Relativistic Jet Dynamics and Calorimetry of Gamma-Ray Bursts
  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.
