### Abstract

Slowly pulsating B (SPB) stars are g-mode pulsators in main-sequence stages with mass ranging from M ∼ 3 to ∼8 M_{⊙}. In this paper, we examine pulsational stability of low-m r modes in SPB stars by calculating fully non-adiabatic oscillations of uniformly rotating stars, where m is an integer representing the azimuthal wavenumber around the rotation axis, r modes are rotationally induced, non-axisymmetric, oscillation modes, whose oscillation frequency strongly depends on the rotation frequency Ω of the star. They are conveniently classified by using two integer indices m and l' ≥ |m| that define the asymptotic oscillation frequency 2mΩ/[l'(l' + 1)] in the limit of Ω → 0. We confirm Savonije's and Townsend's finding that low-m, high-radial order, odd r modes with l' = m in SPB stars are excited by the same iron opacity bump mechanism that excites low-frequency g modes of the variables, when the rotation frequency Ω is sufficiently high. No even r modes with low m are found to be pulsationally unstable. Since the surface pattern of the temperature perturbation of odd modes is antisymmetric about the equator of the star, observed photometric amplitudes caused by the unstable odd r modes with l' = m are strongly dependent on the inclination angle between the axis of rotation and the line of sight. Applying the wave-meanflow interaction formalism to non-adiabatic r modes in rapidly rotating SPB models, we find that because of the rφ component of the Reynolds stress and the radial transport of the eddy fluctuation of density in the rotating star, the surface rotation is accelerated by the forcing due to the low l' = m unstable r modes. We suggest that the amount of angular momentum redistribution in the surface region of the stars can be comparable to that needed to sustain decretion discs found in Be systems. We make a brief comparison between non-adiabatic r-mode calculations done with and without the traditional approximation. In the traditional approximation, the local horizontal component of the rotation vector O is ignored in the momentum conservation equation, which makes it possible to represent the angular dependence of an oscillation mode using a single Hough function. We find that the oscillation frequencies of low-m r modes computed with and without the traditional approximation are qualitatively in good agreement. We also find that the pulsational instability of r modes in the traditional approximation appears weaker than that without the approximation.

Original language | English |
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Pages (from-to) | 677-687 |

Number of pages | 11 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 365 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 Jan 1 |

### Keywords

- Stars: oscillations
- Stars: rotation

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science