Evidence for chromatic X-ray light-curve breaks in Swift gamma-ray burst afterglows and their theoretical implications

The power-law decay of the X-ray emission of gamma-ray burst (GRB) afterglows 050319, 050401, 050607, 050713A, 050802 and 050922C exhibits a steepening at about 1–4 h after the burst which, surprisingly, is not accompanied by a break in the optical emission. If it is assumed that both the optical and X-ray afterglows arise from the same outflow then, in the framework of the standard forward shock model, the chromaticity of the X-ray light-curve breaks indicates that they do not arise solely from a mechanism related to the outflow dynamics (e.g. energy injection) or the angular distribution of the blast-wave kinetic energy (structured outflows or jets). The lack of a spectral evolution accompanying the X-ray light-curve break shows that these breaks do not arise from the passage of a spectral break (e.g. the cooling frequency) either. Under these circumstances, the decoupling of the X-ray and optical decays requires that the microphysical parameters for the electron and magnetic energies in the forward shock evolve in time, whether the X-ray afterglow is synchrotron or inverse-Compton emission. For a steady evolution of these parameters with the Lorentz factor of the forward shock and an X-ray light curve arising cessation of energy injection into the blast wave, the optical and X-ray properties of the above six Swift afterglows require a circumburst medium with a r ⁻² radial stratification, as expected for a massive star origin for long GRBs. Alternatively, the chromatic X-ray light-curve breaks may indicate that the optical and X-ray emissions arise from different outflows. Neither feature (evolution of microphysical parameters or the different origin of the optical and X-ray emissions) was clearly required by pre-Swift afterglows.     

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.     

A statistical study of gamma-ray burst afterglows measured by the Swift Ultraviolet Optical Telescope

We present the first statistical analysis of 27 Ultraviolet Optical Telescope (UVOT) optical/ultraviolet light curves of gamma-ray burst (GRB) afterglows. We have found, through analysis of the light curves in the observer's frame, that a significant fraction rise in the first 500 s after the GRB trigger, all light curves decay after 500 s, typically as a power law with a relatively narrow distribution of decay indices, and the brightest optical afterglows tend to decay the quickest. We find that the rise could be either produced physically by the start of the forward shock, when the jet begins to plough into the external medium, or geometrically where an off-axis observer sees a rising light curve as an increasing amount of emission enters the observers line of sight, which occurs as the jet slows. We find that at 99.8 per cent confidence, there is a correlation, in the observed frame, between the apparent magnitude of the light curves at 400 s and the rate of decay after 500 s. However, in the rest frame, a Spearman rank test shows only a weak correlation of low statistical significance between luminosity and decay rate. A correlation should be expected if the afterglows were produced by off-axis jets, suggesting that the jet is viewed from within the half-opening angle θ or within a core of a uniform energy density  θ_c  . We also produced logarithmic luminosity distributions for three rest-frame epochs. We find no evidence for bimodality in any of the distributions. Finally, we compare our sample of UVOT light curves with the X-ray Telescope (XRT) light-curve canonical model. The range in decay indices seen in UVOT light curves at any epoch is most similar to the range in decay of the shallow decay segment of the XRT canonical model. However, in the XRT canonical model, there is no indication of the rising behaviour observed in the UVOT light curves.     

Are the missing X-ray breaks in gamma-ray burst afterglow light curves merely hidden?

Gamma-ray burst (GRB) afterglow observations in the Swift era have a perceived lack of achromatic jet breaks compared to the BeppoSAX or pre- Swift era. Specifically, relatively few breaks, consistent with jet breaks, are observed in the X-ray light curves of these bursts. If these breaks are truly missing, it has serious consequences on the interpretation of GRB jet collimation and energy requirements, and the use of GRBs as cosmological tools. Here, we address the issue of X-ray breaks that are possibly 'hidden' and hence the light curves are misinterpreted as being single power laws. We do so by synthesizing X-ray telescope (XRT) light curves and fitting both single and broken power laws, and comparing the relative goodness of each fit via Monte Carlo analysis. Even with the well-sampled light curves of the Swift era, these breaks may be left misidentified, hence caution is required when making definite statements on the absence of achromatic breaks.     

Gamma-ray burst efficiency and possible physical processes shaping the early afterglow

The discovery by Swift that a good fraction of gamma-ray bursts (GRBs) have a slowly decaying X-ray afterglow phase led to the suggestion that energy injection into the blast wave takes place several hundred seconds after the burst. This implies that right after the burst the kinetic energy of the blast wave was very low and in turn the efficiency of production of γ-rays during the burst was extremely high, rendering the internal shocks model unlikely. We re-examine the estimates of kinetic energy in GRB afterglows and show that the efficiency of converting the kinetic energy into γ-rays is moderate and does not challenge the standard internal shock model. We also examine several models, including in particular energy injection, suggested to interpret this slow decay phase. We show that with proper parameters, all these models give rise to a slow decline lasting several hours. However, even those models that fit all X-ray observations, and in particular the energy injection model, cannot account self-consistently for both the X-ray and the optical afterglows of well-monitored GRBs such as GRB 050319 and GRB 050401. We speculate about a possible alternative resolution of this puzzle.     

Jet breaks at the end of the slow decline phase of Swift GRB light curves

The Swift mission has discovered an intriguing feature of gamma-ray burst (GRBs) afterglows, a phase of shallow decline of the flux in the X-ray and optical light curves. This behaviour is typically attributed to energy injection into the burst ejecta. At some point this phase ends, resulting in a break in the light curve, which is commonly interpreted as the cessation of the energy injection. In a few cases, however, while breaks in the X-ray light curve are observed, optical emission continues its slow flux decline. This behaviour suggests a more complex scenario. In this paper, we present a model that invokes a double component outflow, in which narrowly collimated ejecta are responsible for the X-ray emission while a broad outflow is responsible for the optical emission. The narrow component can produce a jet break in the X-ray light curve at relatively early times, while the optical emission does not break due to its lower degree of collimation. In our model both components are subject to energy injection for the whole duration of the follow-up observations. We apply this model to GRBs with chromatic breaks, and we show how it might change the interpretation of the GRBs canonical light curve. We also study our model from a theoretical point of view, investigating the possible configurations of frequencies and the values of GRB physical parameters allowed in our model.     

A mini-supernova model for optical afterglows of gamma-ray bursts

An energy deposition of ∼10⁵⁰ erg into the exterior 10⁻³ M⊙ layers of a red giant is calculated to produce an optical phenomenon similar to afterglows of gamma-ray bursts (GRB) recently observed. This mechanism can be realized if a GRB is generated by some mechanism in a close binary system. In contrast to a 'hypernova' scenario for GRB recently proposed by Paczyński, this model does not require huge kinetic energy in the expanding shell to explain optical afterglows of GRB.     

On the optical light curves of afterglows from jetted gamma-ray burst ejecta: effects of parameters

Owing to some refinements in the dynamics, we can follow the overall evolution of a realistic jet numerically until its bulk velocity is as small as c 10³ c . We find no obvious break in the optical light curve during the relativistic phase itself . However, an obvious break does exist at the transition from the relativistic phase to the non-relativistic phase, which typically occurs at time t 10⁶10^6.5 s (i.e. 1030 d). The break is affected by many parameters, such as the electron energy fraction _e, the magnetic energy fraction the initial half-opening angle ₀ and the medium number density n . Increasing any of them to a large enough value will make the break disappear. Although the break itself is parameter-dependent, afterglows from jetted GRB remnants are uniformly characterized by a quick decay during the non-relativistic phase, with power-law timing index 2.1. This is quite different from that of isotropic fireballs, and may be of fundamental importance for determining the degree of beaming in -ray bursts observationally.     

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.     

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.     

Fitting X-ray Afterglow Light curves of Gamma-ray Bursts by Using the Magnetar Energy Injection Model

The central compact object for some gamma-ray bursts (GRBs) may be a strongly magnetized millisecond pulsar. It can inject energy to the outer shock of the GRB by through the magnetic dipole radiation, and therefore causes the shallow decay of the early afterglow. Recently, from a large number of GRB X-ray afterglows observed by Swift/XRT(X-ray telescope), it is revealed that many of them exhibit the shallow decay about 10²∼10⁴ s after the burst prompt emission. We have fitted the X-ray afterglow light curves of 11 GRBs by using the energy injection model of a magnetar with the rotation period in the millisecond order of magnitude. The obtained result shows the validity and universality of the magnetar energy injection model in explaining the shallow decay of afterglows, and simultaneously provides some constraints on the magnetic field strength and rotation period of the central magnetar.     

伽玛暴及其早期X射线余辉的观测特征

Swift卫星的X射线望远镜观测揭示部分伽玛暴的早期余辉光变曲线有一个缓慢衰减的成分,而相当一部分却没有这样的成分.研究比较这两种暴的观测性质发现两类暴的持续时间、伽玛辐射总流量、谱指数、谱硬度比峰值能量等物理量均没有显著差异.然而有该成分的那些伽玛暴谱比较软、早期X射线余辉比较弱、伽玛射线辐射效率显著高于没有这个成分的那些暴.结果表明两类暴的前身星和中心机制一致,是否呈现这个缓慢衰减成分可能取决于外部介质.     

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)  .     

On the anomalous X-ray afterglows of GRB 970508 and 970828

Recently, BeppoSAX and ASCA have observed an unusual resurgence of soft X-ray emission during the afterglows of GRB 970508 and 970828, together with marginal evidence for the existence of Fe lines in both objects. We consider the implications of the existence of a torus of iron-rich material surrounding the sites of gamma-ray bursts, as would be expected in the supra-nova model; in particular, we show that the fireball will quickly hit this torus, and bring it to a temperature of ≈3×10⁷ K. Bremsstrahlung emission from the heated-up torus will cause a resurgence of the soft X-ray emission with all expected characteristics (flux level, duration and spectral hardening with time) identical to those observed during the re-burst. Also, thermal emission from the torus will account for the observed iron line flux. These events are also observable, for instance by new missions such as SWIFT , when beaming away from our line of sight makes us miss the main burst, as fast (soft) X-ray transients, with durations of ≈10³ s and fluences of ≈10⁻⁷–10⁻⁴ erg cm⁻². This model provides evidence in favour of the supra-nova model for gamma-ray bursts.     

Can the early X-ray afterglow of gamma-ray bursts be explained by a contribution from the reverse shock?

We propose to explain the recent observations of gamma-ray burst early X-ray afterglows with SWIFT by the dissipation of energy in the reverse shock that crosses the ejecta as it is decelerated by the burst environment. We compute the evolution of the dissipated power and discuss the possibility that a fraction of it can be radiated in the X-ray range. We show that this reverse shock contribution behaves in a way very similar to the observed X-ray afterglows if the following two conditions are satisfied. (i) The Lorentz factor of the material which is ejected during the late stages of source activity decreases to small values  Γ < 10  and (ii) a large part of the shock-dissipated energy is transferred to a small fraction  (ζ≲ 10⁻²)  of the electron population. We also discuss how our results may help to solve some puzzling problems raised by multiwavelength early afterglow observations such as the presence of chromatic breaks.     

A unifying view of gamma-ray burst afterglows

We selected a sample of 33 gamma-ray bursts detected by Swift , with known redshift and optical extinction at the host frame. For these, we constructed the de-absorbed and K -corrected X-ray and optical rest-frame light curves. These are modelled as the sum of two components: emission from the forward shock due to the interaction of a fireball with the circumburst medium and an additional component, treated in a completely phenomenological way. The latter can be identified, among other possibilities, as a 'late prompt' emission produced by a long-lived central engine with mechanisms similar to those responsible for the production of the 'standard' early prompt radiation. Apart from flares or re-brightenings, that we do not model, we find a good agreement with the data, despite of their complexity and diversity. Although based, in part, on a phenomenological model with a relatively large number of free parameters, we believe that our findings are a first step towards the construction of a more physical scenario. Our approach allows us to interpret the behaviour of the optical and X-ray afterglows in a coherent way, by a relatively simple scenario. Within this context, it is possible to explain why sometimes no jet break is observed; why, even if a jet break is observed, it is often chromatic and why the steepening after the jet break time is often shallower than predicted. Finally, the decay slope of the late prompt emission after the shallow phase is found to be remarkably similar to the time profile expected by the accretion rate of fall-back material (i.e.  ∝ t ^−5/3  ), suggesting that this can be the reason why the central engine can be active for a long time.     

Tail Emission from a Ring-like Jet: Its Application to Shallow Decays of Early Afterglows and GRB 050709

Similar to the case of pulsars the magnetic axis and the spin axis of gamma-ray burst sources may not lie on the same line. This may cause the formation of a ring-like jet due to collimation of the processing magnetic axis. We analyze the tail emission from such a jet, and find that it has a shallow decay phase with a temporal index of -1/2 if the Lorentz factor of the ejecta is not very high, which is consistent with the shallow decay phase of some early X-ray afterglow detected by Swift. The ring-like jet has a tail cusp with sharp rising and very sharp decay. This effect can provide an explanation for the re-brightening and sharp decay of the X-ray afterglow of GRB 050709.     

Optical observations of GRB 050401 afterglow : a case for double-jet model

The afterglow of GRB 050401 presents several novel and interesting features. (i) An initially faster decay in optical band than in X-rays. (ii) A break in the X-ray light curve after ∼0.06 d with an unusual slope after the break. (iii)The X-ray afterglow does not show any spectral evolution across the break while the R -band light curve does not show any break. We have modelled the observed multiband evolution of the afterglow of GRB 050401 as originating in a two-component jet, and interpreting the break in X-ray light curve as due to lateral expansion of a narrow collimated outflow which dominates the X-ray emission. The optical emission is attributed to a wider jet component. Our model reproduces all the observed features of multiband afterglow of GRB 050401. We present optical observations of GRB 050401 using the 104-cm Sampurnanand Telescope at the Aryabhatta Research Institute of Observational Sciences (ARIES), Nainital. Results of the analysis of multiband data are presented and compared with GRB 030329, the first reported case of double jet.     

Evidence for energy injection and a fine-tuned central engine at optical wavelengths in GRB 070419A

We present a comprehensive multiwavelength temporal and spectral analysis of the 'fast rise exponential decay' GRB 070419A. The early-time emission in the γ-ray and X-ray bands can be explained by a central engine active for at least 250 s, while at late times the X-ray light curve displays a simple power-law decay. In contrast, the observed behaviour in the optical band is complex (from 10² up to 10⁶ s). We investigate the light-curve behaviour in the context of the standard forward/reverse shock model; associating the peak in the optical light curve at ∼450 s with the fireball deceleration time results in a Lorenz factor  Γ≈ 350  at this time. In contrast, the shallow optical decay between 450 and 1500 s remains problematic, requiring a reverse shock component whose typical frequency is above the optical band at the optical peak time for it to be explained within the standard model. This predicts an increasing flux density for the forward shock component until   t ∼ 4 × 10⁶ s  , inconsistent with the observed decay of the optical emission from   t ∼ 10⁴ s  . A highly magnetized fireball is also ruled out due to unrealistic microphysic parameters and predicted light-curve behaviour that is not observed. We conclude that a long-lived central engine with a finely tuned energy injection rate and a sudden cessation of the injection is required to create the observed light curves, consistent with the same conditions that are invoked to explain the plateau phase of canonical X-ray light curves of γ-ray bursts.     

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.