Effects of Large-Scale Convection on p-Mode Frequencies

We describe an approach for finding the eigenfrequencies of solar acoustic modes (p-modes) in a convective envelope in the Wentzel-Kramers-Brillouin limit. This approximation restricts us to examining the effects of fluid motions that are large compared with the mode wavelength but allows us to treat the three-dimensional mode as a localized ray. The method of adiabatic switching is then used to investigate the frequency shifts resulting from simple perturbations to a polytropic model of the convection zone as well as from two basic models of a convective cell. We find that although solely depth-dependent perturbations can give frequency shifts that are first order in the strength of the perturbation, models of convective cells generate downward frequency shifts that are second order in the perturbation strength. These results may have implications for resolving the differences between eigenfrequencies derived from solar models and those found from helioseismic observations.