Afterglow light curves, viewing angle and the jet structure of γ-ray bursts

Gamma-ray bursts are often modelled as jet-like outflows directed towards the observer; the cone angle of the jet is then commonly inferred from the time at which there is a steepening in the power-law decay of the afterglow. We consider an alternative model in which the jet has a beam pattern where the luminosity per unit solid angle (and perhaps also the initial Lorentz factor) decreases smoothly away from the axis, rather than having a well-defined cone angle within which the flow is uniform. We show that the break in the afterglow light curve then occurs at a time that depends on the viewing angle. Instead of implying a range of intrinsically different jets – some very narrow, and others with a similar power spread over a wider cone – the data on afterglow breaks could be consistent with a standardized jet, viewed from different angles. We discuss the implication of this model for the luminosity function.     

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.     

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.     

Can all breaks in gamma-ray burst afterglows be explained by jet effects?

Whether gamma-ray bursts are highly beamed or not is a very important question, as it has been pointed out that the beaming will lead to a sharp break in the afterglow light curves during the ultrarelativistic phase, with the breaking point determined by  Γ∼1/ θ ₀  , where Γ is the bulk Lorentz factor and θ ₀ is the initial half opening angle of the ejecta, and such a break is claimed to be present in the light curves of some GRBs. In this paper we will examine whether all the observed breaks in GRB afterglow light curves can be explained by jet effects. Here we present a detailed calculation of the jet evolution and emission, and have obtained a simple formula of bulk Lorentz factor evolution. We show that the light curves are very smoothly steepened by jet effect, and the shape of the light curve is determined by only one parameter –     , where E and n are the fireball energy and surrounding medium density, respectively. We find that for GRB 990123 and GRB 991216, the jet model can approximately fit their light curves, and the values of     are about 0.17 and 0.22, respectively. On the other hand, the light curves of GRB 990510, GRB 000301c, GRB 000926 and GRB 010222 cannot be fitted by the jet model, which suggests that the breaks may be caused by some other reasons, and the jet effect should be not the unique reason.     

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)  .     

The first hours of the optical afterglow from the cosmic gamma-ray burst 030329

We describe the first results of our observations of the exceptionally bright optical afterglow from the cosmic gamma-ray burst (GRB) of March 29, 2003 (030329), with the 1.5-m Russian-Turkish telescope (RTT150) installed at the TUBITAK National Observatory (Turkey) at Mount Bakyrlytepe. RTT150 was one of the first medium-class telescopes pointed at the afterglow. The observations began as early as about six hours after the GRB. During the first five hours of our observations, the BV RI flux fell off exactly as a power law with the same slope ?1.19±0.01. Subsequently, in all of the BV RI bands, we observed the same increase in the power-law slope of the light curve to a value that was later recorded during the observations at observatories in the western hemisphere. The break in the power-law light curve occurs at t ? t ₀ ≈ 0.57 days (13.5 h) and lasts for about 0.2 days. Apart from this smooth decrease in the flux, the afterglow exhibited no flux variability. The upper limits on the variability are 10–1% on time scales of 0.1–1000 s, respectively. The BV RI spectral flux distribution during the first night of our observations closely corresponds to a power-law spectrum with a spectral index α=0.66±0.01. The change in the power-law slope of the light curve at the end of our observations is probably attributable to the deceleration of the ultrarelativistic jet to a gamma factor when its structural features begin to show up in the light curve. The radio, optical, and X-ray broadband spectrum is consistent with the assumption about the synchrotron radiation of the ultrarelativistic jet. This unique object continues to be observed with RTT150.     

Analytical Afterglow Light Curves of Gamma-ray Bursts: the Case of a Flat Electron Spectrum

In the standard afterglow model, the swept electrons have a single power-law energy distribution dn/dγe ∝ γ−p e (p ∼ 2.3), owing to the first order Fermi acceleration process. However, in some events people find a lot of evidence for a flat electron spectrum (i.e., p < 2). In this work, the analytical afterglow light curves in the case of a flat electron energy distribution are presented respectively for a single power-law spectrum and a broken power-law spectrum, then the results are applied to the specific burst GRB 060908. Besides, we have also speculated a possible solution of the so-called low energy spectrum crisis of Gamma-ray Bursts     

The evolution of a beamed gamma-ray-burst afterglow: the non-relativistic case

There has been increasing evidence that at least some gamma-ray bursts (GRBs) are emission beamed. The beamed GRB-afterglow evolution has been discussed by several authors in the ultrarelativistic case. It has been shown that the dynamics of the blast wave will be significantly modified by the sideways expansion, and there may be a sharp break in the afterglow light curves under certain circumstances. However, this is only true when the fireball is still relativistic. Here we present an analytical approach to the evolution of the beamed GRB blast wave expanding in the surrounding medium (density     in the non-relativistic case, our purpose is to explore whether the sideways expansion will strongly affect the blast-wave evolution as in the relativistic case. We find that the blast-wave evolution is strongly dependent on the speed of the sideways expansion. If it expands with the sound speed, then the jet angle θ increases with time as     which means that the sideways expansion has little effect on the afterglow light curves, the flux     for     and     for     It is clear that the light curve of     is not always steeper than that of     as in the relativistic case. We also show that if the expansion speed is a constant, then the jet angle     and the radius     in this case the sideways expansion has the most significant effect on the blast-wave evolution, the flux     independent of s , and we expect that there should be a smooth and gradual break in the light curve.     

Extinction of Beamed Gamma-ray Burst Afterglows in a Dense Circumstellar Cloud

Broadband afterglow observations provide a probe of the density structure of the circumburst medium. In the spreading jet model, prompt and intense X-ray/UV radiation from the reverse shock may destroy and clear the dust in the circumburst cloud out to about 30 pc within the initial solid angle of the jet. Asthe jet expands significantly, optical radiation from the high-latitude part of the jet may suffer extinction by dust outside the initial solid angle, while radiation from the part within the initial solid angle can be observed without extinction. In previous studies, it is usually assumed that the extinction is complete. We calculate the extinction effect by taking the optical depth into account. Our numerical results showthat a break appears in the light curve of optical afterglow but it extends over a factor of ～ 80 in time rather than a factor of ～ 10 in time for the case of strong dust extinction and a factor of ～ 60 in time for the case without dust extinction. These results may provide a way to judge how large the number density of the circumburst cloud is. Finally, we carry out a detailed modeling for the afterglow of GRB 000926. Our model can provide a good fit to the multi-color observations of this event.     

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.     

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.     

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.     

The circumstellar environment of Wolf–Rayet stars and gamma-ray burst afterglows

We study the evolution of the circumstellar medium of massive stars. We pay particular attention to Wolf-Rayet stars that are thought to be the progenitors of some long gamma-ray bursts (GRBs). We detail the mass-loss rates we use in our stellar evolution models and how we estimate the stellar wind speeds during different phases. With these details we simulate the interactions between the wind and the interstellar medium to predict the circumstellar environment around the stars at the time of core-collapse. We then investigate how the structure of the environment might affect the GRB afterglow. We find that when the afterglow jet encounters the free-wind/stalled-wind interface, rebrightening occurs and a bump is seen in the afterglow light curve. However, our predicted positions of this interface are too distant from the site of the GRB to reach while the afterglow remains observable. The values of the final wind density,   A _*  , from our stellar models are of the same order (≲1) as some of the values inferred from observed afterglow light curves. We do not reproduce the lowest   A _*  values below 0.5 inferred from afterglow observations. For these cases, we suggest that the progenitors could have been a WO-type Wolf–Rayet (WR) star or a very low-metallicity star. Finally, we turn our attention to the matter of stellar wind material producing absorption lines in the afterglow spectra. We discuss the observational signatures of two WR stellar types, WC and WO, in the afterglow light curve and spectra. We also indicate how it may be possible to constrain the initial mass and metallicity of a GRB progenitor by using the inferred wind density and wind velocity.     

Supernovae in helium star–compact object binaries: a possible γ-ray burst mechanism

Helium star–compact object binaries, and helium star–neutron star binaries in particular, are widely believed to be the progenitors of the observed double-neutron-star systems. In these, the second neutron star is presumed to be the compact remnant of the helium star supernova. In this paper, the observational implications of such a supernova are discussed, and in particular are explored as a candidate γ-ray burst mechanism. In this scenario, the supernova results in a transient period of rapid accretion on to the compact object, extracting via magnetic torques its rotational energy at highly super-Eddington luminosities in the form of a narrowly beamed, strongly electromagnetically dominated jet. Compton scattering of supernova photons advected within the ejecta, and photons originating at shocks driven into the ejecta by the jet, will cool the jet and can produce the observed prompt emission characteristics, including the peak-inferred isotropic energy relation, X-ray flash characteristics, subpulse light curves, energy-dependent time lags and subpulse broadening, and late time spectral softening. The duration of the burst is limited by the rate of Compton cooling of the jet, eventually creating an optically thick, moderately relativistically expanding fireball that can produce the afterglow emission. If the black hole or neutron star stays bound to a compact remnant, late term light curve variability may be observed as in SN 2003dh.     

Turbulence induced additional deceleration in relativistic shock wave propagation: implications for gamma-ray burst

The late afterglow of gamma-ray burst is believed to be due to progressive deceleration of the forward shock wave driven by the gamma-ray burst ejecta propagating in the interstellar medium. We study the dynamic effect of interstellar turbulence on shock wave propagation. It is shown that the shock wave decelerates more quickly than previously assumed without the turbulence. As an observational consequence, an earlier jet break will appear in the light curve of the forward shock wave. The scatter of the jet-corrected energy release for gamma-ray burst, inferred from the jet-break, may be partly due to the physical uncertainties in the turbulence/shock wave interaction. This uncertainties also exist in two shell collisions in the well-known internal shock model proposed for gamma-ray burst prompt emission. The large scatters of known luminosity relations of gamma-ray burst may be intrinsic and thus gamma-ray burst is not a good standard candle. We also discuss the other implications.     

Variability in GRB afterglows and GRB 021004

We present general analytic expressions for GRB afterglow light curves arising from a variable external density profile and/or a variable energy in the blast wave. The former could arise from a clumpy ISM or a variable stellar wind; The latter could arise from refreshed shocks or from an angular dependent jet structure (patchy shell). Both scenarios would lead to a variable light curve. Our formalism enables us to invert the observed light curve and obtain possible density or energy profiles. The optical afterglow of GRB 021004 was detected 537 s AB (after the burst) [GCN (2002) 1564]. Extensive follow up observations revealed a significant temporal variability. We apply our formalism to the R-band light curve of GRB 021004 and we find that several models provide a good fit to the data. We consider the patchy shell model with p=2.2 as the most likely explanation. According to this model our line of sight was towards a ‘cold spot’ that has lead to a relativity low γ-ray flux and an initially weak afterglow (while the X-ray afterglow flux after a day was above average). Observations above the cooling frequency, ν_c, could provide the best way to distinguish between our different models.     

具平缓电子能谱的伽玛射线暴的解析光变曲线

在标准的伽玛暴余辉模型中,电子通过费米一级加速后形成单幂律能谱分布dn/dγe∝γe-p(p≈2.3),但在某些伽玛暴事件中观测到了平缓的电子能谱分布(即p＜2).在单幂律谱和分段幂律谱两种情况下,分别给出了具有平缓电子能谱的伽玛暴余辉的解析光变曲线,并以GRB 060908为例进行了讨论.同时提出了伽玛暴低能谱危机的...     

Observational signature of a wind bubble environment for double neutron star mergers

During the in-spiral stage of a compact binary, a wind bubble could be blown into the interstellar medium, if electromagnetic radiation due to the binary orbital motion is strong enough. Therefore, shortduration gamma-ray bursts(SGRBs) due to double neutron star mergers would in principle happen in a wind bubble environment, which can influence the propagation of the SGRB jet and consequent afterglow emission. By calculating the dynamics and synchrotron radiation of the jet-driven external shock, we reveal that an abrupt jump could appear in the afterglow light curves of SGRBs and the observational time of the jump is dependent on the viewing angle. This light curve jump provides an observational signature to constrain the radius of the wind bubble and thus the power of the electromagnetic radiation of the binary,by combining with gravitational wave detection.     

Shallow Decay of X-ray Afterglows in Short GRBs： Energy Injection from a Millisecond Magnetar？

With the successful launch of Swift satellite,more and more data of early X-ray afterglows from short gamma-ray bursts have been collected.Some interesting features such as unusual afterglow light curves and unexpected X-ray flares are revealed.Especially,in some cases,there is a fiat segment in the X-ray afterglow light curve.Here we present a simplified model in which we believe that the flattening part is due to energy injection from the central engine.We assume that this energy injection arises from the magnetic dipole radiation of a millisecond pulsar formed after the merger of two neutron stars.We check this model with the short GRB 060313.Our numerical results suggest that energy injection from a millisecond magnetar could make part of the X-ray afterglow light curve flat.     

Afterglow Light Curves of Jetted Gamma-ray Burst Ejecta in Stellar Winds

Optical and radio afterglows arising from shocks by relativistic conical ejecta running into pre-burst massive stellar winds are revisited. Under the homogeneous thin-shell approximation and a realistic treatment for the lateral expansion of jets, our results show that a notable break exists in the optical light curve in most cases we calculated in which the physical parameters are varied within reasonable ranges. For a relatively tenuous wind which cannot decelerate the relativistic jet to cause a light curve break within days, the wind termination shock due to the ram pressure of the surrounding medium occurs at a small radius, namely, a few times 1017 cm. In such a structured wind environment, the jet will pass through the wind within several hours and run into the outer uniform dense medium. The resulting optical light curve flattens with a shallower drop after the jet encounters the uniform medium, and then declines deeply, triggered by runaway lateral expansion.