Amplitude and frequency variations of oscillation modes in the pulsating DB white dwarf star KIC 08626021

Abstract

Context. The signatures of nonlinear effects affecting stellar oscillations are difficult to observe from ground observatories because of the lack of continuous high-precision photometric data spanning extended enough time baselines. The unprecedented photometric quality and coverage provided by the Kepler spacecraft offers new opportunities to search for these phenomena. Aims. We use the Kepler data accumulated on the pulsating DB white dwarf KIC 08626021 to explore in detail the stability of its oscillation modes, searching, in particular, for evidence of nonlinear behaviors. Methods. We analyze nearly two years of uninterrupted short-cadence data, concentrating on identified triplets that are caused by stellar rotation and that show intriguing behaviors during the course of the observations. Results. We find clear signatures of nonlinear effects that could be attributed to resonant mode coupling mechanisms. These couplings occur between the components of the triplets and can induce different types of behaviors. We first notice that a structure at 3681 μHz, identified as a triplet in previous published studies, is in fact forming a doublet, with the third component being an independent mode. We find that a triplet at 4310 μHz and this doublet at 3681 μHz (most likely the two visible components of an incomplete triplet) have clear periodic frequency and amplitude modulations, which are typical of the so-called intermediate regime of the resonance, with timescales consistent with theoretical expectations. Another triplet at 5073 μHz is likely in a narrow transitory regime in which the amplitudes are modulated while the frequencies are locked. Using nonadiabatic pulsation calculations, based on a model representative of KIC 08626021 to evaluate the linear growth rates of the modes in the triplets, we also provide quantitative information that could be useful for future comparisons with numerical solutions of the amplitude equations. Conclusions. The observed modulations are the clearest hints of nonlinear resonant couplings occurring in white dwarf stars identified so far. These should resonate as a warning to projects that aim at measuring the evolutionary cooling rate of KIC 08626021, and of white dwarf stars in general. Nonlinear modulations of the frequencies can potentially jeopardize any attempt to measure such rates reliably, unless they can be corrected beforehand. These results should motivate further theoretical work to develop the nonlinear stellar pulsation theory.

A large oxygen-dominated core from the seismic cartography of a pulsating white dwarf

“…The structure in the 3,677-3,686 μ Hz range, identified previously as a triplet 21,36 , is actually a doublet, f 3 (ref. 18), with an independent mode, f 7 , close by. The seismic modelling is greatly influenced by the addition of this eighth low-order frequency, as it must probe a somewhat different part of the star than the other modes, thus adding to the total information content available from the observations and contributing to a more detailed seismic view of KIC08626021.…”

“…Pulsation properties. To carry out our seismic study, we use a recent thorough analysis 18 , which has shed new light on the 23 months of Kepler photometric data gathered for KIC08626021. In particular, even if the 13 retained frequencies are consistent with previous analyses 21 , interpretation of one of the structures leads to an important correction.…”

“…The list of extracted periods (frequencies) and their specifications are provided in table 1 of ref. 18; we refer the reader to this work for details of the extraction process and the frequencies detected. We use the same convention for the sake of simplicity.…”

“…Out of the remaining four periodicities listed in table 1 of ref. 18, f 8 and f 10 are linear-combination frequencies of two of the eight basic modes, and as such, they are excluded from our analysis. In addition, we do not consider f 11 and f 12 because they do not reach the secure threshold of 5.6σ (ref.…”

“…In addition, we do not consider f 11 and f 12 because they do not reach the secure threshold of 5.6σ (ref. 18). The optimal model.…”