Abstract Using a non-local and time-dependent theory of convection, we have calculated the linear non-adiabatic oscillations of the radial and low-degree F-p39 modes for evolutionary models from the main sequence to the asymptotic giant branch for stars with solar abundance (X = 0.70, Z = 0.02) in the mass range of 0.6–3.0 M⊙. The results show that low luminosity cool stars tend to be solar-like oscillators, whose low-order modes are stable, but intermediate and high order p-modes are pulsationally unstable; their unstable modes have a wide range in frequency and small values for amplitude growth rates. For stars with increasing luminosity and therefore lower temperature, the unstable modes shift towards lower orders, the corresponding range of frequency decreases, and the amplitude growth rate increases. High luminosity red giant stars behave like typical Mira-like oscillators. The effects of the coupling between convection and oscillations on pulsational instability have been carefully analyzed in this work. Our research shows that convection does not simply act as a damping mechanism for oscillations, and the complex nature of the coupling between convection and oscillations makes turbulent convection sometimes behave as damping, and sometimes as excitation. Such a picture can not only naturally account for the red edge of the instability strip, but also the solar-like oscillations in low luminosity red stars and Mira-like ones in high luminosity red giants.

Keywords convection — stars: oscillations — stars: late-type — stars: evolution

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