Post-merger evolution of carbon-oxygen + helium white dwarf binaries and the origin of R Coronae Borealis and extreme helium stars

Orbital decay by gravitational-wave radiation will cause some close-binary white dwarfs (WDs) to merge within a Hubble time. The results from previous hydrodynamical WD-merger simulations have been used to guide calculations of the post-merger evolution of carbon-oxygen + helium (CO+He) WD binaries. Our models include the formation of a hot corona in addition to a Keplerian disc. We introduce a `destroyed-disc' model to simulate the effect of direct disc ingestion into the expanding envelope. These calculations indicate significant lifetimes in the domain of the rare R Coronae Borealis (RCB) stars, before a fast evolution through the domain of the hotter extreme helium (EHe) stars. Surface chemistries of the resulting giants are in partial agreement with the observed abundances of RCB and EHe stars. The production of <sup>3</sup>He, <sup>18</sup>O and <sup>19</sup>F are discussed. Evolutionary time-scales combined with binary WD merger rates from binary-star population synthesis are consistent with present-day numbers of RCBs and EHes, provided that the majority come from relatively recent (<2 Gyr) star formation. However, most RCBs should be produced by CO-WD + low-mass He-WD mergers, with the He WD having a mass in the range 0.20-0.35 M<sub>⊙</sub>. Whilst, previously, a high He-WD mass (≥0.40 M<sub>⊙</sub>) was required to match the carbon-rich abundances of RCB stars, the `destroyed-disc' model yields a high-carbon product with He-WD mass ≥0.30 M_⊙, in better agreement with population synthesis results.