Recent surveys have demonstrated the existence of several short-period binary systems containing two white dwarfs. Following orbital decay by gravitational-wave radiation, such binaries are expected to merge at a rate of two or three per thousand years per galaxy. The consequences of such a merger depend on the individual white dwarf masses, but are believed to include helium-rich subdwarfs, R CrB stars, extreme helium stars and also AM CVn systems and possibly Type Ia supernovae.Whilst the hydrodynamics of the merger process remains difficult to compute, it is possible to compute the evolution of a double white dwarf merger following the destruction of one component. In this paper, we describe the evolution following the merger of two helium white dwarfs. We examine three sets of assumptions concerning the distribution of debris material between a disc and a corona.Our results demonstrate that a model comprising both fast accretion to form a (hot) corona and slow accretion from a (cold) debris disc can reproduce the observed distribution of helium-rich subdwarfs in terms of their surface temperatures, gravities, nitrogen and carbon abundances.

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.

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 Teff–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.

Context. The gravitational wave (GW) background in the range 0.01−30 mHz has been assumed to be dominated by unresolved radiation from double white dwarf binaries (DWDs). Recent investigations indicate that, at short periods, a number of DWDs should be resolvable sources of GW. Aims. We characterize the GW signal which would be detected by LISA from DWDs in the Galaxy. Methods. We have constructed a Galactic model in which we consider distinct contributions from the bulge, thin disc, thick disc, and halo, and subsequently executed a population synthesis approach to determine the birth rates, numbers, and period distributions of DWDs within each component. Results. In the Galaxy as a whole, our model predicts the current birth rate of DWDs to be 3.21 × 10 −2 yr −1 , the local density to be 2.2 × 10 −4 pc −3 and the total number to be 2.76 × 10 8 . Assuming SNIa are formed from the merger of two CO white dwarfs, the SNIa rate should be 0.0013 yr −1 . The frequency spectra of DWD strain amplitude and number distribution are presented as a function of galactic component, DWD type, formation channel, and metallicity. Conclusions. We confirm that CO+He and He+He white dwarf (WD) pairs should dominate the GW signal at very high frequencies (log f Hz −1 > −2.3), while CO+CO and ONeMg WD pairs have a dominant contribution at log f Hz −1 ≤ −2.3. Formation channels involving two common-envelope (CE) phases or a stable Roche lobe overflow phase followed by a CE phase dominate the production of DWDs detectable by LISA at log f Hz −1 > −4.5. DWDs with the shortest orbital periods will come from the CE+CE channel. The Exposed Core plus CE channel is a minor channel. A number of resolved DWDs would be detected, making up 0.012% of the total number of DWDs in the Galaxy. The majority of these would be CO+He and He+He pairs formed through the CE+CE channel.