We have recently obtained the exact analytic solutions for the relativistic equations relating the radial and timecoordinates of a relativistic, thin uniform shell expanding in the interstellar medium in the fully radiative and fully adiabatic regimes. Here we reexamine the validity of the constant-index power-law relation between the Lorentz gamma factor and its radial coordinate, which is usually adopted in the 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 physical and astrophysical parameters and in an asymptotic regime that is reached for a very short time only, if at all, and they are shown to be nonapplicable to GRBs.
Exact versus approximate solutions in gamma-ray burst afterglows / Bianco, Carlo Luciano; Ruffini, Remo. - In: THE ASTROPHYSICAL JOURNAL. - ISSN 0004-637X. - STAMPA. - 633:1 II(2005), pp. L13-L16. [10.1086/498146]
Exact versus approximate solutions in gamma-ray burst afterglows
BIANCO, Carlo Luciano;RUFFINI, Remo
2005
Abstract
We have recently obtained the exact analytic solutions for the relativistic equations relating the radial and timecoordinates of a relativistic, thin uniform shell expanding in the interstellar medium in the fully radiative and fully adiabatic regimes. Here we reexamine the validity of the constant-index power-law relation between the Lorentz gamma factor and its radial coordinate, which is usually adopted in the 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 physical and astrophysical parameters and in an asymptotic regime that is reached for a very short time only, if at all, and they are shown to be nonapplicable to GRBs.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.