A model of the TeV flare of Cygnus X-1: electron acceleration and extended pair cascades

We consider theoretical models of emission of TeV photons by Cyg X-1 during a flare discovered by the Major Atmospheric Gamma Imaging Cherenkov Telescope (MAGIC) detector. We study acceleration of electrons to energies sufficient for TeV emission, and find the emission site is allowed to be close to the black hole. We then consider pair absorption in the photon field of the central X-ray source and a surrounding accretion disc, and find its optical depth is less than or similar to 1, allowing emission close to the black hole. On the other hand, the optical depth in the stellar field is similar to 10 at similar to 1 TeV. However, the optical depth drops with increasing energy, allowing a model with the initial energy of greater than or similar to 3 TeV, in which photons travel far away from the star, initiating a spatially extended pair cascade. This qualitatively explains the observed TeV spectrum, though still not its exact shape.