γ Cas stars: Normal Be stars with discs impacted by the wind of a helium-star companion?

γ Cas 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 identified γ Cas stars and the only imperfect matches between these suggestions and the observations, alternative models should be pursued. Two of the three best-observed γ Cas stars, γ Cas itself and π Aqr , have a low-mass companion with low optical flux, whereas interferometry of BZ Cru is 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 of γ Cas 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 in γ Cas 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 in γ -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 the γ Cas 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.