Spectral lag of gamma-ray burst caused by the intrinsic spectral evolution and the curvature effect

Assuming an intrinsic `Band' shape spectrum and an intrinsic energy-independent emission profile we have investigated the connection between the evolution of the rest-frame spectral parameters and the spectral lags measured in gamma-ray burst (GRB) pulses by using a pulse model. We first focus our attention on the evolution of the peak energy, $E_{0,p}$, and neglect the effect of the curvature effect. It is found that the evolution of $E_{0,p}$ alone can produce the observed lags. When $E_{0,p}$ varies from hard to soft only the positive lags can be observed. The negative lags would occur in the case of $E_{0,p}$ varying from soft to hard. When the evolution of $E_{0,p}$ and the low-energy spectral index $\alpha_{0}$ varying from soft to hard then to soft we can find the aforesaid two sorts of lags. We then examine the combined case of the spectral evolution and the curvature effect of fireball and find the observed spectral lags would increase. A sample including 15 single pulses whose spectral evolution follows hard to soft has been investigated. All the lags of these pulses are positive, which is in good agreement with our theoretical predictions. Our analysis shows that only the intrinsic spectral evolution can produce the spectral lags and the observed lags should be contributed by the intrinsic spectral evolution and the curvature effect. But it is still unclear what cause the spectral evolution.