Early afterglow emission as a probe of the density profile of the medium surrounding gamma-ray bursts

The gamma-ray bursts (GRBs) with durations longer than 2 seconds, namely long gamma-ray bursts, are believed to have a massive star progenitor and should be born in the free stellar wind medium holding up to a radius > 10<SUP>17</SUP>cm. We propose to constrain the density profile of the medium with the early afterglow data and find out that for the interstellar medium (ISM) an early rapid increase of the afterglow flux is possible while in the free wind medium there is no such a signature. For GRB 060418 and GRB 060607A we show that the data is well consistent with the ISM model and the number density is low. While for GRB 081109A, the X-ray and optical data are consistent with the forward shock emission of an ultra-relativistic ejecta expanding into a wind bubble, in which the free wind terminates at a radius ˜ 4.510<SUP>17</SUP>cm, beyond which the medium is ISM-like. The implication of these results has been discussed.