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Recent determinations of the total rate of the 12C+12C nuclear reaction show non-negligible differences with the reference reaction rate commonly used in previous stellar simulations. In addition, the current uncertainties in determining each exit channel constitute one of the main uncertainties in shaping the inner structure of super asymptotic giant branch stars that could have a measurable impact on the properties of pulsating ultra-massive white dwarfs (WDs). We explore how new determinations of the nuclear reaction rate and its branching ratios affect the evolution of WD progenitors. We show that the current uncertainties in the branching ratios constitute the main uncertainty factor in determining the inner composition of ultra-massive WDs and their progenitors. We found that the use of extreme branching ratios leads to differences in the central abundances of 20Ne of at most 17%, which are translated into differences of at most 1.3 and 0.8% in the cooling times and size of the crystallized core. However, the impact on the pulsation properties is small, less than 1 s for the asymptotic period spacing. We found that the carbon burns partially in the interior of ultra-massive WD progenitors within a particular range of masses, leaving a hybrid CONe-core composition in their cores. The evolution of these new kinds of predicted objects differs substantially from the evolution of objects with pure CO cores. Differences in the size of the crystallized core and cooling times of up to 15 and 6%, respectively leading to distinct patterns in the period spacing distribution., Comment: 12 pages, 14 figures. Accepted for publication in ApJ

A central challenge in the field of stellar astrophysics lies in accurately determining the mass of isolated stars. However, for pulsating white dwarf (WD) stars, the task becomes more tractable due to the availability of multiple approaches such as spectroscopy, asteroseismology, astrometry, and photometry. The objective of this work is to compare the asteroseismological and spectroscopic mass values of WDs in detail and, in turn, to compare them with the masses derived using astrometric parallaxes/distances and photometry. Our analysis encompasses a selection of pulsating WDs with different surface chemical abundances that define the main classes of variable WDs. We calculated their spectroscopic masses, compiled seismological masses, and determined astrometric masses. We also derived photometric masses, when possible. Subsequently, we compared all the sets of stellar masses obtained through these different methods. To ensure consistency and robustness in our comparisons, we used identical WD models and evolutionary tracks across all four methods. The analysis suggests a general consensus among the these methods regarding the masses of pulsating WD with H-rich atmospheres, known as DAV or ZZ Ceti stars, especially for objects with masses below approximately $0.75 M_{\sun}$, although notable disparities emerge for certain massive stars. For pulsating WD stars with He-rich atmospheres, called DBV or V777 Her stars, we find that astrometric masses generally exceed seismological, spectroscopic, and photometric masses. Finally, while there is agreement among the sets of stellar masses for pulsating WDs with C-, O-, and He-rich atmospheres (designated as GW Vir stars), outliers exist where mass determinations by various methods show significant discrepancies., Comment: 24 pages, 25 figures, 8 tables. To be published in Astronomy and Astrophysics

Significant advances have been achieved through the latest improvements in the photometric observations accomplished by the recent space missions, substantially boosting the study of pulsating stars via asteroseismology. The TESS mission has already proven to be of relevance for pulsating white dwarf and pre-white dwarf stars. We report a detailed asteroseismic analysis of the pulsating PG 1159 star NGC 246 (TIC3905338), the central star of the planetary nebula NGC 246, based on high-precision photometric data gathered by the TESS space mission. We reduced TESS observations of NGC 246 and performed a detailed asteroseismic analysis using fully evolutionary PG 1159 models computed accounting for the complete prior evolution of their progenitors. We constrained the mass of this star by comparing the measured mean period spacing with the average of the computed period spacings of the models and also employed the observed individual periods to search for a seismic stellar model. We extracted 17 periodicities from the TESS light curves from the two sectors where NGC246 was observed. All the oscillation frequencies are associated with g-mode pulsations, with periods spanning from ~1460 to ~1823s. We found a constant period spacing of $\Delta\Pi= 12.9$s, allowing us to deduce that the stellar mass is larger than ~0.87 Mo if the period spacing is assumed to be associated with l= 1 modes, and ~ 0.568 Mo if it is associated with l= 2 modes. The less massive models are more consistent with the distance constraint from Gaia parallax. Although we were not able to find a unique asteroseismic model for this star, the period-to-period fit analyses suggest a high-stellar mass ($\gtrsim$0.74 Mo) when the observed periods are associated with modes with l= 1 only, and both a high ($\gtrsim$ 0.74 Mo) and intermediate (~0.57 Mo) stellar mass when the observed periods are associated with modes with l= 1 and 2., Comment: 14 pages, 11 figures. Accepted for publication in Astronomy & Astrophysics

Ultra-short period compact binaries are important sources of gravitational waves, which include e.g. the progenitors of type Ia supernovae or the progenitors of merger episodes that may lead to massive and magnetic single white dwarfs. J0526+5934 is an unresolved compact binary star with an orbital period of 20.5 minutes that belongs to this category. The visible component of J0526+5934 has been recently claimed to be a hot sub-dwarf star with a CO white dwarf companion. Our aim is to provide strong observational plus theoretical evidence that the primary star is rather an extremely-low mass white dwarf, although the hot subdwarf nature cannot be completely ruled out. We analyse optical spectra together with time-series photometry of the visible component of J0526+5934 to constrain its orbital and stellar parameters. We also employ evolutionary sequences for low-mass white dwarfs to derive independent values of the primary mass. From the analysis of our observational data, we find a stellar mass for the primary star in J0526+5934 of 0.26+-0.05 Msun, which perfectly matches the 0.237+-0.035 Msun independent measurement we derived from the theoretical evolutionary models. This value is considerably lower than the theoretically expected and generally observed mass range of hot subdwarf stars, but falls well within the mass limit values of extremely low-mass white dwarfs. We conclude J0526+5934 is the fifth ultra-short period detached double white dwarf currently known., Comment: Submitted to A&A

Breathing pulses are mixing episodes that could develop during the core-helium burning phase of low- and intermediate-mass stars. The occurrence of breathing pulses is expected to bear consequences on the formation and evolution of white dwarfs, particularly on the core chemical structure, which can be probed by asteroseismology. We aim to explore the consequences of breathing pulses on the chemical profiles and pulsational properties of variable white-dwarf stars with hydrogen-rich envelopes, known as ZZ Ceti stars. We compute stellar models with masses of $1.0 M_{\odot}$ and $2.5 M_{\odot}$ in the zero-age main sequence, and evolve them through the core-helium burning phase to the thermal pulses on the asymptotic giant branch, and finally to advanced stages of white-dwarf cooling. We compare the chemical structure of the core of white dwarfs whose progenitors have experienced breathing pulses during the core-helium burning phase with the case in which breathing pulses have not occurred. We find that, when breathing pulses occur, the white-dwarf cores are larger and the central abundances of oxygen are higher than for the case in which the breathing pulses are suppressed, in line with previous studies. However, the occurrence of breathing pulses is not sufficient to explain the large cores and the excessive oxygen abundances that characterize recently derived asteroseismological models of pulsating white dwarfs. We find absolute differences of up to $\sim 30$ seconds when we compare pulsation periods of white dwarfs coming from progenitors that have experienced breathing pulses with the case in which the progenitors have not suffered breathing pulses., Comment: 9 pages, 1 table, 7 figures. Accepted for publication in The Astrophysical Journal

G\,29$-$38 (TIC~422526868) is one of the brightest ($V=13.1$) and closest ($d = 17.51$\,pc) pulsating white dwarfs with a hydrogen-rich atmosphere (DAV/ZZ Ceti class). It was observed by the {\sl TESS} spacecraft in sectors 42 and 56. The atmosphere of G~29$-$38 is polluted by heavy elements that are expected to sink out of visible layers on short timescales. The photometric {\sl TESS} data set spans $\sim 51$ days 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 $\sim$ 260 s to $\sim$ 1400 s. We identified %three distinct rotational frequency triplets with a mean separation $\delta \nu_{\ell=1}$ of 4.67 $\mu$Hz and a quintuplet with a mean separation $\delta \nu_{\ell=2}$ of 6.67 $\mu$Hz, from which we estimated a rotation period of about $1.35 \pm 0.1$ days. We determined a constant period spacing of 41.20~s for $\ell= 1$ modes and 22.58\,s for $\ell= 2$ modes. We performed period-to-period fit analyses and found an asteroseismological model with $M_{\star}/M_{\odot}=0.632 \pm 0.03$, $T_{\rm eff}=11\, 635\pm 178$ K, and $\log{g}=8.048\pm0.005$ (with a hydrogen envelope mass of $M_{\rm H}\sim 5.6\times 10^{-5}M_{\star}$), 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 {\sl Gaia} (17.51 pc)., Comment: 17 pages, Accepted for publication in MNRAS

Ultra-massive white dwarf stars are currently being discovered at a considerable rate, thanks to surveys such as the {\it 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 $1.369 M_{\odot}$ 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-V\"ais\"al\"a) 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 in the Newtonian computations, with relative differences of up to $\sim 50$ \% for the highest-mass models ($1.369 M_{\odot}$) 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 $\sim 1.29 M_{\odot}$ cannot be ignored in the asteroseismological analysis of ultra-massive ZZ Ceti stars., Comment: 15 pages, 21 figures, 2 tables. Accepted for publication in MNRAS

We employ the La Plata stellar evolution code, LPCODE, to compute the first set of constant rest-mass carbon-oxygen ultra-massive white dwarf evolutionary sequences for masses higher than 1.29 Msun that fully take into account the effects of general relativity on their structural and evolutionary properties. In addition, we employ the LP-PUL pulsation code to compute adiabatic g-mode Newtonian pulsations on our fully relativistic equilibrium white dwarf models. We find that carbon-oxygen white dwarfs more massive than 1.382 Msun become gravitationally unstable with respect to general relativity effects, being this limit higher than the 1.369 Msun we found for oxygen-neon white dwarfs. As the stellar mass approaches the limiting mass value, the stellar radius becomes substantially smaller compared with the Newtonian models. Also, the thermo-mechanical and evolutionary properties of the most massive white dwarfs are strongly affected by general relativity effects. We also provide magnitudes for our cooling sequences in different passbands. Finally, we explore for the first time the pulsational properties of relativistic ultra-massive white dwarfs and find that the period spacings and oscillation kinetic energies are strongly affected in the case of most massive white dwarfs. We conclude that the general relativity effects should be taken into account for an accurate assessment of the structural, evolutionary, and pulsational properties of white dwarfs with masses above 1.30 Msun., Comment: 12 pages, 12 figures, accepted for publication in MNRAS. arXiv admin note: text overlap with arXiv:2208.14144

The ESA Gaia space mission has revealed a bifurcation of the white dwarf (WD) sequence on the color magnitude diagram in two branches: A and B. While the A branch consists mostly of WDs with H-rich atmospheres, the B branch is not completely understood. Although invoked to be populated mainly by He-rich WDs, the B branch overlaps a $\sim 0.8M_\odot$ evolutionary track with a pure He envelope, fact that would imply an unexpected peak in the WD mass distribution. In cold He-rich WDs, it is expected that the outer convective zone penetrates into deep C-rich layers, thus leading to a slight C contamination in their surfaces at $\sim 10,000$K. Here we aim at studying the Gaia bifurcation as the natural consequence of C dredge-up by convection in cold He-dominated WDs. Relying on accurate atmosphere models, we provide a new set of evolutionary models for He-rich WDs employing different prescriptions for the C enrichment. On the basis of these models, we made a population synthesis study of the Gaia 100pc WD sample to constrain the models that best fit the bifurcation. Our study shows that He-rich WD models with a slight C contamination below the optical detection limit can accurately reproduce the Gaia bifurcation. We refer to these stars as stealth DQ WDs because they do not exhibit detectable C signatures in their optical spectra, but the presence of C in their atmosphere produces a continuum absorption favouring the emission in bluer wavelengths, thereby creating the B branch of the bifurcation. Also, we show that the mass distribution for He-rich WDs obtained when a stealth C contamination is considered is consistent with the mass distribution for H-rich WDs and with the standard evolutionary channels for their formation. We conclude that stealth DQ WDs can account for the lower branch in the Gaia bifurcation. The C signatures of these stars could be detectable in Ultra-Violet spectra., Comment: 9 pages, 8 figures, accepted for publication in Astronomy & Astrophysics

Recently, a new class of white dwarfs (dubbed ``slowly cooling WDs'') has been identified in two globular clusters (namely M13 and NGC 6752) showing a horizontal branch (HB) morphology with an extended blue tail. The cooling rate of these WDs is reduced by stable thermonuclear hydrogen burning in their residual envelope, and they are thought to be originated by stars that populate the blue tail of the HB and then skip the asymptotic giant branch phase. Consistently, no evidence of such kind of WDs has been found in M3, a similar cluster with no blue extension of the HB. To further explore this phenomenon, we took advantage of deep photometric data acquired with the Hubble Space Telescope in the near-ultraviolet and investigate the bright portion of the WD cooling sequence in M5, another Galactic globular cluster with HB morphology similar to M3. The normalized WD luminosity function derived in M5 turns out to be impressively similar to that observed in M3, in agreement with the fact that the stellar mass distribution along the HB of these two systems is almost identical. The comparison with theoretical predictions is consistent with the fact that the cooling sequence in this cluster is populated by canonical (fast cooling) WDs. Thus, the results presented in this paper provide further support to the scenario proposing a direct causal connection between the slow cooling WD phenomenon and the horizontal branch morphology of the host stellar cluster., Comment: 12 pages, 8 figures, accepted in the ApJ

We present APO and Gemini time-series photometry of WD J004917.14$-$252556.81, an ultramassive DA white dwarf with $T_{\rm eff} = 13020$ 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 $M_\star=1.31~M_{\odot}$ (for a CO core) or $1.26~M_{\odot}$ (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 $\gtrsim99$% 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 $\approx1.3~M_{\odot}$ crystallized white dwarf., Comment: MNRAS, in press

(Abridged) We present an exploration of the internal rotation of GD 278, the first pulsating extremely low-mass white dwarf that shows rotational splittings within its periodogram. We assess the theoretical frequency splittings expected for different rotation profiles and compare them to the observed frequency splittings of GD 278. To this aim, we employ an asteroseismological model representative of the pulsations of this star, obtained by using the LPCODE stellar evolution code. We also derive a rotation profile that results from detailed evolutionary calculations carried out with the MESA stellar evolution code and use it to infer the expected theoretical frequency splittings. We found that the best-fitting solution when assuming linear profiles for the rotation of GD 278 leads to values of the angular velocity at the surface and the center that are only slightly differential, and still compatible with rigid rotation. The values of the angular velocity at the surface and the center for the simple linear rotation profiles and for the rotation profile derived from evolutionary calculations are in very good agreement. Also, the resulting theoretical frequency splittings are compatible with the observed frequency splittings, in general, for both cases. The results obtained from the different approaches followed in this work to derive the internal rotation of GD 278 agree. The fact that they were obtained employing two independent stellar evolution codes gives robustness to our results. Our results suggest only a marginally differential behavior for the internal rotation in GD 278, and considering the uncertainties involved, very compatible with the rigid case, as has been observed previously for white dwarfs and pre-white dwarfs. The rotation periods derived for this star are also in line with the values determined asteroseismologically for white dwarfs and pre-white dwarfs in general., Comment: 9 pages, 6 figures. Accepted for publication in Astronomy & Astrophysics

We report a peculiar variable blue star in the globular cluster NGC 6397, using Hubble Space Telescope optical imaging. Its position in the colour-magnitude diagrams, and its spectrum, are consistent with this star being a helium core white dwarf (He WD) in a binary system. The optical light curve shows a periodicity at 18.5 hours. We argue that this periodicity is due to the rotation of the WD and possibly due to magnetic spots on the surface of the WD. This would make this object the first candidate magnetic He WD in any globular cluster (GC), and the first candidate magnetic WD in a detached binary system in any GC and one of the few He WDs with a known rotation period and of magnetic nature. Another possibility is that this system is a He WD in a binary system with another WD or another degenerate object, which would make this object one of the few candidate non-accreting double degenerate binaries in any GC., Comment: Accepted for publication in MNRAS

Ultra-massive H-rich (DA spectral type) white dwarf stars ($M_{\star} > 1.05 M_{\odot}$) are expected to be substantially crystallized by the time they reach the ZZ Ceti instability strip ($T_{\rm eff} \sim 12\,000$ K). Crystallization leads to a separation of $^{16}$O and $^{20}$Ne (or $^{12}$C and $^{16}$O) in the core of ultra-massive WDs, which strongly impacts their pulsational properties. An additional factor to take into account when modeling the evolution and pulsations of WDs in this range of masses are the relativistic effects, which induce changes in the cooling times and the stellar masses derived from the effective temperature and surface gravity. Given the arrival of large amounts of photometric data from space missions such as {\it Kepler}/{\it K2} and {\it TESS}, it is important to assess the impact of General Relativity in the context of pulsations of ultra-massive ZZ Ceti stars. In this work, we present results of Newtonian gravity($g$)-mode pulsation calculations in evolutionary ultra-massive WD models computed in the frame of the General Relativity theory., Comment: 4 pages, 4 figures. Presented as a poster in the 22 European Workshop on White Dwarfs, that took place on August 15-19, 2022, in T\"ubingen, Germany. No proceedings were published at the conference

The {\sl TESS} space mission has recently demonstrated its great potential to discover new pulsating white dwarf and pre-white dwarf stars, and to detect periodicities with high precision in already known white-dwarf pulsators. We report the discovery of two new pulsating He-rich atmosphere white dwarfs (DBVs) and present a detailed asteroseismological analysis of three already known DBV stars employing observations collected by the {\sl TESS} mission along with ground-based data. We extracted frequencies from the {\sl TESS} light curves of these DBV stars using a standard pre-whitening procedure to derive the potential pulsation frequencies. All the oscillation frequencies that we found are associated with $g$-mode pulsations with periods spanning from $\sim 190$ s to $\sim 936$ s. We find hints of rotation from frequency triplets in some of the targets, including the two new DBVs. For three targets, we find constant period spacings, which allowed us to infer their stellar masses and constrain the harmonic degree $\ell$ of the modes. We also performed period-to-period fit analyses and found an asteroseismological model for three targets, with stellar masses generally compatible with the spectroscopic masses. Obtaining seismological models allowed us to estimate the seismological distances and compare them with the precise astrometric distances measured with {\it Gaia}. We find a good agreement between the seismic and the astrometric distances for three stars (PG~1351+489, EC~20058$-$5234, and EC~04207$-$4748), although for the other two stars (WD~J152738.4$-$50207 and WD~1708$-$871), the discrepancies are substantial. The high-quality data from the {\sl TESS} mission continue to provide important clues to determine the internal structure of pulsating pre-white dwarf and white dwarf stars through the tools of asteroseismology., Comment: 22 pages, 27 figures, 21 tables. To be published in Astronomy & Astrophysics

Ultra-massive white dwarfs ($ 1.05 \rm M_\odot \lesssim M_{WD}$) are particularly interesting objects that allow us to study extreme astrophysical phenomena such as type Ia supernovae explosions and merger events. Traditionally, ultra-massive white dwarfs are thought to harbour oxygen-neon (ONe) cores. However, recent theoretical studies and new observations suggest that some ultra-massive white dwarfs could harbour carbon-oxygen (CO) cores. Although several studies have attempted to elucidate the core composition of ultra-massive white dwarfs, to date, it has not been possible to distinguish them through their observed properties. Here, we present a new method for revealing the core-chemical composition in ultra-massive white dwarfs that is based on the study of magnetic fields generated by convective mixing induced by the crystallization process. ONe white dwarfs crystallize at higher luminosities than their CO counterparts. Therefore, the study of magnetic ultra-massive white dwarfs in the particular domain where ONe cores have reached the crystallization conditions but CO cores have not, may provide valuable support to their ONe core-chemical composition, since ONe white dwarfs would display signs of magnetic fields and CO would not. We apply our method to eight white dwarfs with magnetic field measurements and we suggest that these stars are candidate ONe white dwarfs., Comment: Accepted for publication in MNRAS Letters

Asteroseismology is a powerful tool to infer the evolutionary status and chemical stratification of white dwarf (WD) stars, and to explore the physical processes that lead to their formation. This is particularly true for the variable H-rich atmosphere (DA) WDs, known as DAV or ZZ Ceti stars. We present a new grid of DA WD models that take into account the last advances in the modeling and input physics of both the progenitor and the WD stars, thus avoiding and improving several shortcomings present in the set of DA WD models employed in the asteroseismological analyses of ZZ Ceti stars we carried out in our previous works. These new models are derived from a self-consistent way with the changes in the internal chemical distribution that result from the mixing of all the core chemical components induced by mean molecular-weight inversions, from $^{22}$Ne diffusion, Coulomb sedimentation, and from residual nuclearburning. In addition, the expected nuclear-burning history and mixing events along the progenitor evolution are accounted for, in particular the occurrence of third dredge-up, which determines the properties of the core and envelope of post-AGB and white dwarf stars, as well as the WD initial-final mass relation. The range of H envelopes of our new ZZ star models extends from log(M_H/M_*)= -4 to -5, to log(M_H/M_*)= -13.5. This allows, for the first time, to consider seismological solutions for ZZ Ceti stars with extremely thin H envelopes. Our new H-burning post-AGB models predict chemical profiles of O and C near the stellar centre of ZZ Ceti stars substantially different from those we used in our previous works. We find that the pulsation periods of $g$ modes and the mode-trapping properties of the new models differ significantly from those characterizing the ZZ Ceti models of our previous works, particularly for long periods., Comment: 12 pages, 14 figures, 1 table. To be published in Astronomy and Astrophysics

We present two new GW Vir-type pulsating white dwarf stars, TIC\,0403800675 (WD\,J115727.68-280349.64) and TIC\,1989122424 (WD J211738.38-552801.18) discovered in the Transiting Exoplanet Survey Satellite (TESS) photometric data. For both stars, the TESS light curves reveal the presence of oscillations with periods in a narrow range between 400 and 410\,s, which are associated with typical gravity ($g$)-modes. Follow-up ground-based spectroscopy shows that both stars have similar effective temperature ($T_\mathrm{eff} = 110,000 \pm 10,000$\,K) and surface gravity ($\log g = 7.5 \pm 0.5$), but different He/C composition (mass fractions): He\,=\,0.75 and C\,=\,0.25 for TIC\,0403800675, and He\,=\,0.50 and C\,=\,0.50 for TIC\,1989122424. By performing a fit to their spectral energy distributions, we found for both stars radii and luminosities of $R=0.019\pm0.002\,R_\odot$ and $\log(L/L_\odot)=1.68^{+0.15}_{-0.24}$, respectively. By employing evolutionary tracks of PG~1159 stars, we find the masses of both stars to be $0.56\pm0.18 M_{\odot}$ from the $\log g$-$T_\mathrm{eff}$ diagram and $0.60^{+0.11}_{-0.09} M_{\odot}$ from the Hertzsprung Russell diagram., Comment: 8 Pages. arXiv admin note: text overlap with arXiv:2108.11093

Recently a new class of hot subluminous stars strongly enriched in C and O have been discovered (CO-sdOs). These stars show abundances very similar to those observed in PG1159 stars but at lower temperatures. Moreover, it has been recently suggested that C and O enrichment might be the key ingredient driving the pulsations in He-rich hot subdwarf stars (He-sdBVs). Here we argue that these two types of rare stars can be explained by a variant of one of the main channels forming hot subdwarf stars. The scenario involves the formation and merging of a He-core white dwarf and a less massive CO-core white dwarf. We have constructed a simple merger models and computed their subsequent evolution. The merger products are in agreement with the surface parameters and composition of CO-sdOs. In addition, we have performed simulations including the effects of element diffusion and the excitation of pulsations. These simulations show that less massive merger products can form stellar structures that have surface parameters, abundances, and pulsation periods similar to those displayed by He-sdBVs. We conclude that the proposed scenario, or some variant of it, offers a very plausible explanation for the formation of CO-sdOs, pulsating He-sdBs and low-luminosity PG1159 stars., Comment: 6 Pages, 4Figures. Companion paper to "Discovery of hot subdwarfs with extremely high carbon and oxygen abundances" by Klaus Werner et alia

Ultra-massive white dwarfs ($\rm M_{WD} \gtrsim 1.05\, M_{\odot}$) are considered powerful tools to study type Ia supernovae explosions, merger events, the occurrence of physical processes in the Super Asymptotic Giant Branch (SAGB) phase, and the existence of high magnetic fields. Traditionally, ultra-massive white dwarfs are expected to harbour oxygen-neon (ONe) cores. However, new observations and recent theoretical studies suggest that the progenitors of some ultra-massive white dwarfs can avoid carbon burning, leading to the formation of ultra-massive white dwarfs harbouring carbon-oxygen (CO) cores. Here we present a set of ultra-massive white dwarf evolutionary sequences with CO cores for a wide range of metallicity and masses. We take into account the energy released by latent heat and phase separation during the crystallization process and by $^{22}$Ne sedimentation. Realistic chemical profiles resulting from the full computation of progenitor evolution are considered. We compare our CO ultra-massive white dwarf models with ONe models. We conclude that CO ultra-massive white dwarfs evolve significantly slower than their ONe counterparts mainly for three reasons: their larger thermal content, the effect of crystallization, and the effect of $^{22}$Ne sedimentation. We also provide colors in several photometric bands on the basis of new model atmospheres. These CO ultra-massive white dwarf models, together with the ONe ultra-massive white dwarf models, provide an appropriate theoretical framework to study the ultra-massive white dwarf population in our Galaxy., Comment: 9 pages, 6 figures, Accepted for publication in MNRAS

The collection of high-quality photometric data by space telescopes is revolutionizing the area of white-dwarf asteroseismology. Among the different kinds of pulsating white dwarfs, there are those that have He-rich atmospheres, and they are called DBVs or V777 Her variable stars. The archetype of these pulsating white dwarfs, GD~358, is the focus of the present paper. We report a thorough asteroseismological analysis of the DBV star GD~358 (TIC~219074038) based on new high-precision photometric data gathered by the {\it TESS} space mission combined with data taken from the Earth. In total, we detected 26 periodicities from the {\it TESS} light curve of this DBV star using a standard pre-whitening. The oscillation frequencies are associated with nonradial $g$(gravity)-mode pulsations with periods from $\sim 422$ s to $\sim 1087$ s. Moreover, we detected 8 combination frequencies between $\sim 543$ s and $\sim 295$ s. We combined these data with a huge amount of observations from the ground. We found a constant period spacing of $39.25\pm0.17$ s, which helped us to infer its mass ($M_{\star}= 0.588\pm0.024 M_{\sun}$) and constrain the harmonic degree $\ell$ of the modes. We carried out a period-fit analysis on GD~358, and we were successful in finding an asteroseismological model with a stellar mass ($M_{\star}= 0.584^{+0.025}_{-0.019} M_{\sun}$), in line with the spectroscopic mass ($M_{\star}= 0.560\pm0.028 M_{\sun}$). We found that the frequency splittings vary according to the radial order of the modes, suggesting differential rotation. Obtaining a seismological made it possible to estimate the seismological distance ($d_{\rm seis}= 42.85\pm 0.73$ pc) of GD~358, which is in very good accordance with the precise astrometric distance measured by {\it GAIA} EDR3 ($\pi= 23.244\pm 0.024, d_{\rm GAIA}= 43.02\pm 0.04$~pc)., Comment: 15 pages, 10 figures, 5 tables. To be published in Astronomy and Astrophysics. arXiv admin note: text overlap with arXiv:2011.03629

In this paper, we present the observations of two new GW Vir stars from the extended \textit{TESS} mission in both 120\,s short-cadence and 20\,s ultra-short-cadence mode of two pre-white dwarf stars showing hydrogen deficiency. We performed an asteroseismological analysis of these stars on the basis of PG~1159 evolutionary models that take into account the complete evolution of the progenitor stars. We searched for patterns of uniform period spacings in order to constrain the stellar mass of the stars, and employed the individual observed periods to search for a representative seismological model. The analysis of the {\it TESS} light curves of TIC\,333432673 and TIC\,095332541 reveals the presence of several oscillations with periods ranging from 350 to 500~s associated to typical gravity ($g$)-modes. From follow-up ground-based spectroscopy, we find that both stars have similar effective temperature ($T_\mathrm{eff} = 120,000 \pm 10,000$\,K) and surface gravity ($\log g = 7.5 \pm 0.5$) but a different He/C composition. On the basis of PG~1159 evolutionary tracks, we derived a spectroscopic mass of $M_{\star}$ = $0.58^{+0.16}_{-0.08}\,M_{\odot}$ for both stars. Our asteroseismological analysis of TIC\,333432673 allowed us to find a constant period spacing compatible with a stellar mass $M_{\star}\sim 0.60-0.61\,M_{\odot}$, and an asteroseismological model for this star with a stellar mass $M_{\star}$ = $0.589\pm 0.020$ $M_{\odot}$, and a seismological distance of $d= 459^{+188}_{-156}$ pc. For this star, we find an excellent agreement between the different methods to infer the stellar mass, and also between the seismological distance and that measured with {\it Gaia} ($d_{\rm Gaia}= 389^{+5.6}_{-5.2}$ pc). For TIC\,095332541, we have found a possible period spacing that suggests a stellar mass of $M_{\star}\sim 0.55-0.57\,M_{\odot}$., Comment: 12 pages, 13 figures, Accepted for publication in A&A. arXiv admin note: text overlap with arXiv:2011.03629

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 to shed some light on the internal structure of these stars through asteroseismology. 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 $\varepsilon$ mechanism is able to excite gravity-mode pulsations. We carried out a nonadiabatic pulsation analysis for low-mass helium-core white-dwarf models going through CNO flashes during their early cooling phases. We found that the $\varepsilon$ mechanism due to stable hydrogen burning can excite low-order ($\ell= 1, 2$) gravity modes with periods between $\sim 80$ and $500\ $s, for stars with $0.2025 \lesssim M_{\star}/M_{\odot} \lesssim 0.3630$ located in an extended region of the $\log g - T_{\rm eff}$ diagram with effective temperature and surface gravity in the ranges $15\,000 \lesssim T_{\rm eff} \lesssim 38\,000\ $K and $5.8 \lesssim \log g \lesssim 7.1$, respectively. 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. 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 $\varepsilon$ mechanism. In addition, confirming a rapid rate of period change in these pulsations would support that these stars actually experience CNO flashes, as predicted by evolutionary calculations., Comment: 9 pages, 6 figures, 1 table. To be published in Astronomy and Astrophysics

Ultra-massive white dwarfs are relevant for their role as type Ia Supernova progenitors, the occurrence of physical processes in the asymptotic giant-branch phase, the existence of high-field magnetic white dwarfs, and the occurrence of double white dwarf mergers. Some hydrogen-rich ultra-massive white dwarfs are pulsating stars, and as such, they offer the possibility of studying their interiors through asteroseismology. On the other hand, pulsating helium-rich ultra-massive white dwarfs could be even more attractive objects for asteroseismology if they were found, as they should be hotter and less crystallized than pulsating hydrogen-rich white dwarfs, something that would pave the way for probing their deep interiors. We explore the pulsational properties of ultra-massive helium-rich white dwarfs with carbon-oxygen and oxygen-neon cores resulting from single stellar evolution. Our goal is to provide a theoretical basis that could eventually help to discern the core composition of ultra-massive white dwarfs and the scenario of their formation through asteroseismology, anticipating the possible future detection of pulsations in this type of stars. We find that, given that the white dwarf models coming from the three scenarios considered are characterized by distinct core chemical profiles, their pulsation properties are also different, thus leading to distinctive signatures in the period-spacing and mode-trapping properties. Our results indicate that, in case of an eventual detection of pulsating ultra-massive helium-rich white dwarfs, it would be possible to derive valuable information encrypted in the core of these stars in connection with the origin of such exotic objects. The detection of pulsations in these stars has many chances to be achieved soon through observations collected with ongoing space missions., Comment: 8 pages, 10 figures. To be published in A&A. arXiv admin note: text overlap with arXiv:2011.10439

(Abridged abstract) We explore the formation of ultra-massive (M_{\rm WD} \gtrsim 1.05 M_\sun$), carbon-oxygen core white dwarfs resulting from single stellar evolution. We also study their evolutionary and pulsational properties and compare them with those of the ultra-massive white dwarfs with oxygen-neon cores resulting from carbon burning in single progenitor stars, and with binary merger predictions. We consider two single-star evolution scenarios for the formation of ultra-massive carbon-oxygen core white dwarfs that involve rotation of the degenerate core after core helium burning and reduced mass-loss rates in massive asymptotic giant-branch stars. We compare our findings with the predictions from ultra-massive white dwarfs resulting from the merger of two equal-mass carbon-oxygen core white dwarfs, by assuming complete mixing between them and a carbon-oxygen core for the merged remnant. The resulting ultra-massive carbon-oxygen core white dwarfs evolve markedly slower than their oxygen-neon counterparts. Our study strongly suggests the formation of ultra-massive white dwarfs with carbon-oxygen core from single stellar evolution. We find that both the evolutionary and pulsation properties of these white dwarfs are markedly different from those of their oxygen-neon core counterparts and from those white dwarfs with carbon-oxygen core that might result from double degenerate mergers. This can eventually be used to discern the core composition of ultra-massive white dwarfs and their formation scenario., Comment: 15 pages, 10 figures, 2 tables. To be published in Astronomy and Astrophysics

In this paper, we present a detailed asteroseismological analysis of six GW Vir stars including the observations collected by the TESS mission. We processed and analyzed TESS observations of RX J2117+3412, HS 2324+3944, NGC 6905, NGC 1501, NGC 2371, and K 1-16. We carried out a detailed asteroseismological analysis of these stars on the basis of PG 1159 evolutionary models that take into account the complete evolution of the progenitor stars. In total, we extracted 58 periodicities from the TESS light curves using a standard pre-whitening procedure to derive the potential pulsation frequencies. All the oscillation frequencies that we found are associated with g-mode pulsations with periods spanning from $\sim 817$ s to $\sim 2682$ s. We find constant period spacings for all but one star, which allowed us to infer their stellar masses and constrain the harmonic degree $\ell$ of the modes. We performed period-to-period fit analyses on five of the six analyzed stars. For four stars, we were able to find an asteroseismological model with masses in agreement with the stellar-mass values inferred from the period spacings, and generally compatible with the spectroscopic masses. We estimated the seismological distance and compared it with the precise astrometric distance measured with GAIA. Finally, we find that the period spectrum of K 1-16 exhibits dramatic changes in frequency and amplitude. The high-quality data collected by the TESS space mission, considered simultaneously with ground-based observations, are able to provide a very valuable input to the asteroseismology of GW Vir stars, similar to the case of other classes of pulsating white-dwarf stars. The TESS mission, in conjunction with future space missions and upcoming surveys, will make impressive progress in white-dwarf asteroseismology., Comment: 34 pages, 33 figures, 21 tables. Accepted for publication in Astronomy and Astrophysics

Element diffusion is a key physical process that substantially impacts the superficial abundances, internal structure, pulsation properties, and evolution of white dwarfs. We study the effect of Coulomb separation of ions in the cooling times of evolving white dwarfs, their chemical profiles, the Brunt-V\"ais\"al\"a (buoyancy) frequency, and the pulsational periods at the ZZ Ceti instability strip. We follow the full evolution of white-dwarf models derived from their progenitor history on the basis of a time-dependent element diffusion scheme that incorporates the effect of gravitational settling of ions due to Coulomb interactions at high densities. We find that Coulomb sedimentation profoundly alters the chemical profiles of ultra-massive ($M_*> 1 M_{sun}$) white dwarfs along their evolution, preventing helium from diffusing inward toward the core, and thus leading to much narrower chemical transition zones. As a result, significant changes in the $g$-mode pulsation periods as high as $15 \%$ are expected for ultra-massive ZZ Ceti stars. This should be taken into account in detailed asteroseismological analyses of such stars. For less-massive white dwarfs, the impact of Coulomb separation is much less noticeable, inflicting period changes in ZZ Ceti stars that are below the period changes that result from uncertainties in progenitor evolution, albeit larger than typical uncertainties of observed periods., Comment: 6 pages, 4 figures. Accepted for publication in Astronomy and Astrophysics

White dwarf stars are the most common end point of stellar evolution. Of special interest are the ultramassive white dwarfs, as they are related to type Ia Supernovae explosions, merger events, and Fast Radio Bursts. Ultramassive white dwarfs are expected to harbour oxygen-neon (ONe) cores as a result of single standard stellar evolution. However, a fraction of them could have carbon-oxygen (CO) cores. Recent studies, based on the new observations provided by the {\it Gaia} space mission, indicate that a small fraction of the ultramassive white dwarfs experience a strong delay in their cooling, which cannot be attributed only to the occurrence of crystallization, thus requiring an unknown energy source able to prolong their life for long periods of time. In this study we find that the energy released by $^{22}$Ne sedimentation in the deep interior of ultramassive white dwarfs with CO cores and high $^{22}$Ne content is consistent with the long cooling delay of these stellar remnants. On the basis of a synthesis study of the white dwarf population, based on Monte Carlo techniques, we find that the observations revealed by {\it Gaia} can be explained by the existence of these prolonged youth ultramassive white dwarfs. Although such a high $^{22}$Ne abundance is not consistent with the standard evolutionary channels, our results provide sustain to the existence of CO-core ultramassive white dwarfs and to the occurrence of $^{22}$Ne sedimentation., Comment: 5 pages, 4 figures. Accepted for publication in A&A Letters

All evolved stars with masses $M_\star\lesssim 2M_\odot$ undergo a helium(He)-core flash at the end of their first stage as a giant star. Although theoretically predicted more than 50 years ago, this core-flash phase has yet to be observationally probed. We show here that gravity modes (g modes) stochastically excited by He-flash driven convection are able to reach the stellar surface, and induce periodic photometric variabilities in hot-subdwarf stars with amplitudes of the order of a few mmag. As such they can now be detected by space-based photometry with the Transiting Exoplanet Survey Satellite (TESS) in relatively bright stars (e.g. magnitudes $I_C\lesssim 13$). The range of predicted periods spans from a few thousand seconds to tens of thousand seconds, depending on the details of the excitation region. In addition, we find that stochastically excited pulsations reproduce the pulsations observed in a couple of He-rich hot subdwarf stars. These stars, and in particular the future TESS target Feige 46, are the most promising candidates to probe the He-core flash for the first time., Comment: 14 Figures including Supplementary Information. Letter to Nature Astronomy

Two of the possibilities for the formation of low-mass ($M_{\star}\lesssim 0.5\,M_{\odot}$) hydrogen-deficient white dwarfs are the occurrence of a very-late thermal pulse after the asymptotic giant-branch phase or a late helium-flash onset in an almost stripped core of a red giant star. We aim to asses the potential of asteroseismology to distinguish between the hot flasher and the very-late thermal pulse scenarios for the formation of low-mass hydrogen-deficient white dwarfs. We compute the evolution of low-mass hydrogen-deficient white dwarfs from the zero-age main sequence in the context of the two evolutionary scenarios. We explore the pulsation properties of the resulting models for effective temperatures characterizing the instability strip of pulsating helium-rich white dwarfs. We find that there are significant differences in the periods and in the period spacings associated with low radial-order ($k\lesssim 10$) gravity modes for white-dwarf models evolving within the instability strip of the hydrogen-deficient white dwarfs. The measurement of the period spacings for pulsation modes with periods shorter than $\sim500\,$s may be used to distinguish between the two scenarios. Moreover, period-to-period asteroseismic fits of low-mass pulsating hydrogen-deficient white dwarfs can help to determine their evolutionary history., Comment: 7 pages, 7 figures. Accepted for publication in A&A

The possible existence of warm ($T_{\rm eff}\sim19\,000$ K) pulsating DA white dwarf (WD) stars, hotter than ZZ Ceti stars, was predicted in theoretical studies more than 30 yr ago. However, to date, no pulsating warm DA WD has been discovered. 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 TESS satellite up to Sector 9 in order to search for the possible pulsational signal. We compute WD evolutionary sequences with H content in the range $-14.5 \lesssim \log(M_{\rm H}/M_{\star}) \lesssim -10$, appropriate for the study of warm DA WDs. We use a new full-implicit treatment of time-dependent element diffusion. Non-adiabatic pulsations were computed in the effective temperature range of $30\,000-10\,000$ K, focusing on $\ell= 1$ $g$ modes with periods in the range $50-1500$ s. We find that extended He/H transition zones inhibit the excitation of $g$ modes due to partial ionization of He below the H envelope, and only in the case that the H/He transition is assumed much more abrupt, models do exhibit pulsational instability. In this case, instabilities are found only in WD models with H envelopes in the range of $-14.5 \lesssim \log(M_{\rm H}/M_{\star}) \lesssim -10$ and at effective temperatures higher than those typical of ZZ Ceti stars, in agreement with previous studies. None of the 36 warm DAs observed so far by TESS satellite are found to pulsate. Our study suggests that the non-detection 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 an indirect proof that element diffusion indeed operates in the interior of WDs., Comment: 13 pages, 15 figures, 2 tables. Accepted for publication in Astronomy and Astrophysics

Ultra-massive hydrogen-rich (DA) white dwarfs (WD) are expected to have a substantial portion of their cores in a crystalline state at the effective temperatures characterizing the ZZ Ceti instability strip, as a result of Coulomb interactions. Asteroseismological analyses of these WDs can provide valuable information related to the crystallization process, the core chemical composition and the evolutionary origin of these stars. We present a thorough asteroseismological analysis of the ultra-massive ZZ Ceti star BPM~37093, which exhibits a rich period spectrum, on the basis of a complete set of fully evolutionary models that represent ultra-massive oxygen/neon(ONe)-core DA WD stars harbouring a range of hydrogen (H) envelope thicknesses. We also carry out preliminary asteroseismological inferences on two other ultra-massive ZZ Ceti stars that exhibit fewer periods, GD~518, and SDSS~J0840+5222. We found a mean period spacing of $\Delta \Pi \sim 17$ s in the data of BPM~37093, associated to $\ell= 2$ modes. We found asteroseismological models for the three objects under analysis, two of them (BPM~37093 and GD~518) characterized by canonical (thick) H envelopes, and the third one (SDSS~J0840+5222) with a thinner H envelope. We also derive asteroseismological distances which are somewhat different to the astrometric measurements of {\it Gaia} for these stars. Asteroseismological analyses like the one presented in this paper could lead to a more complete knowledge of the processes occurring during crystallization inside WDs. Also, they could make it possible to deduce the core chemical composition of ultra-massive WDs, and in this way, to infer their evolutionary origin, i.e., if the star has a ONe core and then is the result of single-star evolution, or if it harbour a carbon/oxygen (CO) core and is the product of a merger of the two components of a binary system., Comment: 13 pages, 10 figures, 7 tables. To be published in Astronomy and Astrophysics

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 TESS will record pulsation signatures from bright white dwarfs over the entire sky. We aim to demonstrate the sensitivity of TESS data to measuring pulsations of helium-atmosphere white dwarfs in the DBV instability strip, and what asteroseismic analysis of these measurements can constrain about their stellar structures. We present a case study of the pulsating DBV WD 0158$-$160 that was observed as TIC 257459955 with the 2-minute cadence for 20.3 days in TESS Sector 3. We measure the frequencies of variability of TIC 257459955 with an iterative periodogram and prewhitening procedure. The measured frequencies are compared to calculations from two sets of white dwarf models to constrain the stellar parameters: the fully evolutionary models from LPCODE, and the structural models from WDEC. We detect and measure the frequencies of nine pulsation modes and eleven combination frequencies of WD 0158$-$160 to $\sim0.01 \mu$Hz precision. Most, if not all, of the observed pulsations belong to an incomplete sequence of dipole ($\ell=1$) modes with a mean period spacing of $38.1\pm1.0$ s. The global best-fit seismic models from both codes have effective temperatures that are $\gtrsim3000$ 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., Comment: 13 pages, 12 figures, accepted for publication in A&A. The abstract reproduced here has been shorted to meet arXiv's character limit

Asteroseismology of white dwarf (WD) stars is a powerful tool that allows to reveal the hidden chemical structure of WD and infer details about their evolution by comparing the observed periods with those obtained from stellar models. A recent asteroseismological study has reproduced the period spectrum of the helium rich pulsating WD KIC 08626021 with an unprecedented precision. The chemical structure derived from that analysis is notably different from that expected for a WD according to currently accepted formation channels, thus posing a challenge to the theory of stellar evolution. We explore the relevant micro- and macro-physics processes acting during the formation and evolution of KIC 08626021 that could lead to a chemical structure similar to that found through asteroseismology. We quantify to which extent is necessary to modify the physical processes that shapes the chemical structure, in order to reproduce the most important features of the asteroseismic model. We model the previous evolution of KIC 08626021 by exploring specific changes in the 12C+alpha reaction rate, screening processes, microscopic diffusion, as well as convective boundary mixing during core-He burning. We find that, in order to reproduce the core chemical profile derived for KIC 0862602, the 12C+alpha nuclear reaction rate has to be increased by a factor of $\sim$ 10 during the helium-core burning, and reduced by a factor of $\sim$ 1000 during the following helium-shell burning, as compared with the standard predictions for this rate. In addition, the main chemical structures derived for KIC 0862602 cannot be reconciled with our present knowledge of white dwarf formation. We find that within our current understanding of white dwarf formation and evolution, it is difficult to reproduce the most important asteroseismologically-derived features of the chemical structure of KIC 08626021., Comment: 8 pages, 6 figures, accepted for publication in A&A

We analyzed the velocity space of the thin and thick-disk Gaia white dwarf population within 100 pc looking for signatures of the Hercules stellar stream. We aimed to identify those objects belonging to the Hercules stream and, by taking advantage of white dwarf stars as reliable cosmochronometers, to derive a first age distribution. We applied a kernel density estimation to the $UV$ velocity space of white dwarfs. For the region where a clear overdensity of stars was found, we created a 5-D space of dynamic variables. We applied a hierarchichal clustering method, HDBSCAN, to this 5-D space, identifying those white dwarfs that share similar kinematic characteristics. Finally, under general assumptions and from their photometric properties, we derived an age estimate for each object. The Hercules stream was firstly revealed as an overdensity in the $UV$ velocity space of the thick-disk white dwarf population. Three substreams were then found: Hercules $a$ and Hercules $b$, formed by thick-disk stars with an age distribution peaked $4\,$Gyr in the past and extended to very old ages; and Hercules $c$, with a ratio of 65:35 thin:thick stars and a more uniform age distribution younger than 10 Gyr., Comment: 5 pages, 3 figures, accepted for publication in A&A Letters

White dwarf stars constitute the final evolutionary stage for more than 95 per cent of all stars. The Galactic population of white dwarfs conveys a wealth of information about several fundamental issues and are of vital importance to study the structure, evolution and chemical enrichment of our Galaxy and its components ---including the star formation history of the Milky Way. In addition, white dwarfs are tracers of the evolution of planetary systems along several phases of stellar evolution. Also, white dwarfs are used as laboratories for astro-particle physics, being their interest focused on physics beyond the standard model. The last decade has witnessed a great progress in the study of white dwarfs. In particular, a wealth of information of these stars from different surveys has allowed us to make meaningful comparison of evolutionary models with observations. While some information like surface chemical composition, temperature and gravity of isolated white dwarfs can be inferred from spectroscopy, and the total mass and radius can be derived as well when they are in binaries, the internal structure of these compact stars can be unveiled only by means of asteroseismology, an approach based on the comparison between the observed pulsation periods of variable stars and the periods predicted by appropriate theoretical models. The asteroseismological techniques allow us to infer details of the internal chemical stratification, the total mass, and even the stellar rotation profile. In this review, we first revise the evolutionary channels currently accepted that lead to the formation of white-dwarf stars, and then, we give a detailed account of the different sub-types of pulsating white dwarfs known so far, emphasizing the recent observational and theoretical advancements in the study of these fascinating variable stars., Comment: 104 pages, 25 figures, 14 tables. To be published in The Astronomy and Astrophysics Review

We analyze the effect of the sedimentation of $^{22}$Ne on the local white dwarf luminosity function by studying scenarios under different Galactic metallicity models. We make use of an up-to-date population synthesis code based on Monte Carlo techniques to derive the synthetic luminosity function. Constant solar metallicity models are not able to simultaneously reproduce the peak and cut-off of the white dwarf luminosity function. The extra release of energy due to $^{22}$Ne sedimentation piles up more objects in brighter bins of the faint end of the luminosity function. The contribution of a single burst thick disk population increases the number of stars in the magnitude interval centered around $M_{\rm bol}=15.75$. Among the metallicity models studied, the one following a Twarog's profile is disposable. Our best fit model was obtained when a dispersion in metallicities around the solar metallicity value is considered along with a $^{22}$Ne sedimentation model, a thick disk contribution and an age of the thin disk of $8.8\pm0.2$ Gyr. Our population synthesis model is able to reproduce the local white dwarf luminosity function with a high degree of precision when a dispersion in metallicities around the solar value model is adopted. Although the effects of $^{22}$Ne sedimentation are only marginal and the contribution of a thick disk population is minor, both of them help in better fitting the peak and the cut-off regions of the white dwarf luminosity function., Comment: 11 pages, 9 figures and 2 tables; accepted for publication in A&A

Some low-mass white-dwarf (LMWD) stars with H atmospheres show long-period g-mode pulsations, comprising the class of pulsating WDs called extremely low-mass variable (ELMV) stars. It is generally believed that these stars have thick H envelopes. However, from stellar evolution considerations, the existence of LMWDs with thin H envelopes is also possible. We present a thorough asteroseismological analysis of ELMV stars based on a complete set of fully evolutionary models that represents low-mass He-core WD stars harboring a range of H envelope thicknesses. Although there are currently nine ELMVs, here we only focus on those that exhibit more than three periods and whose periods do not show significant uncertainties. We considered g-mode adiabatic pulsation periods for low-mass He-core WD models with $M_*$ in the range [0.1554-0.4352]$M_{\odot}$, $T_{\rm eff}$ in the range [6000-10000]K, and H envelope thicknesses in the range -5.8

The Blue Large-Amplitude Pulsators (BLAPs) constitute a new class of pulsating stars. They are hot stars with effective temperatures of $T_{\rm eff}\sim 30\,000$ K and surface gravities of $\log g \sim 4.9$, that pulsate with periods in the range $\sim 20-40$ min. In Romero et al. (2018), we proposed that BLAPs are hot low-mass He-core pre-white dwarf (WD) stars that pulsate either in high-order non-radial $g$(gravity) modes or low-order radial modes, including the fundamental radial mode. The theoretical modes with periods in the observed range are unstable due to the $\kappa$ mechanism associated with the $Z$ bump in the opacity at $\log T \sim 5.25$. In this work, we extend the study of Romero et al. (2018) by assessing the rate of period changes of nonradial $g$ modes and radial modes and comparing them with the values measured for BLAPs, in an attempt to validate the proposed evolutionary scenario, and to discern whether the observed modes are high-order $g$ modes or radial modes., Comment: 7 pages and 9 figures. Submitted as Proceedings for the 21st European White Dwarf Workshop held July 23-27, 2018, Austin, Texas

Ultra-massive white dwarfs are powerful tools to study various physical processes in the Asymptotic Giant Branch (AGB), type Ia supernova explosions and the theory of crystallization through white dwarf asteroseismology. Despite the interest in these white dwarfs, there are few evolutionary studies in the literature devoted to them. Here, we present new ultra-massive white dwarf evolutionary sequences that constitute an improvement over previous ones. In these new sequences, we take into account for the first time the process of phase separation expected during the crystallization stage of these white dwarfs, by relying on the most up-to-date phase diagram of dense oxygen/neon mixtures. Realistic chemical profiles resulting from the full computation of progenitor evolution during the semidegenerate carbon burning along the super-AGB phase are also considered in our sequences. Outer boundary conditions for our evolving models are provided by detailed non-gray white dwarf model atmospheres for hydrogen and helium composition. We assessed the impact of all these improvements on the evolutionary properties of ultra-massive white dwarfs, providing up-dated evolutionary sequences for these stars. We conclude that crystallization is expected to affect the majority of the massive white dwarfs observed with effective temperatures below $40\,000\, \rm K$. Moreover, the calculation of the phase separation process induced by crystallization is necessary to accurately determine the cooling age and the mass-radius relation of massive white dwarfs. We also provide colors in the GAIA photometric bands for our H-rich white dwarf evolutionary sequences on the basis of new models atmospheres. Finally, these new white dwarf sequences provide a new theoretical frame to perform asteroseismological studies on the recently detected ultra-massive pulsating white dwarfs., Comment: 13 pages, 15 figures, 4 tables. Accepted for publication in Astronomy & Astrophysics

Ultra-massive DA WD stars are expected to harbor ONe cores resulting from the progenitor evolution through the Super-AGB phase. As evolution proceeds during the WD cooling phase, a crystallization process resulting from Coulomb interactions in very dense plasmas is expected to occur, leading to the formation of a highly crystallized core. Pulsating ultra-massive WDs offer a unique opportunity to infer and test the occurrence of crystallization in WD interiors as well as physical processes related with dense plasmas. We aim to assess the adiabatic pulsation properties of ultra-massive DA WD with ONe cores. We studied the pulsation properties of ultra-massive DA WD stars with ONe cores. We employed a new set of ultra-massive WD evolutionary sequences of models with stellar masses in the range 1.10 $\leq M_{star}/M_{sun} \leq$ 1.29 computed by taking into account the complete evolution of the progenitor stars and the WD stage. When crystallization set on in our models, we took into account latent heat release and also the expected changes in the core chemical composition that are due to phase separation according to a phase diagram suitable for O and Ne plasmas. We computed nonradial pulsation g-modes of our sequences of models at the ZZ Ceti phase by taking into account a solid core. We explored the impact of crystallization on their pulsation properties, in particular, the structure of the period spectrum and the distribution of the period spacings. We find that it would be possible, in principle, to discern whether a WD has a nucleus made of CO or a nucleus of ONe by studying the spacing between periods. The features found in the period-spacing diagrams could be used as a seismological tool to discern the core composition of ultra-massive ZZ Ceti stars, something that should be complemented with detailed asteroseismic analysis using the individual observed periods., Comment: 10 pages, 12 figures, 1 table. Accepted for publication in Astronomy \& Astrophysics

We present optical high-speed photometry of three millisecond pulsars with low-mass ($< 0.3 M_{\odot}$) white dwarf companions, bringing the total number of such systems with follow-up time-series photometry to five. We confirm the detection of pulsations in one system, the white dwarf companion to PSR J1738+0333, and show that the pulsation frequencies and amplitudes are variable over many months. A full asteroseismic analysis for this star is under-constrained, but the mode periods we observe are consistent with expectations for a $M_{\star} = 0.16 - 0.19 M_{\odot}$ white dwarf, as suggested from spectroscopy. We also present the empirical boundaries of the instability strip for low-mass white dwarfs based on the full sample of white dwarfs, and discuss the distinction between pulsating low-mass white dwarfs and subdwarf A/F stars., Comment: MNRAS, in press

Pulsating extremely low-mass pre-white dwarf stars (pre-ELMV), with masses between ~0.15 Msun and ~0.30 Msun, constitute a new class of variable stars showing g- and possibly p-mode pulsations with periods between 320 and 6000 s, while main sequence delta Scuti stars, with masses between 1.2-2.5 Msun, pulsate in low-order g and p modes with periods in the range [700-28800] s. Interestingly enough, the instability strips of pre-ELM white dwarf and delta Scuti stars nearly overlap in the Teff vs. log g diagram, leading to a degeneracy when spectroscopy is the only tool to classify the stars and pulsation periods only are considered. We employ adiabatic and non-adiabatic pulsation for models of pre-ELM and delta Scuti stars, and compare their pulsation periods, period spacings and rates of period change. We found substantial differences in the periods spacing of delta Scuti and pre-ELM white dwarf models. Even when the same period range is observed, the modes have distinctive signature in the period spacing and period difference values. For instance, the mean period difference of p- modes of consecutive radial orders for delta Scuti model are at least four times longer than the mean period spacing for the pre-ELM white dwarf model in the period range [2000 - 4600] s. In addition, the rate of period change is two orders of magnitudes larger for the pre-ELM white dwarfs compared to delta Scuti stars. In addition, we also report the discovery of a new variable star, SDSSJ075738.94+144827.50, located in the region of the Teff vs. log g diagram where these two kind of stars coexist. The characteristic spacing between modes of consecutive radial orders (p as well as g modes) and the large differences found in the rates of period change for delta Scuti and pre-ELM white dwarf stars suggest that asteroseismology can be employed to discriminate between these two groups of variable stars., Comment: accepted for publication in Astronomy & Astrophysics

Extremely low-mass white dwarf (ELM WD; $M_{\star}$ $\lesssim$ $0.18-0.20\ $ $M_{\odot}$) stars are thought to be formed in binary systems via stable or unstable mass transfer. Although stable mass transfer predicts the formation of ELM WDs with thick hydrogen (H) envelopes, and hence characterized by dominant residual nuclear burning along the cooling branch, the formation of ELM WDs with thinner H envelopes from unstable mass loss cannot be discarded. We compute new evolutionary sequences for helium (He) core WD stars with thin H envelope with the main aim of assessing the lowest $T_{\rm eff}$ that could be reached by this type of stars. We generate a new grid of evolutionary sequences of He core WD stars with thin H envelope in the mass range from $0.1554$ to $0.2025 M_{\odot}$, and assess the changes in both the cooling times and surface gravity induced by a reduction of the H envelope. We also determine, taking into account the predictions of progenitor evolution, the lowest $T_{\rm eff}$ reached by the resulting ELM WDs. We find that a slight reduction in the H envelope yields a significant increase in the cooling rate of ELM WDs. Because of this, ELM WDs with thin H envelope could cool down to $\sim 2500\ $K, in contrast with their canonical counterparts that cool down to $\sim 7000\ $K. In addition, we find that a reduction of the thickness of the H envelope increases markedly the surface gravity ($g$) of these stars. If ELM WDs are formed with thin H envelopes, they could be detected at very low $T_{\rm eff}$. The detection of such cool ELM WDs would be indicative that they were formed with thin H envelopes, thus opening the possibility of placing constraints to the possible mechanisms of formation of this type of stars. Last but not least, the increase in $g$ due to the reduction of the H envelope leads to consequences in the spectroscopic determinations of these stars., Comment: 7 pages, 4 figures, 1 table. Accepted for publication in Astronomy & Astrophysics

The thermally pulsing phase on the asymptotic giant branch (TP-AGB) is the last nuclear burning phase experienced by most of low and intermediate mass stars. During this phase, the outer chemical stratification above the C/O core of the emerging white dwarf is built up. The chemical structure resulting from progenitor evolution strongly impacts the whole pulsation spectrum exhibited by ZZ Ceti stars, which are pulsating C/O core white dwarfs located on an narrow instability strip at T eff \sim 12000 K. Several physical processes occurring during progenitor evolution strongly affect the chemical structure of these stars, being those found during the TP-AGB phase ones of the most relevant for the pulsational properties of ZZ Ceti stars. We present a study of the impact of the chemical structure built up during the TP-AGB evolution on the stellar parameters inferred from asteroseismological fits of ZZ Ceti stars. Our analysis is based on a set of carbon-oxygen core white dwarf models with masses from 0.534 to 0.6463M_{\odot} derived from full evolutionary computations from the ZAMS to the ZZ Ceti domain. We compute evolutionary sequences that experience different number of thermal pulses. We find that the occurrence or not of thermal pulses during AGB evolution implies an average deviation in the astero- seimological effective temperature of ZZ Ceti stars of at most 8% and of the order of < 5% in the stellar mass. For the mass of the hydrogen envelope, however, we find deviations up to 2 orders of magnitude in the case of cool ZZ Ceti stars. For hot and intermediate temperature ZZ Ceti stars shows no differences in the hydrogen envelope mass in most cases. Our results show that, in general, the impact of the occurrence or not of thermal pulses in the progenitor stars is not negligible and must be taken into account in asteroseismological studies of ZZ Ceti stars., Comment: 8 pages, 8 figures. To be published in A&A

The $\epsilon$ mechanism is a self-excitation mechanism of stellar pulsations which acts in regions inside the star where nuclear burning takes place. It has been shown that the $\epsilon$ mechanism can excite pulsations in models of hot pre-horizontal branch stars, and that the shortest periods of LS IV-14$^{\circ}$116 could be explained that way. We aim to study the $\epsilon$ mechanism in stellar models appropriate for hot pre-horizontal branch stars to predict their pulsational properties and the instability domain in the $\log g-\log T_{\rm eff}$ plane. We perform detailed computations of non-adiabatic non-radial pulsations on stellar models during the helium subflashes just before the helium-core burning phase. We find an instability domain of long-period gravity modes due to the $\epsilon$ mechanism in the $\log g-\log T_{\rm eff}$ plane at roughly $22000\,{\rm K} \lesssim T_{\rm eff}\lesssim 50000\,$K and $4.67 \lesssim \log g \lesssim 6.15$. Consequently, we find instabilities due to the $\epsilon$ mechanism on pre-extreme horizontal branch stellar models ($T_{\rm eff}\gtrsim 22000\,$K), but not on pre-blue horizontal branch stellar models ($T_{\rm eff}\lesssim 21000\,$K). The periods of excited modes range between $\sim 200$ and $\sim2000\,$s. Comparison with the three known pulsating He-rich subdwarfs shows that $\epsilon$ mechanism can excite gravity modes in stars with similar surface properties, but in our models it is only able to excite modes in the range of the shortest observed periods. We predict a new instability strip for hot-subdwarf stars of which LS IV-14$^{\circ}$116 could be the first inhabitant. Based on simple estimates we expect 1 to 10 stars in the current samples of hot-subdwarf stars to be pulsating by the $\epsilon$ mechanism. Our results could constitute a theoretical basis for future searches of pulsators in the Galactic field., Comment: 13 pages, 11 figures, accepted for publication in A&A

Many pulsating low-mass white-dwarf stars have been detected in the last years in the field of our Galaxy. Given that some of them exhibit multiperiodic variation of brightness, it is possible to probe their interiors through asteroseismology. We present a detailed asteroseismological study of all the known low-mass variable white dwarf stars based on a complete set of fully evolutionary models representative of low-mass He-core white dwarf stars. We employed adiabatic radial and nonradial pulsation periods for low-mass white dwarf models with stellar masses ranging from $0.1554$ to $0.4352\ M_{\odot}$, that were derived by simulating the nonconservative evolution of a binary system consisting of an initially $1 M_{\odot}$ ZAMS star and a $1.4 M_{\odot}$ neutron star companion. We estimated the mean period spacing for the stars under study and then we used the comparison between the observed period spacing with the average of the computed period spacings for our grid of models to constrain the stellar mass. We also employed the individual observed periods of every known pulsating low-mass white dwarf star, to search for a representative seismological model. We found that even though the stars under analysis exhibit few periods and the period fits show multiplicity of solutions, it is possible to find seismological models whose mass and effective temperature are in agreement with the values given by spectroscopy, for most of the cases. In the two cases where we could extract the period spacing from the set of observed periods, this method led to values of the stellar masses substantially larger than expected for this type of stars. The results presented in this work show in the one hand, the need for further photometric searches, and on the other hand, some improvements of the theoretical models, in order to place the asteroseismological results on a firmer ground., Comment: 16 pages, 16 figures, 30 tables. Accepted for publication in Astronomy & Astrophysics

We present a set of full evolutionary sequences for white dwarfs with hydrogen-deficient atmospheres. We take into account the evolutionary history of the progenitor stars, all the relevant energy sources involved in the cooling, element diffusion in the very outer layers, and outer boundary conditions provided by new and detailed non-gray white dwarf model atmospheres for pure helium composition. These model atmospheres are based on the most up-to-date physical inputs. Our calculations extend down to very low effective temperatures, of $\sim 2\,500$~K, provide a homogeneous set of evolutionary cooling tracks that are appropriate for mass and age determinations of old hydrogen-deficient white dwarfs, and represent a clear improvement over previous efforts, which were computed using gray atmospheres., Comment: 40 pages, 13 figures. To be published in ApJ

We present a theoretical assessment of the expected temporal rates of change of periods ($\dot{\Pi}$) for low-mass ($M_{\star}/M_{\sun} \lesssim 0.45$) and extremely low-mass (ELM, $M_{\star}/M_{\sun} \lesssim 0.18-0.20$) white-dwarf stars, based on fully evolutionary low-mass He-core white dwarf and pre-white dwarf models. Our analysis is based on a large set of adiabatic periods of radial and nonradial pulsation modes computed on a suite of low-mass He-core white dwarf and pre-white dwarf models with masses ranging from $0.1554$ to $0.4352 M_{\sun}$. We compute the secular rates of period change of radial ($\ell= 0$) and nonradial ($\ell= 1, 2$) $g$ and $p$ modes for stellar models representative of ELMV and pre-ELMV stars, as well as for stellar objects that are evolving just before the occurrence of CNO flashes at the early cooling branches. We found that the theoretically expected magnitude of $\dot{\Pi}$ of $g$ modes for pre-ELMVs are by far larger than for ELMVs. In turn, $\dot{\Pi}$ of $g$ modes for models evolving before the occurrence of CNO flashes are larger than the maximum values of the rates of period change predicted for pre-ELMV stars. Regarding $p$ and radial modes, we found that the larger absolute values of $\dot{\Pi}$ correspond to pre-ELMV models. We conclude that any eventual measurement of a rate of period change for a given pulsating low-mass pre-white dwarf or white dwarf star could shed light about its evolutionary status. Also, in view of the systematic difficulties in the spectroscopic classification of stars of the ELM Survey, an eventual measurement of $\dot{\Pi}$ could help to confirm that a given pulsating star is an authentic low-mass white dwarf and not a star from another stellar population., Comment: 22 pages, 14 figures, 2 tables. To be published in Astronomy & Astrophysics