γCas stars are a ∼1% minority among classical Be stars with hard (≥5−10 keV), but only moderately strong continuous thermal X-ray flux, and mostly very early-B spectral type. The X-ray flux has been suggested to originate from matter accelerated via magnetic disc-star interaction, by a rapidly rotating neutron star (NS) companion via the propeller effect, or by accretion onto a white dwarf (WD) companion. In view of the growing number of identifiedγCas stars and the only imperfect matches between these suggestions and the observations, alternative models should be pursued. Two of the three best-observedγCas stars,γCasitself andπAqr, have a low-mass companion with low optical flux, whereas interferometry ofBZ Cruis inconclusive. Binary-evolution models are examined for their ability to produce such systems. The OB+He-star stage of post-mass transfer binaries, which is otherwise observationally unaccounted, can potentially reproduce many observed properties ofγCas stars. The interaction of the fast wind of helium stars with the circumstellar disc and/or with the wind of Be stars may give rise to the production of hard X-rays. While not modelling this process, it is shown that the energy budget is favourable, and that the wind velocities may lead to hard X-rays, as observed inγCas stars. Furthermore, the observed number of these objects appears to be consistent with the evolutionary models. Within the Be+He-star binary model, the Be stars inγ-Cas stars are conventional classical Be stars. They are encompassed by O-star+Wolf-Rayet systems towards higher mass, where no stable Be decretion discs exist, and by Be+sdO systems at lower mass, where the sdO winds may be too weak to cause theγCas phenomenon. In decreasing order of the helium-star mass, the descendants could be Be+black-hole, Be+NS, or Be+WD binaries. The interaction between the helium-star wind and the disc may provide new diagnostics of the outer disc.
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