Pulsating DA White Dwarf Research Articles

Seismological Studies of Pulsating DA White Dwarfs Observed with the Kepler Space Telescope and K2 Campaigns 1–8

AllS single stars that are born with masses up to 8.5–10 M ⊙ will end their lives as white dwarf (WD) stars. In this evolutionary stage, WDs enter the cooling sequence, where the stars radiate away their thermal energy and are basically cooling. As these stars cool, they reach temperatures and conditions that cause the stars to pulsate. Using differential photometry to produce light curves, we can determine the observed periods of pulsation from the WD. We used the White Dwarf Evolution Code (WDEC) to calculate a grid of over one million models with various temperature, stellar mass, and mass of helium and hydrogen layers and calculated their theoretical pulsation periods. In this paper, we describe our approach to WD asteroseismology using WDEC models, and we present seismological studies for 29 observed DAVs in the Kepler and K2 data sets, 25 of which have never been analyzed using these observations and 19 of which have never been seismically analyzed in any capacity before. Learning about the internal structure of WDs places important constraints on the WD cooling sequence and our overall understanding of stellar evolution for low-mass stars.

Discovery of 74 new bright ZZ Ceti stars in the first three years of TESS

ABSTRACT We report the discovery of 74 new pulsating DA white dwarf stars, or ZZ Cetis, from the data obtained by the Transiting Exoplanet Survey Satellite mission, from Sectors 1 to 39, corresponding to the first 3 cycles. This includes objects from the Southern hemisphere (Sectors 1–13 and 27–39) and the Northern hemisphere (Sectors 14–26), observed with 120 s- and 20 s-cadence. Our sample likely includes 13 low-mass and one extremely low-mass white dwarf candidate, considering the mass determinations from fitting Gaia magnitudes and parallax. In addition, we present follow-up time series photometry from ground-based telescopes for 11 objects, which allowed us to detect a larger number of periods. For each object, we analysed the period spectra and performed an asteroseismological analysis, and we estimate the structure parameters of the sample, i.e. stellar mass, effective temperature, and hydrogen envelope mass. We estimate a mean asteroseismological mass of 〈Msis〉 = 0.635 ± 0.015 M⊙, excluding the candidate low or extremely low-mass objects. This value is in agreement with the mean mass using estimates from Gaia data, which is 〈Mphot〉 = 0.631 ± 0.040 M⊙, and with the mean mass of previously known ZZ Cetis of 〈M*〉 = 0.644 ± 0.034 M⊙. Our sample of 74 new bright ZZ Cetis increases the number of known ZZ Cetis by ∼20 per cent.

Limits on Mode Coherence in Pulsating DA White Dwarfs Due to a Nonstatic Convection Zone

Abstract The standard theory of pulsations deals with the frequencies and growth rates of infinitesimal perturbations in a stellar model. Modes that are calculated to be linearly driven should increase their amplitudes exponentially with time; the fact that nearly constant amplitudes are usually observed is evidence that nonlinear mechanisms inhibit the growth of finite-amplitude pulsations. Models predict that the mass of convection zones in pulsating hydrogen-atmosphere (DAV) white dwarfs is very sensitive to temperature (i.e., ), leading to the possibility that even low-amplitude pulsators may experience significant nonlinear effects. In particular, the outer turning point of finite-amplitude g-mode pulsations can vary with the local surface temperature, producing a reflected wave that is out of phase with what is required for a standing wave. This can lead to a lack of coherence of the mode and a reduction in its global amplitude. In this paper we show that (1) whether a mode is calculated to propagate to the base of the convection zone is an accurate predictor of its width in the Fourier spectrum, (2) the phase shifts produced by reflection from the outer turning point are large enough to produce significant damping, and (3) amplitudes and periods are predicted to increase from the blue edge to the middle of the instability strip, and subsequently decrease as the red edge is approached. This amplitude decrease is in agreement with the observational data while the period decrease has not yet been systematically studied.

About the existence of warm H-rich pulsating white dwarfs

Context.The possible existence of warm (Teff ∼ 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 ofg-mode pulsational instabilities due to theκmechanism acting in the partial ionization zone of He below the H envelope in models of DA WDs with very thin H envelopes (MH/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 0.80M⊙with H content in the range −14.5 ≲ log(MH/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 useLPCODEstellar 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 = 1gmodes 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 ofgmodes 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(MH/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.

White Dwarf Rotation as a Function of Mass and a Dichotomy of Mode Line Widths: Kepler Observations of 27 Pulsating DA White Dwarfs through K2 Campaign 8

We present photometry and spectroscopy for 27 pulsating hydrogen-atmosphere white dwarfs (DAVs, a.k.a. ZZ Ceti stars) observed by the Kepler space telescope up to K2 Campaign 8, an extensive compilation of observations with unprecedented duration (>75 days) and duty cycle (>90%). The space-based photometry reveals pulsation properties previously inaccessible to ground-based observations. We observe a sharp dichotomy in oscillation mode linewidths at roughly 800 s, such that white dwarf pulsations with periods exceeding 800 s have substantially broader mode linewidths, more reminiscent of a damped harmonic oscillator than a heat-driven pulsator. Extended Kepler coverage also permits extensive mode identification: We identify the spherical degree of 61 out of 154 unique radial orders, providing direct constraints of the rotation period for 20 of these 27 DAVs, more than doubling the number of white dwarfs with rotation periods determined via asteroseismology. We also obtain spectroscopy from 4m-class telescopes for all DAVs with Kepler photometry. Using these homogeneously analyzed spectra we estimate the overall mass of all 27 DAVs, which allows us to measure white dwarf rotation as a function of mass, constraining the endpoints of angular momentum in low- and intermediate-mass stars. We find that 0.51-to-0.73-solar-mass white dwarfs, which evolved from 1.7-to-3.0-solar-mass ZAMS progenitors, have a mean rotation period of 35 hr with a standard deviation of 28 hr, with notable exceptions for higher-mass white dwarfs. Finally, we announce an online repository for our Kepler data and follow-up spectroscopy, which we collect at http://www.k2wd.org.

Asteroseismology of the ultramassive ZZ ceti star WD 0246+326

The internal structures of pulsating white dwarfs can be explored only with asteroseismology. Time series photometric observations were made for the pulsating DA white dwarf (ZZ Ceti star) WD 0246+326 during 9 nights in 2014 with a bi-site observation campaign. Eleven frequencies were detected including 1 triplet, 2 doublets, and 4 single modes, which are identified as either l=1 or l=2 modes with the complementarity of frequencies present in the literature. From the multiplets, the rotation period of WD 0246+326 is derived as 3.78 ± 0.11 days. The average period spacing of the l=1 modes ΔP=29.3±0.2 s, implies that WD 0246+326 may be a massive ZZ Ceti star concerning the ΔP−M* relationship for the DAVs. Preliminary analysis derives the stellar parameters of M*=0.98±0.01M⊙ and Teff=11700±100 K by fitting the theoretical frequencies of the eigen modes to the observed ones.

White Dwarf Rotation as a Function of Mass and a Dichotomy of Mode Line Widths: Kepler Observations of 27 Pulsating DA White Dwarfs through K2 Campaign 8

White Dwarf Rotation as a Function of Mass and a Dichotomy of Mode Line Widths: Kepler Observations of 27 Pulsating DA White Dwarfs through K2 Campaign 8

An asteroseismic constraint on the mass of the axion from the period drift of the pulsating DA white dwarf star L19-2

We employ an asteroseismic model of L19-2, a relatively massive (M⋆ ∼ 0.75 M⊙) and hot (Teff ∼ 12 100 K) pulsating DA (H-rich atmosphere) white dwarf star (DAV or ZZ Ceti variable), and use the observed values of the temporal rates of period change of its dominant pulsation modes (Π ∼ 113 s and Π ∼ 192 s), to derive a new constraint on the mass of the axion, the hypothetical non-barionic particle considered as a possible component of the dark matter of the Universe. If the asteroseismic model employed is an accurate representation of L19-2, then our results indicate hints of extra cooling in this star, compatible with emission of axions of mass ma cos2β ≲ 25 meV or an axion-electron coupling constant of gae ≲ 7 × 10−13.

New insights on pulsating white dwarfs from 3D radiation-hydrodynamical simulations

AbstractWe have recently computed a grid of 3D radiation-hydrodynamical simulations for the atmosphere of pure-hydrogen DA white dwarfs in the range 5.0 < log g < 9.0. Our grid covers the full ZZ Ceti instability strip where pulsating DA white dwarfs are located. We have significantly improved the theoretical framework to study these objects by removing the free parameters of 1D convection, which were previously a major modeling hurdle. We present improved atmospheric parameter determinations based on spectroscopic fits with 3D model spectra, allowing for an updated definition of the empirical edges of the ZZ Ceti instability strip. Our 3D simulations also precisely predict the depth of the convection zones, narrowing down the internal layers where pulsation are being driven. We hope that these 3D effects will be included in asteroseismic models in the future to predict the region of the HR diagram where white dwarfs are expected to pulsate.

RATS-Kepler – a deep high-cadence survey of the Kepler field

We outline the purpose, strategy and first results of a deep, high cadence, photometric survey of the Kepler field using the Isaac Newton Telescope on La Palma and the MDM 1.3m Telescope on Kitt Peak. Our goal was to identify sources located in the Kepler field of view which are variable on a timescale of a few mins to 1 hour. The astrophysically most interesting sources would then have been candidates for observation using Kepler using 1 min sampling. Our survey covered ~42% of the Kepler field of view and we have obtained light curves for 7.1x10^5 objects in the range 13<g<20. We have discovered more than 100 variable sources which have passed our two stage identification process. As a service to the wider community, we make our data products and cleaned CCD images available to download. We obtained Kepler data of 18 sources which we found to be variable using our survey and we give an overview of the currently available data here. These sources include a pulsating DA white dwarf, eleven delta Sct stars which have dominant pulsation periods in the range 24 min to 2.35 hrs, three contact binaries, and a cataclysmic variable (V363 Lyr). One of the delta Sct stars is in a contact binary.

MEASURING THE EVOLUTIONARY RATE OF COOLING OF ZZ Ceti

We have finally measured the evolutionary rate of cooling of the pulsating hydrogen atmosphere (DA) white dwarf ZZ Ceti (Ross 548), as reflected by the drift rate of the 213.13260694 s period. Using 41 yr of time-series photometry from 1970 November to 2012 January, we determine the rate of change of this period with time to be dP/dt = (5.2 ± 1.4) × 10–15 s s–1 employing the O – C method and (5.45 ± 0.79) × 10–15 s s–1 using a direct nonlinear least squares fit to the entire lightcurve. We adopt the dP/dt obtained from the nonlinear least squares program as our final determination, but augment the corresponding uncertainty to a more realistic value, ultimately arriving at the measurement of dP/dt = (5.5 ± 1.0) × 10–15 s s–1. After correcting for proper motion, the evolutionary rate of cooling of ZZ Ceti is computed to be (3.3 ± 1.1) × 10–15 s s–1. This value is consistent within uncertainties with the measurement of (4.19 ± 0.73) × 10–15 s s–1 for another similar pulsating DA white dwarf, G 117-B15A. Measuring the cooling rate of ZZ Ceti helps us refine our stellar structure and evolutionary models, as cooling depends mainly on the core composition and stellar mass. Calibrating white dwarf cooling curves with this measurement will reduce the theoretical uncertainties involved in white dwarf cosmochronometry. Should the 213.13 s period be trapped in the hydrogen envelope, then our determination of its drift rate compared to the expected evolutionary rate suggests an additional source of stellar cooling. Attributing the excess cooling to the emission of axions imposes a constraint on the mass of the hypothetical axion particle.

Hot DAVs: a probable new class of pulsating white dwarf stars

We have discovered a pulsating DA white dwarf at the lower end of the temperature range 45 000–30 000 K where a few helium atmosphere white dwarfs are known. There are now three such pulsators known, suggesting that a new class of theoretically predicted pulsating white dwarf stars exists. We name them the hot DAV stars. From high-speed photometric observations with the ULTRACAM photometer on the 4.2-m William Herschel Telescope, we show that the hydrogen atmosphere white dwarf star WD1017−138 pulsates in at least one mode with a frequency of 1.62 mHz (a period of 624 s). The amplitude of that mode was near 1 mmag at a 10σ confidence level on one night of observation and an 8.4σ confidence level on a second night. The combined data have a confidence level of 11.8σ. This supports the two other detections of hot DAV stars previously reported. From three Very Large Telescope Ultraviolet and Visual Echelle Spectrograph spectra we confirm also that WD1017−138 is a hydrogen atmosphere white dwarf with no trace of helium or metals with Teff = 32 600 K, log g = 7.8 (cgs) and M = 0.55 M⊙. The existence of pulsations in these DA white dwarfs at the cool edge of the 45 000–30 000 K temperature range supports the thin hydrogen layer model for the deficit of helium atmosphere white dwarfs in this range. DA white dwarfs with thick hydrogen layers do not have the superadiabatic, chemically inhomogeneous (μ-gradient) zone that drives pulsation in this temperature range. The potential for higher amplitude hot DAV stars exists; their discovery would open the possibility of a direct test of the explanation for the deficit of helium atmosphere white dwarfs at these temperatures by asteroseismic probing of the atmospheric layers of the hot DAV stars. A search for pulsation in a further 22 candidates with ULTRACAM on the European Southern Observatory New Technology Telescope gave null results for pulsation at precisions in the range 0.5–3 mmag, suggesting that the pulsation amplitudes in such stars are relatively low, hence near the detection limit with the ground-based telescopes used in the survey.

A NEW TIMESCALE FOR PERIOD CHANGE IN THE PULSATING DA WHITE DWARF WD 0111+0018

We report the most rapid rate of period change measured to date for a pulsating DA (hydrogen atmosphere) white dwarf (WD), observed in the 292.9 s mode of WD 0111+0018. The observed period change, faster than 10^{-12} s/s, exceeds by more than two orders of magnitude the expected rate from cooling alone for this class of slow and simply evolving pulsating WDs. This result indicates the presence of an additional timescale for period evolution in these pulsating objects. We also measure the rates of period change of nonlinear combination frequencies and show that they share the evolutionary characteristics of their parent modes, confirming that these combination frequencies are not independent modes but rather artifacts of some nonlinear distortion in the outer layers of the star.

A new kind of pulsator in the DB valley of white dwarf stars

Recent systematic surveys providing massive datasets of white dwarf stars show that there is still a deficit of a factor of 2.5 in the ratio of white dwarfs showing helium absorption lines to those with hydrogen absorption lines in the temperature range 30 000 K T eff < 45 000 K. Since all white dwarfs have to evolve through this temperature range along similar sequences in the color-magnitude diagram, this implies that most of the helium atmosphere white dwarfs evolve into hydrogen atmosphere hot DA stars in that temperature range and then back again to helium atmosphere white dwarfs. I describe possible scenarios for this chameleon-like disguises of white dwarfs with helium dominant atmospheres and a new kind of pulsating white dwarfs predicted to appear near the lower end of the temperature range 45 000–30 000 K from these scenarios. Recently searches have discovered a pulsating DA white dwarf, WD1017−138, in the predicted temperature range. This discovery opens the possibility of a direct test of the explanation for the deficit of helium atmosphere white dwarfs at these temperatures by asteroseismic probing of the atmospheric layers of the hot DAV stars.

Asteroseismology of pulsating DA white dwarfs with fully evolutionary models

We present a new approach for asteroseismology of DA white dwarfs that consists in the employment of a large set of non-static, physically sound, fully evolutionary models representative of these stars. We already have applied this approach with success to pulsating PG1159 stars (GW Vir variables). Our white dwarf models, which cover a wide range of stellar masses, effective temperatures, and envelope thicknesses, are the result of fully evolutionary computations that take into account the complete history of the progenitor stars from the ZAMS. In particular, the models are characterized by self-consistent chemical structures from the centre to the surface, a crucial aspect of white dwarf asteroseismology. We apply this approach to an ensemble of 44 bright DAV (ZZ Ceti) stars.

The DB gap and a new class of pulsating white dwarfs

The recent systematic surveys providing enormously massive datasets of white dwarfs show that there is still a deficit of a factor of 2.5 in the DA/non-DA ratio within the temperature range of 30 000 K eff < 45 000 K, which has been regarded as the “DB gap” meaning a range with almost no helium atmosphere white dwarfs. Since all white dwarfs have to evolve through this temperature range along almost the identical sequence on the color-magnitude diagram, this implies that most of the helium atmosphere DO stars once evolve into hydrogen atmosphere hot DA stars in the temperature range of the DB gap and then back to helium atmosphere DB stars. Possible scenarios for this chameleon-like disguises of white dwarfs with helium dominant atmospheres are described and a new class of pulsating white dwarfs, named the hot-DAV stars, is predicted from these scenarios. One pulsating DA white dwarf, being consistent with the prediction, has been discovered indeed.

Asteroseismology of the ZZ Ceti star HS 0507+0434B★

The pulsating DA white dwarfs (ZZ Ceti stars) are $g$-mode non-radial pulsators. Asteroseismology provides strong constraints on their global parameters and internal structure. Since all the DA white dwarfs falling in the ZZ Ceti instability strip do pulsate, the internal structure derived from asteroseismology brings knowledge for the DA white dwarfs as a whole group. HS 0507+0434B is one of the ZZ Ceti stars which lies approximately in the middle of the instability strip for which we have undertaken a detailed asteroseismological study. We carried out multisite observation campaigns in 2007 and from December 2009 to January 2010. In total, 206 hours of photometric time-series have been collected. They have been analysed by means of Fourier analysis and simultaneous multi-frequency sine-wave fitting. In total, 39 frequency values are resolved including 6 triplets and a number of linear combinations. We identify the triplets as $\ell$=1 $g$-modes split by rotation. We derived the period spacing, the rotational splitting and the rotation rate. From the comparison of the observed periods with the theoretical periods of a series of models we estimate the fundamental parameters of the star: its total mass M$_{*}$/M$_{\odot}$ = 0.675, its luminosity L/L$_{\odot}$=3.5$\times 10^{-3}$, and its hydrogen mass fraction M$_{H}$/M$_{*}$= 10$^{-8.5}$.

EMPIRICAL DETERMINATION OF CONVECTION PARAMETERS IN WHITE DWARFS. I. WHOLE EARTH TELESCOPE OBSERVATIONS OF EC14012-1446

We report on analysis of 308.3 hrs of high speed photometry targeting the pulsating DA white dwarf EC14012-1446. The data were acquired with the Whole Earth Telescope (WET) during the 2008 international observing run XCOV26. The Fourier transform of the light curve contains 19 independent frequencies and numerous combination frequencies. The dominant peaks are 1633.907, 1887.404, and 2504.897 microHz. Our analysis of the combination amplitudes reveals that the parent frequencies are consistent with modes of spherical degree l=1. The combination amplitudes also provide m identifications for the largest amplitude parent frequencies. Our seismology analysis, which includes 2004--2007 archival data, confirms these identifications, provides constraints on additional frequencies, and finds an average period spacing of 41 s. Building on this foundation, we present nonlinear fits to high signal-to-noise light curves from the SOAR 4.1m, McDonald 2.1m, and KPNO 2m telescopes. The fits indicate a time-averaged convective response timescale of 99.4 +/- 17 s, a temperature exponent 85 +/- 6.2 and an inclination angle of 32.9 +/- 3.2 degrees. We present our current empirical map of the convective response timescale across the DA instability strip.

DISCOVERY OF A ZZ CETI IN THE KEPLER MISSION FIELD

We report the discovery of the first identified pulsating DA white dwarf in the field of the Kepler mission, WD J1916+3938 (Kepler ID 4552982). This ZZ Ceti star was first identified through ground-based, time-series photometry, and follow-up spectroscopy confirm it is a hydrogen-atmosphere white dwarf with an effective temperature = 11,129 $\pm$ 115 K and log g = 8.34 $\pm$ 0.06, placing it within the empirical ZZ Ceti instability strip. The object shows up to 0.5 percent amplitude variability at several periods between 800 -- 1450 s. Extended Kepler observations of this object could yield the best lightcurve, to-date, of any pulsating white dwarf, allowing us to directly study the interior of an evolved object representative of the fate of the majority of stars in our Galaxy.

New pulsating ZZ ceti stars

Over the last four years the number of known pulsating DA white dwarf stars increased from 32 to a total of 147; 87 are white dwarf stars identified by the Sloan Digital Sky Survey and selected from fits of synthetic spectra from model atmospheres to the S/N<30 optical spectra. With time series photometric observations at the SOAR 4.1m telescope, we found 42 new pulsators, extending the instability strip in terms of effective temperature and surface gravity, but mainly in terms of very low amplitude pulsators. The discovery of 1.5 mma pulsators raises the necessity to re-observe all stars previously classified as non-pulsators close to or inside the instability strip, as their detection limits, in general, were above 3 mma. The real extent of the instability strip and its possible contamination with non-pulsators, specially at the borders, are still open questions.