2003A&A...400..415W

It is widely believed that gamma-ray bursts are produced by a jet-like outflows directed towards the observer, and the jet opening angle (θ_j) is often inferred from the time at which there is a break in the afterglow light curves. Here we calculate the GRB afterglow light curves from a relativistic jet as seen by observers at a wide range of viewing angles (θ_v) from the jet axis, and the jet is uniform or non-uniform (the energy per unit solid angle decreases smoothly away from the axis ε(θ)∝(θ/θ_ c_)^–k). We find that, for uniform jet (k=0), the afterglow light curves for different viewing angles are somewhat different: in general, there are two breaks in the light curve, the first one corresponds to the time at which γ~(θ_ j_–θv_)^–1, and the second one corresponds to the time when γ~(θ_j+θ_v)^–1. However, for non-uniform jet, the things become more complicated. For the case θ_v=0, we can obtain the analytical results, for k<8/(p+4) (where p is the spectral index of electron energy distribution) there should be two breaks in the light curve correspond to γ~θ_c^–1 and γ~θ_j^–1 respectively, while for k>8/(p+4) there should be only one break corresponds to γ~θ_c^–1, and this provides a possible explanation for some rapidly fading afterglows whose light curves have no breaks since the time at which γ~θ_ c_^–1 is much earlier than our first observation time. For the case θ_v≠0, our numerical results show that, the afterglow light curves are strongly affected by the values of θ_v, θ_c and k. If θ_v is close to θ_c and k is small, then the light curve is similar to the case of k=0, except the flux is somewhat lower. However, if the values of θ_v/θ_c and k are larger, there will be a prominent flattening in the afterglow light curve, which is quite different from the uniform jet, and after the flattening a very sharp break will be occurred at the time γ~(θ_v+θ_c)^–1.