THE PHASE FUNCTION FOR STELLAR ACOUSTIC-OSCILLATIONS .1. THEORY

The influence of the upper layers of a star on p-mode frequencies can be described asymptotically by means of a phase function, which depends essentially only on the frequency of the mode. Here we investigate the extent to which the phase function may provide information about the superficial layers of a star. In particular, we derive a linear relation between the phase-function differences and differences in equilibrium structure of the upper layers of two models. We have tested this relation by comparing with a normal solar model two modified models: a chemically homogeneous model and a model with a modified treatment of the superadiabatic gradient in the convection zone. In both cases the linear relation is satisfied with reasonable precision. This allows us to separate the contributions from different layers near the surface of the star to the phase-function differences, and hence to the differences in the mode frequencies. In general a major contribution, which varies slowly with frequency, comes from the layers localized just beneath the photosphere; but the region around the second helium ionization zone may also make a significant contribution, which is characterized by a more rapid frequency dependence.