Produced photon spectrum (blue) for a proton injected spectrum of Γ_p = 2 and E_cut,p = 10¹⁵ eV (black, scaled by an arbitrary factor). The red dotted line represents the best fit of the photon spectra with a simple power law in the energy range [1–300] GeV. The behaviour at low energy follows the increase in the cross section at E_p ~ 1 GeV (see Eq. (A.3)). Note that the proton spectrum is expressed as function of the kinetic energy, E_cin = E_tot − m_pc², with m_p ~ 1 GeV/ c².