GRB afterglow light curves from uniform and non-uniform jets

Abstract

Here we calculate the GRB afterglow light curves from a relativistic jet as seen by observers at a wide range of viewing angles from the jet axis, and the jet is uniform or non-uniform. We find that, for uniform jet the afterglow light curves for different viewing angles are somewhat different: in general, there are two breaks in the light curve, corresponding to the time ${\hat{I}}^3\sim (\hat{I}{¸}_j-\hat{I}{¸}_v{)}^{-1}$ and ${\hat{I}}^3\sim (\hat{I}{¸}_j+\hat{I}{¸}_v{)}^{-1}$ respectively. However, for non-uniform jet, the things become more complicated. For the case $\hat{I}{¸}_v=0$, we can obtain the analytical results, for $k<8/(p+4)$ there should be two breaks in the light curve correspond to ${\hat{I}}^3\sim \hat{I}{¸}_c^{-1}$ and ${\hat{I}}^3\sim \hat{I}{¸}_j^{-1}$ respectively, while for $k>8/(p+4)$ there should be only one break corresponds to ${\hat{I}}^3\sim \hat{I}{¸}_c^{-1}$, and this provides a possible explanation for some rapidly fading afterglows whose light curves have no breaks since the time at which ${\hat{I}}^3\sim \hat{I}{¸}_c^{-1}$ is much earlier than our first observation time. For the case $\hat{I}{¸}_v\ne 0$, our numerical results show that, the afterglow light curves are strongly affected by the values of $\hat{I}{¸}_v$, $\hat{I}{¸}_c$ and $k$. If the values of $\hat{I}{¸}_v/\hat{I}{¸}_c$ 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\sim (θ_v + θ_c)^{-1}.

Latex, 5 pages, accepted for publication by A&A