Rapid fading of optical afterglows as evidence for beaming in gamma-ray bursts

Based on the refined dynamical model proposed by us earlier for beamed γ-ray burst ejecta, we carry out detailed numerical procedure to study those γray bursts with rapidly fading afterglows (i.e., ∼ t). It is found that optical afterglows from GRB 970228, 980326, 980519, 990123, 990510 and 991208 can be satisfactorily fitted if the γ-ray burst ejecta are highly collimated, with a universal initial half opening angle θ0 ∼ 0.1. The obvious light curve break observed in GRB 990123 is due to the relativistic-Newtonian transition of the beamed ejecta, and the rapidly fading optical afterglows come from synchrotron emissions during the mildly relativistic and nonrelativistic phases. We strongly suggest that the rapid fading of afterglows currently observed in some γ-ray bursts is evidence for beaming in these cases.