GRB afterglow light curves from uniform and non-uniform jets

It is widely believed that gamma-ray bursts are produced by a jet-like outflows directed towards the observer, and the jet opening angle (θj) 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 (θv) 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/θc)-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 ∼ (θj - θv)-1, and the second one corresponds to the time when γ ∼ (θj + θv)-1. However, for non-uniform jet, the things become more complicated. For the case θv = 0, we can obtain the analytical results, for k c-1 and γ ∼ θj-1 respectively, while for k > 8/(p+4) there should be only one break corresponds to γ ∼ θc-1, and this provides a possible explanation for some rapidly fading afterglows whose light curves have no breaks since the time at which γ ∼ θc-1 is much earlier than our first observation time. For the case θv 0, our numerical results show that, the afterglow light curves are strongly affected by the values of θv, θc and k. If θv is close to θc 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 θv/θc 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 ∼ (θv - θc)-1.