1999ApJ...525..737R

The energy requirements of gamma-ray bursts have in past been poorly constrained because of three major uncertainties: the distances to bursts, the degree of burst beaming, and the efficiency of gamma-ray production. The first of these has been resolved, with both indirect evidence (the distribution of bursts in flux and position) and direct evidence (redshifted absorption features in the afterglow spectrum of GRB 970508) pointing to cosmological distances. We now wish to address the second uncertainty. Afterglows allow a statistical test of beaming, described in an earlier paper. In this paper, we modify a standard fireball afterglow model to explore the effects of beaming on burst remnant dynamics and afterglow emission. If the burst ejecta are beamed into angle ζ_m, the burst remnant's evolution changes qualitatively once its bulk Lorentz factor Γ≲1/ζ_m: before this, Γ declines as a power law of radius, while afterward, it declines exponentially. This change results in a broken power-law light curve whose late-time decay is faster than expected for a purely spherical geometry. These predictions disagree with afterglow observations of GRB 970508. We explored several variations on our model, but none seems to be able to change this result. We therefore suggest that this burst is unlikely to have been highly beamed and that its energy requirements were near those of isotropic models. More recent afterglows may offer the first practical applications for our beamed models.