Effects of differential rotation on stellar oscillations - A second-order theory

A complete formalism, valid through second order in differential rotation, is developed and applied to calculate the frequencies of stellar oscillations. The derivation is improved and the asymptotic formulas for g-mode splittings are generalized. In application to solar oscillations, it is found that the second-order effects are dominated by distortion for l less than 500. Further, these effects are sufficiently large that they must be accounted for in any effort to seismically determine the sun's internal magnetic field. In the solar oscillation spectrum, accidental degeneracies happen but cannot lead to large frequency shifts. For evolved delta Scuti stars, calculated spectra are dense, and, under the perturbing effect of rotation, members of neighboring multiplets may overlap. The seismic potential of modes of mixed p-mode and g-mode character is emphasized for these stars.