Nonlinear behaviour of pulsating white dwarfs
Using a phenomenological approach, I have investigated the nonlinear properties of the pulsations of two white dwarfs, namely DA G29-38 and DB GD358. The data at my disposal comprised numerous single- and multi-sites time series photometric campaigns, including light curves from four Whole Earth Telescope runs conducted respectively in 1988 and 1992 on G29-38, and in 1990 and 1994 on GD358. Thanks to their length and quality, several of these individual data sets have the beating between the excited eigenmodes resolved. Amplitude changes are nevertheless visible between these various amplitude spectra, suggesting the presence of intrinsic nonlinear processes. However, I showed that only when the spectral changes are drastic have time-dependent nonlinear phenomena to be invoked; no matter how long the data sets, mild seasonal amplitude variations can often be accounted for by beating between the eigen-modes and high order cross-frequencies when harmonic distortion is strong enough. From third order of perturbation, cross-frequencies naturally appear in the direct vicinity of the normal modes, which not only alter the simple eigenmultiplet structures thus rendering the mode identification more difficult, but also generate long and complex beating processes. In GD358, for instance, 153 such third order combination frequencies are expected to appear in the frequency range of each eigentriplet; a light curve spanning at least 9 months is thus necessary to resolve the period structure of this star. Drastic spectral changes were nevertheless recorded in both G29s38 and GD358 which could not be accounted for by such high order beating processes. I could securely conclude that the pulsations of both these stars experience intrinsic amplitude variations on time-scales ranging from days to years, suggesting that different nonlinear processes dominate the evolution of the pulsations at different time.
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