The physics of pulses in gamma-ray bursts: emission processes, temporal profiles and time lags

Abstract

We present a simple, semi-analytical model to explain GRB temporal and spectral properties in the context of the internal shock model. Each individual pulse in the temporal profiles is produced by the deceleration of fast moving material by a comparatively slower layer within a relativistic wind. The spectral evolution of synthetic pulses is first obtained with standard equipartition assumptions to estimate the post-shock magnetic field and electron Lorentz factor. We get Ep propto t^-delta with delta=7/2 which is much steeper than the observed slopes delta(obs) <= 1.5. We therefore consider the possibility that the equipartition parameters depend on the shock strength and post-shock density. We then get a much better agreement with the observations and our synthetic pulses satisfy both the hardness-intensity and hardness-fluence correlations. We also compute time lags between profiles in different energy channels and we find that they decrease with increasing hardness. We finally compare our predicted time lag - luminosity relation to the Norris et al. (2000) result obtained from 6 bursts with known redshift.