Cygnus X-3 (Cyg?X-3) is a remarkable Galactic microquasar (X-ray binary) emitting from radio to γ-ray energies. In this paper, we consider the hadronic model of emission of γ-rays above 100?MeV and their implications. We focus on the joint γ-ray and neutrino production resulting from proton-proton interactions within the binary system. We find that the required proton injection kinetic power, necessary to explain the γ-ray flux observed by AGILE and Fermi-LAT, is Lp ~ 1038 erg s–1, a value in agreement with the average bolometric luminosity of the hypersoft state (when Cyg X-3 was repeatedly observed to produce transient γ-ray activity). If we assume an increase of the wind density at the superior conjunction, the asymmetric production of γ-rays along the orbit can reproduce the observed modulation. According to observational constraints and our modeling, a maximal flux of high-energy neutrinos would be produced for an initial proton distribution with a power-law index α = 2.4. The predicted neutrino flux is almost two orders of magnitude less than the two-month IceCube sensitivity at ~1?TeV. If the protons are accelerated up to PeV energies, the predicted neutrino flux for a prolonged "soft X-ray state" would be a factor of about three lower than the one-year IceCube sensitivity at ~10?TeV. This study shows that, for a prolonged soft state (as observed in 2006) possibly related to γ-ray activity and a hard distribution of injected protons, Cyg?X-3 might be close to being detectable by cubic-kilometer neutrino telescopes such as IceCube.
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