Abstract
We calculate gamma-ray burst (GRB) afterglow light curves from a relativistic jet as seen by observers at various viewing angles, θobs, relative to the jet axis. We describe three increasingly more realistic models and compare the resulting light curves. An observer at θobs < θ0, where θ0 is the initial jet opening angle, should see a light curve very similar to that for an on-axis observer. An observer at θobs > θ0 sees a rising light curve at early times, peaking when the jet Lorentz factor is ~1/θobs, and approaching that seen by an on-axis observer, at later times. A strong linear polarization (≲40%) may occur near the peak in the light curve and slowly decay with time. We show that, if GRB jets have a universal energy, then orphan afterglows are detectable up to a maximum offset angle that is independent of the jet initial aperture and thus at a rate proportional to the true GRB rate. We also discuss the implications of the proposed connection between SN 1998bw and GRB 980425.
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