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Recent reports claiming association of the massive star binary system$\gamma^2 $Velorum (WR 11) with a high-energy $\gamma$-ray source observed by\textit{Fermi}-LAT contrast the so-far exclusive role of $\eta$ Carinae as thehitherto only detected $\gamma$-ray emitter in the source class ofparticle-accelerating colliding-wind binary (CWB) systems. We offer support tothis claim of association by providing dedicated model predictions for thenonthermal photon emission spectrum of $\gamma^2$ Velorum.  We use three-dimensional magneto-hydrodynamic modeling (MHD) to investigatethe structure and conditions of the wind-collision region (WCR) of $\gamma^2$Velorum including the important effect of radiative braking in the stellarwinds. A transport equation is then solved throughout the computational domainto study the propagation of relativistic electrons and protons. The resultingdistributions of particles are subsequently used to compute nonthermal photonemission components.  In agreement with observation in X-ray spectroscopy, our simulations yield alarge shock-cone opening angle. We find the nonthermal $\gamma$-ray emission of$\gamma^2$ Velorum to be of hadronic origin owing to the strong radiationfields in the binary system which inhibit the acceleration of electrons toenergies sufficiently high for efficient inverse Compton radiation. We alsodiscuss the strong dependence of a hadronic $\gamma$-ray component on theenergy-dependent diffusion used in the simulations. Of two mass-loss rates forthe WR star found in literature, only the higher one is able to accommodate theobserved $\gamma$-ray spectrum with reasonable values for important simulationparameters such as the injection ratio of high-energy particles within the WCR.

3D magneto-hydrodynamic models of non-thermal photon emission in the binary system $\gamma^2$ Velorum