On the Optical Light Curves of Afterglows from Jetted Gamma-ray Burst Ejecta: Effects of Parameters

Due to some refinements in the dynamics, we can follow the overall evolution of a realistic jet numerically till its bulk velocity being as small as βc ∼ 10c. 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 nonrelativistic phase, which typically occurs at time t ∼ 10 — 10 s (i.e., 10 — 30 d). The break is affected by many parameters, such as the electron energy fraction ξe, the magnetic energy fraction ξ B , the initial half opening angle θ0, and the medium number density n. Increase of 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 nonrelativistic 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.