Turbulent Convection and Pulsational Stability of Variable Stars. II. Oscillations of RR Lyrae and Horizontal Branch Red Variable Stars

Using a nonlocal time-dependent theory of convection, we have calculated the linear nonadiabatic oscillations of horizontal branch (HB) stars, carefully treating both the dynamic and thermodynamic coupling between convection and oscillations. Turbulent pressure and turbulent viscosity have been included consistently in our equations of nonadiabatic pulsation. When the coupling between convection and oscillations is ignored, for all models with Te ≤ 7350 K, the fundamental through the second overtone are pulsationally unstable, while for Te ≤ 6200 K all the models are unstable up to (at least) the 9th overtone. When the coupling between convection and oscillations is included, the RR Lyrae instability strip is very well predicted. Within the strip, most models are pulsationally unstable only for the fundamental and the first few low-order overtones. The turbulent viscosity is an important damping mechanism. Being exclusively distinct from the luminous red variables (long-period variables), the HB stars to the right of the RR strip are pulsationally stable for the fundamental and low-order overtones, but become unstable for some of the high-order overtones. This may provide a valuable clue to the short-period, low-amplitude red variables found outside the red edge of the RR strip on the H-R diagram of globular clusters. We also present a new radiation-modulated excitation mechanism functioning in a zone of radiation flux gradient. The effects of nonlocal convection and the dynamic coupling between convection and oscillations are discussed. The spatial oscillations of the thermal variables in the pulsational calculations have been effectively suppressed.