A Dense-Cloud Model for Gamma-Ray Bursts to Explain Bimodality

In this model a collimated ultra-relativistic ejecta collides with an amorphous dense cloud surrounding the central engine, producing gamma-rays via synchrotron process. The ejecta is taken as a standard candle, while assuming a gaussian distribution in thickness and density of the surrounding cloud. Due to the cloud high density, the synchrotron emission would be an instantaneous phenomenon (fast cooling synchrotron radiation), so a GRB duration corresponds to the time that the ejecta takes to pass through the cloud. Fitting the model with the observed bimodal distribution of GRBs' durations, the ejecta's initial Lorentz factor, and its initial opening angle are obtained as $\Gamma_{0}\lesssim 10^{3}$, and $\zeta_{0} \approx 10^{-2}$, and the mean density and mean thickness of the surrounding cloud as $\bar{n} \sim 3 \times 10^{17} cm^{-3}$ and $\bar{L} \sim 2 \times 10^{13} cm$. The clouds maybe interpreted as the extremely amorphous envelops of Thorne-Zytkow objects. In this model the two classes of long and short duration GRBs are explained in a unique frame.