Convection Theory and Related Problems in Stellar Structure, Evolution, and Pulsational Stability II. Turbulent Convection and Pulsational Stability of Stars - Xiong, Da-run (Frontiers in Astronomy and Space Sciences, 2021)
Using our non-local and time-dependent theory of convection and a fixed set of convective parameters calibrated to the Sun, the linear non-adiabatic oscillations for evolutionary models with masses 1-20 M_⊙ are calculated. Almost all the classical instability strips can be reproduced. The excitation and damping mechanism of oscillations for low-temperature stars is studied in detail. Convective flux and turbulent viscosity are always damping mechanisms. The damping effect of the convective flux is inversely proportional to the frequency of the modes, so it plays an important role for stabilizing the low-order modes and defining the red edge of the instability strip. The damping effect of turbulent viscosity reaches its maximum at 3ωτ_c/16~1, where τ_c is the 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 red variables. The turbulent pressure is, in general, an excitation mechanism; it reaches maximum at 3ωτ_c/4~1, and plays an important role for excitation of red variables. The relative contributions of turbulent pressure, viscosity and convective flux for excitation and damping change with stellar parameters (M, L and Te) and with the radial order and spherical harmonic degree of the oscillation mode; therefore, the combined effect of convection is sometimes damping, and sometimes excitation of oscillations. For low-luminosity red giants, the low-order modes are pulsationally stable, while the intermediate- and high-order modes are unstable. These are the pulsations characteristic of the solar-like oscillators. Towards higher luminosity, the range of unstable modes shifts gradually towards lower order. All of the intermediate- and high-order modes become stable, and a few low-order modes are unstable for high-luminosity red giants. These are the pulsations characteristic of Mira-like variables. The low-order modes of most high- and intermediate-luminosity red giants are self-excited. Stochastic excitation is necessary only for the high-frequency modes of low-luminosity solar-like oscillators; their intermediate-frequency modes can be self-excited (Xiong, et al., 2018, 2013).