Very high energy gamma - ray production inside the massive binary system Cyg X - 1 / HDE 226868

TeV γ-ray emission has been recently discovered by Cherenkov telescopes from two microquasars, LS 5039 and LS I +61303. This emission is likely to be produced inside the binary system since in both cases variability with the orbital period of the binary has been discovered. In fact, such emission features have been recently predicted by the inverse Compton (IC) e pair cascade model. In this model, electrons accelerated in the jet develop a cascade in the anisotropic radiation of the massive star. The γ-ray spectra emerging from the cascade strongly depend on the location of the observer with respect to the orbital plane of the binary. Here we apply this model in order to investigate the possible γ-ray emission features from another compact massive binary of the microquasar type, Cyg X-1. We conclude that the observational constraints at lower energies (from MeV to GeV) suggest that the spectrum of electrons injected in the jet is likely steeper than in other TeV γ-ray microquasars. The cascade γ-ray spectrum produced by electrons with such spectrum in Cyg X-1 should be below the sensitivities of the MAGIC and VERITAS class Cherenkov telescopes. However, if the electron spectrum is flatter, then the highest TeV γ-ray fluxes are predicted at ∼7 hrs before and after the phase when the compact object is in front of the massive star. We suggest that Cherenkov telescopes should concentrate on these range of phases since the TeV flux can vary by a factor of ∼20 with the period of the Cyg X-1 binary system. Moreover, the model predicts clear anticorrelation of the GeV and TeV γ-ray emission. This feature can be tested by the future multiwavelength observations with the AGILE and GLAST telescopes in the GeV energy range and the MAGIC and VERITAS telescopes in the TeV energy range.