Oscillations of the solar radial p - modes

We have calculated the radial non-adiabatic p-mode oscillations of the solar models. Based on a statistical theory of non-local convection, both the thermodynamic and kinetic couplings between convection and oscillations are finely treated. The turbulent pressure, turbulent viscosity, turbulent thermal flux and turbulent kinetic flux are all self-consistently included in the equations. The departure from the radiative equilibrium is treated exactly in the Eddington's approximation. The radiation field and gas are separately considered throughout, and they are coupled by the gaseous absorption and radiation. The generalized Mihalas' radiative hydrodynamic equations, and the dynamic equations of the auto-and the cross-correlations of the turbulent temperature and velocity fluctuations together form a set of self-consistent complete equations. It is shown by numeric calculation that all p-modes with n = 0 – 13 are pulsational unstable when the coupling between convection and oscillations was neglected, and the p-modes with n = 6 – 32 are unstable while that coupling was included. The thermodynamic coupling between convection and oscillations is the chief excitation mechanism, which occurs predominantly in the superadiabatic convection region. Turbulent pressure is always a destabilization factor. With increasing frequency, the turbulent viscosity increases more rapidly than the turbulent pressure does and becomes a dominate damping factor. The non-adiabatic effects on oscillation frequencies are not negligible, they caused a change of the frequencies up to several microhertzs. The departure from the radiative equilibrium has significant effects on stability of the solar p-modes. But these effects usually only alter the value of the stability coefficient but not its sign. The influence of the non-adiabatic effects and non-radiative equilibrium increases with increasing frequency of p-mode oscillations.