Relativistic expansions in gamma-ray bursts: Constraints from photon-photon pair production

Abstract

A significant fraction of bright gamma-ray bursts detected by BATSE have also been seen at much higher energies by EGRET, implying that they are optically thin to photon-photon pair production out to 100 MeV or more. For sources more than about 10 pc away, this can be achieved only if the source is moving with a relativistic bulk Lorentz factor Γ≫1. Early calculations of γγ→e + e − constraints for bursts were limited to cases of a beam with opening angle Θ B ∼1/Γ, or expansions of infinitely thin spherical shells. This paper presents our extension of pair production optical depth calculations in relativistically expanding sources to more general geometries, including shells of finite thickness and arbitrary opening angle. We find that the minimum Lorentz factor for EGRET sources to be optically thin, i.e., to display no spectral attenuation above 1 MeV, is only moderately dependent on the shell thickness and virtually independent of its opening solid angle if Θ B ≳1/Γ. This insensitivity to Θ B relieves the number problem for non-repeating sources at cosmological distances, i.e., it is not necessary to invoke small Θ B to effect photon escape.