## Abstract

We investigate the properties of relativistic r-modes of slowly rotating neutron stars by using a relativistic version of the Cowling approximation. In our formalism, we take into account the influence of the Coriolis-like force on the stellar oscillations but ignore the effects of the centrifugal-like force. For three neutron star models, we calculate the fundamental r-modes with l′ = m = 2 and 3. We find that the oscillation frequency σ̄ of the fundamental r-mode is given in a good approximation by σ̄ K _{0}Ω, where σ̄ is defined in the corotating frame at spatial infinity and Ω is the angular frequency of rotation of the star. The proportional coefficient K_{0} is only weakly dependent on Ω, but it strongly depends on the relativistic parameter GM/c^{2}R, where M and R are the mass and the radius of the star. All the fundamental r-modes with l′ = m computed in this study are discrete modes with distinct regular eigen-functions, and they all fall in the continuous part of the frequency spectrum associated with Kojima's equation. These relativistic r-modes are obtained by including the effects of rotation higher than the first order of Ω so that the buoyant force plays a role, the situation of which is quite similar to that for Newtonian r-modes.

Original language | English |
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Pages (from-to) | 1112-1120 |

Number of pages | 9 |

Journal | Astrophysical Journal |

Volume | 567 |

Issue number | 2 I |

DOIs | |

Publication status | Published - 2002 Mar 10 |

## Keywords

- Instabilities
- Stars: neutron
- Stars: oscillations
- Stars: rotation

## ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science