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.     

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.     

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

The purpose of this work is to explore the evolution of helium-core white dwarf stars in a self-consistent way with the predictions of detailed non-grey model atmospheres and element diffusion. To this end, we consider helium-core white dwarf models with stellar masses of 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 M _V ≈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.     

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.     

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.     

Merged binary white dwarf evolution: rapidly accreting carbon–oxygen white dwarfs and the progeny of extreme helium stars

We have examined the evolution of merged low-mass double white dwarfs that become luminous helium stars. We have approximated the merging process by the rapid accretion of matter, consisting mostly of helium, on to a carbon–oxygen (CO) white dwarf. After a certain mass is accumulated, a helium shell flash occurs, the radius and luminosity increase and the star becomes a yellow giant. Mass accretion is stopped artificially when the total mass reaches a pre-determined value. When the mass above the helium-burning shell becomes small enough, the star evolves blueward almost horizontally in the Hertzsprung–Russell diagram. The theoretical models for the merger of a 0.6-M_⊙ CO white dwarf with a 0.3-M_⊙ He white dwarf agree very well with the observed locations of extreme helium stars in the  log  T _eff–log  g   diagram, with their observed rates of blueward evolution, and with luminosities and masses obtained from their pulsations. Together with predicted merger rates for  CO+He  white dwarf pairs, the evolutionary time-scales are roughly consistent with the observed numbers of extreme helium stars. Predicted surface carbon and oxygen abundances can be consistent with the observed values if carbon and oxygen produced in the helium shell during a previous asymptotic giant branch phase are assumed to exist in the helium zone of the initial CO white dwarfs. These results establish the  CO+He  white dwarf merger as the best, if not only, viable model for the creation of extreme helium stars and, by association, the majority of R Coronae Borealis stars.     

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.     

Optimal filters for the construction of the ensemble pulsar time

An algorithm of the ensemble pulsar time based on the optimal Wiener filtration method has been constructed. This algorithm allows the separation of the contributions to the post-fit pulsar timing residuals of the atomic clock and the pulsar itself. Filters were designed using the cross- and auto-covariance functions of the timing residuals. The method has been applied to the timing data of millisecond pulsars PSR B1855+09 and B1937+21 and allowed the filtering out of the atomic-scale component from the pulsar data. Direct comparison of the terrestrial time TT(BIPM06) and the ensemble pulsar time PT_ens revealed that the fractional instability of TT(BIPM06)−PT_ens is equal to  σ _z = (0.8 ± 1.9) × 10⁻¹⁵  . Based on the  σ _z   statistics of TT(BIPM06)−PT_ens, a new limit of the energy density of the gravitational wave background was calculated to be equal to  Ω_g h ²∼ 3 × 10⁻⁹  .