Cygnus X-3 ( Cyg X-3 ) is a remarkable Galactic microquasar ( X-ray binary ) emitting from radio to \gamma -ray energies .
In this paper , we consider hadronic model of emission of \gamma -rays above 100 MeV and their implications .
We focus here on the joint \gamma -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 \gamma -ray flux observed by AGILE and Fermi -LAT , is L _ { p } \sim 10 ^ { 38 } \ > { erg\ > s ^ { -1 } } , a value in agreement with the average bolometric luminosity of the hypersoft state ( when Cygnus X-3 was repeatedly observed to produce transient \gamma -ray activity ) .
If we assume an increase of the wind density at the superior conjunction , the asymmetric production of \gamma -rays along the orbit can reproduce the observed modulation .
According to observational constraints and our modelling , a maximal flux of high-energy neutrinos would be produced for an initial proton distribution with a power-law index \alpha = 2.4 .
The predicted neutrino flux is almost two orders of magnitude less than the 2-month IceCube sensitivity at \sim 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 3 lower than the 1-year IceCube sensitivity at \sim 10 TeV .
This study shows that , for a prolonged soft state ( as observed in 2006 ) possibly related with \gamma -ray activity and a hard distribution of injected protons , Cygnus X-3 might be close to being detectable by cubic-kilometer neutrino telescopes such as IceCube .