GRB afterglow light curves from uniform and non-uniform jets

Free access article

Issue		A&A Volume 400, Number 2, March III 2003


Page(s)		415 - 419
Section		Cosmology
DOI		http://dx.doi.org/10.1051/0004-6361:20030007

A&A 400, 415-419 (2003)
DOI: 10.1051/0004-6361:20030007

GRB afterglow light curves from uniform and non-uniform jets

D. M. Wei^{1, 2} and Z. P. Jin^{1, 2}

¹ Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, PR China
² National Astronomical Observatories, Chinese Academy of Sciences, PR China

(Received 15 November 2002 / Accepted 23 December 2002 )

Abstract
It is widely believed that gamma-ray bursts are produced by a jet-like outflows directed towards the observer, and the jet opening angle ( $\theta_{\rm j}$ ) 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 ( $\theta_{\rm v}$ ) from the jet axis, and the jet is uniform or non-uniform (the energy per unit solid angle decreases smoothly away from the axis $\epsilon (\theta)\propto (\theta/\theta_{\rm c})^{-k}$ ). 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 $\gamma\sim (\theta_{\rm j}-\theta_{\rm v})^{-1}$ , and the second one corresponds to the time when $\gamma\sim (\theta_{\rm j}+\theta_{\rm v})^{-1}$ . However, for non-uniform jet, the things become more complicated. For the case $\theta_{\rm v}=0$ , 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 $\gamma\sim\theta_{\rm c}^{-1}$ and $\gamma\sim\theta_{\rm j}^{-1}$ respectively, while for k>8/(p+4) there should be only one break corresponds to $\gamma\sim\theta_{\rm c}^{-1}$ , and this provides a possible explanation for some rapidly fading afterglows whose light curves have no breaks since the time at which $\gamma\sim\theta_{\rm c}^{-1}$ is much earlier than our first observation time. For the case $\theta_{\rm v}\neq 0$ , our numerical results show that, the afterglow light curves are strongly affected by the values of $\theta_{\rm v}$ , $\theta_{\rm c}$ and k. If $\theta_{\rm v}$ is close to $\theta_{\rm c}$ 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 $\theta_{\rm v}/\theta_{\rm c}$ 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 $\gamma\sim (\theta_{\rm v} + \theta_{\rm c})^{-1}$ .

Key words: gamma rays: bursts -- ISM: jets and outflows

Offprint request: D. M. Wei, dmwei@pmo.ac.cn

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