On the optical light curves of afterglows from jetted gamma-ray burst ejecta: effects of parameters

Owing to some refinements in the dynamics, we can follow the overall evolution of a realistic jet numerically until its bulk velocity is as small as βc∼10−3c. We find no obvious break in the optical light curve during the relativistic phase itself. However, an obvious break does exist at the transition from the relativistic phase to the non-relativistic phase, which typically occurs at time t∼106–106.5s (i.e. 10–30 d). The break is affected by many parameters, such as the electron energy fraction ξe, the magnetic energy fraction the initial half-opening angle θ0 and the medium number density n. Increasing any of them to a large enough value will make the break disappear. Although the break itself is parameter-dependent, afterglows from jetted GRB remnants are uniformly characterized by a quick decay during the non-relativistic phase, with power-law timing index α ≥ 2.1. This is quite different from that of isotropic fireballs, and may be of fundamental importance for determining the degree of beaming in γ-ray bursts observationally.