We have performed linear pulsational stability analysis for a 1 Modot long period variable star, which is 5000 more luminous than the sun and has solar metal abundance (Z=0.02), within the effective temperature interval of 2400-3800K. Both of the dynamical and thermodynamic coupling between convection and oscillations is treated using a statistical theory of nonlocal and time-dependent convection. The results show that, the fundamental and all the low overtones are always pulsational unstable for the low temperature models when not considering the coupling between convection and pulsation; When convection and pulsation are coupled, there is indeed a limited sized low temperature "Mira" pulsational instability zone, just to the right of the Cepheid instability strip on the H-R diagram. The position and the width of such a instability zone on the H-R diagram depend on the mass, luminosity and metal abundance of the star in a very complex manner, the overall properties of the dependence are: 1). The zone becomes wider and moves to the lower effective temperature when the metal abundance increases; 2). For a model with solar mass and chemical abundance, L=5000Lodot, the size of the zone reaches its maximum. The dimension of the instability zone in temperature for the fundamental mode is 2400 <= T_e <= 3050K, first overtone 2600K <= T_e <= 3580K. The sizes of these "Mira" zones decrease when the luminosity vary towards both higher and lower directions, and may eventually disappear. 3). For the coolest models, the only pulsational unstable mode is the fundamental. For slightly higher temperature, linear instability for the fundamental mode and the first overtone will be established. For even higher temperatures, higher mode (2-4) may become linearly pulsational unstable. This possibly explains the observational fact for the long period variables that, the pulsation become gradually none-periodic from single mode when the effective temperature increases. For variables close to the red edge of the Cepheid instability strip, the thermodynamic coupling between convection and pulsation becomes dominant. For the red variables seated outside the instability strip, however, the dynamic coupling between convection and pulsation balances or may even overtake the thermodynamic coupling, therefore turbulent viscosity can no longer be omitted for the instability analysis of the low temperature red variables. The effect of turbulent viscosity becomes more and more important for higher mode, and may finally become the main damping mechanism against the pulsation.
New Eyes to See Inside the Sun and Stars
- Pub Date: