THE SEISMOLOGY OF STELLAR CORES - A SIMPLE THEORETICAL DESCRIPTION OFTHE SMALL FREQUENCY SEPARATIONS

We present a new theoretical description of the 'small frequency separ ations' deltaomega(l,n) = omega(l,n) - omega(l+2,n-1) for high-frequen cy stellar p-modes of low degree, these separations being the observab le quantities that are primarily sensitive to the structure of the dee p stellar interior. The description is based on an integral representa tion of the phase shift of acoustic waves due to scattering off the st ellar core, taking into account the effects of buoyancy and gravitatio nal perturbations. The accuracy of the theoretical description is test ed by comparing the predicted frequency separations with values determ ined by numerically solving the full set of eigenfrequency equations f or a standard solar model and for simple zero-age and evolved models o f a 3-M. main-sequence star with a convective core.