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A new class of pulsating white dwarf of extremely low mass: The fourth and fifth members
Abstract and Figures
We report the discovery of two new pulsating extremely low-mass (ELM) white dwarfs (WDs), SDSS J161431.28+191219.4 (hereafter
J1614) and SDSS J222859.93+362359.6 (hereafter J2228). Both WDs have masses <0.25 M⊙ and thus likely harbour helium cores. Spectral fits indicate these are the two coolest pulsating WDs ever found. J1614 has
Teff = 8880 ± 170 K and log g = 6.66 ± 0.14, which corresponds to a ∼0.19 M⊙ WD. J2228 is considerably cooler, with a Teff = 7870 ± 120 K and log g = 6.03 ± 0.08, which corresponds to an ∼0.16 M⊙ WD, making it the coolest and lowest mass pulsating WD known. There are multiple ELM WDs with effective temperatures between
the warmest and coolest known ELM pulsators that do not pulsate to observable amplitudes, which questions the purity of the
instability strip for low-mass WDs. In contrast to the CO-core ZZ Ceti stars, which are believed to represent a stage in the
evolution of all such WDs, ELM WDs may not all evolve as a simple cooling sequence through an instability strip. Both stars
exhibit long-period variability (1184-6235 s) consistent with non-radial g-mode pulsations. Although ELM WDs are preferentially found in close binary systems, both J1614 and J2228 do not exhibit significant
radial-velocity variability, and are perhaps in low-inclination systems or have low-mass companions. These are the fourth
and fifth pulsating ELM WDs known, all of which have hydrogen-dominated atmospheres, establishing these objects as a new class
of pulsating WD.
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... Neither the canonical ZZ Ceti instability strips (Gianninas, Bergeron & Ruiz 2011 ;Gianninas et al. 2015 ;C órsico et al. 2016 ) nor the hot subdwarf instability strip (Heber 2016 ) co v ers the parameters of J0338 properly. Currently only about twenty ELMs are known to be pulsating (Hermes et al. 2013 ;Gianninas et al. 2016 ;Zhang et al. 2016 ;Wang, Zhang & Dai 2020b ). More photometric observations on larger ELM sample might be helpful to solve this issue more convincingly. ...
Double white dwarf systems are of great astrophysical importance in the field of gravitational wave and Type Ia supernova. While the binary fraction of CO core white dwarf is about a few percents, the extremely low mass white dwarfs are all thought to be within binary systems. In this work, we report the orbital solution of a double degenerate system: J033847.06+413424.24, an extremely low mass He core white dwarf orbiting a CO core white dwarf. With LAMOST and P200, time domain spectroscopic observations have been made and spectral atmosphere parameters are estimated to be Teff ∼ 22500 K and log g ∼ 5.6 dex. Combining Gaia parallax, 3D extinction, and evolution tracks, we estimate a radius of ∼0.12 R⊙ and a mass of ∼0.22 M⊙. With the 37 single exposure spectra, the radial velocities are measured and the orbital parameters are estimated to be P = 0.1253132(1) days, K1 = 289 ± 4 km/s and Vsys = −41 ± 3 km/s. The radial velocity based system ephemeris is also provided. The light curves from several photometric surveys show no orbital modulation. The orbital solution suggests that the invisible companion has a minimum mass of about 0.60 M⊙ and is ∼0.79 M⊙ for an inclination of 60.0○, indicating most probably a CO core white dwarf. The system is expected to merge in about 1 Gyr. With present period and distance (∼596 pc) it can not irradiate strong enough gravitational wave for LISA. More double degenerate systems are expected to be discovered and parameterized as the LAMOST survey goes on.
... We do this using a Gaussian process (GP) implemented through Figure 7. The ZZ Ceti instability strip (blue region) with known pulsating (dark grey) and non-pulsating (light grey) WDs from Gianninas et al. ( 2011), Steinfadt et al. ( 2012, Hermes et al. ( 2012Hermes et al. ( , 2013aHermes et al. ( , 2013bHermes et al. ( , 2013c, Romero et al. ( 2022 ). Points in red show the measured parameters of the WD components of binaries fit in this work, with the confirmed pulsators, ZTF J1407 + 2115 and ZTF J0528 + 2156, shown by the yellow and cyan stars, respectively. ...
Wide-field time-domain photometric sky surveys are now finding hundreds of eclipsing white dwarf plus M dwarf binaries, a population encompassing a wealth of information and potential insight into white dwarf and close binary astrophysics. Precise follow-up observations are essential in order to fully constrain these systems and capitalise on the power of this sample. We present the first results from our program of high-speed, multi-band photometric follow-up. We develop a method to measure temperatures, (model-dependent) masses, and radii for both components from the eclipse photometry alone and characterize 34 white dwarf binaries, finding general agreement with independent estimates using an alternative approach while achieving around a factor of two increase in parameter precision. In addition to these parameter estimates, we discover a number of interesting systems – finding four with sub-stellar secondaries, doubling the number of eclipsing examples, and at least six where we find the white dwarf to be strongly magnetic, making these the first eclipsing examples of such systems and key to investigating the mechanism of magnetic field generation in white dwarfs. We also discover the first two pulsating white dwarfs in detached and eclipsing post-common-envelope binaries – one with a low-mass, likely helium core, and one with a relatively high mass, towards the upper end of the known sample of ZZ Cetis. Our results demonstrate the power of eclipse photometry, not only as a method of characterising the population, but as a way of discovering important systems that would have otherwise been missed by spectroscopic follow-up.
... The ZZ Ceti instability strip (blue region) with known pulsating (dark grey) and non-pulsating (light grey) WDs fromGianninas et al. (2011);Steinfadt et al. (2012);Hermes et al. (2012Hermes et al. ( , 2013a;Romero et al. (2022). Points in red show the measured parameters of the WD components of binaries fit in this work, with the confirmed pulsators, ZTF J1407+2115 and ZTF J0528+2156, shown by the yellow and cyan stars respectively. ...
Wide-field time-domain photometric sky surveys are now finding hundreds of eclipsing white dwarf plus M dwarf binaries, a population encompassing a wealth of information and potential insight into white dwarf and close binary astrophysics. Precise follow-up observations are essential in order to fully constrain these systems and capitalise on the power of this sample. We present the first results from our program of high-speed, multi-band photometric follow-up. We develop a method to measure temperatures, (model-dependent) masses, and radii for both components from the eclipse photometry alone and characterize 34 white dwarf binaries, finding general agreement with independent estimates using an alternative approach while achieving around a factor of two increase in parameter precision. In addition to these parameter estimates, we discover a number of interesting systems -- finding four with sub-stellar secondaries, doubling the number of eclipsing examples, and at least six where we find the white dwarf to be strongly magnetic, making these the first eclipsing examples of such systems and key to investigating the mechanism of magnetic field generation in white dwarfs. We also discover the first two pulsating white dwarfs in detached and eclipsing post-common-envelope binaries -- one with a low-mass, likely helium core, and one with a relatively high mass, towards the upper end of the known sample of ZZ Cetis. Our results demonstrate the power of eclipse photometry, not only as a method of characterising the population, but as a way of discovering important systems that would have otherwise been missed by spectroscopic follow-up.
... The remnant of the component with a helium core would not go through the asymptotic giant branch phase and would directly contract toward a WD (see, e.g., Althaus et al. 2013;Istrate et al. 2016;Li et al. 2019). Some ELM WDs have been known to exhibit pulsations (e.g., Hermes et al. 2012Hermes et al. , 2013aHermes et al. , 2013bBell et al. 2015;Kilic et al. 2015;Bell et al. 2017;Pelisoli et al. 2018). They constitute a separate class of pulsating WDs, commonly referred to as extremely low-mass variables (ELMVs). ...
SDSS J111215.82+111745.0 is the second pulsating extremely low-mass white dwarf discovered. Two short-period pulsations, 107.56 and 134.275 s, were detected on this star, which would be the first observed pressure mode ( p -mode) pulsations observed on a white dwarf. While the two potential p -modes have yet to be confirmed, they make SDSS J111215.82+111745.0 an interesting object. In this work, we analyzed the whole set of seven periods observed on SDSS J111215.82+111745.0. We adopt three independent period-spacing tests to reveal a roughly 93.4 s mean period spacing of ℓ = 1 g -modes, which gives added credence to the ℓ = 1 identifications. Then we perform asteroseismic modeling for this star, in which the H chemical profile is taken as a variable. The stellar parameters M = 0.1650 ± 0.0137 M ☉ and T eff = 9750 ± 560 K are determined from the best-fit model, and the H/He chemical profiles are also defined. The two suspected p -modes are also well represented in the best-fit model, and both the stellar parameters and the pulsation frequencies are in good agreement with the values derived from spectroscopy.
In recent years, about 150 low-mass white dwarfs (WDs), typically with masses below $0.4M_ odot $, have been discovered. The majority of these low-mass WDs are observed in binary systems as they cannot be formed through single-star evolution within Hubble time. In this work, we present a comprehensive analysis of the double low-mass WD eclipsing binary system J2102-4145. Our investigation encompasses an extensive observational campaign, resulting in the acquisition of approximately 28 hours of high-speed photometric data across multiple nights using NTT/ULTRACAM, SOAR/Goodman, and SMARTS-1m telescopes. These observations have provided critical insights into the orbital characteristics of this system, including parameters such as inclination and orbital period. To disentangle the binary components of J2102-4145, we employed the GRID spectral fitting method with GMOS/Gemini-South and X-Shooter data. Additionally, we used the PHOEBE package for light curve analysis on NTT/ULTRACAM high-speed time-series photometry data to constrain the binary star properties. Our analysis unveils remarkable similarities between the two components of this binary system. For the primary star, we determine $T_ eff,1 $ K, $ g_1 = 7.36 $R_1=0.0211 and $M_1 = 0.375 odot $, while, the secondary star is characterised by $T_ eff,2 $ K, $ g_2 = 7.32 $\,R$_ and $M_2 = 0.314 odot $. Furthermore, we found a notable discrepancy between $T_ eff $ and $R$ of the less massive WD, compared to evolutionary sequences for WDs from the literature, which has significant implications for our understanding of WD evolution. We discuss a potential formation scenario for this system which might explain this discrepancy and explore its future evolution. We predict that this system will merge in sim 800\,Myr, evolving into a helium-rich hot subdwarf star and later into a hybrid He/CO WD.
G 29−38 (TIC 422526868) is one of the brightest (V = 13.1) and closest (d = 17.51 pc) pulsating white dwarfs with a hydrogen-rich atmosphere (DAV/ZZ Ceti class). It was observed by the TESS spacecraft in sectors 42 and 56. The atmosphere of G 29−38 is polluted by heavy elements that are expected to sink out of visible layers on short timescales. The photometric TESS data set spans ∼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 ∼ 260 s to ∼ 1400 s. We identified rotational frequency triplets with a mean separation δνℓ = 1 of 4.67 μHz and a quintuplet with a mean separation δνℓ = 2 of 6.67 μHz, from which we estimated a rotation period of about 1.35 ± 0.1 days. We determined a constant period spacing of 41.20 s for ℓ = 1 modes and 22.58 s for ℓ = 2 modes. We performed period-to-period fit analyses and found an asteroseismological model with M⋆/M⊙ = 0.632 ± 0.03, Teff = 11 635 ± 178 K, and log g = 8.048 ± 0.005 (with a hydrogen envelope mass of MH ∼ 5.6 × 10−5M⋆), in good agreement with the values derived from spectroscopy. We obtained an asteroseismic distance of 17.54 pc, which is in excellent agreement with that provided by Gaia (17.51 pc).
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).
Context. The advent of high-quality space-based photometry, brought about by missions such as Kepler /K2 and TESS, makes it possible to unveil the fundamental parameters and properties of the interiors of white dwarf stars, particularly extremely low-mass white dwarfs, using the tools of asteroseismology.
Aims. We present an exploration of the internal rotation of GD 278, the first known pulsating extremely low-mass white dwarf to show rotational splittings within its periodogram.
Methods. We assessed the theoretical frequency splittings expected for different rotation profiles and compared them to the observed frequency splittings of GD 278. To this aim, we employed an asteroseismological model representative of the pulsations of this star, obtained by using the LPCODE stellar evolution code and the LP-PUL non-radial pulsation code. We also derived a rotation profile that results from detailed evolutionary calculations carried out with the MESA stellar evolution code and used it to infer the expected theoretical frequency splittings.
Results. We find that the best-fitting solution when assuming linear profiles for the rotation of GD 278 leads to angular velocity values at the surface and center that are only slightly differential, and still compatible with rigid rotation. Additionally, 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.
Conclusions. 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 by employing two independent stellar evolution codes gives our results robustness. Our results suggest only a marginally differential behavior for the internal rotation in GD 278 and, considering the uncertainties involved, this is 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.
Context. Gaia DR3 contains 1.8 billion sources with G -band photometry, 1.5 billion of which with G BP and G RP photometry, complemented by positions on the sky, parallax, and proper motion. The median number of field-of-view transits in the three photometric bands is between 40 and 44 measurements per source and covers 34 months of data collection.
Aims. We pursue a classification of Galactic and extra-galactic objects that are detected as variable by Gaia across the whole sky.
Methods. Supervised machine learning (eXtreme Gradient Boosting and Random Forest) was employed to generate multi-class, binary, and meta-classifiers that classified variable objects with photometric time series in the G , G BP , and G RP bands.
Results. Classification results comprise 12.4 million sources (selected from a much larger set of potential variable objects) and include about 9 million variable stars classified into 22 variability types in the Milky Way and nearby galaxies such as the Magellanic Clouds and Andromeda, plus thousands of supernova explosions in distant galaxies, 1 million active galactic nuclei, and almost 2.5 million galaxies. The identification of galaxies was made possible by the artificial variability of extended objects as detected by Gaia , so they were published in the galaxy_candidates table of the Gaia DR3 archive, separate from the classifications of genuine variability (in the vari_classifier_result table). The latter contains 24 variability classes or class groups of periodic and non-periodic variables (pulsating, eclipsing, rotating, eruptive, cataclysmic, stochastic, and microlensing), with amplitudes from a few milli-magnitudes to several magnitudes.
Context. In current astronomical surveys with ever-increasing data volumes, automated methods are essential. Objects of known classes from the literature are necessary to train supervised machine-learning algorithms and to verify and validate their results.
Aims. The primary goal of this work is to provide a comprehensive data set of known variable objects from the literature that we cross-match with Gaia DR3 sources, including a large number of variability types and representatives, in order to cover sky regions and magnitude ranges relevant to each class in the best way. In addition, non-variable objects from selected surveys are targeted to probe their variability in Gaia and possible use as standards. This data set can be the base for a training set that can be applied to variability detection, classification, and validation.
Methods. A statistical method that employed astrometry (position and proper motion) and photometry (mean magnitude) was applied to selected literature catalogues in order to identify the correct counterparts of known objects in the Gaia data. The cross-match strategy was adapted to the properties of each catalogue, and the verification of results excluded dubious matches.
Results. Our catalogue gathers 7 841 723 Gaia sources, 1.2 million of which are non-variable objects and 1.7 million are galaxies, in addition to 4.9 million variable sources. This represents over 100 variability (sub)types.
Conclusions. This data set served the requirements of the Gaia variability pipeline for its third data release (DR3) from classifier training to result validation, and it is expected to be a useful resource for the scientific community that is interested in the analysis of variability in the Gaia data and other surveys.
We present the discovery of 17 low-mass white dwarfs (WDs) in short-period (P ≤ 1 day) binaries. Our sample includes four objects with remarkable log g 5 surface gravities and orbital solutions that require them to be double degenerate binaries. All of the lowest surface gravity WDs have metal lines in their spectra implying long gravitational settling times or ongoing accretion. Notably, six of the WDs in our sample have binary merger times <10 Gyr. Four have 0.9 M
☉ companions. If the companions are massive WDs, these four binaries will evolve into stable mass transfer AM CVn systems and possibly explode as underluminous supernovae. If the companions are neutron stars, then these may be millisecond pulsar binaries. These discoveries increase the number of detached, double degenerate binaries in the ELM Survey to 54; 31 of these binaries will merge within a Hubble time.
Most millisecond pulsars with low-mass companions are in systems with either
helium-core white dwarfs or non-degenerate ("black widow" or "redback") stars.
A candidate counterpart to PSR J1816+4510 was identified by Kaplan et al.
(2012) whose properties were suggestive of both types of companions although
identical to neither. We have assembled optical spectroscopy of the candidate
companion and confirm that it is part of the binary system with a radial
velocity amplitude of 343+/-7 km/s, implying a high pulsar mass,
Mpsr*sin^3i=1.84+/-0.11 Msun, and a companion mass Mc*sin^3i=0.192+/-0.012
Msun, where i is the inclination of the orbit. The companion appears similar to
proto-white dwarfs/sdB stars, with a gravity log(g)=4.9+/-0.3, and effective
temperature 16000+/-500 K. The strongest lines in the spectrum are from
hydrogen, but numerous lines from helium, calcium, silicon, and magnesium are
present as well, with implied abundances of roughly ten times solar (relative
to hydrogen). As such, while from the spectrum the companion to PSR J1816+4510
is superficially most similar to a low-mass white dwarf, it has much lower
gravity, is substantially larger, and shows substantial metals. Furthermore, it
is able to produce ionized gas eclipses, which had previously been seen only
for low-mass, non-degenerate companions in redback or black widow systems. We
discuss the companion in relation to other sources, but find we understand
neither its nature nor its origins. Thus, the system is interesting for
understanding unusual stellar products of binary evolution, as well as,
independent of its nature, for determining neutron-star masses.
Aims: The determination of the location of the theoretical ZZ
Ceti instability strip in the log g - Teff diagram has
remained a challenge over the years due to the lack of a suitable
treatment for convection in these stars. For the first time, a full
nonadiabatic approach including time-dependent convection is applied to
ZZ Ceti pulsators, and we provide the appropriate details related to the
inner workings of the driving mechanism. Methods: We used the
nonadiabatic pulsation code MAD with a representative evolutionary
sequence of a 0.6 M⊙ DA white dwarf. This sequence is
made of state-of-the-art models that include a detailed modeling of the
feedback of convection on the atmospheric structure. The assumed
convective efficiency in these models is the so-called ML2/α = 1.0
version. We also carried out, for comparison purposes, nonadiabatic
computations within the frozen convection approximation, as well as
calculations based on models with standard grey atmospheres.
Results: We find that pulsational driving in ZZ Ceti stars is
concentrated at the base of the superficial H convection zone, but at
depths, near the blue edge of the instability strip, somewhat larger
than those obtained with the frozen convection approach. Despite the
fact that this approach is formally invalid in such stars, particularly
near the blue edge of the instability strip, the predicted boundaries
are not dramatically different in both cases. The revised blue edge for
a 0.6 M⊙ model is found to be around Teff = 11
970 K, some 240 K hotter than the value predicted within the frozen
convection approximation, in rather good agreement with the empirical
value. On the other hand, our predicted red edge temperature for the
same stellar mass is only about 5600 K (80 K hotter than with the frozen
convection approach), much lower than the observed value.
Conclusions: We correctly understand the development of pulsational
instabilities of a white dwarf as it cools at the blue edge of the ZZ
Ceti instability strip. Our current implementation of time-dependent
convection however still lacks important ingredients to fully account
for the observed red edge of the strip. We will explore a number of
possibilities in the future papers of this series.
In light of the exciting discovery of g-mode pulsations in extremely low-mass, He-core DA white dwarfs, we report on the results of a detailed stability survey aimed at explaining the existence of these new pulsators as well as their location in the spectroscopic Hertzsprung-Russell diagram. To this aim, we calculated some 28 evolutionary sequences of DA models with various masses and chemical layering. These models are characterized by the so-called ML2/α = 1.0 convective efficiency and take into account the important feedback effect of convection on the atmospheric structure. We pulsated the models with the nonadiabatic code MAD, which incorporates a detailed treatment of time-dependent convection. On the other hand, given the failure of all nonadiabatic codes, including MAD, to account properly for the red edge of the strip, we resurrect the idea that the red edge is due to energy leakage through the atmosphere. We thus estimated the location of that edge by requiring that the thermal timescale in the driving region—located at the base of the H convection zone—be equal to the critical period beyond which ℓ = 1 g-modes cease to exist. Using this approach, we find that our theoretical ZZ Ceti instability strip accounts remarkably well for the boundaries of the empirical strip, including the low-gravity, low-temperature regime where the three new pulsators are found. We also account for the relatively long periods observed in these stars, and thus conclude that they are true ZZ Ceti stars, but with low masses.
We provide a fine and homogeneous grid of evolutionary sequences for He-core
white dwarfs with masses 0.15-0.45 Msun, including the mass range for ELM white
dwarfs (<0.20Msun). The grid is appropriate for mass and age determination, and
to study their pulsational properties. White dwarf sequences have been computed
by performing full evolutionary calculations that consider the main energy
sources and processes of chemical abundance changes during white dwarf
evolution. Initial models for the evolving white dwarfs have been obtained by
computing the non-conservative evolution of a binary system consisting of a
Msun ZAMS star and a 1.4 Msun neutron star for various initial orbital periods.
To derive cooling ages and masses for He-core white dwarf we perform a least
square fitting of the M(Teff, g) and Age(Teff, g) relations provided by our
sequences by using a scheme that takes into account the time spent by models in
different regions of the Teff-g plane. This is useful when multiple solutions
for cooling age and mass determinations are possible in the case of
CNO-flashing sequences. We also explore the adiabatic pulsational properties of
models near the critical mass for the development of CNO flashes (~0.2 Msun).
This is motivated by the discovery of pulsating white dwarfs with stellar
masses near this threshold value. We obtain reliable and homogeneous mass and
cooling age determinations for 58 very low-mass white dwarfs, including 3
pulsating stars. Also, we find substantial differences in the period spacing
distributions of g-modes for models with stellar masses ~ 0.2 Msun, which could
be used as a seismic tool to distinguish stars that have undergone CNO flashes
in their early cooling phase from those that have not. Finally, for an easy
application of our results, we provide a reduced grid of values useful to
obtain masses and ages of He-core white dwarf.
With a time-series CCD photometric survey, we have demonstrated clearly that the observed red edge for the ZZ Ceti stars instability strip at 11 000 K is real, with the pulsation amplitude decreasing at least by a factor of 50. Previous surveys for variability among hydrogen atmosphere white dwarfs around 11 000 K have been carried out using time-series photoelectric photometry, not differential photometry, insensitive for small amplitude periodicities of 15 min and longer. In our survey we constantly monitor the sky brightness as well as one or more comparison stars through the same color filter, reducing the adverse effects of differential extinction and sky fluctuations, obtaining true differential photometry.
Upper and lower critical frequencies for adiabatic radial and nonradial
oscillations of white dwarfs are established. The ranges of pulsation
frequency where wave leakage may occur are estimated, and the importance
of that leakage for damping pulsation is considered. It is found that
acoustic modes are strongly damped by outwardly propagating running
waves in the atmosphere when periods are less than 0.1-1 sec. For
gravity modes, a similar result holds when periods exceed a certain
approximate value. Applications to observed white dwarf variable periods
are discussed.
We present a summary of what is currently known about the three distinct
families of isolated pulsating white dwarfs. These are the GW Vir stars
(He/C/O-atmosphere stars with Teff ≃ 120,000 K), the
V777 Her stars (He-atmosphere, Teff ≃ 25,000 K), and the ZZ Ceti
stars (H-atmosphere, Teff ≃ 12,000 K), all showing
multiperiodic luminosity variations caused by low-order and low-degree
g-mode instabilities. We also provide, in an Appendix, a very brief
overview of the newly found evidence in favor of the existence of a
fourth category of oscillating white dwarfs bearing strong similarities
with these families of pulsators. We begin our survey with a short
historical introduction, followed by a general discussion of pulsating
white dwarfs as compact pulsators. We then discuss the class properties
of these objects, including an updated census. We next focus on the
instability domains for each family of pulsators in the log g -
Teff diagram, and present their time-averaged properties in
more detail. This is followed by a section on excitation physics, i.e.,
the causes of the pulsational instabilities, with emphasis on the common
properties of the different types of pulsator. We then discuss the
time-dependent properties of the pulsating white dwarfs featuring, among
other things, a brief "picture tour" across the ZZ Ceti instability
strip. We next review the methods used to infer or constrain the angular
geometry of a pulsation mode in a white dwarf. These include multicolor
photometry and time-resolved spectroscopy, the exploitation of the
nonlinear features in the observed light curves, and rotational
splitting. We also consider basic adiabatic asteroseismology starting
with a discussion of the reaction of the period spectrum to variations
of model parameters. We next review the various asteroseismological
inferences that have so far been claimed for white dwarfs. We also
discuss the potential of exploiting the rates of period change. We
finally provide some concluding remarks, including a list with several
suggestions for future progress in the field.
The decrease in the amplitude of the theoretical brightness changes in
ZZ Ceti stars are used as the depth of the convective zone increases in
order to fix the position of the red edge and to explain the
period-temperature correlation in these stars. The width of the ZZ Ceti
instability strip in the T(e)-log g plan is determined at less than 1000
K. It is argued that this value is consistent with the statistics of
these stars and that the much wider spread in temperature which has been
found in several investigations may be due to observational errors.
Calibration for the mixing length theory of convection on the basis of
the mean temperature of the ZZ Ceti stars is in broad agreement with the
solar calibration.