Amplitudes of low frequency modes in rotating B type stars

Abstract

Using weakly non-linear theory of oscillation, we estimate the amplitudes of low frequency modes in a slowly pulsating B (SPB) star, taking account of the effects of rotation on the modes. Applying the formulation by Schenk et al (2002), we compute 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, that is, 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.

14 pages, 6 figures, submitted to Monthly Notices of the Royal Astronomical Society

References in corpus (4)

• Kepler observations of variability in B-type stars
• MOST Detects g-Modes in the Late-Type be Star beta CMi (B8Ve)
• MOST detects SPBe pulsations in HD 127756 & HD 217543: Asteroseismic rotation rates independent of vsini
• Stability of g-modes in rotating B-type stars

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