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 (up to 4 - 6) orders of magnitude, and the event rate increased
correspondingly. The large Lorentz factors (Gamma > 100) inferred from GRB
spectra imply relativistic beaming of the gamma rays into an angle 1/Gamma. We
are at present ignorant of whether there are ejecta outside this narrow cone.
Afterglows allow empirical tests of whether GRBs are well-collimated jets or
spherical fireballs. The bulk Lorentz factor decreases and radiation is beamed
into an ever increasing solid angle as the burst remnant expands. 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.
In addition, a burst whose ejecta are beamed into angle zeta undergoes a
qualitative change in evolution when Gamma < 1/zeta: Before this, Gamma ~
r^{-3/2}, while afterwards, Gamma decays exponentially with r. This change
results in a potentially observable break in the afterglow light curve.
Successful application of either test would eliminate the largest remaining
uncertainty in the energy requirements and space density of gamma ray bursters.Comment: 5 pages, LaTex, uses aipproc and psfig style files. To appear in the
proceedings of the Fourth Huntsville Gamma Ray Burst Symposiu