The seismology of stellar cores: a simple theoretical description of the ‘small frequency separations’

We present a new theoretical description of the ‘small frequency separations’ |δωl,n = ωl,n - ωl+2,n-1| for high-frequency stellar p-modes of low degree, these separations being the observable quantities that are primarily sensitive to the structure of the deep stellar interior. The description is based on an integral representation of the phase shift of acoustic waves due to scattering off the stellar core, taking into account the effects of buoyancy and gravitational perturbations. The accuracy of the theoretical description is tested by comparing the predicted frequency separations with values determined by numerically solving the full set of eigenfrequency equations for a standard solar model and for simple zero-age and evolved models of a 3-M⊙ mass main-sequence star with a convective core.