Non-adiabatic Oscillations of Red Giants
  Using our non-local time-dependent theory of convection, the linear non-adiabatic oscillations of 10 evolutionary model series with masses of 1--3M$_\odot$ are calculated. The results show that there is a red giant instability strip in the lower temperature side of the Hertzsprung-Russel (HR) diagram which goes along the sequences of the red giant branch (RGB) and the asymptotic giant branch (AGB). For red giants of lower luminosities, pulsation instability are found at high order overtones, the lower order modes from the fundamental to the second overtone are stable. Towards higher luminosity and lower effective temperature, instability moves to lower order modes, and the amplitude growth rate of oscillations also grows. At the high luminosity end of the strip, the fundamental and the first overtone become unstable, while all the modes above the 4th order become stable. The excitation mechanism have been sdudied in detail. It is found that turbulent pressure plays a key role for excitating of red variables. The frozen convecttin approximation is unavailaable for the low temperature stars with extended convective envelopes. In any case, this approximation can explain neither the red edge of the Cepheid instability strip, nor the blue edge of the pulsating red giant instability strip. An analytic expression of a pulsation constant as a function of stellar mass, luminosity and effective temperature is presented from this work. 
D. R. Xiong, L. Deng