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Ultra-massive white dwarf stars are currently being discovered at a considerable rate, thanks to surveys such as the Gaia space mission. These dense and compact stellar remnants likely play a major role in Type Ia supernova explosions. It is possible to probe the interiors of ultra-massive white dwarfs through asteroseismology. In the case of the most massive white dwarfs, general relativity could affect their structure and pulsations substantially. In this work, we present results of relativistic pulsation calculations employing relativistic ultra-massive ONe-core white dwarf models with hydrogen-rich atmospheres and masses ranging from 1.29 to $1.369 \ \mathrm{M}_{\odot }$ with the aim of assessing the impact of general relativity on the adiabatic gravity (g)-mode period spectrum of very high mass ZZ Ceti stars. Employing the relativistic Cowling approximation for the pulsation analysis, we find that the critical buoyancy (Brunt–Väisälä) and acoustic (Lamb) frequencies are larger for the relativistic case, compared to the Newtonian case, due to the relativistic white dwarf models having smaller radii and higher gravities for a fixed stellar mass. In addition, the g-mode periods are shorter in the relativistic case than those in the Newtonian computations, with relative differences of up to ∼$50$ per cent for the highest mass models ($1.369 \ \mathrm{M}_{\odot }$) and for effective temperatures typical of the ZZ Ceti instability strip. Hence, the effects of general relativity on the structure, evolution, and pulsations of white dwarfs with masses larger than ∼$1.29 \ \mathrm{M}_{\odot }$ cannot be ignored in the asteroseismological analysis of ultra-massive ZZ Ceti stars.

 

We present Apache Point Observatory (APO) and Gemini time-series photometry of WD J004917.14−252556.81, an ultramassive DA white dwarf with $T_{\rm eff} = 13\, 020$ K and log g = 9.34. We detect variability at two significant frequencies, making J0049−2525 the most massive pulsating white dwarf currently known with M⋆ = 1.31 M⊙ (for a CO core) or 1.26 M⊙ (for an ONe core). J0049−2525 does not display any of the signatures of binary mergers, there is no evidence of magnetism, large tangential velocity, or rapid rotation. Hence, it likely formed through single star evolution and is likely to have an ONe core. Evolutionary models indicate that its interior is ≳99 per cent crystallized. Asteroseismology offers an unprecedented opportunity to probe its interior structure. However, the relatively few pulsation modes detected limit our ability to obtain robust seismic solutions. Instead, we provide several representative solutions that could explain the observed properties of this star. Extensive follow-up time-series photometry of this unique target has the potential to discover a significant number of additional pulsation modes that would help overcome the degeneracies in the asteroseismic fits, and enable us to probe the interior of an ≈1.3 M⊙ crystallized white dwarf.

 

G 29 − 38 (TIC 422526868) is one of the brightest (V = 13.1) and closest (d = 17.51 pc) pulsating white dwarfs with a hydrogen-rich atmosphere (DAV/ZZ Ceti class). It was observed by the TESS spacecraft in sectors 42 and 56. The atmosphere of G 29 − 38 is polluted by heavy elements that are expected to sink out of visible layers on short time-scales. The photometric TESS data set spans ∼51 d in total, and from this, we identified 56 significant pulsation frequencies, that include rotational frequency multiplets. In addition, we identified 30 combination frequencies in each sector. The oscillation frequencies that we found are associated with g-mode pulsations, with periods spanning from ∼ 260 to ∼ 1400 s. We identified rotational frequency triplets with a mean separation δνℓ = 1 of 4.67 μHz and a quintuplet with a mean separation δνℓ = 2 of 6.67 μHz, from which we estimated a rotation period of about 1.35 ± 0.1 d. We determined a constant period spacing of 41.20 s for ℓ = 1 modes and 22.58 s for ℓ = 2 modes. We performed period-to-period fit analyses and found an asteroseismological model with M⋆/M⊙ = 0.632 ± 0.03, $T_{\rm eff}=11\, 635\pm 178$ K, and log g = 8.048 ± 0.005 (with a hydrogen envelope mass of MH ∼ 5.6 × 10−5M⋆), in good agreement with the values derived from spectroscopy. We obtained an asteroseismic distance of 17.54 pc, which is in excellent agreement with that provided by Gaia (17.51 pc).

 

Context. Before reaching their quiescent terminal white-dwarf cooling branch, some low-mass helium-core white dwarf stellar models experience a number of nuclear flashes which greatly reduce their hydrogen envelopes. Just before the occurrence of each flash, stable hydrogen burning may be able to drive global pulsations that could be relevant in shedding some light on the internal structure of these stars through asteroseismology, similarly to what occurs with other classes of pulsating white dwarfs. Aims. We present a pulsational stability analysis applied to low-mass helium-core stars on their early white-dwarf cooling branches going through CNO flashes in order to study the possibility that the ε mechanism is able to excite gravity-mode pulsations. We assess the ranges of unstable periods and the corresponding instability domain in the log g  −  T eff plane. Methods. We carried out a nonadiabatic pulsation analysis for low-mass helium-core white-dwarf models with stellar masses between 0.2025 and 0.3630  M ⊙ going through CNO flashes during their early cooling phases. Results. We found that the ε mechanism due to stable hydrogen burning can excite low-order ( ℓ  = 1, 2) gravity modes with periods between ∼80 and 500 s for stars with 0.2025 ≲  M ⋆ / M ⊙  ≲ 0.3630 located in an extended region of the log g  −  T eff diagram, with effective temperature and surface gravity in the ranges 15 000 ≲  T eff  ≲ 38 000 K and 5.8 ≲ log g  ≲ 7.1, respectively. For the sequences that experience multiple CNO flashes, we found that with every consecutive flash, the region of instability becomes wider and the modes are more strongly excited. The magnitudes of the rate of period change for these modes are in the range of ∼10 −10 –10 −11  [s/s]. Conclusions. Since the timescales required for these modes to reach amplitudes large enough to be observable are shorter than their corresponding evolutionary timescales, the detection of pulsations in these stars is feasible. Given the current problems in distinguishing some stars that populate the same region of the log g  −  T eff plane, the eventual detection of short-period pulsations may help in the classification of such stars. Furthermore, if a low-mass white dwarf star were found to pulsate with low-order gravity modes in this region of instability, it would confirm our result that such pulsations can be driven by the ε mechanism. In addition, confirming a rapid rate of period change in these pulsations would support the idea that these stars actually experience CNO flashes, as has been predicted by evolutionary calculations. 

Context. The possible existence of warm ( T eff  ∼ 19 000 K) pulsating DA white dwarf (WD) stars, hotter than ZZ Ceti stars, was predicted in theoretical studies more than 30 yr ago. These studies reported the occurrence of g -mode pulsational instabilities due to the κ mechanism acting in the partial ionization zone of He below the H envelope in models of DA WDs with very thin H envelopes ( M H / M ⋆  ≲ 10 −10 ). However, to date, no pulsating warm DA WD has been discovered, despite the varied theoretical and observational evidence suggesting that a fraction of WDs should be formed with a range of very low H content. Aims. We re-examine the pulsational predictions for such WDs on the basis of new full evolutionary sequences. We analyze all the warm DAs observed by the TESS satellite up to Sector 9 in order to search for the possible pulsational signal. Methods. We computed WD evolutionary sequences of masses 0.58 and 0.80 M ⊙ with H content in the range −14.5 ≲ log( M H / M ⋆ )≲ − 10, appropriate for the study of pulsational instability of warm DA WDs. Initial models were extracted from progenitors that were evolved through very late thermal pulses on the early cooling branch. We use LPCODE stellar code into which we have incorporated a new full-implicit treatment of time-dependent element diffusion to precisely model the H–He transition zone in evolving WD models with very low H content. The nonadiabatic pulsations of our warm DA WD models were computed in the effective temperature range of 30 000 − 10 000 K, focusing on ℓ = 1 g modes with periods in the range 50 − 1500 s. Results. We find that traces of H surviving the very late thermal pulse float to the surface, eventually forming thin, growing pure H envelopes and rather extended H–He transition zones. We find that such extended transition zones inhibit the excitation of g modes due to partial ionization of He below the H envelope. Only in the cases where the H–He transition is assumed much more abrupt than predicted by diffusion do models exhibit pulsational instability. In this case, instabilities are found only in WD models with H envelopes in the range of −14.5 ≲ log( M H / M ⋆ )≲ − 10 and at effective temperatures higher than those typical for ZZ Ceti stars, in agreement with previous studies. None of the 36 warm DAs observed so far by TESS satellite are found to pulsate. Conclusions. Our study suggests that the nondetection of pulsating warm DAs, if WDs with very thin H envelopes do exist, could be attributed to the presence of a smooth and extended H–He transition zone. This could be considered as indirect proof that element diffusion indeed operates in the interior of WDs. 

Context. Pulsation frequencies reveal the interior structures of white dwarf stars, shedding light on the properties of these compact objects that represent the final evolutionary stage of most stars. Two-minute cadence photometry from the Transiting Exoplanet Survey Satellite (TESS) records pulsation signatures from bright white dwarfs over the entire sky. Aims. As part of a series of first-light papers from TESS Asteroseismic Science Consortium Working Group 8, we aim to demonstrate the sensitivity of TESS data, by measuring pulsations of helium-atmosphere white dwarfs in the DBV instability strip, and what asteroseismic analysis of these measurements can reveal about their stellar structures. We present a case study of the pulsating DBV WD 0158−160 that was observed as TIC 257459955 with the two-minute cadence for 20.3 days in TESS Sector 3. Methods. We measured the frequencies of variability of TIC 257459955 with an iterative periodogram and prewhitening procedure. The measured frequencies were compared to calculations from two sets of white dwarf models to constrain the stellar parameters: the fully evolutionary models from LPCODE and the structural models from WDEC . Results. We detected and measured the frequencies of nine pulsation modes and eleven combination frequencies of WD 0158−160 to ∼0.01  μ Hz precision. Most, if not all, of the observed pulsations belong to an incomplete sequence of dipole (ℓ = 1) modes with a mean period spacing of 38.1 ± 1.0 s. The global best-fit seismic models from both LPCODE and WDEC have effective temperatures that are ≳3000 K hotter than archival spectroscopic values of 24 100–25 500 K; however, cooler secondary solutions are found that are consistent with both the spectroscopic effective temperature and distance constraints from Gaia astrometry. Conclusions. Our results demonstrate the value of the TESS data for DBV white dwarf asteroseismology. The extent of the short-cadence photometry enables reliably accurate and extremely precise pulsation frequency measurements. Similar subsets of both the LPCODE and WDEC models show good agreement with these measurements, supporting that the asteroseismic interpretation of DBV observations from TESS is not dominated by the set of models used. However, given the sensitivity of the observed set of pulsation modes to the stellar structure, external constraints from spectroscopy and/or astrometry are needed to identify the best seismic solutions.