Chinese Journal of Astronomy and Astrophysics The Relationship between the Rise Width and the Full Width of γ-ray Burst Pulses and Its Implications ∗

Abstract 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 Γ−2∆τθ,FWHM Rc c (Γ the Lorentz factor of the bulk motion, ∆τθ,FWHM a local pulse’s width, Rc 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