The Gamma-Ray Horizon Imposed by the Background Light: Horizon Energies from a Scaled Optical Depth

This paper addresses a specific question in the accounting of the cosmic optical and infrared backgrounds: at what gamma-ray energy does the extragalactic background light make the universe opaque, as a function of source redshift? The approach is a transparent computation from stated inputs drawn from the published literature, carried through in a deposited script whose output supplies every number quoted here. The principal computed values are: horizon z0.1 GeV = 200; horizon z0.5 GeV = 77.7; horizon z1.0 GeV = 31.8; tau 1TeV z0.1 = 7.48; tau 300GeV z0.3 = 3.13. These are compared with published measurements and budgets at the same wavelengths, and the agreement or disagreement is stated in each case. The study is computed from stated assumptions, not a new measurement; its contribution is arithmetic that can be checked line by line, with sensitivities reported wherever an input is uncertain.