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 } ^ { \prime } and the fireball radius R .
It is shown that approximately the lag \propto \Gamma ^ { -1 } and \propto t _ { d } ^ { \prime } , 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 .