The early X-ray afterglow of gamma-ray bursts revealed by Swift carried many surprises. We focus in this paper on the plateau phase whose origin remains highly debated. We confront several newly discovered correlations between prompt and afterglow quantities (isotropic emitted energy in gamma-rays, luminosity and duration of the plateau) to several models proposed for the origin of plateaus in order to check if they can account for these observed correlations. We first show that the scenario of plateau formation by energy injection into the forward shock leads to an efficiency crisis for the prompt phase and therefore study two possible alternatives: the first one still takes place within the framework of the standard forward shock model but allows for a variation of the microphysics parameters to reduce the radiative efficiency at early times; in the second scenario the early afterglow results from a long-lived reverse shock. Its shape then depends on the distribution of energy as a function of Lorentz factor in the ejecta. In both cases, we first present simple analytical estimates of the plateau luminosity and duration and then compute detailed light curves. In the two considered scenarios we find that plateaus following the observed correlations can be obtained under the condition that specific additional ingredients are included. In the forward shock scenario, the preferred model supposes a wind external medium and a microphysics parameter epsilon_e that first varies as n^{- u} (n being the external density), with u~1 to get a flat plateau, before staying constant below a critical density n_0. To produce a plateau in the reverse shock scenario the ejecta must contain a tail of low Lorentz factor with a peak of energy deposition at Gamma >~ 10.
Relations linking the temporal or/and spectral properties of the prompt emission of gamma-ray bursts (hereafter GRBs) to the absolute luminosity are of great importance as they both constrain the radiation mechanisms and represent potential distance indicators. Here we discuss two such relations: the lag-luminosity relation and the newly discovered duration-luminosity relation of GRB pulses. We aim to extend our previous work on the origin of spectral lags, using the duration-luminosity relation recently discovered by Hakkila et al. to connect lags and luminosity. We also present a way to test this relation which has originally been established with a limited sample of only 12 pulses. We relate lags to the spectral evolution and shape of the pulses with a linear expansion of the pulse properties around maximum. We then couple this first result to the duration-luminosity relation to obtain the lag-luminosity and lag-duration relations. We finally use a Monte-Carlo method to generate a population of synthetic GRB pulses which is then used to check the validity of the duration-luminosity relation. Our theoretical results for the lag and duration-luminosity relations are in good agreement with the data. They are rather insensitive to the assumptions regarding the burst spectral parameters. Our Monte Carlo analysis of a population of synthetic pulses confirms that the duration-luminosity relation must be satisfied to reproduce the observational duration-peak flux diagram of BATSE GRB pulses. The newly discovered duration-luminosity relation offers the possibility to link all three quantities: lag, duration and luminosity of GRB pulses in a consistent way. Some evidence for its validity have been presented but its origin is not easy to explain in the context of the internal shock model.
The curvature of a relativistic blast wave implies that its emission arrives to observers with a spread in time. This effect is believed to wash out fast variability in the lightcurves of GRB afterglows. We note that the spreading effect is reduced if emission is anisotropic in the rest-frame of the blast wave (i.e. if emission is limb-brightened or limb-darkened). In particular, synchrotron emission is almost certainly anisotropic, and may be strongly anisotropic, depending on details of electron acceleration in the blast wave. Anisotropic afterglows can display fast and strong variability at high frequencies (above the fast-cooling frequency). This may explain the existence of bizarre features in the X-ray afterglows of GRBs, such as sudden drops and flares. We also note that a moderate anisotropy can significantly delay the jet break in the lightcurve, which makes it harder to detect.
