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

Abstract

An analysis of the phase spectrum of the DA pulsating white dwarf G29‐38 over many seasons has been performed. This complements a companion paper which analyses the evolution of the temporal spectrum of G29‐38. We show that, with one exception, the relative phases of the harmonics and combination frequencies are all oscillating in phase with their parent modes. This not only suggests that these non‐linear frequencies owe their presence to harmonic distortion and not to resonant mode coupling, but also explains the typical pulse shapes observed in the light curves of large‐amplitude variable white dwarfs. The one exceptional cross‐frequency that does not show a phasing with its parent modes is thought to be a resonance.

Asteroseismology of the β Cephei star 12 (DD) Lacertae: photometric observations, pulsational frequency analysis and mode identification

“…Consequently, we examined the relative amplitudes A ij /( A i / A j ), where A ij is the amplitude of the combination frequency and A i and A j are the amplitudes of the parent modes, respectively, and phases φ i j − (φ i +φ j ), where φ i j is the phase of the combination signal and φ i and φ j are the phases of the parent modes of the first‐order combination frequency sums with respect to their parents. Such an analysis has been successfully used by Vuille (2000) and Vuille & Brassard (2000) for the pulsating white dwarf star G 29‐38. We show the relative amplitudes and phases of the combination frequencies in Fig.…”

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

“…We therefore believe that the majority of these combination frequencies probably arise from harmonic distortion. This belief is given sound quantitative support in Vuille (2000).…”

“…1, because no linear relation exists between their frequencies. Furthermore, their combination frequencies, which could play the role of the naturally stable modes excited by direct resonance, are not systematically observed in each season, and, when they are, their relative phases are all consistent with harmonic distortion rather than mode coupling (Vuille 2000). Mode coupling between these observed modes is therefore not likely to be responsible for the amplitude changes observed.…”

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

“…2). This difference frequency, which corresponds to the combination 8–17, was already standing out when a phase analysis was performed (Vuille 2000b), which led to the suspicion that this frequency might be a resonant mode rather than a harmonic distortion peak. The fact that it is also standing out in the present analysis strengthens this suspicion.…”

“…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.…”