Convection Theory and Related Problems in Stellar Structure, Evolution, and Pulsational Stability II. Turbulent Convection and Pulsational Stability of Stars
Authors: Xiong Da-run 
Published: March 2021

Using our non-local and time-dependent theory of convection and a fixed set of convective parameters (C1,  C2/C1 ,   C3)= (0.70,   0.50,   3.0) calibrated against the Sun, the linear non-adiabatic oscillations for evolutionary models with masses 1–20 M⊙ are calculated. The results show that almost all the classical instability strips can be reproduced. The theoretical instability strips of δ Scuti and γ Doradusvariables agree well with Kepler spacecraft observations. There is no essential difference in the excitation mechanism for δ Scuti and γ Doradus stars. They are excited by the combined effects of the radiative κ-mechanism and coupling between convection and oscillations. They represent two subgroups of a broader type of δ Scuti and  γ Doradus stars, located in the lower part of the Cepheid instability strip. δ Scuti is the p-mode subgroup and γ Doradus is the g-mode subgroup. The luminous variable red giants observed by MACHO and OGLE are low-order radial pulsators among low-mass red giant and asymptotic giant branch stars. The excitation and damping mechanism of oscillations for low-temperature stars is studied in detail. Convective flux and turbulent viscosity are consistent damping mechanisms. The damping effect of the convective enthalpy flux is inversely proportional to the frequency of the modes, so it plays an important role in stabilizing the low-order modes and defining the red edge of the Cepheid instability strip. The damping effect of turbulent viscosity reaches its maximum at 3ωτc/16∼1, where τc is the dynamic time scale of turbulent convection and ω is the angular frequency of the modes. Turbulent viscosity is the main damping mechanism for stabilizing the high-order modes of low-temperature variables. The turbulent pressure is, in general, an excitation mechanism; it reaches maximum at 3ωτc/4∼1, and it plays an important role for the excitation of red variables. Convection is not, in fact, a pure damping effect for stellar oscillations. The relative contributions of turbulent pressure, turbulent viscosity, and convective enthalpy flux for excitation and damping effects change with stellar parameters (mass, luminosity, effective temperature) and with the radial order and spherical harmonic degree of the oscillation mode; therefore, the combined effect of convection is sometimes damping, and sometimes the excitation of oscillations. Our research shows that, for low-luminosity red giants, the low-order modes are pulsationally stable, while the intermediate- and high-order modes are unstable. Toward higher luminosity, the range of unstable modes shifts gradually toward the lower order. All of the intermediate- and high-order modes become stable, and a few low-order modes become unstable for high-luminosity red giants. They show the typical pulsational characteristics of Mira-like variables. The variable red giants are, at least for the high-luminosity RGs, self-excited. For red giants, the frequency of the maximally unstable modes predicted by our theory is similar to that given by the semi-empirical scaling relation.