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Keywords:

  • instabilities;
  • stars: early-type;
  • stars: oscillations;
  • stars: rotation

ABSTRACT

Using the weakly non-linear theory of oscillation, we estimate the amplitudes of low-frequency modes in a slowly pulsating B star, taking account of the effects of rotation on the modes. Applying the formulation by Schenk et al., we compute the non-linear coupling coefficient between the low-frequency modes and estimate the equilibrium amplitudes of the modes excited in the star, assuming the amplitudes of the unstable modes are saturated as a result of non-linear coupling with stable modes, i.e. as a result of parametric instability expected between one unstable mode and two stable modes. We use the traditional approximation to calculate adiabatic and non-adiabatic oscillations in a rotating star. We find r-modes in a rapidly rotating star play a significant role in the amplitude determination through non-linear coupling. We also find that for low-m modes, the fractional amplitudes of the radiative luminosity caused by the low-frequency modes are of order 10−4 to 10−3 at the surface.