Relationship between the rise width and the full width of gamma-ray burst pulses and its implications in terms of the fireball model

Kocevski et al. (2003) found that there is a linear relation between the rise width and the full width of gamma-ray burst pulses detected by the BATSE instrument based on their empirical functions. Motivated by this, we investigate the relationship based on Qin et al. (2004) model. Theoretical analysis shows that each of the two quantities, the rise width and the full width of observed pulse, is proportional to $\Gamma^{-2}\Delta\tau_{\theta,\rm FWHM}\frac{R_c}{c}$, where $\Gamma$ is the Lorentz factor for the bulk motion, $\Delta \tau_{\theta,\rm FWHM}$ is a local pulse's width, $R_{c}$ is the radius of fireballs and c is the velocity of light. We employ the observed pulses coming from four samples to study the relationship and find that: (1) Merely the curvature effect could produce the relationship with the same slope as those derived from Qin et al. (2004) model in the rise width vs. the full width panel. (2) Gamma-ray burst pulses, long or short ones (selected from the short and long GRBs), follow the same sequence in the rise width vs. the full width panel, with the shorter pulses at the end of this sequence. (3) All GRBs may intrinsically result from local Gaussian pulses. These features place constraints on the physical mechanism(s) for producing long and short GRBs.