The relationship between the rise width and the full width of γ-ray burst pulses and its implications

We investigate the relationship between the rise width and the full width of gamma-ray burst pulses. Theoretical analysis shows that either width is proportional to Gamma(-2) Delta(T theta), FWHM (Rc)/(c) (Gamma the Lorentz factor of the bulk motion, Delta(T theta), FWHM a local pulse's width, R-c the radius of fireballs and c the velocity of light). We study the relationship for four samples of observed pulses. We find: (1) merely the curvature effect could reproduce the relationship between the rise and full widths with the same slope as derived from the model of Qin et al.; (2) gamma-ray burst pulses, selected from both the short and long GRBs, follow the same sequence in the rise width vs. full width diagram, with the shorter pulses at one end; (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.