Solar seismology. I. The stability of the solar p-modes

We investigate the stability of the radial p-modes of the Sun by computing nonadiabatic eigen-values and e1genfunctions for a solar envelope model which extends from an inner radius r ≈ 0.3 R_☉ out to an optical depth r ≈ 3 x 10^(-4). Our calculations take into account in a crude fashion the response of the convective flux to the oscillation. The dynamical effect of turbulence in the convection zone is parametrized in terms of a turbulent shear viscosity. The results of our calculations are as follows. If damping by turbulent viscosity is neglected, all modes with penriods longer than 6 minutes are unstable. The familiar K-mechanism, which operates in the H ionization-H^- opacity region, is the dominant source of driving of the oscillations. Modes with periods shorter than 6 minutes are stabilized by radiative damping in the solar atmosphere. When turbulent dissipation of pulsational energy is included, all modes are predicted to be stable. However, the margin of stability is very small. In view of the large uncertainty that must be assigned to our estimate of turbulent damping, we conclude that theoretical calculations cannot unequivocally resolve the question of the stability of the solar p-modes.