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 beta c similar to 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 similar to 10(6)-10(6.5) s (i.e. 10-30 d). The break is affected by many parameters, such as the electron energy fraction xi(e), the magnetic energy fraction xi(B)(2), the initial half-opening angle theta(0) 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 alpha greater than or equal to 2.1. This is quite different from that of isotropic fireballs, and may be of fundamental importance for determining the degree of beaming in gamma-ray bursts observationally.