### 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 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.

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

Title of host publication | Proceedings of the 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006 |

Pages | 86-89 |

Number of pages | 4 |

Publication status | Published - 2006 |

Externally published | Yes |

Event | 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006 - Niigata Duration: 2006 Nov 27 → 2006 Dec 1 |

### Other

Other | 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006 |
---|---|

City | Niigata |

Period | 06/11/27 → 06/12/1 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Proceedings of the 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006*(pp. 86-89)

**Secular bar mode instabilities in rotating relativistic stars.** / Saijo, Motoyuki; Gourgoulhon, Eric.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Proceedings of the 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006.*pp. 86-89, 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006, Niigata, 06/11/27.

}

TY - CHAP

T1 - Secular bar mode instabilities 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 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.

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 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.

UR - http://www.scopus.com/inward/record.url?scp=84887348430&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887348430&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:84887348430

SP - 86

EP - 89

BT - Proceedings of the 16th Workshop on General Relativity and Gravitation in Japan, JGRG 2006

ER -