RINGS IN FIREBALL AFTERGLOWS

We derive the equation for the surface of equal arrival time of radiat ion from a thin relativistic shell interacting with an external medium , representing the afterglow of a gamma-ray burst produced by a fireba ll. Due to the deceleration, these surfaces become distorted ellipsoid s and, at late times, most of the light comes from a ringlike region w hose width depends only on age. We analyze the shape of these surfaces for different dynamic and radiative regimes and homogeneous or power- law external densities. We tabulate the most relevant parameters descr ibing the surfaces and the source brightness distribution, both for bo lometric and fixed frequency observations, which are useful for more a ccurate analytic estimates of the afterglow evolution.