A. M. Serenelli

The ages and colours of cool helium-core white dwarf stars

0.406, 0.360, 0.327, 0.292, 0.242, 0.196 and 0.169 M( and follow their evolution from the end of mass-loss episodes, during their pre-white dwarf evolution, down to very low surface luminosities. We find that when the effective temperature decreases below 4000 K, the emergent spectrum of these stars becomes bluer within time-scales of astrophysical interest. In particular, we analyse the evolution of our models in the colour ‐ colour and in the colour ‐ magnitude diagrams and find that helium-core white dwarfs with masses ranging from ,0.18 to 0.3 M( can reach the turn-off in their colours and become blue again within cooling times much less than 15 Gyr and then remain brighter than MV < 16:5. In view of these results, many low-mass helium white dwarfs could have had enough time to evolve to the domain of collision-induced absorption from molecular hydrogen, showing blue colours.

New evolutionary models for massive ZZ Ceti stars. I. First results for their pulsational properties

We present new and improved evolutionary calculations for carbon-oxygen white dwarf (WD) stars appropriate for the study of massive ZZ Ceti stars. We follow the complete evolution of massive WD progenitors from the zero-age main sequence through the thermally pulsing and mass loss phases to the WD regime. Abundance changes are accounted for by means of a full coupling between nuclear evolution and time-dependent mixing due to diffusive overshoot, semiconvection and salt fingers. In addition, time-dependent element diffusion for multicomponent gases has been considered during the WD stage. We find that before the ZZ Ceti stage is reached, element diffusion has strongly smoothed out the chemical profile to such a degree that the resulting internal abundance distribution does not depend on the occurrence of overshoot episodes during the thermally pulsing phase. The mass of the hydrogen envelope left at the ZZ Ceti domain amounts to

Evolution and colours of helium-core white dwarf stars: the case of low-metallicity progenitors

M_H \approx 2.3 \times 10^{-6}

New DA white dwarf evolutionary models and their pulsational properties

\msun. This is about half as large as for the case when element diffusion is neglected. The implications of our new models for the pulsational properties of massive ZZ Ceti stars are discussed. In this regard, we find that the occurrence of core overshooting during central helium burning leaves strong imprints on the theoretical period spectrum of massive ZZ Ceti stars. Finally, we present a simple new prescription for calculating the He/H profile which goes beyond the trace element approximation.

Evolution of a 3-M⊙ star from the main sequence to the ZZ Ceti stage: the role played by element diffusion

The present work is designed to explore the evolution of helium-core white dwarf (He WD) stars for the case of metallicities much lower than the solar metallicity (Z= 0.001 and 0.0002). Evolution is followed in a self-consistent way with the predictions of detailed and new non-grey model atmospheres, time-dependent element diffusion and the history of the white dwarf progenitor. Reliable initial models for low-mass He WDs are obtained by applying mass-loss rates to a 1-M⊙ stellar model in such a way that the stellar radius remains close to the Roche lobe radius. The loss of angular momentum caused by gravitational wave emission and magnetic stellar wind braking are considered. Model atmospheres, based on a detailed treatment of the microphysics entering the WD atmosphere (such as the formalism of Hummer–Mihalas to deal with non-ideal effects) and hydrogen line and pseudo-continuum opacities, enable us to provide accurate colours and magnitudes at both early and advanced evolutionary stages. We find that most of our evolutionary sequences experience several episodes of hydrogen thermonuclear flashes. In particular, the lower the metallicity, the larger the minimum stellar mass for the occurrence of flashes induced by CNO cycle reactions. The existence of a mass threshold for the occurrence of diffusion-induced CNO flashes leads to a marked dichotomy in the age of our models. Another finding of this study is that our He WD models experience unstable hydrogen burning via PP nuclear reactions at late cooling stages as a result of hydrogen chemically diffusing inwards. Such PP flashes take place in models with very low metal content. We also find that models experiencing CNO flashes exhibit a pronounced turn-off in most of their colours at MV≈ 16. Finally, colour–magnitude diagrams for our models are presented and compared with recent observational data of He WD candidates in the globular clusters NGC 6397 and 47 Tucanae.

Formation and Evolution of a 0.242 M☉ Helium White Dwarf in the Presence of Element Diffusion

In this letter we investigate the pulsational properties of ZZ Ceti stars on the basis of new white dwarf evolutionary models calculated in a self-consistent way with the predictions of time dependent element diusion and nuclear burning. In addition, full account is taken of the evolutionary stages prior to the white dwarf formation. Emphasis is placed on the trapping properties of such models. By means of adiabatic, non-radial pulsation calculations, we nd, as a result of time dependent diusion, a much weaker mode trapping eect, particularly for the high-period regime of the pulsation g-spectrum. This result is valid at least for models with massive hydrogen-rich envelopes. Thus, mode trapping would not be an eective mechanism to explain the fact that all the high periods expected from standard models of stratied white dwarfs are not observed in the ZZ Ceti stars.

Time dependent diffusion in pulsating white dwarf stars: asteroseismology of g117-b15a

The purpose of this paper is to present new full evolutionary calculations for DA white dwarf stars with the major aim of providing a physically sound reference frame for exploring the pulsation properties of the resulting models in future communications. Here, white dwarf evolution is followed in a self-consistent way with the predictions of time-dependent element diffusion and nuclear burning. In addition, full account is taken of the evolutionary stages prior to white dwarf formation. In particular, we follow the evolution of a 3-M⊙ model from the zero-age main sequence (the adopted metallicity is Z=0.02), all the way from the stages of hydrogen and helium burning in the core up to the thermally pulsing phase. After experiencing 11 thermal pulses, the model is forced to evolve towards its white dwarf configuration by invoking strong mass loss episodes. Further evolution is followed down to the domain of the ZZ Ceti stars on the white dwarf cooling branch. Emphasis is placed on the evolution of the chemical abundance distribution caused by diffusion processes and the role played by hydrogen burning during the white dwarf evolution. We find that discontinuities in the abundance distribution at the start of the cooling branch are considerably smoothed out by diffusion processes by the time the ZZ Ceti domain is reached. Nuclear burning during the white dwarf stage does not represent a major source of energy, as expected for a progenitor star of initially high metallicity. We also find that thermal diffusion lessens even further the importance of nuclear burning. Furthermore, the implications of our evolutionary models for the main quantities relevant for adiabatic pulsation analysis are discussed. Interestingly, the shape of the Ledoux term is markedly smoother compared with previous detailed studies of white dwarfs. This is translated into a different behaviour of the Brunt–Vaisala frequency.

The effects of element diffusion on the pulsational properties of variable DA white dwarf stars

The evolution of a 0.242 M☉ object that finally becomes a helium white dwarf is modeled from Roche lobe detachment down to very low luminosities (log L/L☉ = -5). In doing so, we employ our stellar code, to which we have added a set of routines that compute the effects due to gravitational settling and chemical and thermal diffusion. Initial models are constructed by abstracting mass from a 1 M☉ red giant branch model up to the moment at which the model begins to evolve blueward. From then on, two detailed sequences have been computed: one sequence with element diffusion and the other without that phenomenon. Results without diffusion are very similar to those of Driebe and collaborators. We find that element diffusion introduces important changes in the internal structure of the star. In particular, models with diffusion undergo three thermonuclear flashes, whereas models without diffusion experience only one. This fact has a large effect on the fraction of total hydrogen mass left in the star (about 3 times less hydrogen compared to models without diffusion) at the start of the final cooling track. As a result, at late stages of evolution models with diffusion are characterized by a much smaller nuclear energy release. Consequently, the star has to take energy from its relic thermal content, causing its further evolution to be significantly faster compared with the standard treatment. Notably, these new, more detailed structures strongly resemble those we have assumed in previous work on helium white dwarfs with hydrogen envelopes. Conventional wisdom indicates that a millisecond pulsar is recycled during the mass transfer stage in a binary system. Usually, the companion to the pulsar is a low-mass white dwarf. If zero ages are set at the end of mass transfer, the ages of both objects should be the same. Available models characterized by dominant hydrogen burning lead to a strong discrepancy between the ages of PSR B1855+09 and its white dwarf companion. We interpret such a discrepancy as a direct consequence of ignoring element diffusion in the stellar models. We show that in the frame of models in which diffusion is properly accounted for, ages naturally come into a nice agreement. Consequently, we do not have to invoke any ad hoc mass loss or exotic mechanisms to account for the ages of the stars that belong to the binary system PSR B1855+09.

Addendum: Calculation of the masses of the binary star HD 93205 by application of the theory of apsidal motion

ABSTRA C T We study the structural characteristic of the variable DA white dwarf G117-B15A by applying the methods of asteroseismology. For such a purpose, we construct white dwarf evolutionary models considering a detailed and up-to-date physical description as well as several processes responsible for the occurrence of element diffusion. We have considered several thicknesses for the outermost hydrogen layer, whereas for the inner helium-, carbon- and oxygen-rich layers we considered realistic profiles predicted by calculations of the white dwarf progenitor evolution. The stellar masses we have analysed cover the mass range of 0:50 # M * /M( # 0:60. The evolution of each of the considered model sequences was followed down to very low effective temperatures; in particular, from 12 500 K on we computed the dipolar, linear, adiabatic oscillations with radial order ka 1;...; 4. We find that asteroseismological results are not univocal regarding mode identification for the case of G117-B15A. However, our asteroseismological results are compatible with spectroscopic data only if the observed periods of 215.2, 271.0 and 304.4 s are due to dipolar modes with ka 2; 3; 4, respectively. Our calculations indicate that the best fit to the observed period pattern of G117-B15A corresponds to a DA white dwarf structure with a stellar mass of 0.525 M(, with a hydrogen mass fraction logOMH/M * U *2 3:83 at an effective temperature T eff < 11 800 K. The value of the stellar mass is consistent with that obtained spectroscopically by Koester & Allard.

On mode trapping in pulsating DA white dwarf stars

We explore the effects of element diffusion due to gravitational settling and thermal and chemical diffusion on the pulsational properties of DA white dwarfs. To this end, we employ an updated evolutionary code coupled with a pulsational, finite difference code for computing the linear, non-radial g-modes in the adiabatic approximation. We follow the evolution of a 0.55-M⊙ white dwarf model in a self-consistent way with the evolution of chemical abundance distribution as given by time-dependent diffusion processes. Results are compared with the standard treatment of diffusive equilibrium in the trace element approximation. Appreciable differences are found between the two employed treatments. We conclude that time-dependent element diffusion plays an important role in determining the whole oscillation pattern and the temporal derivative of the periods in DAV white dwarfs. In addition, we discuss the plausibility of the standard description employed in accounting for diffusion in most white dwarf asteroseismological studies.