The dynamics of gamma-ray burst ( GRB ) jets during the afterglow phase is most reliably and accurately modeled using hydrodynamic simulations .
All published simulations so far , however , have considered only a uniform external medium , while a stratified external medium is expected around long duration GRB progenitors .
Here we present simulations of the dynamics of GRB jets and the resulting afterglow emission for both uniform and stratified external media with \rho _ { ext } \propto r ^ { - k } for k = 0 , 1 , 2 .
The simulations are performed in two dimensions using the special relativistic version of the Mezcal code .
Common to all calculations is the initiation of the GRB jet as a conical wedge of half-opening angle \theta _ { 0 } = 0.2 whose radial profile is taken from the self-similar Blandford-McKee solution .
The dynamics for stratified external media ( k = 1 , 2 ) are broadly similar to those derived for expansion into a uniform external medium ( k = 0 ) .
The jet half-opening angle is observed to start increasing logarithmically with time ( or radius ) once the Lorentz factor \Gamma drops below \theta _ { 0 } ^ { -1 } .
For larger k values , however , the lateral expansion is faster at early times ( when \Gamma > \theta _ { 0 } ^ { -1 } ) and slower at late times with the jet expansion becoming Newtonian and slowly approaching spherical symmetry over progressively longer timescales .
We find that contrary to analytic expectations , there is a reasonably sharp jet break in the lightcurve for k = 2 ( a wind-like external medium ) although the shape of the break is affected more by the viewing angle ( for \theta _ { obs } \leq \theta _ { 0 } ) than by the slope of the external density profile ( for 0 \leq k \leq 2 ) .
Steeper density profiles ( i.e .
increasing k values ) are found to produce more gradual jet breaks while larger viewing angles cause smoother and later appearing jet breaks .
The counter-jet becomes visible as it becomes sub-relativistic , and for k = 0 this results in a clear bump-like feature in the light curve .
However , for larger k values the jet decelerates more gradually , causing only a mild flattening in the radio light curve that might be hard to discern when k = 2 .
Late time radio calorimetry , which makes use of a spherical flow approximation near the non-relativistic transition , is likely to consistently over-estimate the true energy by up to a factor of a few for k = 2 , but either over-predict or under-predict it by a smaller factor for k = 0 , 1 .