Turbulent convection and pulsational stability of variable stars: non-adiabatic oscillations of the solar p-modes

By using a non-local time-dependent theory of convection, the non-adiabatic oscillations of the radial p-modes of the Sun were calculated. The coupling between convection and oscillation and the influence of departure from radiative equilibrium on oscillations of p-modes were investigated in detail. The results of numerical calculations show that when the coupling between convection and oscillations is ignored, all the low-order radial p-modes with n less than or similar to 10 are pulsationally unstable and all the intermediate- and high-order (n greater than or similar to 11) radial p-modes are pulsationally stable. When the coupling between convection and oscillations is taken into consideration, only the intermediate-order p-modes with 11 n less than or similar to 23 are pulsationally unstable and all the low-order (n less than or similar to 10) and high-order (n greater than or similar to 24) p-modes are pulsationally stable. The behaviour of stability of the solar p-mode oscillations described above is the result of the joint action of radiation and convection on oscillations. In the interior of the convection zone, the thermodynamic coupling between convection and oscillations gives rise to damping of solar oscillations, but at the top of the convection zone, it causes excitation. The thermodynamic coupling between convection and oscillations plays a key role in the stabilization of low-frequency solar p-modes and also in the excitation of the intermediate-order solar p-mode oscillations with periods of about 5 min. The turbulent pressure generally causes excitation. The radiative damping in the outer atmosphere and the turbulent viscosity are the main damping mechanisms of the high-order (nu greater than or similar to 4000 mu Hz) solar p-modes. For the low-order p-mode oscillations with nu less than or similar to 1000 mu Hz, the departure from radiative equilibrium (DRE) does not have a significant effect. With the increase of frequency, the influence of the outer atmosphere and the DRE grows rapidly. The generalized Eddington approximations (GEA) developed by Unno & Spiegel and Mihalas are much better than the usual radiative diffusion approximation. Our conclusion is as follows: the coupling between convection and oscillations is an important excitation and damping mechanism for solar 5-min oscillations. However, it cannot be used to interpret all the observational characteristics of solar p-modes. There must be excitation and damping mechanisms other than the radiation and the 'regular' coupling between convection and oscillations.