2013MNRAS.432.3245D

Using the most recent observational data concerning the extragalactic background light and the radio background for a source at an arbitrary redshift in the range zs ≤ 3, we compute the energy E0 of an observed γ-ray photon in the range 10 ≤ E0 ≤ 1013GeV such that the resulting optical depth τγ(E0, zs) takes the values 1, 2, 3 and 4.6 corresponding to an observed flux dimming of e-1 ≃ 0.37, e-2 ≃ 0.14, e-3 ≃ 0.05 and e-4.6 ≃ 0.01, respectively. Below a distance D ≃ 8kpc, we find that τγ(E0, DH0/c) < 1 for any value of E0. In the limiting case of a local Universe (zs ≃ 0), we compare our result with the one derived in 1997 by Coppi and Aharonian. The present achievement is of paramount relevance for the planned ground-based detectors like Cherenkov Telescope Array, High Altitude Water Cherenkov Experiment and Hundred Square-km Cosmic ORigin Explorer.