Non-linear behaviour of the pulsating white dwarf G29-38 — I. Evolution of the temporal spectrum

Abstract

An analysis of the evolution of the amplitude spectrum over many seasons of the DA pulsating white dwarf G29‐38 has been performed. Neither beating nor resonant mode coupling can account for the observed appearance and disappearance of modes, although some of them clearly grow while others get damped. Therefore some unknown non‐adiabatic, non‐linear process has to be invoked that affects both the mode selection mechanism and the driving efficiency on a time‐scale as short as a day.

Non-linear behaviour of the pulsating white dwarf G29-38 — II. Analysis of the phase spectrum

“…No obvious trend or correlated evolution can be seen in the phases over the years. This is, in a sense, expected as the peaks are not found at exactly the same frequency in each season, but experience slight frequency shifts up to about 2 μHz (Kleinman 1995; Vuille 2000). This may easily induce large phase shifts as, from one season to the next, each oscillation mode goes through a few tens of thousands of cycles.…”

“…Only if a mode is stable enough in frequency and well resolved in each season can the gaps between the data sets be bridged, and its phase possibly monitored. Even though the mode k =4, which corresponds to a 283‐s period, seems to satisfy these criteria [its seasonal shift does not exceed 0.18 μHz (Vuille 2000)], the evolution of its phase still appears erratic (Fig. 1).…”

Observational white dwarf seismology

“…The filter mechanism that selects which modes get excited to observable amplitudes, mode trapping, was studied by Winget et al (1981) and Córsico et al (2002). Some pulsators have small amplitudes and sinusoidal light curves (Stover et al 1980;Kepler et al , 1983Kepler 1984), while others are high amplitude pulsators, with many harmonics and combination peaks detected (McGraw & Robinson 1975;Robinson et al 1978;Kleinman et al 1998;Vuille 2000;Dolez et al 2006).…”

Non-linear behaviour of the pulsating white dwarf G29-38 — III. Relative amplitudes of the cross-frequencies

“…combinations of three modes. Based on the frequency table of Vuille (2000a), we have measured the amplitude ratio A c A 1 A 2 for each of these 31 first‐order cases according to the rule that the smallest of the three peaks forming each combination is assumed to be the non‐linear frequency, while the other two are the ‘parent’ normal modes. The results are plotted in Fig.…”

“…Although the period spectrum of this star has shown tremendous qualitative changes from season to season, numerous combination frequencies could always been identified. Various analyses (Vuille 2000a,b) have led to the conclusion that most of the combination frequencies are due to harmonic distortion and not to resonant mode coupling. However, because none of the different harmonic distortion processes bears a distinctive signature, it is difficult to disentangle them and determine which one, if any, is dominating in G29‐38.…”