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

Vuille, François; Brassard, P.

doi:10.1046/j.1365-8711.2000.03202.x

Cited by 10 publications

(16 citation statements)

References 19 publications

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“…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.…”

Section: Discussionmentioning

confidence: 99%

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

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Jerzykiewicz

Rodríguez‐López

et al. 2006

Monthly Notices of the Royal Astronomical Society

104

114

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We report a multisite photometric campaign for the β Cephei star 12 Lacertae. 750 h of high‐quality differential photoelectric Strömgren, Johnson and Geneva time‐series photometry were obtained with nine telescopes during 190 nights. Our frequency analysis results in the detection of 23 sinusoidal signals in the light curves. Ten of those correspond to independent pulsation modes, and the remainder are combination frequencies. We find some slow aperiodic variability such as that seemingly present in several β Cephei stars. We perform mode identification from our colour photometry, derive the spherical degree ℓ for the five strongest modes unambiguously and provide constraints on ℓ for the weaker modes. We find a mixture of modes of 0 ≤ℓ≤ 4. In particular, we prove that the previously suspected rotationally split triplet within the modes of 12 Lac consists of modes of different ℓ; their equal frequency splitting must thus be accidental. One of the periodic signals we detected in the light curves is argued to be a linearly stable mode excited to visible amplitude by non‐linear mode coupling via a 2:1 resonance. We also find a low‐frequency signal in the light variations whose physical nature is unclear; it could be a parent or daughter mode resonantly coupled. The remaining combination frequencies are consistent with simple light‐curve distortions. The range of excited pulsation frequencies of 12 Lac may be sufficiently large that it cannot be reproduced by standard models. We suspect that the star has a larger metal abundance in the pulsational driving zone, a hypothesis also capable of explaining the presence of β Cephei stars in the Large Magellanic Cloud.

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Section: Discussionmentioning

confidence: 99%

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

Handler

Jerzykiewicz

Rodríguez‐López

et al. 2006

Monthly Notices of the Royal Astronomical Society

104

114

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“…This does not necessarily invalidate the theory, but suggests that some other mechanism is at work, at least in G29-38. Vuille & Brassard (2000) left open the question of low amplitude pulsators, which have much smaller combination frequencies. In one case at least (G117-B15A), the BFW theory was able to account for the amplitude of the combination frequencies (Brassard et al 1993).…”

Section: Introductionmentioning

confidence: 99%

“…These radiative nonlinearities can be larger than expected from the T 4 dependence of flux because of the sensitivity of the H absorption lines to temperature. Vuille & Brassard (2000) compared the predictions of this theory to those of Brickhill for the large amplitude pulsator G29-38, and found that the combination frequencies in that star are too large to be explained by the BFW theory. This does not necessarily invalidate the theory, but suggests that some other mechanism is at work, at least in G29-38.…”

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confidence: 99%

Mode Identification from Combination Frequency Amplitudes in ZZ Ceti Stars

Clemens

Thompson

et al. 2005

ApJ

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The lightcurves of variable DA stars are usually multi-periodic and nonsinusoidal, 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 paper, 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 analysis 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 four-meter class telescopes.

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“…The latter eigenmode is a good candidate to be a coupled mode, not only because its relative phase stands out, but also because its relative amplitude does as well (Vuille & Brassard 2000, hereafter Paper III). The measured amplitude of k =8−17 is indeed larger than that of k =8.…”

Section: Relative Phases Of the Combination Frequenciesmentioning

confidence: 99%

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

Vuille¹

2000

Monthly Notices of the Royal Astronomical Society

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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.

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

Cited by 10 publications

References 19 publications

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

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

Mode Identification from Combination Frequency Amplitudes in ZZ Ceti Stars

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

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