Scaling of oscillation frequencies in rotating stars

Abstract

We have studied oscillation frequencies of two-dimensional uniformly rotating zero-age main sequence stellar models in the delta Scuti mass range. We identified 370 p and g axisymmetric modes for non-rotating models and then traced their evolution as the rotational velocity was increased. For each mass we considered a rotation sequence of ten models, with the largest rotation rate being about 200 km s⁻¹. We constrained the models to have the same surface shape, which can be characterized for uniform rotation by the ratio between the polar and the equatorial radii. We find that scaling relationships exist among the oscillation frequencies calculated for models with the same shape. For p modes, this scaling closely follows the period root-mean-density relation found in spherical stars. The g modes also scale between models of the same shape, with the scaling reflecting the change in properties outside the convective core as the stellar mass increases. These scaling relationships can be particularly useful in finding specific stellar models to match the oscillation frequencies of individual stars.