Mode Identification from Combination Frequency Amplitudes in ZZ Ceti Stars

The lightcurves of variable DA stars are usually multi-periodic andnon-sinusoidal, so that their Fourier transforms show peaks at eigenfrequenciesof the pulsation modes and at sums and differences of these frequencies. Thesecombination frequencies provide extra information about the pulsations, bothphysical and geometrical, that is lost unless they are analyzed. Severaltheories provide a context for this analysis by predicting combinationfrequency amplitudes. In these theories, the combination frequencies arise fromnonlinear mixing of oscillation modes in the outer layers of the white dwarf,so their analysis cannot yield direct information on the global structure ofthe star as eigenmodes provide. However, their sensitivity to mode geometrydoes make them a useful tool for identifying the spherical degree of the modesthat mix to produce them. In this paper, we analyze data from eight hot,low-amplitude DAV white dwarfs and measure the amplitudes of combinationfrequencies present. By comparing these amplitudes to the predictions of thetheory of Goldreich & Wu, we have verified that the theory is crudelyconsistent with the measurements. We have also investigated to what extent thecombination frequencies can be used to measure the spherical degree (ell) ofthe modes that produce them. We find that modes with ell > 2 are easilyidentifiable as high ell based on their combination frequencies alone.Distinguishing between ell=1 and 2 is also possible using harmonics. Theseresults will be useful for conducting seismological analysis of large ensemblesof ZZ Ceti stars, such as those being discovered using the Sloan Digital SkySurvey. Because this method relies only on photometry at optical wavelengths,it can be applied to faint stars using 4 m class telescopes.Comment: 73 pages, 22 figures, accepted in the Ap