TY - JOUR

T1 - The evolution of a structured relativistic jet and gamma-ray burst afterglow light curves

AU - Kumar, Pawan

AU - Granot, Jonathan

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 2003/7/10

Y1 - 2003/7/10

N2 - 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 one-dimensional 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, ε, and the Lorentz factor, Γ, 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 gamma-ray burst 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 (vt) and the speed of sideways expansion for smooth jet profiles is typically much smaller than the speed of sound (cs) throughout much of the evolution of the jet; v t approaches cs when Γ along the jet axis becomes of order a few (for a large angular gradient of ε, vt ∼ cs while Γ is still large). This result suggests that the dynamics of relativistic structured jets may be reasonably described by a simple analytic model in which γ is independent of time, as long as Γ along the jet axis is larger than a few.

AB - 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 one-dimensional 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, ε, and the Lorentz factor, Γ, 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 gamma-ray burst 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 (vt) and the speed of sideways expansion for smooth jet profiles is typically much smaller than the speed of sound (cs) throughout much of the evolution of the jet; v t approaches cs when Γ along the jet axis becomes of order a few (for a large angular gradient of ε, vt ∼ cs while Γ is still large). This result suggests that the dynamics of relativistic structured jets may be reasonably described by a simple analytic model in which γ is independent of time, as long as Γ along the jet axis is larger than a few.

KW - Gamma rays: bursts

KW - Gamma rays: theory

UR - http://www.scopus.com/inward/record.url?scp=0141726594&partnerID=8YFLogxK

U2 - 10.1086/375186

DO - 10.1086/375186

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AN - SCOPUS:0141726594

SN - 0004-637X

VL - 591

SP - 1075

EP - 1085

JO - Astrophysical Journal

JF - Astrophysical Journal

IS - 2 I

ER -