The initial Lorentz factors of fireballs inferred from the early X-ray data of SWIFT GRBs

Abstract

We intend to determine the type of circumburst medium and measure directly the initial Lorentz factor ${\Gamma }_0$ of GRB outflows. If the early X-ray afterglow lightcurve has a peak and the whole profile across the peak is consistent with the standard external shock model, the early rise profile of light curves can be used to differentiate whether the burst was born in interstellar medium (ISM) or in stellar wind. In the thin shell case, related to a sub-relativistic reverse shock, the peak time occurring after the end of the prompt emission, can be used to derive an accurate ${\Gamma }_0$, especially for the ISM case. The afterglow lightcurves for a flat electron spectrum $1<p<2$ have been derived analytically. In our GRB sample, we obtain ${\Gamma }_0\sim 300$ for the bursts born in ISM. We did not find any good case for bursts born in stellar wind and behaving as a thin shell that can be used to constrain ${\Gamma }_0$ reliably.

6 pages,1 figure,3 tables,accepted for publication in Astronomy & Astrophysics

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