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

We present a simple, semi-analytical model to explain gamma-ray burst 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 the electron Lorentz factor. We find E_p α t ^-δ with δ = 7/2, which is much steeper than the observed slopes δobs ≲ 1.5. We therefore consider the possibility that the equipartition parameters depend on the shock strength and post-shock density. We then obtain 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. Finally, we compare our predicted time-lagluminosity relation with the result of Morris, Marani & Bonnell obtained from six bursts with known redshift.