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Gamma~Cas stars are early-type Be stars that exhibit an unusually hard andbright thermal X-ray emission. One of the proposed scenarios to explain theseproperties postulates the existence of a neutron star companion in thepropeller stage, during which the magnetosphere of a rapidly rotating neutronstar repels infalling material. To test this model, we examined the fluorescentFe K$\alpha$ emission line at $\sim 6.4$\,keV in the X-ray spectra of$\gamma$~Cas stars, which offers a powerful diagnostic of both the primarysource of hard X-rays and the reprocessing material. We computed synthetic lineprofiles of the fluorescent Fe K$\alpha$ emission line in the framework of thepropelling neutron star scenario. Two reservoirs of material contribute to thefluorescence in this case: the Be circumstellar decretion disk and a shell ofcool material that surrounds the shell of X-ray-emitting plasma around theputative propelling neutron star. We analysed the synthetic line profiles andexpected equivalent widths of the lines for three well-studied $\gamma$~Casstars. The predicted line strengths fall short of the observed values by atleast an order of magnitude. Pushing the model parameters to reproduce theobserved line strengths led to column densities towards the primary X-raysource that exceed the observationally determined values by typically a factorof 20, and would further imply a higher X-ray luminosity than observed. Thestrengths of the observed Fe K$\alpha$ fluorescent emission lines in$\gamma$~Cas stars are inconsistent with the expected properties of a propellerscenario as proposed in the literature.

Fluorescent Fe K line emission of gamma Cas stars I. Do gamma Cas stars host propelling neutron stars?