Exact versus approximate solutions in Gamma-Ray Burst afterglows

Details Exact versus approximate solutions in Gamma-Ray Burst afterglows Exact versus approximate solutions in Gamma-Ray Burst afterglows

2005-09-21

arxiv.org/abs/astro-ph/0509621v1

Astrophys.J.633:L13-L16,2005

Astronomy and Astrophysics

Astrophysics

4 pages, 2 figures, to appear on ApJ Letters

Scientific paper

10.1086/498146

We have recently obtained the exact analytic solutions of the relativistic equations relating the radial and time coordinate of a relativistic thin uniform shell expanding in the interstellar medium in the fully radiative and fully adiabatic regimes. We here re-examine the validity of the constant-index power-law relations between the Lorentz gamma factor and its radial coordinate, usually adopted in the current Gamma-Ray Burst (GRB) literature on the grounds of an "ultrarelativistic" approximation. Such expressions are found to be mathematically correct but only approximately valid in a very limited range of the physical and astrophysical parameters and in an asymptotic regime which is reached only for a very short time, if any, and are shown to be not applicable to GRBs.

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