The impact of element diffusion on the formation and evolution of helium white dwarf stars

The aim of this work is to investigate the effect of element diffusion on the evolution of helium white dwarfs. To this end, we couple the multicomponent flow equations that describe gravitational settling, chemical and thermal diffusion to an evolutionary code. We compute the evolution of a set of helium white dwarf models with masses ranging from 0.169 to 0.406 M_⊙. In particular, several low-mass white dwarfs have been found in binary systems as companion to millisecond pulsars. In these systems, pulsar emission is activated by mass transfer episodes so that, if we place the zero-age point at the end of such mass transfer, then the pulsar and the white dwarf ages should be equal. Interestingly enough, available models of helium white dwarfs neglect element diffusion. Using such models, good agreement has been found between the ages of the components of the PSR J1012+5307 system. However, recent observations of the PSR B1855+09 system cast doubts on the correctness of such models, which predict a white dwarf age twice as long as the spin-down age of the pulsar. In this work, we find that element diffusion induces thermonuclear hydrogen shell flashes for models in the mass interval 0.18≲ M /M_⊙ ≲ 0.41 . We show, in particular, that the occurrence of these diffusion-induced flashes eventually leads to white dwarf models with hydrogen envelope masses too small to support any further nuclear burning, thus implying much shorter cooling ages than in the case when diffusion is neglected. In particular, excellent agreement is found between the ages of PSR B1855+09 system components, solving the age discrepancy from first principles.     

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.     

Cooling curves and initial models for low-mass white dwarfs (<0.25 M⊙) with helium cores

We present a detailed calculation of the evolution of low-mass (<0.25 M_⊙) 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 and 0.06 M_⊙. As a result of mixing between the core and outer envelope, the surface hydrogen content ( X _surf) is 0.5–0.35 , depending on the initial value of the heavy element Z and the initial secondary mass. We found that the majority of our computed models experience one or two hydrogen shell flashes. We found that the mass of the helium dwarf in which the hydrogen shell flash occurs depends on the chemical composition. The minimum helium white dwarf mass in which a hydrogen flash takes place is 0.213 M_⊙ ( Z =0.003), 0.198 M_⊙ ( Z =0.01), 0.192 M_⊙ ( Z =0.02) or 0.183 M_⊙ ( Z =0.03). The duration of the flashes (independent of chemical composition) is between a few ×10⁶ and a few ×10⁷ yr. In several flashes the white dwarf radius will increase so much that it forces the model to fill its Roche lobe again. Our calculations show that the cooling history of the helium white dwarf depends dramatically on the thickness of the hydrogen layer. We show that the transition from a cooling white dwarf with a temporarily stable hydrogen-burning shell to a cooling white dwarf in which almost all residual hydrogen is lost in a few thermal flashes (via Roche lobe overflow) occurs between 0.183 and 0.213 M_⊙ (depending on the heavy element value).     

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.     

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.     

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.     

Stellar forensics — I. Cooling curves

The presence of low-mass, degenerate secondaries in millisecond pulsar binaries offers the opportunity to determine an age for the binary system independently of the rotational properties of the pulsar. To this end, we present here a detailed calculation of the evolution of a grid of low-mass (< 0.05 M⊙) helium core white dwarfs. We investigate the effects of different hydrogen layer masses and provide results for well-known optical bandpasses. We supplement the OPAL opacity calculations with our own calculations for low effective temperatures ( T _eff < 6000 K) and also provide fitting formulae for the gravity as a function of mass and effective temperature. In Paper II we apply these results to individual cases.     

The evolution of a rapidly accreting helium white dwarf to become a low-luminosity helium star

We have examined the evolution of merged low-mass double white dwarfs which become low-luminosity (or high-gravity) extreme helium stars. We have approximated the merging process by the rapid accretion of matter, consisting mostly of helium, on to a helium 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. As the helium-burning shell moves inwards with repeating shell flashes, the effective temperature gradually increases as the star evolves towards the helium main sequence. When the mass interior to the helium‐burning shell is approximately 0.25 M_⊙, the star enters a regime where it is pulsationally unstable. We have obtained radial pulsation periods for these models.
These models have properties very similar to those of the pulsating helium star V652 Her. We have compared the rate of period change of the theoretical models with that observed in V652 Her, as well as with its position on the Hertzsprung–Russell diagram. We conclude that the merger between two helium white dwarfs can produce a star with properties remarkably similar to those observed in at least one extreme helium star, and is a viable model for their evolutionary origin. Such helium stars will evolve to become hot subdwarfs close to the helium main sequence. We also discuss the number of low-luminosity helium stars in the Galaxy expected for our evolution scenario.     

Hydrogen-model atmospheres for white dwarf stars

We present a detailed calculation of model atmospheres for DA white dwarfs. Our atmosphere code solves the atmosphere structure in local thermodynamic equilibrium with a standard partial linearization technique, which takes into account the energy transfer by radiation and convection. This code incorporates recent improved and extended data base of collision-induced absorption by molecular hydrogen. We analyse the thermodynamic structure and emergent flux of atmospheres in the range 2500 T _eff60 000 K and 6.5log  g 9.0. Bolometric correction and colour indices are provided for a subsample of the model grid. Comparison of the colours is made with published observational material and results of other recent model calculations.
Motivated by the increasing interest in helium-core white dwarfs, we analyse the photometric characteristics of these stars during their cooling, using evolutionary models recently available. Effective temperatures, surface gravities, masses and ages have been determined for some helium-core white dwarf candidates, and their possible binary nature is briefly discussed.     

The case and fate of HD 75767 – neutron star or supernova?

We report the discovery of the nearby  ( d = 24 pc)  HD 75767 as an eight billion year old quadruple system consisting of a distant M dwarf pair, HD 75767 C–D, in orbit around the known short-period   P = 10.25 d  single-lined binary HD 75767 A–B, the primary of which is a solar-like G star. On the reasonable assumption of synchronous orbital rotation as well as rotational and orbital coplanarity for the inner pair, we get   M _B= 0.96 M_⊙  for the unseen HD 75767 B, that is, the case of a massive white dwarf. Upon future evolution, mass transfer towards HD 75767 B will render the   M _A= 0.96 M_⊙  G-type primary, now a turnoff star, to become a helium white dwarf of   M _A∼ 0.33 M_⊙  . Depending on the mass accretion rate, accretion efficiency and composition of the massive white dwarf, this in turn may result in a collapse of HD 75767 B with the formation of a millisecond pulsar, i.e. the creation of a low-mass binary pulsar (LMBP), or, instead, a Type Ia supernova explosion and the complete disruption of HD 75767 B. Irrespective of which scenario applies, we point to the importance of the distant M dwarfs as the likely agents for the formation of the inner, short-period HD 75767 A–B pair, and hence a path that particularly avoids preceding phases of common envelope evolution.     

A possible detection mechanism for pre-low-mass X-ray binaries

This work presents a possible detection mechanism for close, detached, neutron star–red dwarf binaries, which are expected to be the evolutionary precursors of low-mass X-ray binaries (LMXBs). Although this pre-low-mass X-ray binary (pre-LMXB) phase of evolution is predicted theoretically, as yet no such systems have been identified observationally. The calculations presented here suggest that the X-ray luminosity of neutron star wind accretion in a pre-LMXB system can be expected to exceed the intrinsic X-ray luminosity of the red dwarf secondary star. Furthermore, the temperature of the radiation emitted from the neutron star wind accretion process is expected, within the confines of a reasonable set of conditions, to lie within the detection range of X-ray satellites. Sources with X-ray luminosities greater than that expected for a red dwarf star, but the positions of which coincide with that of a red dwarf star, are then candidate pre-LMXB systems. These candidate systems should be surveyed for the radial velocity shifts that would occur as a result of the orbital motion of a red dwarf star within a close binary system containing a high-mass compact object.     

Relation of Velocity Distribution and Mass for DA White Dwarfstwo

White dwarfs are the evolutionary endpoint of the low-and-medium mass stars. In the studies of white dwarfs, the mass of white dwarf is an important physical parameter. In this paper, we give an analysis about the velocity distribution of DA white dwarfs in the Sloan Digital Sky Survey (SDSS), and hope to find the relation between mass and velocity distribution of white dwarfs. We get the radial velocity and tangential velocity of every DA white dwarf according to their proper motion and spectral shift. Through analyzing the velocity distribution of DA white dwarfs, we find that the small-mass white dwarfs, which are produced from the single-star evolution channel, have a relatively large velocity dispersion.     

The DODO survey – II. A Gemini direct imaging search for substellar and planetary mass companions around nearby equatorial and Northern hemisphere white dwarfs

The aim of the Degenerate Objects around Degenerate Objects (DODO) survey is to search for very low-mass brown dwarfs and extrasolar planets in wide orbits around white dwarfs via direct imaging. The direct detection of such companions would allow the spectroscopic investigation of objects with temperatures much lower  (<500 K)  than the coolest brown dwarfs currently observed. These ultra-low-mass substellar objects would have spectral types >T8.5, and so could belong to the proposed Y dwarf spectral sequence. The detection of a planet around a white dwarf would prove that such objects can survive the final stages of stellar evolution and place constraints on the frequency of planetary systems around their progenitors (with masses between 1.5 and 8   M_⊙  , i.e. early B to mid-F). This paper presents the results of a multi epoch J band common proper motion survey of 23 nearby equatorial and Northern hemisphere white dwarfs. We rule out the presence of any common proper motion companions, with limiting masses determined from the completeness limit of each observation, to 18 white dwarfs. For the remaining five targets, the motion of the white dwarf is not sufficiently separated from the non-moving background objects in each field. These targets require additional observations to conclusively rule out the presence of any common proper motion companions. From our completeness limits, we tentatively suggest that  ≲5 per cent  of white dwarfs have substellar companions with   T _eff≳ 500 K  between projected physical separations of 60–200 au.     

Population Synthesis of Binary Be Stars with Degenerate Companions in the Galaxy

Using the numerical code (`Scenario Machine') we study of number and physical properties of binary Be stars. Evolutionary tracks leading to a formation of the observational binary systems are presented. We conclude that synchronization must be taken into account when calculating binary Be star evolution and calculate the minimal orbital period for Be/evolved companion binary. The obtained distributions over orbital parameters are in good agreement with the observational lack of short-period Be/X-ray binaries. According to our calculations 70% of all Be stars must have a white dwarf. The white dwarfs in these systems should be hot enough with the surface temperature distribution peaking at 10000–20000 K. Their detection is possible during the period of the lack of Be star envelope by the detection of white dwarf extremely UV and soft X-ray emission. This method of registration appears to be particularly promising for `single' early-type Be stars because in these systems the white dwarfs must have a very high surface temperature. However, the loss of the Be disc-like envelope does not often occur and it is a rather rare event for many Be stars. The best possibility of white dwarf detection is given by the study of helium spectral lines found in emission from several Be stars. The ultraviolet continuum energy of these Be stars is found to be not enough to produce the observed helium emission. Besides, we also discuss the orbital properties of binary Be star systems with other evolved companions such as helium stars and neutron stars and give a possible explanation for the lack of Be/black hole binaries. This revised version was published online in July 2006 with corrections to the Cover Date.     

Accretion and dynamical interactions in small-N star-forming clusters: N= 5

We present results from high-resolution hydrodynamical simulations that explore the effects of small-scale clustering in star-forming regions. A large ensemble of small- N clusters with five stellar seeds have been modelled and the resulting properties of stars and brown dwarfs statistically derived and compared with observational data.
Close dynamical interactions between the protostars and competitive accretion driven by the cloud collapse are shown to produce a distribution of final masses that is bimodal, with most of the mass residing in the binary components. When convolved with a suitable core mass function, the final distribution of masses resembles the observed initial mass function, in both the stellar and substellar regimes. Binaries and single stars are found to constitute two kinematically distinct populations, with about half of the singles attaining velocities ≥2 km s⁻¹, which might deprive low-mass star-forming regions of their lightest members in a few crossing times. The eccentricity distribution of binaries and multiples is found to follow a distribution similar to that of observed long-period (uncircularized) binaries.
The results obtained support a mechanism in which a significant fraction of brown dwarfs form under similar circumstances as those of normal stars but are ejected from the common envelope of unstable multiple systems before their masses exceed the hydrogen burning limit. We predict that many close binary stars should have wide brown dwarf companions. Brown dwarfs, and, in general, very low-mass stars, would be rare as pure binary companions. The binary fraction should be a decreasing function of primary mass, with low-mass or substellar primaries being scarce. Where such binaries exist, they are expected either to be close enough (semimajor axis ∼10 au) to survive strong interactions with more massive binaries or to be born in very small molecular cloud cores.     

The triple degenerate star WD 1704+481

WD 1704+481 is a visual binary in which both components are white dwarfs. We present spectra of the H α line of both stars which show that one component (WD 1704+481.2=Sanduleak B=GR 577) is a close binary with two white dwarf components. Thus, WD 1704+481 is the first known triple degenerate star. From radial velocity measurements of the close binary we find an orbital period of 0.1448 d, a mass ratio, q M _bright M _faint, of 0.70±0.03 and a difference in the gravitational redshifts of 11.5±2.3 km s⁻¹. The masses of the close pair of white dwarfs predicted by the mass ratio and gravitational redshift difference combined with theoretical cooling curves are 0.39±0.05 and 0.56±0.07 M_⊙. WD 1704+481 is therefore also likely to be the first example of a double degenerate in which the less massive white dwarf is composed of helium and the other white dwarf is composed of carbon and oxygen.     

A search for hidden white dwarfs in the ROSAT EUV survey — II. Discovery of a distant DA+F6/7V binary system in a direction of low-density neutral hydrogen

The ROSAT Wide Field Camera (WFC) survey of the extreme ultraviolet (EUV) has provided us with evidence for the existence of a previously unidentified sample of hot white dwarfs in unresolved, detached binary systems. These stars are invisible at optical wavelengths due to the close proximity of their much more luminous companions (spectral type K or earlier). However, for companions of spectral type ∼A5 or later the white dwarfs are easily visible at far-ultraviolet wavelengths, and can be identified in spectra taken by IUE . 16 such systems have been discovered in this way through ROSAT EUVE IUE observations, including four identified by us in Paper I. In the present paper we report the results of our continuing search during the final year of IUE operations. One new system, RE J0500−364 (DA+F6/7V), has been identified. This star appears to lie at a distance of ∼500−1000 pc, making it one of the most distant white dwarfs, if not the most distant, to be detected in the EUV surveys. The very low line-of-sight neutral hydrogen volume density to this object could place a lower limit on the length of the β CMa interstellar tunnel of diffuse gas, which stretches away from the Local Bubble in a similar direction to RE J0500−364. In this paper we also analyse a number of the stars observed where no white dwarf companion was found. Some of these objects show evidence for chromospheric and coronal activity. Finally, we present an analysis of the previously known WD+active F6V binary HD 27483 (Bo¨hm-Vitense 1993), and show that, at T  ≈ 22 000 K, the white dwarf may be contributing significantly to the observed EUV flux. If so, it is one of the coolest such stars to be detected in the EUV surveys.     

A search for radio pulsars around low-mass white dwarfs

Low-mass white dwarfs can be produced either in low-mass X-ray binaries by stable mass transfer to a neutron star, or in a common envelope phase with a heavier white dwarf companion. We have searched eight low-mass white dwarf candidates recently identified in the Sloan Digital Sky Survey for radio pulsations from pulsar companions, using the Green Bank Telescope at 340 MHz. We have found no pulsations down to flux densities of 0.6–0.8 mJy kpc⁻² and conclude that a given low-mass helium-core white dwarf has a probability of  <0.18 ± 0.05  of being in a binary with a radio pulsar.