Spectral lags and the energy dependence of pulse width in gamma-ray   bursts: contributions from the relativistic curvature effect
  We compute the temporal profiles of the gamma-ray burst pulse in the four Burst and Transient Source Experiment (BATSE) Large Area Detector (LAD) discriminator energy channels, with the relativistic curvature effect of a expanding fireball being explicitly investigated. Assuming an intrinsic 'Band' shape spectrum and an intrinsic energy-independent emission profile, we show that merely the curvature effect can produce detectable spectral lags if the intrinsic pulse profile has a gradually decaying phase. We examine the spectral lag's dependences on some physical parameters, such as the Lorentz factor \Gamma, the low-energy spectral index, \alpha, of the intrinsic spectrum, the duration of the intrinsic radiation t_d' and the fireball radius R. It is shown that approximately the lag \propto \Gamma ^{-1} and \propto t_d', and a spectrum with a more extruded shape (a larger \alpha) causes a larger lag. We find no dependence of the lag on R. Quantitatively, the lags produced from the curvature effect are marginally close to the observed ones, while larger lags require extreme physical parameter values, e.g., \Gamma < 50, or \alpha > -0.5. The curvature effect causes an energy-dependent pulse width distribution but the energy dependence of the pulse width we obtained is much weaker than the observed W \propto E^{-0.4} one. This indicates that some intrinsic mechanism(s), other than the curvature effect, dominates the pulse narrowing of GRBs. 
R.-F. Shen, L.-M. Song, Z. Li