2 v 1 2 0 A ug 1 99 7 Absorption of High Energy Gamma Rays by Interactions with Extragalactic Starlight Photons at High Redshifts

We extend earlier calculations of the attenuation suffered by γ-rays during their propagation from extragalactic sources, obtaining new extinction curves for γ-rays down to 10 GeV in energy, from sources up to a redshift of z = 3. The recognition that high energy γ-rays, propagating over cosmological distances, suffer electron-pair-producing interactions with photons from the extragalactic background radiation fields dates back to the 1960s [1–4]. The reaction γγ → e + e − between a γ-ray of energy E and a background photon of energy ǫ can occur when the center-of-mass square energy s is above threshold, s = 2Eǫ(1 − cos θ) > 4m 2 e c 4 , where θ is the angle between the two photons' direction vectors. A γ-ray of energy E TeV TeV therefore interacts only with background photons above a threshold energy ǫ thr ≈ 0.3eV/E TeV. Since the number density of background photons decreases roughly as a power law in energy, most of the collisions occur near threshold. Thus, when estimating the extinction of 1 TeV gamma rays, it is the density of the in-frared background which dominates; at 20 GeV, however, only UV photons near the Lyman limit can act as targets. This mechanism was recently invoked [5] to explain why many EGRET blazars are not seen at ∼TeV energies by ground-based instruments such as Whipple, in spite of the fact that an extrapolation of the EGRET power-law spectra places them above the sensitivity limit of these ground-based detectors. The opacity τ seen by a γ-ray in its propagation from source to Earth is roughly τ ∼ Nσ T d, where N is the number of target soft photons above threshold, σ T is the Thompson cross section, and d is the distance to the source. For sources with redshift z > 0.1 (corresponding to most of the EGRET blazar sources), based on estimates of the