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).     

The possible companions of young radio pulsars

We discuss the formation of pulsars with massive companions in eccentric orbits. We demonstrate that the probability for a non-recycled radio pulsar to have a white dwarf as a companion is comparable to that of having an old neutron star as a companion. Special emphasis is given to PSR B1820−11 and PSR B2303+46. Based on population synthesis calculations we argue that PSR B1820−11 and PSR B2303+46 could very well be accompanied by white dwarfs with mass ≳1.1 M_⊙. For PSR B1820−11, however, we cannot exclude the possibility that its companion is a main-sequence star with a mass between ∼0.7 M_⊙ and ∼5 M_⊙.     

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.     

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.     

PSR J1012+5307: younger than it looks?

Lorimer et al. have recently reported that the spin-down age (∼7 × 10⁹ yr) of the low-mass binary pulsar PSR J1012+5307 is much higher than the cooling age (3 × 10⁸ yr) of its white dwarf companion. The proposed solutions for this discrepancy are outlined and discussed. In particular, the revised cooling age estimate proposed by Alberts et al. agrees with data from other low-mass binary pulsar systems if a transition to the 'classical' cooling regime occurs between ∼0.14 and ∼0.28 M_⊙. If this transition is excluded, PSR J1012+5307 seems to have finished its accretion phase far from the spin-up line.     

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.     

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.     

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.     

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.     

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.     

Models for the formation of binary and millisecond radio pulsars

The peculiar combination of a relatively short pulse period and a relatively weak surface dipole magnetic field strength of binary radio pulsars finds a consistent explanation in terms of (i) decay of the surface dipole component of neutron-star magnetic fields on a timescale of (2–5) × 10⁶ yr, in combination with (ii) spin-up of the rotation of the neutron star during a subsequent mass-transfer phase. The four known binary radio pulsars appear to fall into two different categories. Two of them, PSR 0655 + 64 and PSR 1913 + 16, have short orbital periods (<25 h) and high mass functions, indicating companion masses 0.7M⊙ (∼1 (± 0.3) M⊙ and 1.4 M⊙, respectively). The other two, PSR 0820 + 02 and PSR 1953 + 29, have long orbital periods (117d), nearly circular orbits, and low, almost identical mass functions of about 3×10^-3 M⊙, suggesting companion masses of about 0.3M⊙. It is pointed out that these two classes of systems are expected to be formed by the later evolution of binaries consisting of a neutron star and a normal companion star, in which the companion was (considerably) more massive than the neutron star, or less massive than the neutron star, respectively. In the first case the companion of the neutron star in the final system will be a massive white dwarf, in a circular orbit, or a neutron star in an eccentric orbit. In the second case the final companion to the neutron star will be a low-mass (∼ 0.3 M⊙) helium white dwarf in a wide and nearly circular orbit. In systems of the second type the neutron star was most probably formed by the accretion-induced collapse of a white dwarf. This explains in a natural way why PSR 1953 + 29 has a millisecond rotation period and PSR 0820 + 02 has not. Among the binary models proposed for the formation of the 1.5-millisecond pulsar, the only ones that appear to be viable are those in which the companion disappeared by coalescence with the neutron star. In such models the companion may have been a red dwarf of mass 0.03M⊙, a neutron star, or a massive (>0.7M⊙) white dwarf. Only in the last-mentioned case is a position of the pulsar close to the galactic plane a natural consequence. In the first-mentioned case the progenitor system most probably was a cataclysmic-variable binary in which the white dwarf collapsed by accretion.     

PSR J1740−3052: a pulsar with a massive companion

We report on the discovery of a binary pulsar, PSR J1740−3052, during the Parkes multibeam survey. Timing observations of the 570-ms pulsar at Jodrell Bank and Parkes show that it is young, with a characteristic age of 350 kyr, and is in a 231-d, highly eccentric orbit with a companion whose mass exceeds 11 M_⊙. An accurate position for the pulsar was obtained using the Australia Telescope Compact Array. Near-infrared 2.2-μm observations made with the telescopes at the Siding Spring observatory reveal a late-type star coincident with the pulsar position. However, we do not believe that this star is the companion of the pulsar, because a typical star of this spectral type and required mass would extend beyond the orbit of the pulsar. Furthermore, the measured advance of periastron of the pulsar suggests a more compact companion, for example, a main-sequence star with radius only a few times that of the Sun. Such a companion is also more consistent with the small dispersion measure variations seen near periastron. Although we cannot conclusively rule out a black hole companion, we believe that the companion is probably an early B star, making the system similar to the binary PSR J0045−7319.     

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.     

The mass of the neutron star in the binary millisecond pulsar PSR J 1012 + 5307

We have measured the radial velocity variation of the white dwarf secondary in the binary system containing the millisecond pulsar PSR J 1012 + 5307. Combined with the orbital parameters of the radio pulsar, we infer a mass ratio q (≡ M ₁/ M ₂) = 10.5 ± 0.5. Our optical spectroscopy has also allowed us to determine the mass of the white dwarf companion by fitting the spectrum to a grid of DA model atmospheres: we estimate M ₂ = 0.16 ± 0.02 M⊙, and hence the mass of the neutron star is 1.64 ± 0.22 M⊙, where the error is dominated by that of M ₂. The orbital inclination is 52 ± 4°. For an initial neutron star mass of ∼ 1.4 M⊙, only a few tenths of a solar mass at most has been successfully accreted over the lifetime of the progenitor low-mass X-ray binary. If the initial mass of the secondary was ∼ 1 M⊙, our result suggests that the mass transfer may have been non-conservative.     

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.     

New Praesepe white dwarfs and the initial mass–final mass relation

We report the spectroscopic confirmation of four further white dwarf members of Praesepe. This brings the total number of confirmed white dwarf members to 11, making this the second largest collection of these objects in an open cluster identified to date. This number is consistent with the high-mass end of the initial mass function of Praesepe being Salpeter in form. Furthermore, it suggests that the bulk of Praesepe white dwarfs did not gain a substantial recoil kick velocity from possible asymmetries in their loss of mass during the asymptotic giant branch phase of evolution. By comparing our estimates of the effective temperatures and the surface gravities of WD0833+194, WD0840+190, WD0840+205 and WD0843+184 to modern theoretical evolutionary tracks, we have derived their masses to be in the range  0.72–0.76 M_⊙  and their cooling ages ∼300 Myr. For an assumed cluster age of 625 ± 50 Myr, the inferred progenitor masses are between 3.3 and  3.5 M_⊙  . Examining these new data in the context of the initial mass–final mass relation, we find that it can be adequately represented by a linear function  ( a ₀= 0.289 ± 0.051,  a ₁= 0.133 ± 0.015)  over the initial mass range 2.7–6  M_⊙  . Assuming an extrapolation of this relation to larger initial masses is valid and adopting a maximum white dwarf mass of  1.3 M_⊙  , our results support a minimum mass for core-collapse supernovae progenitors in the range  ∼6.8–8.6 M_⊙  .     

The Parkes Multibeam Pulsar Survey: PSR J1811−1736, a pulsar in a highly eccentric binary system

We are undertaking a high-frequency survey of the Galactic plane for radio pulsars, using the 13-element multibeam receiver on the 64-m Parkes radio telescope. We describe briefly the survey system and some of the initial results. PSR J1811−1736, one of the first pulsars discovered with this system, has a rotation period of 104 ms. Subsequent timing observations using the 76-m radio telescope at Jodrell Bank show that it is in an 18.8-d, highly eccentric binary orbit. We have measured the rate of advance of periastron which indicates a total system mass of 2.6±0.9 M_⊙, and the minimum companion mass is about 0.7 M_⊙. This, the high orbital eccentricity and the recycled nature of the pulsar suggest that this system is composed of two neutron stars, only the fourth or fifth such system known in the disc of the Galaxy.     

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.