1 Introduction

The cosmological origin of GRBs, established as a result of optical follow-up observations of fading X-ray counterparts to GRBs, requires an extraordinarily large amount of energy to flood the entire universe with gamma rays. The lack of apparent photon-photon attenuation of high energy photons implies substantial bulk relativistic motion. The bulk Lorentz factor, $\Gamma=(1-\beta^{2})^{-1/2}$, must be on the order of 10² to 10³. Two major scenarios involving relativistic shells have been developed. In the external shock models, a relativistic shell, that expands outward for a long period of time, is generated by a single release of energy during the merger. The shell coasts in a gamma-ray quiet phase for a certain period. Eventually, the shell becomes gamma-ray active due to the interactions with the external medium. If the shell has a velocity, $v=\beta c$, then the photons emitted on axis over a period t' ("proper time'' in the comoving frame of the shell) arrive at a detector over a much shorter period, $T={t' \over 2\Gamma}$. The duration of the event is set by the expansion of the shell and the complex temporal structure is due to inhomogeneities in the shell and/or the ambient material. The alternative theory is that a central site releases energy in the form of a wind or multiple shells over a period of time commensurate with the observed duration of GRB. Each subpeak in the GRB is the result of a separate explosive event in the central site. If the emission sites do indeed lie on a relativistically expanding shell, the pulse width in the time GRBs histories scales as $\Delta T=\Lambda\Delta t'$, where $\Lambda$ is the Doppler factor, $\Lambda=\Gamma(1-\beta \cos\theta)$. Here $\theta$ is the angle of the motion of the emitting region with respect to the direction of the emission. In this paper, we proposed to determine the angular spread of the emitting region and the amount of deceleration from the time histories of many GRBs.

  

Figure 1: Average peak alignment from 53 bright BATSE bursts with durations longer than 20 s. The three curves show the average pulse shape for the largest peak in the first third, second third, and last third of the bursts. We find no significant change, during the gamma-ray phase, in the average peak width over at least 2/3 of T90. Models should account this empirical trend in GRB physics