Different features of jets and isotropic fireballs in gamma-ray burst phase

We investigated physical quantities including the spectrum, emission lilies and pulse profiles expected from a uniform jet, a spherical fireball and the 1/Gamma region (the portion of the spherical fireball with opening angle 1/Gamma) in the prompt emission phase, after taking into consideration of the Doppler effect under the fireball framework. Our study shows that: a) for these physical quantities the spherical fireball and the uniform jets do not present obvious differences, so we cannot use these to distinguish a spherical fireball from a uniform jet; b) for the spherical fireball and a uniform jet, the observed quantities mainly come from the 1/Gamma region, so we can simply use the 1/Gamma region in approximate calculations; c) broadening of emission lines is a general phenomena, which mainly comes from the curvature effect; d) the 1/Gamma region plays different roles in different frequency ranges, and the radiation from the 1/Gamma region is greater in the higher than in the lower frequencies.