White Dwarf luminosities are powerful age indicators, whose calibration should be based on reliable models. We discuss the uncertainty of some chemical and physical parameters and their influence on the age estimated by means of white dwarf cooling sequences. Models at the beginning of the white dwarf sequence have been obtained on the base of progenitor evolutionary tracks computed starting from the zero age horizontal branch and for a typical halo chemical composition (Z=0.0001, Y=0.23). The uncertainties due to nuclear reaction rates, convection, mass loss and initial chemical composition are discussed. Then, various cooling sequences for a typical white dwarf mass (M=0.6 Mo) have been calculated under different assumptions on some input physics, namely: conductive opacity, contribution of the ion-electron interaction to the free energy and microscopic diffusion. Finally we present the evolution of white dwarfs having mass ranging between 0.5 and 0.9 Mo. Much effort has been spent to extend the equation of state down to the low temperature and high density regime. An analysis of the latest improvement in the physics of white dwarf interiors is presented. We conclude that at the faint end of the cooling sequence (log L/Lo=-5.5) the present overall uncertainty on the age is of the order of 20%, which correspond to about 3 Gyr. We suggest that this uncertainty could be substantially reduced by improving our knowledge of the conductive opacity (especially in the partially degenerate regime) and by fixing the internal stratification of C and O.
We summarize recent improvements in model atmosphere and internal structure of faint white dwarfs. We derive an analytical cooling theory which illustrates the effects of various physical processes on the energy budget and the cooling history of cool white dwarfs. We consider in particular the effect of chemical fractionation at crystallization. This process, although it liberates a small amount of energy, affects significantly the cooling time of white dwarfs at their low-luminosity stages. This modifies the age of the faintest white dwarf ever observed, ESO 439-26, and bears important conseq…
We use the irradiated secondary star in the remnant of Nova Cyg 1975 as a probe of the cooling white dwarf. At superior conjunction the flux in the B band is dominated by the irradiated face of the secondary star. The heated face produces an orbital modulation which is dependent on the strength of the irradiating source. We demonstrate that the cooling rate of the white dwarf is consistent with the theoretical model of Prialnik (1986).
In this paper we demonstrate that the puzzling bright peak in the luminosity function of the white dwarf (WD) cooling sequence of NGC6791 can be naturally accounted for if ~34% of the observed WDs are WD+WD binary systems.
We have used deep HST WFPC2 observations of two fields in NGC 2420 to produce a cluster CMD down to V = 27. After imposing morphological selection criteria we find eight candidate white dwarfs in NGC 2420. Our completeness estimates indicate that we have found the terminus of the WD cooling sequence. We argue that the cluster distance modulus is likely to be close to 12.10 with E(B-V) = 0.04. With these parameters we find a white dwarf cooling age for NGC 2420 of 2.0 +- 0.20 (1 sigma) Gyrs. The 0.20 Gyr uncertainty includes errors in the photometry, sequence fitting, precursor time scales, and…
We discuss the importance of pure hydrogen white dwarf atmosphere models with Ly-$\rm α$ far red wing opacity in the analysis of the white dwarf cooling sequence of the globular cluster NGC 6397. Our recently improved atmosphere models account for the previously missing opacity from the Ly-$\rm α$ hydrogen line broadened by collisions of the absorbing hydrogen atoms with molecular and atomic hydrogen. These models are the first that well reproduce the UV colors and spectral energy distributions of cool white dwarfs with $T_{\rm eff}<6000 \rm K$ observed in the Galactic Disk. Fitting the observ…
We develop the white dwarf luminosity function (LF) of the old open cluster NGC 188 in order to determine a lower limit to the age of the cluster by using the faint end of the cooling sequence. To produce an extensive sequence of the cooling white dwarfs we imaged four contiguous HST-WFPC2 fields in the center of the cluster in the F555W and F814W filters. After imposing selection criteria on the detected objects we found a white dwarf cooling sequence (down to V ~26.5) including 28 candidate white dwarfs in the cluster. The exposures are not deep enough to reach the end of this sequence, but …
In the old, populous, and metal-rich open cluster NGC 6791 we have used deep HST/ACS images to track the white dwarf cooling sequence down to m_F606W~28.5. The white dwarf luminosity function shows a well defined peak at m_F606W~27.4, and a bending to the blue in the color--magnitude diagram. If this peak corresponds to the end of the white dwarf cooling sequence the comparison with theoretical isochrones provides a cluster age estimate of ~2.4 Gyr, in sharp contrast with the age of 8--9 Gyr inferred from the main-sequence turn-off. If the end is at fainter magnitudes, the peak at m_F606W~27.4…
The evolution of white dwarfs is essentially a cooling process that depends primarily on the energy stored in their degenerate cores and on the transparency of their envelopes. In this paper we compute accurate cooling sequences for carbon-oxygen white dwarfs with hydrogen dominated atmospheres for the full range of masses of interest. For this purpose we use the most accurate available physical inputs for both the equation of state and opacities of the envelope and for the thermodynamic quantities of the degenerate core. We also investigate the role of the latent heat in the computed cooling …
We present new cooling sequences, color-magnitude diagrams, and color-color diagrams for cool white dwarfs with pure hydrogen atmospheres down to an effective temperature $\te=1500$ K. We include a more detailed treatment of the physics of the fully-ionized interior, particularly an improved discussion of the thermodynamics of the temperature-dependent ion-ion and ion-electron contributions of the quantum, relativistic electron-ion plasma. The present calculations also incorporate accurate boundary conditions between the degenerate core and the outermost layers as well as updated atmosphere mo…
We respond to the paper by De Marchi, Paresce, Straniero and Moroni (2003) on the white dwarf cooling age of M4. The authors question the data analysis and interpretation that led to the conclusions in Hansen et al. (2002). In their paper, De Marchi et al. are unable to obtain photometry as deep as ours from the same data set and therefore assert that only a lower limit to the white dwarf cooling age for this cluster of approximately 9 Gyr can be obtained. In this short contribution we show that shortcomings in the data analysis and reduction techniques of De Marchi et al. are responsible for …
I explore the current ability of both white dwarf cooling theory and main sequence stellar evolution theory to accurately determine stellar population ages by comparing ages derived using both techniques for open clusters ranging from 0.1 to 4 Gyr. I find good agreement between white dwarf and main sequence evolutionary ages over the entire age range currently available for study. I also find that directly comparing main sequence turn-off ages to white dwarf ages is only weakly sensitive to realistic levels of errors in cluster distance, metallicity, and reddening. Additional detailed comparis…
We investigate in detail the white dwarf cooling sequence of the globular cluster Messier 4. In particular we study the influence of various systematic uncertainties, both observational and theoretical, on the determination of the cluster age from the white dwarf cooling sequence. These include uncertainties in the distance to the cluster and the extinction along the line of sight, as well as the white dwarf mass, envelope and core compositions and the white dwarf --main sequence mass relation. We find that fitting to the full two-dimensional colour-magnitude diagram offers a more robust metho…
We present new white dwarf cooling models which incorporate an accurate outer boundary condition based on new opacity and detailed radiative transfer calculations. We find that helium atmosphere dwarfs cool considerably faster than has previously been claimed, while old hydrogen atmosphere dwarfs will deviate significantly from black body appearance. We use our new models to derive age limits for the Galactic disk. We find that the Liebert, Dahn & Monet (1988) luminosity function yields an age of only 6 Gyr if it is complete to stated limits. However, age estimates of individual dwarfs and the…
We report on Keck and {\em Hubble Space Telescope} observations of the binary millisecond pulsar PSR B1855+09. We detect its white-dwarf companion and measure $\mv=25.90\pm0.12$ and $\mi=24.19\pm0.11$ (Vega system). From the reddening-corrected color, $(\mv-\mi)_0=1.06\pm0.21$, we infer a temperature $\Teff=4800\pm800 $K. The white-dwarf mass is known accurately from measurements of the Shapiro delay of the pulsar signal, $\Mcomp=0.258^{+0.028}_{-0.016} \Msun$. Hence, given a cooling model, one can use the measured temperature to determine the cooling age. The main uncertainty in the cooling m…
We present the results of a deep Hubble Space Telescope (HST) exposure of the nearby globular cluster NGC6397, focussing attention on the cluster's white dwarf cooling sequence. This sequence is shown to extend over 5 magnitudes in depth, with an apparent cutoff at magnitude F814W=27.6. We demonstrate, using both artificial star tests and the detectability of background galaxies at fainter magnitudes, that the cutoff is real and represents the truncation of the white dwarf luminosity function in this cluster. We perform a detailed comparison between cooling models and the observed distribution…
White dwarfs are the end-product of the lifes of intermediate- and low-mass stars and their evolution is described as a simple cooling process. Recently, it has been possible to determine with an unprecedented precision their luminosity function, that is, the number of stars per unit volume and luminosity interval. We show here that the shape of the bright branch of this function is only sensitive to the averaged cooling rate of white dwarfs and we propose to use this property to check the possible existence of axions, a proposed but not yet detected weakly interacting particle. Our results in…
We present the white dwarf sequence of the globular cluster M4, based on a 123 orbit Hubble Space Telescope exposure, with limiting magnitude V = 30, I = 28. The white dwarf luminosity function rises sharply for I >25.5, consistent with the behaviour expected for a burst population. The white dwarfs of M4 extend to approximately 2.5 magnitudes fainter than the peak of the local Galactic disk white dwarf luminosity function. This demonstrates a clear and significant age difference between the Galactic disk and the halo globular cluster M4. Using the same standard white dwarf models (Hansen 1999…
In this paper we compute detailed evolutionary models providing chemical profiles for white dwarfs having progenitors in the mass range from 1.0 to $7 M_{\sun}$ and we examine the influence of such profiles in the cooling process. The influence of the process of separation of carbon and oxygen during crystallization is decreased as a consequence of the initial stratification, but it is still important and cannot be neglected. As an example, the best fit to the luminosity functions of Liebert et al. (1988) and Oswalt et al. (1996) gives and age of the disk of 9.3 and 11.0 Gyr, respectively, whe…
We report on Keck optical BVRI images and spectroscopy of the companion of the binary millisecond pulsar PSR J0218+4232. A faint bluish (V=24.2, B-V=0.25) counterpart is observed at the pulsar location. Spectra of this counterpart reveal Balmer lines which confirm that the companion is a Helium-core white dwarf. We find that the white dwarf has a temperature of Teff=8060+-150 K. Unfortunately, the spectra are of insufficient quality to put a strong constraint on the surface gravity, although the best fit is for low log g and hence low mass (~0.2 Msun), as expected. We compare predicted white d…
We present a detailed calculation of the evolution of low-mass ($< 0.25~M_\odot $) helium white dwarfs. These white dwarfs (the optical companions to binary millisecond pulsars) are formed via long-term, low-mass binary evolution. After detachment from the Roche lobe, the hot helium cores have a rather thick hydrogen layer with mass between 0.01 to 0.06$~M_\odot $. Due to mixing between the core and outer envelope, the surface hydrogen content is 0.5 to 0.35, depending on the initial value of the heavy element (Z) and the initial secondary mass. We found that the majority of our computed model…
A deep imaging survey covering the entire $23\arcmin$ diameter of the old open cluster M67 to $V = 25$ has been carried out using the mosaic imager (UHCam) on the Canada-France-Hawaii Telescope. The cluster color-magnitude diagram (CMD) can be traced from stars on its giant branch at $M_{V} = +1$ down through main sequence stars at least as faint as $M_{V} = 13.5$. Stars this low in luminosity have masses below $0.15 M_{\odot}$. A modest white dwarf (WD) cooling sequence is also observed commencing slightly fainter than $M_V = 10$ and, after correction for background galaxy and stellar field c…
We present new observations of the white dwarf sequence of the old open cluster NGC 6791. The brighter peak previously observed in the white dwarf luminosity function (WDLF) is now better delineated, and the second, fainter peak that we suggested earlier is now confirmed. A careful study suggests that we have reached the end of the white dwarf sequence. The WDs that create the two peaks in the WDLF show a significant turn to the blue in the color-magnitude diagram. The discrepancy between the age from the WDs and that from the main sequence turnoff remains, and we have an additional puzzle in …
We discuss the cooling history of the low-mass, helium core white dwarfs in short orbital period millisecond pulsars PSR J0751+1807 and PSR J1012+5307. The revised cooling age estimated by Alberts et al. agrees with the age estimation for PSR J1012+5307, removing the discrepancy between the spin-down age and the cooling age. However, if we accept this model then the helium white dwarf in the binary pulsar system PSR J0751+1807 must be much hotter than is observed. We propose that this discrepancy may be resolved if, after detachment of the secondary star from its Roche lobe in PSR J0751+1807, …
The white dwarf luminosity function of a stellar cluster will have a sharp truncation at a luminosity which is determined by the time since formation of the first white dwarfs in that cluster. Calculation of the dependence of this limiting luminosity on age requires relatively well-understood physics and is independent of stellar evolutionary models. Thus, measurement of the termination of the white dwarf luminosity function provides an independent method to determine the age of a cluster, and thereby to calibrate stellar evolutionary ages. We have obtained HST WFPC2 data in two open clusters,…
Given the importance of white dwarfs (WDs) in many fields of modern astrophysics, the precise knowledge of the actual degree of accuracy of the associated theoretical predictions is a primary task. In the first paper of a series dedicated to the modeling of WD structure and evolution we discussed the limits of the available theoretical studies of cooling sequences. In the present work we extend this analysis to isochrones and luminosity functions of WDs belonging to old stellar systems, like globular or old disk clusters. The discussion is focused on the most common DA, those with a CO core an…
We have investigated the ionisation structure of the post-shock regions of magnetic cataclysmic variables using an analytic density and temperature structure model in which effects due to bremsstrahlung and cyclotron cooling are considered. We find that in the majority of the shock-heated region where H- and He-like lines of the heavy elements are emitted, the collisional-ionisation and corona-condition approximations are justified. We have calculated the line emissivity and ionisation profiles for Iron as a function of height within the post-shock flow. For low-mass white dwarfs, line emissio…
We assess the impact of the trace element ^{22}Ne on the cooling and seismology of a liquid C/O white dwarf (WD). Due to this elements' neutron excess, it sinks towards the interior as the liquid WD cools. The subsequent gravitational energy released slows the cooling of the WD by 0.25--1.6 Gyrs by the time it has completely crystallized, depending on the WD mass and the adopted sedimentation rate. The effects will make massive WDs or those in metal rich clusters (such as NGC 6791) appear younger than their true age. Our diffusion calculations show that the ^{22}Ne mass fraction in the crystal…
We present seven evolutionary tracks for low-mass white dwarfs with helium cores, ranging in mass from 0.179 to 0.414 Msol. We generated the pre-white dwarf models from a 1 Msol sequence extending up to the tip of its red-giant branch by applying high mass-loss rates at appropriate positions, and we followed their evolution across the Hertzsprung-Russell diagram and down the cooling path. We discuss the internal structures and cooling properties of these new models and compare them with those of recently published models for low-mass white dwarfs which are based on simplified initial configura…
We obtained Hubble GHRS medium resolution (G160M grating) phase-resolved spectroscopic observations of the prototype dwarf nova U Geminorum during dwarf nova quiescence, 13 days and 61 days following the end of a narrow outburst. The spectral wavelength ranges were centered upon three different line regions: N V (1238Å, 1242Å), Si III (1300Å) and He II (1640Å). All of the quiescent spectra at both epochs are dominated by absorption lines and show no emission features. The Si III and He II absorption line velocities versus orbital phase trace the orbital motion of the white dwarf but the N~V ab…
The evolution of white dwarfs is a cooling process that depends on the energy stored in the core and on the way in which it is transferred through the envelope. In this paper we show that despite some (erroneous) claims, the redistribution of chemical elements ensuing the crystallization of C/O white dwarfs provides between the 10% and the 20% of the total energy released during the crystallization process, depending on the internal chemical composition, which is not negligible at all, given the present state of the art of the white dwarf cooling theory.
We assess the impact of the trace element Ne-22 on the cooling and seismology of a liquid C/O white dwarf (WD). Due to this element's neutron excess, it sinks towards the interior as the liquid WD cools. The gravitational energy released slows the WD's cooling by 0.5-1.6 Gyr. In addition the Ne-22 abundance gradient changes the periods of the high radial order g-modes at the 1% level.
White dwarfs can be used as galactic chronometers and, therefore, provide important information about galactic evolution if good theoretical models of their cooling are available. Consequently, it is natural to wonder if all the sources or sinks of energy are correctly taken into account. One of these sources is partial differentiation of the chemical components of the white dwarf upon crystallization. In this paper we use a new formalism to show that if there is a redistribution of the elements inside the star, there is a net release of energy that has to be radiated away and that slows down …
FUSE and HST/STIS spectra of the dwarf nova WZ Sge, obtained during and following the early superoutburst of July 2001 over a time span of 20 months, monitor changes in the components of the system during its different phases. The synthetic spectral fits to the data indicate a cooling in response to the outburst of about 12,000K, from about 28,000K down to about 16,000K. The cooling time scale tau (of the white dwarf temperature excess) is of the order of about 100 days in the early phase of the cooling period, and increases to about 850 days toward the end of the second year following the out…
We present a grid of evolutionary tracks for low-mass white dwarfs with helium cores in the mass range from 0.179 to 0.414 M_sun. The lower mass limit is well suited for comparison with white dwarf companions of millisecond pulsars (MSP). The derived cooling ages are of the order of 10^9 yrs due to residual nuclear burning. The cooling ages are consistent with age estimations of MSP systems based on the pulsars' spin-down. For example, for the system PSR 1012+5307 we derived a white dwarf cooling age of 6 +/-1 Gyr in good agreement with the spin-down age of 7 Gyr. For the companion mass we fou…
The 3-body crystallization diagrams of C/O/Ne ionic mixtures characteristic of white dwarf interiors are examined within the framework of the density-functional theory of freezing. The crystallization process is described more accurately than in former calculations where the three-component system was treated as an effective two-component mixture (Segretain et al. 1994). The distillation process due to neon-crystallization is found to occur only for the late stages of crystallization. At the beginning, the presence of neon plays only a minor role and the phase diagram resembles a pure carbon-o…
With the Wide Field Planetary Camera 2 (WFPC2) on the Hubble Space Telescope, we have discovered in M4 (NGC 6121, C 1620-264) the first extensive sequence of cooling white dwarfs seen in a globular cluster. Adopting a distance modulus of (m-M)_V = 12.65 and a reddening of E(B-V) = 0.37, we show that the sequence, which extends over 9 < M_U < 13, is comprised of white dwarfs of mass \sim 0.5 M_{\odot}. The total mass loss from the present turnoff to the white dwarf sequence is 0.31 M_{\odot} and the intrinsic dispersion in the mean mass appears to be < 0.05 M_{\odot}. Both the location of the w…
We present deep CCD photometry of the very rich, intermediate aged (similar to the Hyades) open star cluster NGC 2099 (M37). The V, B-V color-magnitude diagram (CMD) for the cluster shows an extremely well populated and very tightly constrained main-sequence extending over 12 magnitudes from the turn-off. The CFH12K photometry for this cluster is faint enough (V ~ 24.5) to detect the remnants of the most massive progenitor cluster stars under the Type I SNe limit. Therefore, the CMD of the cluster also exhibits a well defined white dwarf `clump' caused by the decreased rate of cooling of these…
Following an outburst in 2001 July, the UV flux of WZ Sge has declined slowly toward pre-outburst levels. Here, we describe new 1150-1710 Angstrom HST/STIS spectra of WZ Sge obtained between 2002 April and 2003 March to follow the decline. A combined analysis of these and spectra obtained in the fall of 2001 show that if log g=8.5, then the white dwarf temperature decreased from 23,400 K in 2001 October, shortly after the steady decline of the system began, to 15,900 K 17 months later. The UV flux in 2003 March was still 2.4 times higher than measured prior to the outburst and so the system wa…
We present deep and precise photometry (F435, F625W, F658N) of Omega Cen collected with the Advanced Camera for Surveys (ACS) on board the Hubble Space Telescope (HST). We have identified ~ 6,500 white dwarf (WD) candidates, and the ratio of WD and Main Sequence (MS) star counts is found to be at least a factor of two larger than the ratio of CO-core WD cooling and MS lifetimes. This discrepancy is not explained by the possible occurrence of a He-enhanced stellar population, since the MS lifetime changes by only 15% when changing from a canonical (Y=0.25) to a He-enhanced composition (Y=0.42).…
We employed recently computed evolutionary white-dwarf models with helium cores, supplemented by heavier models with carbon-oxygen cores, in order to investigate the ages of millisecond pulsar systems based on the cooling properties of the compact companions. Contrary to the behaviour of more massive white dwarfs, the evolutionary speed of low-mass white-dwarf models is substantially slowed down by ongoing hydrogen burning. By comparing the cooling ages of these models with the spin-down ages of the pulsars for those systems for which reasonable information about the compact companions is avai…
The present work is designed to explore the evolutionary and pulsational properties of low-mass white dwarfs with carbon/oxygen cores. In particular, we follow the evolution of a 0.33 Msun white dwarf remnant in a self-consistent way with the predictions of nuclear burning, element diffusion and the history of the white dwarf progenitor. Attention is focused on the occurrence of hydrogen shell flashes induced by diffusion processes during cooling phases. The evolutionary stages prior to the white dwarf formation are also fully accounted for by computing the conservative binary evolution of an …
Using a new grid of models of cooling white dwarfs, we calculate isochrones and luminosity functions in the Johnson-Kron/Cousins and HST filter sets for systems containing old white dwarfs. These new models incorporate a non-grey atmosphere which is necessary to properly describe the effects of molecular opacity at the cool temperatures of old white dwarfs. The various functions calculated and extensively tabulated and plotted are meant to be as utilitarian as possible for observers so all results are listed in quantities that observers will obtain. The tables and plots developed should eventu…
We have cross-correlated the 2dF QSO Redshift Survey (2QZ) white dwarf catalog with the GALEX 2nd Data Release and the Sloan Digital Sky Survey (SDSS) data release 5 to obtain ultraviolet photometry (FUV, NUV) for approximately 700 objects and optical photometry (ugriz) for approximately 800 objects. We have compared the optical-ultraviolet colors to synthetic white dwarf colors to obtain temperature estimates for approximately 250 of these objects. These white dwarfs have effective temperatures ranging from 10 000 K (cooling age of about 1Gyr) up to about 40 000 K (cooling age of about 3 Myrs…
We examine the recent results of the MACHO collaboration towards the Large Magellanic Cloud (Alcock et al. 1996) in terms of a halo brown dwarf or white dwarf population. The possibility for most of the microlensing events to be due to brown dwarfs is totally excluded by large-scale kinematic properties. The white dwarf scenario is examined in details in the context of the most recent white dwarf cooling theory (Segretain et al. 1994) which includes explicitely the extra source of energy due to carbon-oxygen differentiation at crystallization, and the subsequent Debye cooling. We show that the…
We present evolutionary calculations and colors for massive white dwarfs with oxygen-neon cores for masses between 1.06 and 1.28 Mo. The evolutionary stages computed cover the luminosity range from log(L/Lo) approx. 0.5 down to -5.2. Our cooling sequences are based on evolutionary calculations that take into account the chemical composition expected from massive white dwarf progenitors that burned carbon in partially degenerate conditions. The use of detailed non-gray model atmospheres provides us with accurate outer boundary conditions for our evolving models at low effective temperatures. We…
G39-27/289 is a common proper motion pair formed by a white dwarf (WD0433+270) and a main-sequence star (BD+26 730) that apparently has been classified as a member of the Hyades open cluster. Previous studies of the white dwarf component yielded a cooling time of ~4 Gyr. Although it has not been pointed out before explicitly, this result is 6 times larger than the age of the Hyades cluster, giving rise to an apparent conflict between the physics of white dwarfs and cluster main-sequence fitting. We investigate whether this system belongs to the Hyades cluster and, accordingly, give a plausible…
The interpretation of microlensing results towards the Large Magellanic Cloud (LMC) still remains controversial. White dwarfs have been proposed to explain these results and, hence, to contribute significantly to the mass budget of our Galaxy. However, several constraints on the role played by regular carbon-oxygen white dwarfs exist. Massivewhite dwarfs are thought to be made of a mixture of oxygen and neon. Correspondingly, their cooling rate is larger than those of typical carbon-oxygen white dwarfs and they fade to invisibility in short timescales. Consequently, they constitute a good cand…
Theories of fundamental interactions with large extra dimensions have recently become very popular. Astrophysical bounds from the Sun, red-giants and SN1987a have already been derived by other authors for the theory proposed by Arkani-Hamed, Dimopoulos and Dvali. In this paper we consider G117-B15A pulsating white dwarf (ZZ Ceti star) for which the secular rate at which the period of its fundamental mode increases has been accurately measured and claimed that this mode of G117-B15A is perhaps the most stable oscillation ever recorded in the optical band. Because an additional channel of energy…
We considered recently as a new axion production mechanism the process $e^- \to e^- +a$ in a strong magnetic field $B$. Requiring that for a strongly magnetized neutron star the axion luminosity is smaller than the neutrino luminosity we obtained the bound $g_{ae} \lsim 10^{-10}$ for the axion electron coupling constant. This limit is considerably weaker than the bound derived earlier by Borisov and Grishina using the same method. Applying a similar argument to magnetic white dwarf stars we obtained $g_{ae}\lsim 9 \cdot 10^{-13} (T/10^7)^{5/4} (B/10^{10})^{-2}$, where $T$ is the internal tempe…
