How to tell a jet from a balloon: A proposed test for beaming in gamma-ray bursts

If gamma-ray bursts are highly collimated, radiating into only a small fraction of the sky, the energy requirements of each event may be reduced by several (similar to 4-6) orders of magnitude, and the event rate is increased correspondingly. Extreme conditions in gamma-ray bursters lead to highly relativistic motions (bulk Lorentz factors of Gamma greater than or similar to 100). This results in strong forward beaming of the emitted radiation in the observer's rest frame. Thus, all information on gamma-ray bursts comes from those ejecta emitted in a narrow cone (opening angle of similar to/Gamma)) pointing toward the observer. We are at present ignorant of whether there are ejecta outside that cone or not. The recent detection of longer wavelength transients following gamma-ray bursts allows an empirical test of whether gamma-ray bursts are well-collimated jets or spherical fireballs. The bulk Lorentz factor of the burst ejecta will decrease with time after the event, as the ejecta sweep up the surrounding medium. Thus, radiation from the ejecta is beamed into an ever-increasing solid angle as the burst remnant evolves. It follows that if gamma-ray bursts are highly collimated, many more optical and radio transients should be observed without associated gamma rays than with them. Published supernova searches may contain enough data to test the most extreme models of gamma-ray beaming. We close with a brief discussion of other possible consequences of beaming, including its effect on the evolution of burst remnants.