The possible high-energy emission from GRB 080319B and origins of the GeV emission of GRBs 080514B, 080916C and 081024B

We calculate the high-energy (sub-GeV to TeV) prompt and afterglow emission of GRB 080319B that was distinguished by a naked-eye optical flash and by an unusual strong early X-ray afterglow. There are three possible sources for high-energy emission: the prompt optical and γ-ray photons IC scattered by the accelerated electrons, the prompt photons IC scattered by the early external reverse-forward shock electrons, and the higher band of the synchrotron and the synchrotron self-Compton emission of the external shock. There should have been in total hundreds of high-energy photons detectable for the Large Area Telescope onboard the Fermi satellite, and tens of photons of those with energy >10 GeV. The >10 GeV emission had a duration about twice that of the soft γ-rays. Astro-rivelatore Gamma a Immagini Leggero (AGILE) could have observed these energetic signals if it was not occulted by the Earth at that moment. The physical origins of the high-energy emission detected in GRB 080514B, GRB 080916C and GRB 081024B are also discussed. These observations seem to be consistent with the current high-energy emission models.     

Relativistic blast waves and synchrotron emission

Relativistic shocks can accelerate particles by the first-order Fermi mechanism; the particles then emit synchrotron emission in the post-shock gas. This process is of particular interest in the models used for the afterglow of gamma-ray bursts. In this paper we use recent results in the theory of particle acceleration at highly relativistic shocks to model the synchrotron emission in an evolving, inhomogeneous and highly relativistic flow. We have developed a numerical code that integrates the relativistic Euler equations for fluid dynamics with a general equation of state, together with a simple transport equation for the accelerated particles. We present tests of this code and, in addition, we use it to study the gamma-ray burst afterglow predicted by the fireball model, along with the hydrodynamics of a spherically-symmetric relativistic blast wave.
We find that, while broadly speaking the behaviour of the emission is similar to that already predicted with semi-analytic approaches, the detailed behaviour is somewhat different. The 'breaks' in the synchrotron spectrum behave differently with time, and the spectrum above the final break is harder than had previously been expected. These effects are due to the incorporation of the geometry of the (spherical) blast wave, along with relativistic beaming and adiabatic cooling of the energetic particles leading to a mix, in the observed spectrum, between recently injected 'uncooled' particles and the older 'cooled' population in different parts of the evolving, inhomogeneous flow.     

The Prompt Ultraviolet/Soft X-ray Emission of GRBs

We discuss the prompt emission of gamma-ray bursts (GRBs), allowing for γγ pair production and synchrotron self-absorption. The observed hard spectra suggest heavy pair-loading in GRBs. The re-emission of the generated pairs results in the energy transmission from high-energy gamma-rays to long-wavelength radiation. Due to strong self-absorption, the synchrotron radiation by pairs is in optically thick regime. Thus, the re-emission would appear as a thermal-like spectral bump in the extreme-ultraviolet/soft X-ray band, other than the peak from the main burst. The confirmation of the thermal-like feature and the double-peak structure by future satellites, such as Swift, would indicate that the dominant radiation mechanism in GRBs is synchrotron rather than inverse-Compton radiation.     

Adiabatic expansion, early X-ray data and the central engine in GRBs

The Swift satellite early X-ray data show a very steep decay in most of the gamma-ray bursts light curves. This decay is either produced by the rapidly declining continuation of the central engine activity or by some leftover radiation starting right after the central engine shuts off. The latter scenario consists of the emission from an 'ember' that cools via adiabatic expansion and, if the jet angle is larger than the inverse of the source Lorentz factor, the large angle emission. In this work, we calculate the temporal and spectral properties of the emission from such a cooling ember, providing a new treatment for the microphysics of the adiabatic expansion. We use the adiabatic invariance of   p ²_⊥/ B ( p _⊥  is the component of the electrons' momentum normal to the magnetic field, B ) to calculate the electrons' Lorentz factor during the adiabatic expansion; the electron momentum becomes more and more aligned with the local magnetic field as the expansion develops. We compare the theoretical expectations of the adiabatic expansion (and the large angle emission) with the current observations of the early X-ray data and find that only ∼20 per cent of our sample of 107 bursts are potentially consistent with this model. This leads us to believe that, for most bursts, the central engine does not turn off completely during the steep decay of the X-ray light curve; therefore, this phase is produced by the continued rapidly declining activity of the central engine.     

Overall temporal synchrotron emissions from relativistic jets: adiabatic and radiative breaks

We discuss the afterglow emission from a relativistic jet that is initially in the radiative regime, in which the accelerated electrons are fast-cooling. We note that such a 'semiradiative' jet decelerates faster than an adiabatic jet does. We also take into account the effect of strong inverse-Compton scattering on the cooling frequency in the synchrotron component and therefore on the light-curve decay index. We find that there are two kinds of light-curve break for the jet effect. The first is an 'adiabatic break', if the electrons become slow-cooling before the jet enters a spreading phase, and the second is a 'radiative break', which appears in the contrary case. We then show how a relativistic jet evolves dynamically and derive the overall temporal synchrotron emission in both cases, focusing on the change in the light-curve decay index around the break time. Finally, in view of our results, we rule out two cases for relativistic jets which do not account for the observed light-curve breaks in a few afterglows : (i) an adiabatic jet with strong Compton cooling  ( Y >1)  and with the cooling frequency ν _c locating in the observed energy range; (ii) a radiative jet with a significant fraction of total energy occupied by electrons  ( ε _e ∼1)  .     

Possible effects of pair echoes on gamma-ray burst afterglow emission

High-energy emission from gamma-ray bursts (GRBs) is widely expected but had been sparsely observed until recently when the Fermi satellite was launched. If >TeV gamma-rays are produced in GRBs and can escape from the emission region, they are attenuated by the cosmic infrared background photons, leading to regeneration of ∼GeV–TeV secondary photons via inverse-Compton scattering. This secondary emission can last for a longer time than the duration of GRBs, and it is called a pair echo. We investigate how this pair echo emission affects spectra and light curves of high-energy afterglows, considering not only prompt emission but also afterglow as the primary emission. Detection of pair echoes is possible as long as the intergalactic magnetic field (IGMF) in voids is weak. We find (1) that the pair echo from the primary afterglow emission can affect the observed high-energy emission in the afterglow phase after the jet break and (2) that the pair echo from the primary prompt emission can also be relevant, but only when significant energy is emitted in the TeV range, typically     . Even non-detections of the pair echoes could place interesting constraints on the strength of IGMF. The more favourable targets to detect pair echoes may be the 'naked' GRBs without conventional afterglow emission, although energetic naked GRBs would be rare. If the IGMF is weak enough, it is predicted that the GeV emission extends to >30–300 s.     

GeV emission from gamma-ray burst afterglows

We calculate the GeV afterglow emission expected from a few mechanisms related to gamma-ray bursts (GRBs) and their afterglows. Given the brightness of the early X-ray afterglow emission measured by Swift /X-Ray Telescope, Gamma-ray Large Area Space Telescope (GLAST)/Large Area Telescope (LAT) should detect the self-Compton emission from the forward shock driven by the GRB ejecta into the circumburst medium. Novel features discovered by Swift in X-ray afterglows (plateaus and chromatic light-curve breaks) indicate the existence of a pair-enriched, relativistic outflow located behind the forward shock. Bulk and inverse-Compton upscattering of the prompt GRB emission by such outflows provide another source of GeV afterglow emission detectable by LAT. The large-angle burst emission and synchrotron forward-shock emission are, most likely, too dim at high photon energy to be observed by LAT. The spectral slope of the high-energy afterglow emission and its decay rate (if it can be measured) allow the identification of the mechanism producing the GeV transient emission following GRBs.     

X-ray flares, plateaus and chromatic breaks of GRB afterglows from up-scattered forward-shock emission

Scattering of the forward-shock synchrotron emission by a relativistic outflow located behind the leading blast wave may produce an X-ray emission brighter than that coming directly from the forward shock and may explain four features displayed by Swift X-ray afterglows: flares, plateaus (slow decays), chromatic light-curve breaks and fast post-plateau decays. For a cold scattering outflow, the reflected flux overshines the primary one if the scattering outflow is nearly baryon-free and highly relativistic. These two requirements can be relaxed if the scattering outflow is energized by weak internal shocks, so that the incident forward-shock photons are also inverse-Compton scattered, in addition to bulk scattering. Sweeping-up of the photons left behind by the forward shock naturally yields short X-ray flares. Owing to the boost in photon energy produced by bulk scattering, the reflected emission is more likely to overshine that coming directly from the forward shock at higher photon energies, yielding light-curve plateaus and breaks that appear only in the X-ray. The brightness, shape and decay of the X-ray light-curve plateau depend on the radial distribution of the scatterer's Lorentz factor and mass flux. Chromatic X-ray light-curve breaks and sharp post-plateau decays cannot be accommodated by the direct forward-shock emission and argue in favour of the scattering-outflow model proposed here. On the other hand, the X-ray afterglows without plateaus, those with achromatic breaks and those with very long lived power-law decays are more naturally accommodated by the standard forward-shock model. Thus, the diversity of X-ray light curves arises from the interplay of the scattered and direct forward-shock emissions.     

Reverse shock emission as a probe of gamma-ray burst ejecta

We calculate the reverse shock (RS) synchrotron emission in the optical and the radio wavelength bands from electron–positron pair-enriched gamma-ray burst ejecta with the goal of determining the pair content of gamma-ray bursts (GRBs) using early-time observations. We take into account an extensive number of physical effects that influence radiation from the RS-heated GRB ejecta. We find that optical/infrared flux depends very weakly on the number of pairs in the ejecta, and there is no unique signature of ejecta pair enrichment if observations are confined to a single wavelength band. It may be possible to determine if the number of pairs per proton in the ejecta is ≳100 by using observations in optical and radio bands; the ratio of flux in the optical and radio at the peak of each respective RS light curve is dependent on the number of pairs per proton. We also find that over a large parameter space, RS emission is expected to be very weak; GRB 990123 seems to have been an exceptional burst in that only a very small fraction of the parameter space produces optical flashes this bright. Also, it is often the case that the optical flux from the forward shock is brighter than the RS flux at deceleration. This could be another possible reason for the paucity of prompt optical flashes with a rapidly declining light curve at early times as was seen in GRBs 990123 and 021211. Some of these results are a generalization of similar results reported in Nakar & Piran.     

Gamma-ray burst afterglows: effects of radiative corrections and non-uniformity of the surrounding medium

The afterglow of a gamma-ray burst (GRB) is commonly thought to be the result of continuous deceleration of a relativistically expanding fireball in the surrounding medium. Assuming that the expansion of the fireball is adiabatic and that the density of the medium is a power-law function of shock radius, i.e. n _ext ∝  R ^{− k} , we study the effects of the first-order radiative correction and the non-uniformity of the medium on a GRB afterglow analytically. We first derive a new relation among the observed time, the shock radius and the Lorentz factor of the fireball: t _⊕ =  R /4(4− k ) γ²c, and also derive a new relation among the comoving time, the shock radius and the Lorentz factor of the fireball: t _co = 2 R /(5− k ) γc. We next study the evolution of the fireball by using the analytic solution of Blandford &38; McKee. The radiation losses may not significantly influence this evolution. We further derive new scaling laws both between the X-ray flux and observed time and between the optical flux and observed time. We use these scaling laws to discuss the afterglows of GRB 970228 and GRB 970616, and find that if the spectral index of the electron distribution is p  = 2.5, implied from the spectra of GRBs, the X-ray afterglow of GRB 970616 is well fitted by assuming k  = 2.     

A unified picture for the γ-ray and prompt optical emissions of GRB 990123

The prompt optical emission of GRB 990123 was uncorrelated to the γ-ray light curve and exhibited temporal properties similar to those of the steeply decaying, early X-ray emission observed by Swift at the end of many bursts. These facts suggest that the optical counterpart of GRB 990123 was the large-angle emission released during (the second pulse of) the burst. If the optical and γ-ray emissions of GRB 990123 have, indeed, the same origin then their properties require that (i) the optical counterpart was synchrotron emission and γ-rays arose from inverse-Compton scatterings (the 'synchrotron self-Compton model'), (ii) the peak energy of the optical-synchrotron component was at ∼20 eV and (iii) the burst emission was produced by a relativistic outflow moving at Lorentz factor  ≳450  and at a radius  ≳10¹⁵  cm, which is comparable to the outflow deceleration radius. Because the spectrum of GRB 990123 was optically thin above 2 keV, the magnetic field behind the shock must have decayed on a length-scale of  ≲1  per cent  of the thickness of the shocked gas, which corresponds to  10⁶–10⁷  plasma skin depths. Consistency of the optical counterpart decay rate and its spectral slope (or that of the burst, if they represent different spectral components) with the expectations for the large-angle burst emission represents the most direct test of the unifying picture proposed here for GRB 990123.     

Testing the blast wave model with Swift GRBs

The complex structure of the light curves of Swift Gamma-Ray Bursts (GRBs) has made the identification of breaks, and the interpretation of the blast wave caused by the burst, more difficult than in the pre- Swift era. We aim to identify breaks, which are possibly hidden, and to constrain the blast wave parameters; electron energy distribution, p , density profile of the circumburst medium, k , and the continued energy injection index, q . We do so by comparing the observed multiwavelength light curves and X-ray spectra of our sample to the predictions of the blast wave model. We can successfully interpret all of the bursts in our sample of 10, except two, within this framework and we can estimate, with confidence, the electron energy distribution index for 6 of the sample. Furthermore, we identify jet breaks in a number of the bursts. A statistical analysis of the distribution of p reveals that, even in the most conservative case of least scatter, the values are not consistent with a single, universal value. The values of k suggest that the circumburst density profiles are not drawn from only one of the constant density or wind-like media populations.