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 (
) 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
(
) from the jet axis, and the jet is uniform or
non-uniform (the energy per unit solid angle decreases smoothly
away from the axis
). 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
, and the second one corresponds to the
time when
.
However, for non-uniform jet, the things become more complicated.
For the case
, 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
and
respectively, while for
*k*>8/(*p*+4) there should be only one break corresponds to
, and this provides a possible
explanation for some rapidly fading afterglows whose light curves
have no breaks since the time at which
is much earlier than our first observation time. For the
case
, our numerical results show that, the
afterglow light curves are strongly affected by the values of
,
and
*k*. If
is
close to
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
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
.

**Key words:**gamma rays: bursts

**--**ISM: jets and outflows

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

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*ESO 2003*