The Relationship between the Power-Law Indices of the Temporal Properties on Energy and the Spectral Lag and Photon Flux of Gamma-Ray Burst Pulses

Abstract

Abstract Previous studies have shown that the dependence of the pulse temporal properties (pulse width, pulse rise width, pulse decay width, and pulse peak time) on energy is a power-law function. In this work we demonstrate that the power-law indices of the pulse width, pulse rise width, pulse decay width, and pulse peak time on energy are correlated with the spectral lag and the relative spectral lag, $ \bigtriangleup t_{31}/w_{3}$ (where $ \bigtriangleup t_{31}$ and $ w_{3}$ are the spectral lag between BATSE channels 1 and 3 and the pulse width of BATSE channel 3, respectively), using a sample including 102 well-separated long-duration gamma-ray burst pulses. In addition, the correlations of the power-law indices with the relative spectral lags are much more tighter than those with the spectral lags. We further find that the power-law indices are also correlated with the pulse photon flux. The possible origins of these correlations are also discussed. We argue that the kinematic effect can explain the correlated properties.