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EVOLUTION MODELS

Several scenarios have been proposed to account for the depletion of surface hydrogen in extreme helium stars. Those which may be successful in producing extremely hydrogen-poor surfaces are the following:

Case BB mass transfer in a binary. Following main-sequence evolution, a red giant star in a close binary system may expand to fill its Roche lobe. Transferring mass to the less massive companion (Case B) will reduce but not remove the H-rich envelope. If core-helium burning is completed before the secondary completes its main-sequence evolution and the primary expands to the giant region for a second time, then a further phase of mass transfer (case BB) can completely remove the H-rich envelope, exposing CNO-processed helium (Plavec 1973, Schönberner & Drilling 1983). Although Iben & Tutukov (1984) used this model to account for the EHes, the latter are not binaries (Jeffery et al. 1987). Case BB mass transfer does account successfully for the observations of hydrogen-deficient binaries such as $\upsilon$ Sgr and KSPer.

Final helium-shell flash in a post-AGB star. The model proposed by Iben et al. (1983) derives from evolutionary calculations of post-AGB stars. At some point during contraction from the AGB to the white dwarf (WD) track, some models were found to experience a late thermal pulse - or helium-shell flash. The energy output of this last shell flash causes large-scale mixing and a brief expansion of the envelope to giant dimensions. Strong evidence that such late shell flashes do occur comes from three objects, V652 Aql, FG Sge and V4334 Sge, all of which have been observed to evolve from faint blue star to a red supergiant on timescales of 3 - 50 years. In the case of V652 Aql, contraction after the shell flash to the WD track was also rapid. Recently, more detailed evolutionary calculations have been carried out for WDs which experience a late shell flash (Herwig et al 1999). The post-expansion tracks have been compared favourably with observations of other H-deficient objects including some central stars of PN ([WC] stars) and very hot pre-WDs (PG1159 stars). All of these objects have a surface carbon abundance of $\sim10\%$ or greater. If the final shell-flash model successfully explains such stars, the question is whether it can also explain EHes, with $\sim1\%$ carbon abundances and apparently slower evolutionary timescales.

Merger of CO and He white dwarf. While most proposed models for EHes invoke post-AGB evolution, the model introduced by Webbink (1984) is completely different. A binary system with appropriate initial masses and orbital separation can evolve to the point where both stars are WDs, one being a carbon-oxygen WD of $\sim0.6$     $\rm M_{\odot}$, the other a helium WD of 0.3-0.4 $\rm M_{\odot}$, with an orbital period in the range 1-10 hours. Over a long interval, the orbital angular momentum can be reduced by a combination of gravitational-wave radiation and magnetic-wind braking to the point at which the less massive WD fills its Roche lobe. Tidal disruption will follow on a dynamical timescale, the WD being transformed into a thick disk around the more massive companion. Accretion from the disk onto the surviving WD creates a star with a degenerate CO core and a helium envelope. Depending on the accretion rate, helium may be ignited either explosively (slow accretion) or quiescently (fast accretion), resulting in either a type Ib supernova or a helium giant (Iben & Tutukov 1985). Numerical models for the mergers of two CO WDs and two He WDs have been computed (Saio & Nomoto 1998, Saio & Jeffery 2000), but the CO+He case has yet to be treated successfully.
Other models. Schönberner (1986) discusses a variety of unsuccessful models which have been proposed at one time or another. Only the final-flash and WD-merger models currently seem capable of reproducing most of the observed properties of EHes.