### Abstract

We study the r-modes propagating in steadily mass accreting, nuclear burning, and geometrically thin envelopes on the surface of rotating neutron stars. For the modal analysis, we construct envelope models that are fully radiative or have a convective region. We simply call the former radiative models and the latter convective models in this paper. As the angular rotation frequency Ω is increased, the oscillation frequency ω of the r-modes in the thin envelopes deviates appreciably from the asymptotic frequency ω = 2mΩ/l′(l′ + 1) defined in the limit of Ω → 0, where ω is the frequency observed in the corotating frame of the star, and m and l′ are the indices of the spherical harmonic function Y_{l′}^{m} representing the angular dependence of the modes. We find that the amplitudes of the fundamental r-modes with no radial nodes of the eigenfunctions are strongly confined to the equatorial region, and ω becomes only weakly dependent on Ω, gathering in a frequency range of ω/2π ≲ 10 Hz, at rapid rotation rates. We also find that the fundamental r-modes in the convective models are destabilized by strong nuclear burning in the convective region. Because of excessive heating by nuclear burning, the corotating-frame oscillation frequency ω of the r-modes in the convective models becomes larger, and hence the inertial-frame oscillation frequency |σ| becomes smaller than those of the corresponding r-modes in the radiative models, where σ = ω - mΩ is negative for the r-modes of positive m. We find that the relative frequency change f = -(σ_{conv} -σ_{rad})/σ_{rad} is always positive and becomes less than ∼0.01 for the fundamental r-modes of l′ > |m| + 1 at |sigma;_{rad}|/2π ∼ 300 Hz for m = 1 or at |σ_{rad}|/2π ∼ 600 Hz for m = 2, and that we need to consider the r-modes of l′ much larger than |m| for values of f as small as ∼0.001, where σ_{conv} and σ_{rad} denote the oscillation frequencies for the convective and the radiative envelope models, respectively.

Original language | English |
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Pages (from-to) | 914-926 |

Number of pages | 13 |

Journal | Astrophysical Journal |

Volume | 600 |

Issue number | 2 I |

DOIs | |

Publication status | Published - 2004 Jan 10 |

### Keywords

- Instabilities
- 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*,

*600*(2 I), 914-926. https://doi.org/10.1086/380122