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.
In the neutron-rich internal shocks model for gamma-ray bursts (GRBs), the Lorentz factors (LFs) of ion shells are variable, and so are the LFs of accompanying neutron shells. For slow neutron shells with a typical LF of approximate tens, the typical
$beta$-decay radius is $sim 10^{14}-10^{15}$ cm. As GRBs last long enough [$T_{90}>14(1+z)$ s], one earlier but slower ejected neutron shell will be swept successively by later ejected ion shells in the range $sim10^{13}-10^{15}$ cm, where slow neutrons have decayed significantly. Part of the thermal energy released in the interaction will be given to the electrons. These accelerated electrons will be mainly cooled by the prompt soft $gamma-$rays and give rise to GeV emission. This kind of GeV emission is particularly important for some very long GRBs and is detectable for the upcoming satellite {it Gamma-Ray Large Area Space Telescope} (GLAST).
The dust extinction of gamma-ray bursts (GRBs) host galaxies, containing important clues to the nature of GRB progenitors and crucial for dereddening, is still poorly known. Here we propose a straightforward method to determine the extinction of GRB
host galaxies by comparing the observed optical spectra to the intrinsic ones extrapolated from the X-ray spectra. The rationale for this method is from the standard fireball model: if the optical flux decay index equals to that of the X-ray flux, then there is no break frequency between the optical and X-ray bands, therefore we can derive the intrinsic optical flux from the X-ray spectra. We apply this method to three GRBs of which the optical and X-ray fluxes have the same decay indices and another one with inferred cooling break frequency, and obtain the rest-frame extinction curves of their host galaxies. The derived extinction curves are gray and do not resemble any extinction curves of local galaxies (e.g. the Milk Way, the Small/Large Magellanic Clouds, or nearby starburst galaxies). The amount of extinction is rather large (with visual extinction $A_V$ $sim$ 1.6--3.4$magni$). We model the derived extinction curves in terms of the silicate-graphite interstellar grain model. As expected from the ``gray nature of the derived extinction curve, the dust size distribution is skewed to large grains. We determine, for the first time, the local dust-to-gas ratios of GRB host galaxies using the model-derived dust parameters and the hydrogen column densities determined from X-ray absorptions.
