the rotational kinetic energy and W is the gravitational binding energy, mainly depends on the compactness of the star and takes values around 0.13-0.16, which differ slightly 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. This is significantly larger than the uniformly rotating case with the same compactness of the star. Finally we discuss a possibility of detecting gravitational waves from viscosity driven instability with ground-based interferometers.

AB - We investigate the viscosity driven instability in rotating relativistic stars by means of an iterative approach. We focus on polytropic rotating equilibrium stars and impose a m=2 perturbation in the lapse. We vary both the stiffness of the equation of state and the compactness of the star to study those effects on the value of the threshold. For a uniformly rotating star, the criterion T/W, where T is the rotational kinetic energy and W is the gravitational binding energy, mainly depends on the compactness of the star and takes values around 0.13-0.16, which differ slightly 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. This is significantly larger than the uniformly rotating case with the same compactness of the star. Finally we discuss a possibility of detecting gravitational waves from viscosity driven instability with ground-based interferometers.

UR - http://www.scopus.com/inward/record.url?scp=33749459730&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749459730&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.74.084006

DO - 10.1103/PhysRevD.74.084006

M3 - Article

AN - SCOPUS:33749459730

VL - 74

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 8

M1 - 084006

ER -