Light and line profile variations due to r-mode pulsations with an application to the ZZ Ceti star G117-B15A

A general formulation is presented for the effects of r-mode nonradial pulsations on the light curves and line profiles of a slowly rotating star, given a pulsation model, and model atmospheres. It is shown that the temperature perturbation, the gravity perturbation, and the light variations are proportional to the spheroidal component of the displacement, while the velocity perturbation is proportional to the toroidal component. Therefore, when calculating the observable effects of r-mode pulsations, it is necessary to include both the toroidal and the spheroidal components of the displacement in the calculations. The formalism is applied to the ZZ Ceti star G117-B15A. The results indicate that the observed variations of G117-B15A are not caused by r-mode pulsations, but are consistent with g-mode pulsations.