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

TeV gamma-ray emission has recently been discovered by Cherenkov telescopes from two microquasars, LS 5039 and LS I + 61 degrees 303. 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 recently been 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 gamma-ray spectra emerging from the cascade strongly depends on the location of the observer with respect to the orbital plane of the binary. Here we apply this model to investigate the possible gamma-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 gamma-ray microquasars. The cascade gamma-ray spectrum produced by electrons with such a 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 gamma-ray fluxes are predicted at similar to 7 h 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 ranges of phases since the TeV flux can vary by a factor of similar to 20 with the period of the Cyg X-1 binary system. Moreover, the model predicts clear anticorrelation of the GeV and TeV gamma-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.