Escape of high-energy photons from relativistically expanding gamma-ray burst sources

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Abstract
Four bright gamma‐ray bursts detected by BATSE have also been detected at higher energies by EGRET. All are consistent with power‐law spectra extending to energies as high as, in the case of GRB930131, 1 GeV. The optical depth to photon‐photon pair production in these sources is extremely large for distances more than a few pc away if the radiation is emitted isotropically in the observer’s frame. While it has been shown that the pair production optical depth can be dramatically reduced if the source is moving with a relativistic bulk Lorentz factor Γ, calculations have been limited to cases of a beam with opening angle 1/Γ. The beaming angles required for optically thin sources are so small for Galactic halo or cosmological distances that the implied number of non‐repeating sources is unreasonably high. Spherical expansion has also been considered but only in the case of an infinitely thin shell. We have investigated the pair production optical depth in relativistically expanding sources for more general cases, including shells of finite thickness and arbitrary opening angle. The new limits on required velocity for given beaming angles and thickness will place realistic constraints on gamma‐ray burst source models.

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