The Dynamics and Light Curves of Beamed Gamma‐Ray Burst Afterglows

The energy requirements of gamma ray bursts have in past been poorlyconstrained because of three major uncertainties: The distances to bursts, thedegree of burst beaming, and the efficiency of gamma ray production. The firstof these has been resolved, with both indirect evidence (the distribution ofbursts in flux and position) and direct evidence (redshifted absorptionfeatures in the afterglow spectrum of GRB 970508) pointing to cosmologicaldistances. We now wish to address the second uncertainty. Afterglows allow astatistical test of beaming, described in an earlier paper. In this paper, wemodify a standard fireball afterglow model to explore the effects of beaming onburst remnant dynamics and afterglow emission. If the burst ejecta are beamedinto angle zeta, the burst remnant's evolution changes qualitatively once itsbulk Lorentz factor Gamma < 1/zeta: Before this, Gamma declines as a power lawof radius, while afterwards, it declines exponentially. This change results ina broken power law light curve whose late-time decay is faster than expectedfor a purely spherical geometry. These predictions disagree with afterglowobservations of GRB 970508. We explored several variations on our model, butnone seems able to change this result. We therefore suggest that this burst isunlikely to have been highly beamed, and that its energy requirements were nearthose of isotropic models. More recent afterglows may offer the first practicalapplications for our beamed models.Comment: 18 pages, uses emulateapj.sty, four embedded postscript figures. Submitted to The Astrophysical Journal, 199