### 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.

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

Pages (from-to) | 481-485 |

Number of pages | 5 |

Journal | Astrophysics and Space Science |

Volume | 308 |

Issue number | 1-4 |

DOIs | |

Publication status | Published - 2007 Apr |

Externally published | Yes |

### Fingerprint

### Keywords

- Gravitational waves
- Instabilities
- Relativity
- Stars: rotation

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysics and Space Science*,

*308*(1-4), 481-485. https://doi.org/10.1007/s10509-007-9357-3

**Instabilities in rotating relativistic stars driven by viscosity.** / Saijo, Motoyuki; Gourgoulhon, Eric.

Research output: Contribution to journal › Article

*Astrophysics and Space Science*, vol. 308, no. 1-4, pp. 481-485. https://doi.org/10.1007/s10509-007-9357-3

}

TY - JOUR

T1 - Instabilities in rotating relativistic stars driven by viscosity

AU - Saijo, Motoyuki

AU - Gourgoulhon, Eric

PY - 2007/4

Y1 - 2007/4

N2 - 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.

AB - 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.

KW - Gravitational waves

KW - Instabilities

KW - Relativity

KW - Stars: rotation

UR - http://www.scopus.com/inward/record.url?scp=34248142176&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34248142176&partnerID=8YFLogxK

U2 - 10.1007/s10509-007-9357-3

DO - 10.1007/s10509-007-9357-3

M3 - Article

AN - SCOPUS:34248142176

VL - 308

SP - 481

EP - 485

JO - Astrophysics and Space Science

JF - Astrophysics and Space Science

SN - 0004-640X

IS - 1-4

ER -