Modelling the hardening of gamma-ray spectra by extragalactic background light

The interactions of Extragalactic Background Light (EBL) photons and γ-rays from distant quasars result in the steepening of the γ-ray spectrum at very high energies. The underlying process is the γ-ray absorption induced by pair production (γ + γ→e + e−) which is dependent on γ-ray energy and EBL energy density. We present a realistic model of the EBL based on the semi-analytical galaxy catalogues from the Millennium data base plus a homogeneous component assumed to be the accumulated light from distant galaxies. This approach reflects the fluctuations in the EBL due to the inhomogeneous galaxy distribution in a realistic manner. Our model predicts well the steepening of the spectral index of distant γ-ray sources as a function of redshift. In agreement with our previous purely analytical results the differences in the opacity due to individual γ-ray paths experiencing different EBL fluctuations are negligible.