The apparent size of gamma-ray burst afterglows as a test of the fireball model

Taylor et al. reported recently on the first direct measurement of the apparent size of a gamma-ray burst (GRB) afterglow. Here we confront these observations with the predictions of the fireball model. We use a simple model to study numerically the evolution of the fireball and determine its apparent size, starting at the early spherical expansion phase through the jet break and into the Newtonian regime. We perform these calculations on the background of a uniform interstellar medium and a massive stellar wind environment. We find that the calculated apparent size at the time of the measurements taken by Taylor et al. depends only weakly on the chosen parameters (the jet opening angle, the energy and the external density profile). Thus it is reassuring that the only possible outcome of the model, within the plausible range of parameters, agrees very well with the data. These measurements therefore present us with a strong test of possible GRB models, which the fireball model passes successfully.