Off-Axis Afterglow Emission from Jetted Gamma-Ray Bursts

We calculate the Gamma-Ray Burst (GRB) afterglow light-curves from a relativistic jet as seen by observers at a wide range of viewing angles, $\theta_{obs}$, from the jet axis. We describe three increasingly more realistic models and compare the resulting light-curves. An off-axis observer at $\theta_{obs}>\theta_0$ (outside the initial opening of the jet) should see a rising light curve at early times, the flux peaking when the jet Lorentz factor $\sim 1/\theta_{obs}$. After this time the flux is not very different from that seen by an observer along the jet axis ($\theta_{obs}=0$). A strong linear polarization ($\lesssim 40%$) may occur near the peak in the light curve, and slowly decay with time. An observer at $\theta_{obs}<\theta_0$ should see a light curve very similar to that for an on-axis observer ($\theta_{obs}=0$). We apply our results to the recently reported observation of a very bright optical transient by the SDSS, whose isotropic luminosity was a factor $\sim 50$ larger than the peak brightness of supernovae. We find that the data for this event are consistent with a GRB afterglow provided that the observer is located off-axis at $\theta_{obs} \approx 2-5 \theta_0$, and that the burst occurred $\sim$1.5--3 days before the first SDSS observation. We also discuss the proposed connection between supernova 1998bw and GRB 980425.