### Abstract

We discuss the effects of rotation (spin) on a variety of the oscillation modes of a neutron star model which has both solid and fluid regions in the interior. Within the framework of Newtonian dynamics, we derive oscillation equations for wave propagation in the solid crust and fluid regions of the rotating neutron star. We include the Coriolis force and neglect both the centrifugal force and the rotational deformation of the star. Applying a perturbation technique to the oscillation equations, we calculate the first order rotational corrections to the eigenfrequency and eigenfunction for a variety of the oscillation modes. Using a different computational method, we generally confirm the previous results of Strohmayer (1991) for the first order rotational corrections. Because of the effects of rotation the spheroidal modes associated with l acquire toroidal components (associated with l′ = l ± 1) of the displacement at the first order in Ω. Similarly the toroidal modes associated with l in the solid crust acquire spheroidal components (associated with l′ = l ± 1) of the displacement, which generates the temperature and density variations associated with the oscillations. We solve the differential equations describing the oscillations in order to investigate some other aspects of the rotational effects which are not sufficiently described by the perturbation method. For example, we consider avoided crossings between several different oscillation modes. We show that avoided crossings between the f mode, p modes, shear s modes, and toroidal t modes are likely to occur since the f and low radial order p mode frequencies are interspersed with those of the high radial order s and t modes of the neutron star. We also calculate the r modes propagating in the surface fluid region above the solid crust. Although the r-mode oscillation periods observed in an inertial frame are essentially determined by the rotation period of the star, we show that the r mode associated with m = -1 and l = 1 is an exception to this rule.

Original language | English |
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Pages (from-to) | 155-171 |

Number of pages | 17 |

Journal | Astronomy and Astrophysics |

Volume | 311 |

Issue number | 1 |

Publication status | Published - 1996 Jul 1 |

### Keywords

- Oscillations
- Rotation
- Stars: neutron

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

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## Cite this

*Astronomy and Astrophysics*,

*311*(1), 155-171.