Steepening of the GRB afterglows : one clue to the initial condition of the fireball

Whether gamma-ray bursts are highly beamed or not is a very important question, since it has been pointed out that the beaming will lead to a sharp break in the afterglow light curves during the ultra-relativistic phase, with the breaking point determined by Γ ∼ 1/θ 0 , where Γ is the bulk Lorentz factor and θ 0 is the initial half opening angle of the ejecta, and such a break is claimed to be present in the light curves of some GRBs. Here we present a detailed calculation of the jet evolution and emission, we show that the light curves are very smoothly steepened by jet effect, and the sharpness of the light curve is determined by only one parameter — Γ 0 θ 0 , where Γ 0 is the initial Lorentz factor. So we can obtain the value of Γ 0 θ 0 through fitting the light curves. We find that for GRB990123 and GRB000926, the jet model can fit the light curves well, and the values of Γ 0 θ 0 is about 15 and 10 respectively. While for GRB990510 and GRB000301c, their light curves cannot be fitted by the jet model , which suggests that the breaks may be caused by some other reasons , jet may be not the unique reason.