### Abstract

We have developed a new numerical scheme to solve r-mode oscillations of rapidly rotating polytropic stars in Newtonian gravity. In this scheme, Euler perturbations of the density, three components of the velocity are treated as four unknown quantities together with the oscillation frequency. For the basic equations of oscillations, the compatibility equations are used instead of the linearized equations of motion. By using this scheme, we have solved the classical r-mode oscillations of rotational equilibrium sequences of polytropes with the polytropic indices N=0.5, 1.0, and 1.5 for m=2, 3, and 4 modes. Here m is the rank of the spherical harmonics Y_{l}^{m}. These results have been applied to investigate the evolution of uniformly rotating hot young neutron stars by considering the effect of gravitational radiation and viscosity. We have found that the maximum angular velocities of neutron stars are around 10-20% of the Keplerian angular velocity irrespective of the softness of matter. This confirms the results obtained from the analysis of r-modes with the slow rotation approximation employed by many authors.

Original language | English |
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Article number | 084012 |

Pages (from-to) | 1-11 |

Number of pages | 11 |

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

Volume | 62 |

Issue number | 8 |

Publication status | Published - 2000 Oct 15 |

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

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

*62*(8), 1-11. [084012].