### Abstract

We investigate the properties of r-modes characterized by the regular eigenvalue problem in slowly rotating, relativistic polytropes. Our numerical results suggest that discrete r-mode solutions for the regular eigenvalue problem exist only for restricted polytropic models. In particular, the r-mode associated with l = m = 2, which is considered to be the most important for gravitational radiation-driven instability, does not have a discrete mode as a solution of the regular eigenvalue problem for polytropes with polytropic index N > 1.18, even in the post-Newtonian order. Furthermore, for an N = 1 polytrope, which is employed as a typical neutron star model, discrete r-mode solutions for the regular eigenvalue problem do not exist for stars whose relativistic factor M/R is larger than about 0.1, where M and R are stellar mass and stellar radius, respectively.

Original language | English |
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Pages (from-to) | 263-269 |

Number of pages | 7 |

Journal | Astrophysical Journal |

Volume | 558 |

Issue number | 1 PART 1 |

DOIs | |

Publication status | Published - 2001 Sep 1 |

### Keywords

- Relativity
- Stars: Neutron
- Stars: Oscillations
- Stars: Rotation

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Astrophysical Journal*,

*558*(1 PART 1), 263-269. https://doi.org/10.1086/322275