THE EVOLUTION OF GAMMA-RAY BURST REMNANTS

The detection of the delayed emission in X-ray, optical, and radio ban ds, i.e., the afterglow of gamma-ray bursts (GRBs), suggests that the sources of GRBs are likely to be at cosmological distances. Here we ex plore the interaction of a relativistic shell with a uniform interstel lar medium (ISM) and obtain the exact solution of the evolution of gam ma-ray burst remnants, including the radiative losses. We show that in general the evolution of the bulk Lorentz factor, gamma, satisfies ga mma proportional to t(-alpha t) when gamma much greater than 1; here, alpha(t) is mainly in the range 9/22-3/8, the latter corresponding to adiabatic expansion. So it is clear that adiabatic expansion is a good approximation even when radiative loss is considered. However, in fac t, alpha(t) is slightly larger than 3/8, which may have some effects o n a detailed data analysis. Synchrotron self-absorption is also calcul ated, and it is demonstrated that the radio emission may become optica lly thin during the afterglow. Our solution can also apply to the nonr elativistic case (gamma similar to 1); at that time, the observed flux decreases more rapidly than that in the relativistic case.