Hydrodynamics of a relativistic fireball in early afterglow phase

Abstract

We discuss the reference time t<inf>0</inf> of afterglow light curves in the context of the standard internal-external shock model. The decay index of early afterglow is very sensitive to the reference time one chooses. In order to understand the nature of early afterglow, it is essential to take a correct reference time. Our simple analytic model provides a framework to understand special relativistic effects involved in the early afterglow phase. We evaluate light curves of reverse shock emission as well as those of forward shock emission, based on full hydrodynamic calculations. We show that the reference time does not shift significantly even in the thick-shell case. For external shock emission components, measuring times from the beginning of the prompt emission is a good approximation and it does not cause an early steep decay. In the thin-shell case, the energy transfer time from fireball ejecta to ambient medium typically extends to thousands of seconds. This might be related to the shallow decay phases observed in early X-ray afterglow at least for some bursts. A full discussion of the t<inf>0</inf> issue including implications for inhomogeneous fireballs is given by S. Kobayashi and B. Zhang in Astrophys. J., 655 (2007) 973. © Società Italians di Fisica.