We review at length the longstanding problem in the spectroscopic analysis of cool hydrogen-line (DA) white dwarfs (Teff < 13,000 K) where gravities are significantly higher than those found in hotter DA stars. The first solution that has been proposed for this problem is a mild and systematic helium contamination from convective mixing that would mimic the high gravities. We constrain this scenario by determining the helium abundances in six cool DA white dwarfs using high-resolution spectra from the Keck I 10-m telescope. We obtain no detections, with upper limits as low as He/H = 0.04 in some cases. This allows us to put this scenario to rest for good. We also extend our model grid to lower temperatures using improved Stark profiles with non-ideal gas effects from Tremblay & Bergeron and find that the gravity distribution of cool objects remains suspiciously high. Finally, we find that photometric masses are, on average, in agreement with expected values, and that the high-log g problem is so far unique to the spectroscopic approach.
It is not known how single white dwarfs with masses less than 0.5Msolar -- low-mass white dwarfs -- are formed. One way in which such a white dwarf might be formed is after the merger of a helium-core white dwarf with a main-sequence star that produces a red giant branch star and fails to ignite helium. We use a stellar-evolution code to compute models of the remnants of these mergers and find a relation between the pre-merger masses and the final white dwarf mass. Combining our results with a model population, we predict that the mass distribution of single low-mass white dwarfs formed throug…
The article covers the physical properties and evolution of single white dwarfs ranging in temperature from 20,000K to 200,000 and higher, the hottest know electron-degenerate stars. After discussing the classification of their spectra, the author reviews the known properties, parameters, evolutionary state, as well as persisting and new puzzles regarding all spectroscopic subclasses of hot white dwarfs: the hot DA white dwarfs, the DAO white dwarfs, the PG1159 degenerates, the DO white dwarfs, the DB white dwarfs, the DBA white dwarfs, and the Hot DQ white dwarfs (an entirely new class). The …
The origin of strong magnetic fields in white dwarfs has been a puzzle for decades. Recently, a dynamo mechanism operating in rapidly rotating and crystallizing white dwarfs has been suggested to explain the occurrence rates of strong magnetic fields in white dwarfs with close low-mass main sequence star companions. Here we investigate whether the same mechanism may produce strong magnetic fields in close double white dwarfs. The only known strongly magnetic white dwarf that is part of a close double white dwarf system, the magnetic component of NLTT 12758, is rapidly rotating and likely cryst…
The Southern African Large Telescope (SALT) survey of helium-rich hot subdwarfs aims to explore evolutionary pathways amongst groups of highly-evolved stars. The selection criteria mean that several hot white dwarfs and related objects have also been included. This paper reports the discovery and analysis of eight new very hot white dwarf and pre-white dwarf stars with effective temperatures exceeding 100,000 K. They include two PG1159 stars, one DO white dwarf, three O(He) and two O(H) stars. One of the O(H) stars is the central star of a newly-discovered planetary nebula, the other is the ho…
We report the discovery of 9 089 new spectroscopically confirmed white dwarfs and subdwarfs in the Sloan Digital Sky Survey Data Release 10. We obtain Teff, log g and mass for hydrogen atmosphere white dwarf stars (DAs) and helium atmosphere white dwarf stars (DBs), and estimate the calcium/helium abundances for the white dwarf stars with metallic lines (DZs) and carbon/helium for carbon dominated spectra DQs. We found 1 central star of a planetary nebula, 2 new oxygen spectra on helium atmosphere white dwarfs, 71 DQs, 42 hot DO/PG1159s, 171 white dwarf+main sequence star binaries, 206 magneti…
We identify Gaia0007-1605AC as the first inner brown dwarf-white dwarf binary of a hierarchical triple system in which the outer component is another white dwarf (Gaia0007-1605B). From optical/near-infrared spectroscopy obtained at the Very Large Telescope with the X-Shooter instrument and/or from Gaia photometry plus SED fitting, we determine the effective temperatures and masses of the two white dwarfs (12018+-68 K, 0.54+-0.01 Msun for Gaia0007-1605A and 4445+-116 K, 0.56+-0.05 Msun for Gaia0007-1605B) and the effective temperature of the brown dwarf (1850+-50 K; corresponding to a spectral …
The spectral distribution of field white dwarfs shows a feature called the "non-DA gap". As defined by Bergeron et al., this is a temperature range (5100K--6100K) where relatively few non-DA stars are found, even though such stars are abundant on either side of the gap. It is usually viewed as an indication that a significant fraction of white dwarfs switch their atmospheric compositions back and forth between hydrogen-rich and helium-rich as they cool. In this paper, we present a Monte Carlo model of the Galactic disk white dwarf population, based on the spectral evolution model of Chen and H…
White dwarf stars are the final stage of most stars, born single or in multiple systems. We discuss the identification, magnetic fields, and mass distribution for white dwarfs detected from spectra obtained by the Sloan Digital Sky Survey up to Data Release 13 in 2016, which lead to the increase in the number of spectroscopically identified white dwarf stars from 5000 to 39000. This number includes only white dwarf stars with log g >= 6.5 stars, i.e., excluding the Extremely Low Mass white dwarfs, which are necessarily the byproduct of stellar interaction.
The origin of magnetic fields in white dwarfs remains a fundamental unresolved problem in stellar astrophysics. In particular, the very different fractions of strongly (exceeding 1 MG) magnetic white dwarfs in evolutionarily linked populations of close white dwarf binary stars cannot be reproduced by any scenario suggested so far. Strongly magnetic white dwarfs are absent among detached white dwarf binary stars that are younger than approximately 1 Gyr. In contrast, in semi-detached cataclysmic variables in which the white dwarf accretes from a low-mass star companion, more than one third host…
The Sloan Digital Sky Survey has allowed us to increase the number of known white dwarfs by a factor of five and consequently the number of known pulsating white dwarfs also by a factor of five. It has also led to the discovery of new types of variable white dwarfs, as the variable hot DQs, and the pulsating Extremely Low Mass white dwarfs. With the Kepler Mission, it has been possible to discover new phenomena, the outbursts present in a few pulsating white dwarfs.
The emission of the white dwarf-M dwarf binary AR Sco is driven by the rapid synchronization of its white dwarf, rather than by accretion. This requires a comparatively large magnetic field $\sim 100$ gauss at the M dwarf and $\sim 10^8$ gauss on the white dwarf, larger than the fields of most intermediate polars but within the range of fields of known magnetic white dwarfs. The spindown power is dissipated in the atmosphere of the M dwarf by magnetic reconnection, accelerating particles that produce the observed synchrotron radiation. The displacement of the optical maximum from conjunction m…
We consider the effects of rotation and temperature on the structure of white dwarfs in order to compare them with the estimated data from observations.
We present the first white dwarf mass distributions of a large and homogeneous sample of post-common envelope binaries (PCEBs) and wide white dwarf-main sequence binaries (WDMS) directly obtained from observations. Both distributions are statistically independent, with PCEBs showing a clear concentration of systems towards the low-mass end of the distribution, and the white dwarf mass distribution of wide WDMS binaries being similar to those of single white dwarfs. Our results provide evidence that the majority of low-mass (Mwd < 0.5Msun) white dwarfs are formed in close binaries.
The ESO Supernova Ia Progenitor Survey (SPY) took high-resolution spectra of more than 1000 white dwarfs and pre-white dwarfs. About two thirds of the stars observed are hydrogen-dominated DA white dwarfs. Here we present a catalog and detailed spectroscopic analysis of the DA stars in the SPY. Atmospheric parameters effective temperature and surface gravity are determined for normal DAs. Double-degenerate binaries, DAs with magnetic fields or dM companions, are classified and discussed. The spectra are compared with theoretical model atmospheres using a chi^2 fitting technique. Our final samp…
The number of spatially unresolved white dwarf plus main-sequence star binaries has increased rapidly in the last decade, jumping from only ~30 in 2003 to over 3000. However, in the majority of known systems the companion to the white dwarf is a low mass M dwarf, since these are relatively easy to identify from optical colours and spectra. White dwarfs with more massive FGK type companions have remained elusive due to the large difference in optical brightness between the two stars. In this paper we identify 934 main-sequence FGK stars from the Radial Velocity Experiment (RAVE) survey in the s…
By introducing a simplified transport model of outer layers of white dwarfs we derive an analytical semi-empirical relation which constrains effective temperature-mass-radius for white dwarfs. This relation is used to classify recent data of white dwarfs according to their time evolution in non-accretion process of cooling. This formula permit us to study the population map of white dwarfs in the central temperature and mass plane, and discuss the relation with the ignition temperature for C-O material. Our effective temperature-mass-radius relation provide a quick method to estimate the mass …
It has long been suspected that metal polluted white dwarfs (types DAZ, DBZ, and DZ) and white dwarfs with dusty disks possess planetary systems, but a specific physical mechanism by which planetesimals are perturbed close to a white dwarf has not yet been fully posited. In this paper we demonstrate that mass loss from a central star during post main sequence evolution can sweep planetesimals into interior mean motion resonances with a single giant planet. These planetesimals are slowly removed through chaotic excursions of eccentricity that in time create radial orbits capable of tidally disr…
We report the discovery of 6576 new spectroscopically confirmed white dwarf and subdwarf stars in the Sloan Digital Sky Survey Data Release 12. We obtain Teff, log g and mass for hydrogen atmosphere white dwarf stars (DAs) and helium atmosphere white dwarf stars (DBs), estimate the calcium/helium abundances for the white dwarf stars with metallic lines (DZs) and carbon/helium for carbon dominated spectra DQs. We found one central star of a planetary nebula, one ultra-compact helium binary (AM CVn), one oxygen line dominated white dwarf, 15 hot DO/PG1159s, 12 new cataclysmic variables, 36 magne…
Observations of white dwarfs in the globular clusters NGC 6397 and Omega Centauri indicate that these stars may get a velocity kick during their time as giants. If the mass loss while on the asymptotic giant branch is slightly asymmetric, the resulting white dwarf could be born with such a velocity kick. These energetic white dwarfs will impart their excess energy on other stars as they travel through the cluster. A Monte-Carlo simulation of the white-dwarfs kicks combined with estimate of the phase-space diffusion of the white dwarfs reveals that as the white dwarfs equilibrate, they lose mos…
Recently, a class of Roche-lobe-filling binary systems consisting of hot subdwarf stars and white dwarfs with sub-hour periods has been discovered. At present, the hot subdwarf is in a shell He burning phase and is transferring some of its remaining thin H envelope to its white dwarf companion. As the evolution of the hot subdwarf continues, it is expected to detach, leaving behind a low mass C/O core white dwarf secondary with a thick He layer. Then, on a timescale of $\sim 10$ Myr, gravitational wave radiation will again bring the systems into contact. If the mass transfer is unstable and re…
Spectroscopically identified white dwarfs from the SDSS data release 1 are matched against SDSS data release 1 proper motion survey in the search for common proper motion companions
Binary systems containing a magnetic white dwarf and a main-sequence star are considered extremely rare, perhaps non-existent. In the course of a search of magnetic fields in high-mass white dwarfs we have discovered a Sirius-like wide binary system composed of a main-sequence G0 star and a $M\sim 1.1\,M_\odot$ white dwarf with a huge (hundreds of MG) magnetic field. This star, WDS J03038+0608B, shows a circular polarisation amplitude of 5% in the continuum, with no evidence of variability in a 1d time-scale, little or no linear polarisation in the blue part of the spectrum, and about 2% linea…
We use Gaia Data Release 2 to identify 13,928 white dwarfs within 100 pc of the Sun. The exquisite astrometry from Gaia reveals for the first time a bifurcation in the observed white dwarf sequence in both Gaia and the Sloan Digital Sky Survey (SDSS) passbands. The latter is easily explained by a helium atmosphere white dwarf fraction of 36%. However, the bifurcation in the Gaia colour-magnitude diagram depends on both the atmospheric composition and the mass distribution. We simulate theoretical colour-magnitude diagrams for single and binary white dwarfs using a population synthesis approach…
As a result of competing physical mechanisms, the atmospheric composition of white dwarfs changes throughout their evolution, a process known as spectral evolution. Because of the ambiguity of their atmospheric compositions and the difficulties inherent to the modeling of their dense atmospheres, no consensus exists regarding the spectral evolution of cool white dwarfs ($T_{\rm eff}<6000$ K). In the previous papers of this series, we presented and observationally validated a new generation of cool white dwarf atmosphere models that include all the necessary constitutive physics to accurately m…
We used the revised New Luyten Two-Tenths (rNLTT) catalog to select high proper motion white dwarf candidates. We studied the spectra of 70 hydrogen-rich (DA) white dwarfs, which were obtained at the Cerro Tololo Inter-American Observatory (CTIO) and extracted from the Sloan Digital Sky Survey (SDSS). We determined their effective temperature and surface gravity by fitting their Balmer line profiles to model white dwarf spectra. Using evolutionary mass-radius relations we determined their mass and cooling age. We also conducted a kinematical study of the white dwarf sample and found that most …
In this work, cold and hot, static and rotating white dwarf stars are investigated within the framework of classical physics, employing the Chandrasekhar equation of state. The main parameters of white dwarfs such as the central density, pressure, total mass and radius are calculated fulfilling the stability criteria for hot rotating stars. To construct rotating configurations the Hartle approach is involved. It is shown that the effects of finite temperatures become crucial in low-mass white dwarfs, whereas rotation is relevant in all mass range. The simultaneous accounting for temperature an…
There are no known examples of magnetic white dwarfs with fields larger than about 3MG paired with a non-degenerate companion in detached binary systems. The suggestion is that highly magnetic, isolated white dwarfs may originate from stars that coalesce during common envelope evolution while those stars that emerge from a common envelope on a close orbit may evolve into double degenerate systems consisting of two white dwarfs, one or both magnetic. The presence of planets or planetary debris around white dwarfs is also a new and exciting area of research that may give us important clues on th…
White dwarfs carry information on the structure and evolution of the Galaxy, especially through their luminosity function and initial-to-final mass relation. Very cool white dwarfs provide insight into the early ages of each population. Examining the spectra of all stars with $3σ$ proper motion in the Sloan Digital Sky Survey Data Release 14, we report the classification for 20 088 spectroscopically confirmed white dwarfs, plus 415 hot subdwarfs, and 311 cataclysmic variables. We obtain Teff, log g and mass for hydrogen atmosphere white dwarf stars (DAs), warm helium atmosphere white dwarfs (D…
White dwarfs are the final remnants of low- and intermediate-mass stars. Their evolution is essentially a cooling process that lasts for $\sim 10$ Gyr. Their observed properties provide information about the history of the Galaxy, its dark matter content and a host of other interesting astrophysical problems. Examples of these include an independent determination of the past history of the local star formation rate, identification of the objects responsible for the reported microlensing events, constraints on the rate of change of the gravitational constant, and upper limits to the mass of wea…
Hot DQ white dwarfs constitute a new class of white dwarf stars, uncovered recently within the framework of the SDSS project. Recently, three hot DQ white dwarfs have been reported to exhibit photometric variability with periods compatible with pulsation g-modes. Here, we present a nonadiabatic pulsation analysis of the recently discovered carbon-rich hot DQ white dwarf stars. One of our main aims is to test the convective-mixing picture for the origin of hot DQs through the pulsational properties. Our study relies on the full evolutionary models of hot DQ white dwarfs recently developed by Al…
In Gentile Fusillo et al. (2015) we developed a selection method for white dwarf candidates which makes use of photometry, colours and proper motions to calculate a probability of being a white dwarf (Pwd). The application of our method to the Sloan Digital Sky Survey (SDSS) data release 10 resulted in nearly 66,000 photometrically selected objects with a derived Pwd, approximately 21000 of which are high confidence white dwarf candidates. Here we present an independent test of our selection method based on a sample of spectroscopically confirmed white dwarfs from the LAMOST (Large Sky Area Mu…
A new relative orbit solution with new dynamical masses is determined for the nearby white dwarf - red dwarf pair 40 Eri BC. The period is 230.09+/-0.68y. It is predicted to close slowly over the next half-century getting as close as 1.32" in early 2066. We determine masses of 0.575+/-0.018 $m_\odot$ for the white dwarf and 0.2041+/-0.0064 $m_\odot$ for the red dwarf companion. The inconsistency of the masses determined by gravitational redshift and dynamical techniques, due to a premature orbit calculation, no longer exists.
The equilibrium configurations of uniformly rotating white dwarfs at finite temperatures are investigated, exploiting the Chandrasekhar equation of state for different isothermal cores. The Hartle-Thorne formalism is applied to construct white dwarf configurations in the framework of Newtonian physics. The equations of structure are considered in the slow rotation approximation and all basic parameters of rotating hot white dwarfs are computed to test the so-called moment of inertia, tidal Love number and quadrupole moment ($I$-Love-$Q$) relations. It is shown that even within the same equatio…
White dwarf and pre-white dwarf atmospheres are one of the best examples for the application of Stark broadening research results in astrophysics, due to plasma conditions very favorable for this line broadening mechanism. For example in hot hydrogen-deficient (pre-) white dwarf stars Teff = 75 000 K - 180 000 K and log g = 5.5-8 [cgs]. Even for much cooler DA and DB white dwarfs with typical effective temperatures of 10 000 K - 20 000 K, Stark broadening is usually the dominant broadening mechanism. In this review, Stark broadening in white dwarf spectra is considered and the attention is dra…
Limits on the companions of white dwarfs in the single degenerate scenario for the origin of Type Ia supernovae (SNIa) have gotten increasingly tight. The only type of non-degenerate stars that survive the limits on the companions of SNIa in SNR 0509-67.5 and SN1572 are M dwarfs. M dwarfs have special properties that have not been considered in most work on the progenitors of SNIa: they have small but finite magnetic fields, and they flare frequently. These properties are explored in the context of SNIa progenitors. White dwarf/M dwarf pairs may be sufficiently plentiful to provide an adequate…
We present a spectroscopically identified catalogue of 72 DA white dwarfs from the LAMOST pilot survey. 35 are found to be new identifications after cross-correlation with the Eisenstein et al. and Villanova catalogues. The effective temperature and gravity of these white dwarfs are estimated by Balmer lines fitting. Most of them are hot white dwarfs. The cooling times and masses of these white dwarfs are estimated by interpolation in theoretical evolution tracks. The peak of mass distribution is found to be $\sim$ 0.6 $M_\odot$ which is consistent with prior work in the literature. The distan…
Observations of main sequence stars conducted over the last several decades have clearly shown that something like 50 per cent of stars of spectral types G and F occur in multiple systems. For earlier spectral types, the incidence of multiplicity is even higher. Thus, a volume limited sample of white dwarfs should reflect the percentage of binarity observed in stars of F to late B spectral types, which are their Main Sequence progenitors. However, a study of the local volume limited sample of white dwarfs (20 pc from the Sun) conducted by Holberg has shown that a white dwarf has a probability …
We identify a likely member of the NGC 752 open cluster (based on Gaia DR2 proper motions and parallax) having photometry consistent with being a white dwarf and a relatively low-mass main sequence star. If confirmed, this would be the first white dwarf known in this nearby cluster, and the brightest.
With the Cosmic Origins Spectrograph onboard the Hubble Space Telescope, we have detected molecular hydrogen in the atmospheres of three white dwarfs with effective temperatures below 14,000 K, G29-38, GD 133 and GD 31. This discovery provides new independent constraints on the stellar temperature and surface gravity of white dwarfs.
White dwarfs are the burnt out cores of Sun-like stars and are the final fate of 97% of all stars in our Galaxy. The internal structure and composition of white dwarfs are hidden by their high gravities, which causes all elements, apart from the lightest ones, to settle out of their atmospheres. The most direct method to probe the inner structure of stars and white dwarfs in detail is via asteroseismology. Here we present the first known pulsating white dwarf in an eclipsing binary system, enabling us to place extremely precise constraints on the mass and radius of the white dwarf from the lig…
As they evolve, white dwarfs undergo major changes in surface composition, a phenomenon known as spectral evolution. In particular, some stars enter the cooling sequence with helium atmospheres (type DO) but eventually develop hydrogen atmospheres (type DA), most likely through the upward diffusion of residual hydrogen. Our empirical knowledge of this process remains scarce: the fractions of white dwarfs that are born helium-rich and that experience the DO-to-DA transformation are poorly constrained. We tackle this issue by performing a detailed model-atmosphere investigation of 1806 hot ($T_{…
A significant fraction of white dwarfs harbour a magnetic field with strengths ranging from a few kG up to about 1000 MG. The fraction appears to depend on the specific class of white dwarfs being investigated and may hold some clues to the origin of their magnetic field. The number of white dwarfs with variable fields as a function of their rotation phase have revealed a large field structure diversity, from a simple offset dipole to structures with spots or multipoles. A review of the current challenges in modelling white dwarf atmospheres in the presence of a magnetic field is presented, an…
SDSSJ125733.63+542850.5 (hereafter SDSSJ1257+5428) is a compact white dwarf binary from the Sloan Digital Sky Survey that exhibits high-amplitude radial velocity variations on a period of 4.56 hours. While an initial analysis suggested the presence of a neutron star or black-hole binary companion, a follow-up study concluded that the spectrum was better understood as a combination of two white dwarfs. Here we present optical spectroscopy and ultraviolet fluxes which directly reveal the presence of the second white dwarf in the system. SDSSJ1257+5428's spectrum is a composite, dominated by the …
Context: About 10% of white dwarfs have magnetic fields with strength in the range between about 10^5 and 3x10^8 G. It is not known whether the remaining white dwarfs are not magnetic, or if they have a magnetic field too weak to be detected with the techniques adopted in the large surveys. Aims. We describe the results of the first survey specifically devised to clarify the detection frequency of kG-level magnetic fields in cool DA white dwarfs. Methods: Using the FORS1 instrument of the ESO VLT, we have obtained Balmer line circular spectropolarimetric measurements of a small sample of cool …
We present optical high-speed photometry of three millisecond pulsars with low-mass ($< 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…
With the Keck I Low-Resolution Imaging Spectrometer we have observed nine white dwarf candidates in the very rich open cluster NGC 2099 (M37). The spectroscopy shows seven to be DA white dwarfs, one to be a DB white dwarf, and one to be a DZ white dwarf. Three of these DA white dwarfs are consistent with singly evolved cluster membership: an ultramassive (1.28$^{+0.05}_{-0.08}$ M$_\odot$) and two intermediate-mass (0.70 and 0.75 M$_\odot$) white dwarfs. Analysis of their cooling ages allows us to calculate their progenitor masses and establish new constraints on the initial-final mass relation…
It has been recently proposed that very massive white dwarfs endowed with strongly quantizing magnetic fields might be the progenitors of overluminous type Ia supernovae like SN 2006gz and SN 2009dc. In this work, we show that the onset of electron captures and pycnonuclear reactions in these putative super-Chandrasekhar white dwarfs may severely limit their stability.
We present new spectroscopic observations of the polluted, dusty, helium-dominated atmosphere white dwarf star HE1349-2305. Optical spectroscopy reveals weak CaII infrared triplet emission indicating that metallic gas debris orbits and is accreted by the white dwarf. Atmospheric abundances are measured for magnesium and silicon while upper limits for iron and oxygen are derived from the available optical spectroscopy. HE1349-2305 is the first gas disk-hosting white dwarf star identified amongst previously known polluted white dwarfs. Further characterization of the parent body polluting this s…
We present some of the results of a survey aimed at exploring the asteroseismological potential of the newly-discovered carbon-atmosphere white dwarfs. We show that, in certains regions of parameter space, carbon-atmosphere white dwarfs may drive low-order gravity modes. We demonstrate that our theoretical results are consistent with the recent exciting discovery of luminosity variations in SDSS J1426+5752 and some null results obtained by a team of scientists at McDonald Observatory. We also present follow-up photometric observations carried out by ourselves at the Mount Bigelow 1.6-m telesco…
Using our newly developed model atmosphere code appropriate for magnetic white dwarfs with metal lines in the Paschen-Back regime, we study various magnetic white dwarfs and explore the effects of various parameters such as the field geometry and the convective efficiency
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 the…
The evolution of white dwarfs is a simple gravothermal process. This process can be tested in two ways, through the luminosity function of these stars and through the secular variation of the period of pulsation of those stars that are variable. Here we show how the mass of the axion can be constrained using the white dwarf luminosity function.
