Relativistic Jet Dynamics and Calorimetry of Gamma-Ray Bursts

TL;DR

This paper provides numerical solutions for relativistic jet dynamics in gamma-ray bursts, showing how sideways expansion affects jet evolution and how calorimetric energy estimates can be simplified after a certain phase.

Contribution

It offers new numerical modeling of relativistic jet expansion, clarifies the significance of sideways expansion, and demonstrates simplified energy estimation methods for GRB blast waves.

Findings

Relativistic sideways expansion becomes significant beyond a specific radius.

Emission from the jet resembles that of a spherical blast wave after a certain time.

Calorimetric energy estimates are accurate with observations taken after R/c.

Abstract

We present numerical solutions of the 2D relativistic hydrodynamics equations describing the deceleration and expansion of highly relativistic conical jets, of opening angles 0.05<theta<0.2, propagating into a medium of uniform density. Jet evolution is followed from a collimated relativistic outflow through to the quasi-spherical non-relativistic phase. We show that relativistic sideways expansion becomes significant beyond the radius R at which the expansion Lorentz factor drops to 1/theta. This is consistent with simple analytic estimates, which predict faster sideways expansion than has been claimed based on earlier numerical modeling. For t>R/c the emission of radiation from the jet blast wave is similar to that of a spherical blast wave carrying the same energy. Thus, the total (calorimetric) energy of GRB blast waves may be estimated with only a small fractional error based on t>R/c observations.