Normal modes and discovery of high-order cross-frequencies in the DBV white dwarf GD 358

We present a detailed mode identification performed on the 1994 Whole Earth Telescope (WET) run on GD 358. The results are compared with that obtained for the same star from the 1990 WET data. The two temporal spectra show very few qualitative differences, although amplitude changes are seen in most modes, including the disappearance of the mode identified as k =14 in the 1990 data. The excellent coverage and signal-to-noise ratio obtained during the 1994 run lead to the secure identification of combination frequencies up to fourth order, i.e. peaks that are sums or differences of up to four parent frequencies, including a virtually complete set of second-order frequencies, as expected from harmonic distortion. We show how the third-order frequencies are expected to affect the triplet structure of the normal modes by back-interacting with them. Finally, a search for ℓ=2 modes was unsuccessful, not verifying the suspicion that such modes had been uncovered in the 1990 data set.     

The evolution of iron-core white dwarfs

Recent measurements by Hipparcos present observational evidence supporting the existence of some white dwarf (WD) stars with iron-rich core composition. In connection with this, the present paper is aimed at exploring the structure and evolution of iron-core WDs by means of a detailed and updated evolutionary code. In particular, we examined the evolution of the central conditions, neutrino luminosity, surface gravity, crystallization, internal luminosity profile and ages. We find that the evolution of iron-rich WDs is markedly different from that of their carbon–oxygen counterparts. In particular, cooling is strongly accelerated (up to a factor of 5 for models with pure iron composition) as compared with the standard case. Thus, if iron WDs were very numerous, some of them would have had time enough to evolve at lower luminosities than that corresponding to the fall-off in the observed WD luminosity function.     

Full evolution of low-mass white dwarfs with helium and oxygen cores

We study the full evolution of low-mass white dwarfs with helium and oxygen cores. We revisit the age dichotomy observed in many white dwarf companions to millisecond pulsar on the basis of white dwarf configurations derived from binary evolution computations. We evolve 11 dwarf sequences for helium cores with final masses of 0.1604, 0.1869, 0.2026, 0.2495, 0.3056, 0.3333, 0.3515, 0.3844, 0.3986, 0.4160 and  0.4481 M_⊙  . In addition, we compute the evolution of five sequences for oxygen cores with final masses of 0.3515, 0.3844, 0.3986, 0.4160 and  0.4481 M_⊙  . A metallicity of   Z = 0.02  is assumed. Gravitational settling, chemical and thermal diffusion are accounted for during the white dwarf regime. Our study reinforces the result that diffusion processes are a key ingredient in explaining the observed age and envelope dichotomy in low-mass helium-core white dwarfs, a conclusion we arrived at earlier on the basis of a simplified treatment for the binary evolution of progenitor stars. We determine the mass threshold where the age dichotomy occurs. For the oxygen white dwarf sequences, we report the occurrence of diffusion-induced, hydrogen-shell flashes, which, as in the case of their helium counterparts, strongly influence the late stages of white dwarf cooling. Finally, we present our results as a set of white dwarf mass–radius relations for helium and oxygen cores.     

Evolutionary calculations of carbon dredge-up in helium envelope white dwarfs

We investigate the evolution of cooling helium atmosphere white dwarfs using a full evolutionary code, specifically developed to follow the effects of element diffusion and gravitational settling on white dwarf cooling. The major difference between this work and previous work is that we use more recent opacity data from the OPAL project. Since, in general, these opacities are higher than those available 10 years ago, at a given effective temperature, convection zones go deeper than in models with older opacity data. Thus convective dredge-up of observationally detectable carbon in helium atmosphere white dwarfs can occur for thicker helium layers than found by Pelletier et al. We find that the range of observed C to He ratios in different DQ white dwarfs of similar effective temperature is well explained by a range of initial helium layer mass between 10⁻³ and 10⁻² M⊙, in good agreement with stellar evolution theory, assuming a typical white dwarf mass of 0.6 M⊙. We also predict that oxygen will be present in DQ white dwarf atmospheres in detectable amounts if the helium layer mass is near the lower limit compatible with stellar evolution theory. Determination of the oxygen abundance has the potential of providing information on the profile of oxygen in the core and hence on the important ¹²C(α,γ)¹⁶O reaction rate.     

Photospheric phosphorus in the FUSE spectra of GD71 and two similar DA white dwarfs

We report the detection, from the Far Ultraviolet Spectroscopic Explorer (FUSE) data, of phosphorus in the atmospheres of GD71 and two similar DA white dwarfs. This is the first detection of a trace metal in the photosphere of the spectrophotometric standard star GD71. Collectively, these objects represent the coolest DA white dwarfs in which photospheric phosphorus has been observed. We use a grid of homogeneous non-local thermodynamic equilibrium synthetic spectra to measure abundances of  [P/H]=−8.57^+0.09_−0.13, −8.70^+0.23_−0.37  and  −8.36^+0.14_−0.19  in GD71, RE J1918+595 and RE J0605−482 respectively. At the observed level we find that phosphorus has no significant impact on the overall energy distribution of GD71. We explore possible mechanisms responsible for the presence of this element in these stars, concluding that the most likely is an interplay between radiative levitation and gravitational settling, possibly modified by weak mass loss.     

Lessons for asteroseismology from white dwarf stars

The interpretation of pulsation data for sun-like stars is currently facing challenges quite similar to those faced by white dwarf modelers ten years ago. The observational requirements for uninterrupted long-term monitoring are beginning to be satisfied by successful multi-site campaigns and dedicated satellite missions. But exploration of the most important physical parameters in theoretical models has been fairly limited, making it difficult to establish a detailed best-fit model for a particular set of oscillation frequencies. I review the past development and the current state of white dwarf asteroseismology, with an emphasis on what this can tell us about the road to success for asteroseismology of other types of stars.     

Diffusion in helium white dwarf stars

This paper is aimed at exploring the effects of diffusion on the structure and evolution of low-mass helium white dwarfs. To this end, we solve the multicomponent flow equations describing gravitational settling and chemical and thermal diffusion. The diffusion calculations are coupled to an evolutionary code in order to follow the cooling of low-mass, helium core white dwarf models having envelopes made up of a mixture of hydrogen and helium, as recently suggested by detailed evolutionary calculations for white dwarf progenitors in binary systems. We find that diffusion causes hydrogen to float and the other elements to sink over time-scales shorter than evolutionary time-scales. This produces a noticeable change in the structure of the outer layers, making the star inflate. Thus, in order to compute accurately the mass–radius relation for low-mass helium white dwarfs we need to account for the diffusion processes during (at least) the white dwarf stages of the evolution of these objects. This should be particularly important when studying the general characteristics of binary systems containing a helium white dwarf and a pulsar.
In addition, we present an analytic, approximate model for the outer layers of the white dwarf aimed at interpreting the physical reasons for the change in the surface gravity for low-mass white dwarfs induced by diffusion.     

Combination frequencies in the Fourier spectra of white dwarfs

Combination frequencies are observed in the Fourier spectra of pulsating DA and DB white dwarfs, along with frequencies that are associated with stellar gravity modes. They appear at the sum and difference frequencies of the stellar modes. Brickhill proposed that the combination frequencies result from mixing of the eigenmode signals by a depth-varying surface convection zone when undergoing pulsation. The depth changes cause time-dependent thermal impedance.
Following Brickhill's proposal, we developed analytical expressions for the amplitudes and phases of these combination frequencies. The parameters that appear in these expressions are the depth of the stellar convection zone when at rest, the sensitivity of this depth towards changes in the stellar effective temperature, the inclination angle of the stellar pulsation axis with respect to the line of sight, and lastly the spherical degrees of the eigenmodes involved in the mixing. Adopting credible values for these parameters, we apply our expressions to DA and DB variable white dwarfs. We find reasonable agreement between theory and observation, although some discrepancies remain unexplained. It is possible to identify the spherical degrees of the pulsation modes using the combination frequencies.     

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

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–Väisälä frequency.     

Gravitational signals due to tidal interactions between white dwarfs and black holes

In this paper, we compute the gravitational signal emitted when a white dwarf moves around a black hole on a closed or open orbit using the affine-model approach. We compare the orbital and the tidal contributions to the signal, assuming that the star moves in a safe region where, although very close to the black hole, the strength of the tidal interaction is insufficient to provoke the stellar disruption. We show that for all considered orbits the tidal signal presents sharp peaks corresponding to the excitation of the non-radial oscillation modes of the star, the amplitude of which depends on how deep the star penetrates the black hole tidal radius and on the type of orbit. Further structure is added to the emitted signal by the coupling between the orbital and the tidal motions.     

The origin of the magnetic fields in white dwarfs

Magnetic white dwarfs with fields in excess of ∼10⁶ G (the high field magnetic white dwarfs; HFMWDs) constitute about ∼10 per cent of all white dwarfs and show a mass distribution with a mean mass of  ∼0.93 M_⊙  compared to  ∼0.56 M_⊙  for all white dwarfs. We investigate two possible explanations for these observations. First, that the initial–final mass relationship (IFMR) is influenced by the presence of a magnetic field and that the observed HFMWDs originate from stars on the main sequence that are recognized as magnetic (the chemically peculiar A and B stars). Secondly, that the IFMR is essentially unaffected by the presence of a magnetic field, and that the observed HFMWDs have progenitors that are not restricted to these groups of stars. Our calculations argue against the former hypothesis and support the latter. The HFMWDs have a higher than average mass because on the average they have more massive progenitors and not because the IFMR is significantly affected by the magnetic field. A requirement of our model is that ∼40 per cent of main-sequence stars more massive than  ∼4.5 M_⊙  must either have magnetic fields in the range of ∼10–100 G, which is below the current level of detection, or generate fields during subsequent stellar evolution towards the white dwarf phase. In the former case, the magnetic fields of the HFMWDs could be fossil remnants from the main-sequence phase consistent with the approximate magnetic flux conservation.     

A source of high-velocity white dwarfs

We investigate whether the recently observed population of high-velocity white dwarfs can be derived from a population of binaries residing initially within the thin disc of the Galaxy. In particular, we consider binaries where the primary is sufficiently massive to explode as a Type II supernova. A large fraction of such binaries are broken up when the primary then explodes as a supernova, owing to the combined effects of the mass loss from the primary and the kick received by the neutron star on its formation. For binaries where the primary evolves to fill its Roche lobe, mass transfer from the primary leads to the onset of a common envelope phase during which the secondary and the core of the primary spiral together as the envelope is ejected. Such binaries are the progenitors of X-ray binaries if they are not broken up when the primary explodes. For those systems that are broken up, a large number of the secondaries receive kick velocities ∼100–200 km s⁻¹ and subsequently evolve into white dwarfs. We compute trajectories within the Galactic potential for this population of stars and relate the birth rate of these stars over the entire Galaxy to those seen locally with high velocities relative to the local standard of rest (LSR) . We show that for a reasonable set of assumptions concerning the Galactic supernova rate and the binary population, our model produces a local number density of high-velocity white dwarfs compatible with that inferred from observations. We therefore propose that a population of white dwarfs originating in the thin disc may make a significant contribution to the observed population of high-velocity white dwarfs.     

IRTF observations of white dwarfs with possible near-infrared excess

Near-infrared photometry and spectroscopy are obtained for a heterogeneous sample of nearby white dwarfs with possible excess flux as identified primarily in the Two Micron All Sky Survey. Among the sample of 43 stars are a number of white dwarfs that are either metal-rich, magnetic or binary suspects. With a few notable exceptions in four (or possibly five) distinct categories, the newly obtained JHK photometric data fail to corroborate the putative excesses, with  〈 K _IRTF− K _2MASS〉=+0.31  mag. Where available, Galaxy Evolution Explorer photometric data are used to better constrain the overall spectral energy distribution of the white dwarfs, enabling any excess near-infrared flux to stand out more readily against the expected stellar photosphere.
With superior data, a near-infrared photometric excess is confirmed at three metal-rich white dwarfs and ruled out at nine others. Several new binaries are confirmed or suggested; five white dwarf–red dwarf pairs and five double degenerates. Four apparently single magnetic white dwarfs – two DA and two DQp – display modest to strong near-infrared excess (relative to non-magnetic models), which may be better described as two effective temperatures owing to a redistribution of energy in highly magnetic or peculiar atmospheres.