A Simple Analytic Treatment of the Intergalactic Absorption Effect in Blazar Gamma-ray Spectra

Abstract

We derive a new and user friendly simple analytic approximation for determining the effect of intergalactic absorption in the energy range 0.2-2 TeV and the redshift range 0.05-0.4. In these ranges, the form of the absorption coeeficient is approximately logarithmic in energy. The effect of this energy dependence is to steepen intrinsic source spectra such that a source with an approximate power-law intrinsic spectrum in this energy range with spectral index $\Gamma_{s}$ is steepened to a power-law with an observed spectral index $\Gamma_{o} = $\Gamma_{s} + $\Delta \Gamma (z)$ where $\Delta \Gamma (z)$ is a linear function of z in the redshift range 0.05-0.4. We apply this approximation to the spectra of seven TeV blazars.