ANGULAR SIZE AND EMISSION TIMESCALES OF RELATIVISTIC FIREBALLS

The detection of delayed X-ray, optical, and radio emission, ''aftergl ow,'' associated with gamma-ray bursts (GRBs) is consistent with model s in which the bursts are produced by relativistic expanding blast wav es, driven by expanding fireballs at cosmological distances; In partic ular, the timescales over which radiation is observed at different wav ebands 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/2y(2)(r)c, where y is the fluid Lorentz factor, should be replaced with t = r/16 gamma(2)(r)c because of blast wave decelera tion. Applying the suggested deceleration modification would make it d ifficult to reconcile observed timescales with model predictions. It w ould also imply an apparent source size too large to allow attributing observed radio variability to diffractive scintillation. We present a detailed analysis of the implications of the relativistic hydrodynami cs of expanding blast waves to the observed afterglow. We find that mo difications clue to shock deceleration are small, therefore allowing f or both the observed afterglow timescales and for diffractive scintill ation. We show that at time r the fireball appears on the sky as a nar row ring of radius h = r/gamma(r) and width Delta h/h similar to 0.1, where r and t are related by t = r/2 gamma(2)(r)c.