Astron. Astrophys. 355, L43-L46 (2000)

1. Introduction

The cosmological origin of -ray bursts (GRBs) has been well established due to recent discovery of multi-wavelength afterglows (Costa et al. 1997; Metzger et al. 1997; Galama et al. 1997; Wijers, Rees & Mészáros 1997; Piran 1999). However, we are still far from resolving the puzzle of GRBs, because their "inner engines" are well hidden from direct afterglow observations. Some GRBs localized by BeppoSAX satellite have implied isotropic energy release of more than ergs (Kulkarni et al. 1998, 1999; Andersen et al. 1999; Harrison et al. 1999), which forces many theorists to deduce that GRB radiation must be highly collimated. Obviously, whether GRBs are beamed or not has become one of the most important problems that need to be solved urgently.

In the literature, it is generally believed that afterglows from jetted GRB remnant are characterized by an obvious break in the light curve during the relativistic phase , due to both the jet edge effect (Panaitescu & Mészáros 1999; Kulkarni et al. 1999; Mészáros & Rees 1999) and the lateral expansion effect (Rhoads 1997, 1999). The breaking point is determined by , where is the Lorentz factor of the jet and is the half opening angle. Recently we have developed a refined dynamical model that can correctly describe the overall evolution of an ultra-relativistic jet to non-relativisitic phase with the expanding velocity as small as (Huang et al. 2000a). Surprisingly enough, our detailed numerical results (Huang, Dai & Lu 2000b) show that the break theoretically predicted in light curve does not appear during the relativistic phase , i.e., the time determined by is not a breaking point. However, an obvious break does appear within the relativistic-Newtonian transition region, the degree of which is found to be parameter dependent (Huang, Dai & Lu 2000b). Generally speaking, the Newtonian phase of jet evolution is characterized by a rapid decay of optical afterglows, with the power-law timing index - 2.1.

In practical observations, the power-law decay indices of afterglows from GRB 980326, 980519 and 991208 are anomalously large, (Groot et al. 1998; Owens et al. 1998; Castro-Tirado et al. 1999b), and optical light curves of GRB 990123 and 990510 even show obvious steepening at observing time - 2 d (Kulkarni et al. 1999; Harrison et al. 1999; Castro-Tirado et al. 1999a). Recently GRB 970228 was also reported to have a large index of (Galama et al. 1999b). These phenomena have been widely regarded as evidence for beaming (Sari, Piran & Halpern 1999; Castro-Tirado et al. 1999a). The purpose of this Letter is to study these cases numerically, based on our refined beaming model (Huang et al. 2000a). It is found that optical afterglows from these GRBs can be easily reproduced, thus a jet model is strongly favored.

© European Southern Observatory (ESO) 2000

Online publication: March 21, 2000
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