Mode identification from combination frequency amplitudes in pulsating white dwarf stars

The lightcurves of variable DA and DB white dwarf stars are usually multiperiodic and non-sinusoidal, so that their Fourier transforms show peaks at eigenfrequencies of the pulsation modes and at sums and differences of these frequencies. These combination frequencies provide extra information about the pulsations, both physical and geometrical, that is lost unless they are analyzed. Several theories provide a context for this analysis by predicting combination frequency amplitudes. In these theories, the combination frequencies arise from nonlinear mixing of oscillation modes in the outer layers of the white dwarf, so their analysis cannot yield direct information on the global structure of the star as eigenmodes provide. However, their sensitivity to mode geometry does make them a useful tool for identifying the spherical degree of the modes that mix to produce them. In this dissertation, we analyze data from eight hot, low-amplitude DAV white dwarfs and measure the amplitudes of combination frequencies present. By comparing these amplitudes to the predictions of the theory of Goldreich and Wu, we have verified that the theory is crudely consistent with the measurements. We have also investigated to what extent the combination frequencies can be used to measure the spherical degree (ℓ) of the modes that produce them. We find that modes with ℓ > 2 are easily identifiable as high ℓ based on their combination frequencies alone. Distinguishing between ℓ = 1 and 2 is also possible using harmonics. These results will be useful for conducting seismological analyses of large ensembles of ZZ Ceti stars, such as those being discovered using the Sloan Digital Sky Survey. Because this method relies only on photometry at optical wavelengths, it can be applied to faint stars using 4 m class telescopes. We present new data from the 4.1 m Southern Astrophysical Research Telescope for the ZZ Ceti star L19-2. We use these data to determine the limits for application of this theory on data from a 4 m class telescope. We also analyze data for the hot, low-amplitude DBV EC 20058-5234 and demonstrate that the theory is applicable to both DAV and DBV white dwarf stars