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

Abstract

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 ${\hat{I}}^{2}c\sim 10^{-3}c$. 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 $t\sim 10^6$ --- $10^{6.5}$ s (i.e., 10 --- 30 d). The break is affected by many parameters, such as the electron energy fraction $\hat{I}{¾}_{\mathrm{e}}$, the magnetic energy fraction $\hat{I}{¾}_{\mathrm{B}}^2$, the initial half opening angle $\hat{I}{¸}_0$, 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 non-relativistic phase, with power law timing index $\hat{I}\pm \ge 2.1$. This is quite different from that of isotropic fireballs, and may be of fundamental importance for determining the degree of beaming in ${\hat{I}}^3$-ray bursts observationally.

8 pages, 10 embedded eps figures, MNRAS in press, using epsfig.sty and mn.sty