Turbulent Convection and pulsational Stability of Variable Stars I. Oscillations of Long-Period Variables

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Abstract
We have performed a linear pulsational stability survey of 6 series of long period variable models with M=1.0 Msun, L=3000 - 8000Lsun, and (X,Z)= (0.700,0.020),(0.735,0.005). The dynamic and thermodynamic couplings between convection and oscillations are treated by using a statistical theory of nonlocal and time-dependent convection. The results show that the fundamental and all the low overtones are always pulsationally unstable for the low temperature models when the coupling between convection and oscillations is ignored. When the coupling is considered, there is indeed a "Mira" pulsationally instability region outside of the Cepheid instability strip on the H-R diagram. The coolest models near the Hayashi track are pulsationally stable. Towards high temperature the fundamental mode first becomes unstable, and then the first overtone. Some one of the 2nd -4th overtone may become unstable for the hotter models. All the modes higher than 4th (n > 4) are pulsationally stable. The position and the width of such an instability region on the H-R diagram critically depends on the mass, luminosity and metal abundance of the star.

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