The Evolution of a Structured Relativistic Jet and GRB Afterglow Light-Curves

Authors:
Pawan Kumar,
Jonathan Granot

Comments: 22 pages, 6 figures. Accepted for publication in ApJ (scheduled for
the v590, June 20, 2003 issue)

We carry out a numerical hydrodynamical modeling for the evolution of a
relativistic collimated outflow, as it interacts with the surrounding medium,
and calculate the light-curve resulting from synchrotron emission of the
shocked fluid. The hydrodynamic equations are reduced to 1-D by assuming axial
symmetry and integrating over the radial profile of the flow, thus considerably
reducing the computation time. We present results for a number of different
initial jet structures, including several different power-laws and a Gaussian
profile for the dependence of the energy per unit solid angle, $epsilon$, and
the Lorentz factor, $Gamma$, on the angle from the jet symmetry axis. Our
choice of parameters for the various calculations is motivated by the current
knowledge of relativistic outflows from gamma-ray bursts and the observed
afterglow light-curves. Comparison of the light curves for different jet
profiles with GRB afterglow observations provides constraints on the jet
structure. One of the main results we find is that the transverse fluid
velocity in the comoving frame ($v_t$) and the speed of sideways expansion, for
smooth jet profiles, is typically much smaller than the speed of sound ($c_s$)
throughout much of the evolution of the jet; $v_t$ approaches $c_s$ when
$Gamma$ along the jet axis becomes of order a few (for large angular gradient
of $epsilon$, $v_tsim c_s$ while $Gamma$ is still large). This result
suggests that the dynamics of relativistic structured jets may be reasonably
described by a simple analytic model where $epsilon$ is independent of time,
as long as $Gamma$ along the jet-axis is larger than a few.

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