Pulse width evolution in gamma-ray bursts: Evidence for internal shocks

Many cosmological models of gamma-ray bursts (GRBs) envision the energy sou rce to be a cataclysmic stellar event leading to a relativistically expandi ng fireball. Particles are thought to be accelerated at shocks and produce nonthermal radiation. The highly variable temporal structure observed in mo st GRBs has significantly constrained models. By using different methods of statistical analysis in the time domain, we find that the width of the lar ge-amplitude pulses in GRB time histories remains remarkably constant throu ghout the classic GRB phase. This is also true for small-amplitude pulses. However, small and large pulses do not have the same pulse width within a s ingle time history. We find a quantitative relationship between pulse ampli tude and pulse width: the smaller amplitude peaks tend to be wider, with th e pulse width following a power law with an index of about -2.8. Internal s hocks simulated by randomly selecting the Lorentz factor and energy per she ll are consistent with a power-law relationship. This is strong quantitativ e evidence that GRBs are indeed caused by internal shocks. The dependency o f the width-versus-intensity relationship on the maximum Lorentz factor pro vides a way to estimate that elusive parameter. Our observed power-law inde x indicates that Gamma(max) is less than or similar to 10(3). We also inter pret the narrowness of the pulse width distribution as indicating that the emission that occurs when one shell overtakes another is produced over a sm all range of distances from the central site.