The origin of the hard, bright X-ray emission that defines the $\gamma $ Cas analog class of Be stars remains an outstanding question in Be star literature. This work explores the possibility that the X-ray flux is produced by accretion onto a white dwarf companion. We use three-dimensional smoothed particle hydrodynamics simulations to model the prototype $\gamma $ Cas system assuming a white dwarf companion and investigate the accretion of the circumstellar material by the secondary star. We contrast these results to a model for 59 Cyg, a non- $\gamma $ Cas Be star system with a stripped companion. We find that the secondary stars in both systems form disk-like accretion structures with Keplerian characteristics, similar to those seen in the Be decretion disks. We also find that white dwarf accretion can produce X-ray fluxes that are consistent with the observed values for $\gamma $ Cas, while the predicted X-ray luminosities are significantly lower for the non-degenerate companion in 59 Cyg. In addition, using the three-dimensional radiative transfer code, hdust, we find that these models produce H $\alpha $ emission consistent with the observations for both $\gamma $ Cas and 59 Cyg, and that the predicted polarization degrees across optical and UV wavelengths are at detectable levels. Finally, we discuss the impact that future UV spectropolarimetry missions could have on our understanding of these systems.
