Effects of spatial fluctuations in the extragalactic background light on hard gamma-ray spectra

Abstract

This study investigates the impact of the fluctuations in the extra galactic background light (EBL) on the attenuation of the hard $\gamma$-ray spectra of distant blazars. EBL fluctuations occur on the scales up to 100 Mpc and are caused by clustering of galaxies. The EBL photons interact with high energy $\gamma$-rays via the electron-positron pair production mechanism: $\gamma + \gamma' \rightarrow e^+ + e^-$. The attenuation of $\gamma$-rays depends on their energy and the density of the intervening EBL photon field. Using a simple model for the evolution of the mean EBL photon density, we implement an analytical description of the EBL fluctuations. We find that the amplitudes of the EBL energy density can vary by $\pm 1\%$ as a function of environment. The EBL fluctuations lead to mild alterations of the optical depth or equivalently the transmissivity for $\gamma$-rays from distant blazars. Our model predicts maximum changes of $\pm 10\%$ in the $\gamma$-ray transmissivity. However, this translates into marginal differences in the power law slopes of currently observed $\gamma$-ray spectra. The slopes of deabsorbed $\gamma$-ray spectra differ by not more than $\pm 1\%$ if EBL fluctuations are included.