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 qu
antities (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.
We study the observed correlations between the duration and luminosity of the early afterglow plateau and the isotropic gamma-ray energy release during the prompt phase. We discuss these correlations in the context of two scenarios for the origin of
the plateaus. In the first one the afterglow is made by the forward shock and the plateau results from variations of the microphysics parameters while in the second one the early afterglow is made by a long-lived reverse shock propagating in a low Lorentz factor tail of the ejecta.
GRB spectra appear non-thermal, but recent observations of a few bursts with Fermi GBM have confirmed previous indications from BATSE of the presence of an underlying thermal component. Photospheric emission is indeed expected when the relativistic o
utflow emerging from the central engine becomes transparent to its own radiation, with a quasi-blackbody spectrum in absence of additional sub-photospheric dissipation. However, its intensity strongly depends on the acceleration mechanism - thermal or magnetic - of the flow. We aim to compute the thermal and non-thermal emissions produced by an outflow with a variable Lorentz factor, where the power injected at the origin is partially thermal (fraction epsilon_th) and partially magnetic (fraction 1-epsilon_th). The thermal emission is produced at the photosphere, and the non-thermal emission in the optically thin regime. Apart from the value of epsilon_th, we want to test how the other model parameters affect the observed ratio of the thermal to non-thermal emission. If the non-thermal emission is made by internal shocks, we self-consistently obtained the light curves and spectra of the thermal and non-thermal components for any distribution of the Lorentz factor in the flow. If the non-thermal emission results from magnetic reconnection we were unable to produce a light curve and could only compare the respective non-thermal and thermal spectra. In the different considered cases, we varied the model parameters to see when the thermal component in the light curve and/or spectrum is likely to show up or, on the contrary, to be hidden. We finally compared our results to the proposed evidence for the presence of a thermal component in GRB spectra. Focussing on GRB 090902B and GRB 10072B, we showed how these observations can be used to constrain the nature and acceleration mechanism of GRB outflows.
The Swift-XRT observations of the early X-ray afterglow of GRBs show that it usually begins with a steep decay phase. A possible origin of this early steep decay is the high latitude emission that subsists when the on-axis emission of the last dissip
ating regions in the relativistic outflow has been switched-off. We wish to establish which of various models of the prompt emission are compatible with this interpretation. We successively consider internal shocks, photospheric emission, and magnetic reconnection and obtain the typical decay timescale at the end of the prompt phase in each case. Only internal shocks naturally predict a decay timescale comparable to the burst duration, as required to explain XRT observations in terms of high latitude emission. The decay timescale of the high latitude emission is much too short in photospheric models and the observed decay must then correspond to an effective and generic behavior of the central engine. Reconnection models require some ad hoc assumptions to agree with the data, which will have to be validated when a better description of the reconnection process becomes available.
GRB 080503, detected by Swift, belongs to the class of bursts whose prompt phase consists of an initial short spike followed by a longer soft tail. It did not show any transition to a regular afterglow at the end of the prompt emission but exhibited
a surprising rebrightening after one day. We aim to explain this rebrightening with two different scenarios - refreshed shocks or a density clump in the circumburst medium - and two models for the origin of the afterglow, the standard one where it comes from the forward shock, and an alternative one where it results from a long-lived reverse shock. We computed afterglow light curves either using a single-zone approximation for the shocked region or a detailed multizone method that more accurately accounts for the compression of the material. We find that in several of the considered cases the detailed model must be used to obtain a reliable description of the shock dynamics. The density clump scenario is not favored. We confirm previous results that the presence of the clump has little effect on the forward shock emission, except if the microphysics parameters evolve when the shock enters the clump. Moreover, we find that the rebrightening from the reverse shock is also too weak when it is calculated with the multi-zone method. On the other hand, in the refreshed-shock scenario both the forward and reverse shock models provide satisfactory fits of the data under some additional conditions on the distribution of the Lorentz factor in the ejecta and the beaming angle of the relativistic outflow.
Recent detections of GeV photons in a few GRBs by Fermi-LAT have led to strong constraints on the bulk Lorentz factor in GRB outflows. To avoid a large gamma-gamma optical depth, minimum values of the Lorentz factor have been estimated to be as high
as 800-1200 in some bursts. Here we present a detailed calculation of the gamma-gamma optical depth taking into account both the geometry and the dynamics of the jet. In the framework of the internal shock model, we compute lightcurves in different energy bands and the corresponding spectrum and we show how the limits on the Lorentz factor can be significantly lowered compared to previous estimates. Our detailed model of the propagation of high energy photons in GRB outflows is also appropriate to study many other consequences of gamma-gamma annihilation in GRBs: (i) the gamma-gamma cutoff transition in a time-integrated spectrum is expected to be closer to a power-law steepening of the spectrum than to a sharp exponential decay; (ii) the temporal evolution of the gamma-gamma opacity during a burst favors a delay between the MeV and GeV light curves; (iii) for complex GRBs, the gamma-gamma opacity suppresses the shortest time-scale features in high energy light curves (above 100 MeV). Finally we also consider GRB scenarii where MeV and GeV photons are not produced at the same location, showing that the gamma-gamma opacity could be further lowered, reducing even more the constraint on the minimum Lorentz factor.
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.
Recent detections of GeV photons in a few GRBs by Fermi-LAT imply huge bulk Lorentz factors to avoid a large gamma gamma optical depth at high energy. Estimates can be as high as Gamma ~ 1000 in the most extreme cases. This puts severe constraints on
models of the central engine and the jet acceleration in GRBs. These estimates are however obtained from a simplified single zone model. We present here a more realistic calculation which takes into account the time, space and direction dependent photon field existing in an outflow with several relativistically moving emitting zones. The formalism is general and can be applied to many models of the prompt GRB emission. We present results obtained for a numerical implementation in the framework of the internal shock model. We show that (i) the minimum Lorentz factor Gamma_min in bright LAT GRBs is reduced by a factor ~ 2-3 compared to previous estimates if the GeV and MeV emission are produced in the same region, and by an additional factor ~ 2-8 if the GeV emission is produced at larger radii. We provide an improved approximate formula for Gamma_min which is in good agreement with our numerical results and can be directly applied to LAT GRB data; (ii) a delayed GeV onset can be due to the time evolution of the opacity. As an illustration of these two first results, we present a synthetic GRB that reproduces most features of GRB 080916C with a mean Lorentz factor of ~ 340, an optically thin regime for gamma gamma opacity at 3GeV in bin b, a variability timescale of 0.5s in the MeV lightcurve and a delayed onset of ~ 5s of the GeV emission; (iii) the gamma gamma opacity can smooth the short timescale variability in the GeV lightcurve. This last result implies that the observed variability at high energy is not necessarily a good test to distinguish between an internal and an external origin for the GeV emission in GRBs. [abridged]
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 i
f 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.
(abridged) The association of GRB 980425 with SN 1998bw at z=0.0085 implies the existence of a population of GRBs with an isotropic-equivalent luminosity which is about 10^4 times smaller than in the standard cosmological case. We investigate two sce
narios to explain a weak GRB : a normal (intrinsically bright) GRB seen off-axis or an intrinsically weak GRB seen on-axis. For each of these two scenarios, we first derive the conditions to produce a GRB 980425-like event and we then discuss the consequences for the event rate. If we exclude the possibility that GRB 980425 is an occurence of an extremely rare event observed by chance during the first eight years of the afterglow era, the first scenario implies that (i) the local rate of standard bright GRBs is much higher than what is usually expected; (ii) the typical opening angle is much narrower than what is derived from observations of a break in the afterglow lightcurve. In addition, we show that the afterglow of GRB 980425 in this scenario should have been very bright and easily detected. For these reasons the second scenario appears more realistic. We show that the parameter space of the internal shock model indeed allows GRB 980425-like events, in cases where the outflow is only mildly-relativistic and mildly-energetic. The rate of such weak events in the Universe has to be much higher than the rate of standard bright GRBs to allow the discovery of GRB 980425 during a short period of a few years. However it is still compatible with the observations as the intrinsic weakness of these GRB 980425-like bursts does not allow detection at cosmological redshift. We finally briefly discuss the consequences of such a high local rate of GRB 980425-like events for the future prospects of detecting non-electromagnetic radiation, especially gravitational waves.
