Off-Axis Afterglow Emission from Jetted Gamma-Ray Bursts

We calculate gamma-ray burst (GRB) afterglow light curves from a relativistic jet as seen by observers at various viewing angles, θ_obs, relative to the jet axis. We describe three increasingly more realistic models and compare the resulting light curves. An observer at θ_obs < 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 θ_obs > θ₀ sees a rising light curve at early times, peaking when the jet Lorentz factor is ~1/θ_obs, 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.