  The detection of delayed X-ray, optical and radio emission, ``afterglow,''
associated with gamma-ray bursts (GRBs) is consistent with models, where the
bursts are produced by relativistic expanding blast waves, driven by expanding
fireballs at cosmological distances. In particular, the time scales over which
radiation is observed at different wave bands agree with model predictions. It
had recently been claimed that the commonly used relation between observation
time t and blast wave radius r, t=r/2\gamma^{2}c where \gamma(r) is the fluid
Lorentz factor, should be replaced with t=r/16\gamma^{2}c due to blast wave
deceleration. Applying the suggested deceleration modification would make it
difficult to reconcile observed time scales with model predictions. It would
also imply an apparent source size which is too large to allow attributing
observed radio variability to diffractive scintillation. We present a detailed
analysis of the implications of the relativistic hydrodynamics of expanding
blast waves to the observed afterglow. We find that modifications due to shock
deceleration are small, therefore allowing for both the observed afterglow time
scales and for diffractive scintillation. We show that at time t the fireball
appears on the sky as a narrow ring of radius h=r/\gamma and width 0.1h, where
r and t are related by t=r/2\gamma^{2}c.

Astrophysics