Astronomy and Astrophysics – Astrophysics
Scientific paper
1997-12-31
ApJ, Vol. 499(1998), 754
Astronomy and Astrophysics
Astrophysics
15pages,1 figure, accepted by ApJ,aasms4 style
Scientific paper
10.1086/305686
The detection of the delayed emission in X-ray, optical and radio band, i.e. the afterglow of $\gamma$-ray bursts (GRBs), suggestes that the sources of GRBs are likely to be at cosmological distances. Here we explore the interaction of a relativistic shell with a uniform interstellar medium (ISM) and obtain the exact solution of the evolution of $\gamma$-ray burst remnants, including the radiative losses. We show that in general the evolution of bulk Lorentz factor $\gamma$ satisfies $\gamma \propto t^{-\alpha_{t}}$ when $\gamma \gg 1$, here $\alpha_{t}$ is mainly in the range $9/22 \sim 3/8$, the latter corresponds to adiabatic expansion. So it is clear that adiabatic expansion is a good approximation even when radiative loss is considered. However, in fact, $\alpha_{t}$ is slightly larger than 3/8, which may have some effects on a detailed data analysis. Synchrotron-self-absorption is also calculated and it is demonstrated that the radio emission may become optically thin during the afterglow. Our solution can also apply to the nonrelativistic case ($\gamma \sim 1$), at that time the observed flux decrease more rapidly than that in the relativistic case.
Lu Tan
Wei Da-Ming
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