The principal discovery of the Compton Gamma-Ray Observatory (GRO) concerning gamma-ray bursts is that these sources are isotropic but with a comparative deficiency of fainter sources, suggesting that they are probably cosmological in origin. If they are at such large distances from Earth then they are extremely luminous and compact. A consequence of this is that two-photon pair production attenuation of the gamma-ray continuum cannot be avoided unless the source radiation is substantially beamed. Most sources do not display gamma-ray turnovers although a few GRB detected by GRO exhibit distinct spectral breaks in the MeV range. A derivation of the relationship defining of the degree of beaming in burst sources with spectral breaks due to γ-γ attenuation, as a function of source spectral index and break energy, is presented. It is found that sources at distances of ~1 Gpc must typically be beamed with bulk Lorentz factors of around 103 -104 , indicating powerful bulk acceleration in bursts, although these Lorentz factors are reduced markedly for steep source spectra. Since the source spectra are not strongly Comptonized, such beaming will blueshift the γ-γ attenuation breaks to energies much higher than 1 MeV; an absolute lower bound to the source bulk Lorentz factor is determined from this additional constraint. This blueshifting suggests that those sources with MeV breaks may not be cosmological, or that their breaks are produced by a mechanism that dominates γ-γ attenuation at these energies.

Subject headings: gamma-rays: bursts — radiation mechanisms: nonthermal