Mixing-length theory and the excitation of solar acoustic oscillations

Abstract

The stability of radial solar acoustic oscillations is studied using a time-dependent formulation of mixing-length theory. Though the radiation field is treated somewhat simplistically with the Eddington approximation, and we appreciate that any coupling of the pulsation to the radiation field is important, for the lower frequency radial modes that have been computed this should not produce too serious an error. Instead, we have concentrated upon treating the coupling with convection as accurately as is currently possible with generalized mixing-length theory in order to learn something about its pertinence. Our principal conclusion is that, according to this theory, solar radial acoustic oscillations are expected to be stable and generated by turbulence. Moreover, the theory predicts changes in mode frequency that may, in part, explain the discrepancy between solar observations and the adiabatic pulsation frequencies of theoretical models. We also compute the amplitudes of the modes using a theory of stochastic excitation. These are in good agreement with observed power spectra.