The Optical Afterglow of GW170817: An Off-axis Structured Jet and Deep Constraints on a Globular Cluster Origin
Wen-fai Fong, P. K. Blanchard, K. D. Alexander, J. Strader, R. Margutti, A. Hajela, V. A. Villar, Y. Wu, C. S. Ye, E. Berger, R. Chornock, D. Coppejans, P. S. C… 展开作者
Wen-fai Fong, P. K. Blanchard, K. D. Alexander, J. Strader, R. Margutti, A. Hajela, V. A. Villar, Y. Wu, C. S. Ye, E. Berger, R. Chornock, D. Coppejans, P. S. Cowperthwaite, T. Eftekhari, D. Giannios, C. Guidorzi, A. Kathirgamaraju, T. Laskar, A. MacFadyen, B. D. Metzger, M. Nicholl, K. Paterson, G. Terreran, D. J. Sand, L. Sironi, P. K. G. Williams, X. Xie, J. Zrake
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11 pages, 6 figures, 2 tables. Accepted to ApJ Letters
We present a revised and complete optical afterglow light curve of the binary neutron star merger GW170817, enabled by deep Hubble Space Telescope (HST) F606W observations at $\approx\!584$ days post-merger, which provide a robust optical template. The light curve spans $\approx 110-362$ days, and is fully consistent with emission from a relativistic structured jet viewed off-axis, as previously indicated by radio and X-ray data. Combined with contemporaneous radio and X-ray observations, we find no spectral evolution, with a weighted average spectral index of $\langle β\rangle = -0.583 \pm 0.013$, demonstrating that no synchrotron break frequencies evolve between the radio and X-ray bands over these timescales. We find that an extrapolation of the post-peak temporal slope of GW170817 to the luminosities of cosmological short GRBs matches their observed jet break times, suggesting that their explosion properties are similar, and that the primary difference in GW170817 is viewing angle. Additionally, we place a deep limit on the luminosity and mass of an underlying globular cluster of $L \lesssim 6.7 \times 10^{3}\,L_{\odot}$, or $M \lesssim 1.3 \times 10^{4}\,M_{\odot}$, at least 4 standard deviations below the peak of the globular cluster mass function of the host galaxy, NGC4993. This limit provides a direct and strong constraint that GW170817 did not form and merge in a globular cluster. As highlighted here, HST (and soon JWST) enables critical observations of the optical emission from neutron star merger jets and outflows.
For gravitational wave (GW) detected neutron star mergers, one of the leading candidates for electromagnetic (EM) counterparts is the afterglow from an ultra-relativistic jet. Where this afterglow is observed, it will likely be viewed off-axis, such as the afterglow following GW170817/GRB 170817A. The temporal behaviour of an off-axis observed GRB afterglow can be used to reveal the lateral jet structure, and statistical model fits can put constraints on the various model free-parameters. Amongst these parameters is the inclination of the system to the line of sight. Along with the GW detectio…
Gamma-ray bursts (GRBs) are fascinating extragalactic objects. They represent a fantastic opportunity to investigate unique properties not exhibited in other sources. Multi-wavelength afterglow observations from some short- and long-duration GRBs reveal an atypical long-lasting emission that evolves differently from the canonical afterglow light curves favoring the off-axis emission. We present an analytical synchrotron afterglow scenario, and the hydrodynamical evolution of an off-axis top-hat jet decelerated in a stratified surrounding environment. The analytical synchrotron afterglow model …
We verified the off-axis jet model of X-ray flashes (XRFs) and examined a discovery of off-axis orphan gamma-ray burst (GRBs) afterglows. The XRF sample was selected on the basis of the following three factors: (1) a constraint on the lower peak energy of the prompt spectrum $E^{src}_{obs}$, (2) redshift measurements, and (3) multi-color observations of an earlier (or brightening) phase. XRF020903 was the only sample selected basis of these criteria. A complete optical multi-color afterglow light curve of XRF020903 obtained from archived data and photometric results in literature showed an ach…
With the launch of Gaia satellite, detection of many different types of transient sources will be possible, one of them being optical afterglows of gamma-ray bursts (GRBs). Using the knowledge of the satellites dynamics and properties of GRB optical afterglows we performed a simulation in order to estimate an average GRB detection rate with Gaia. Here we present the simulation results for two types of GRB optical afterglows, differing in the observer's line-of-sight compared to a GRB jet axis: regular (on-axis) and orphan afterglows. Results show that for on-axis GRBs, less than 10 detections …
The gravitational wave event GW170817 and the slowly-rising afterglows of short gamma-ray burst GRB 170817A clearly suggest that the GRB jet has an angular structure. However the actual jet structure remains unclear as different authors give different structures. We formulate a novel method to inversely reconstruct the jet structure from off-axis GRB afterglows, without assuming any functional form of the structure in contrast to the previous studies. The jet structure is uniquely determined from the rising part of a light curve for a given parameter set by integrating an ordinary differential…
Gamma-ray burst (GRB) afterglows are likely produced in the shock that is driven as the GRB jet interacts with the external medium. Long-duration GRBs are also associated with powerful supernovae (SNe). We consider the optical and radio afterglows of long GRBs for both blasts viewed along the jet axis ("on-axis" afterglows) and misaligned observes ("off-axis" afterglows). Comparing the optical emission from the afterglow with that of the accompanying SN, using SN 1998bw as an archetype, we find that only a few percent of afterglows viewed off-axis are brighter than the SN. For observable optic…
Particle acceleration is expected to be different between relativistic and non-relativistic collisionless shocks. We show that electromagnetic counterparts to gravitational waves (GWs), gamma-ray burst (GRB) afterglows, are ideal targets for observing trans-relativistic evolution of accelerated electron distribution because the GWs spot nearby GRBs with off-axis jets, otherwise missed in gamma-ray observations. We find that the relativistic spectral slope begins to change steeply near the peak time of the light curve and approaches the non-relativistic limit in about 10 times the peak time. Th…
CDF-S XT1 is a fast-rising non-thermal X-ray transient detected by \textit{Chandra} in the Deep-Field South Survey. Although various hypotheses have been suggested, the origin of this transient remains unclear. Here, we show that the observations of CDF-S XT1 are well explained as the X-ray afterglow produced by a relativistic structured jet viewed off-axis. We measure properties of the jet, showing that they are similar to those of GRB170817A, albeit at cosmological distances. We measure the observers viewing angle to be $θ_{\textrm{obs}} = 10^{\circ}\pm3^{\circ}$ and the core of the ultra-re…
The jet structure of short gamma-ray bursts (GRBs) has been controversial after the detection of GRB 170817A as the electromagnetic counterparts to the gravitational wave event GW170817. Different authors use different jet structures for calculating the afterglow light curves. We formulated a method to inversely reconstruct a jet structure from a given off-axis GRB afterglow, without assuming any functional form of the structure. By systematically applying our inversion method, we find that more diverse jet structures are consistent with the observed afterglow of GRB 170817A within errors: suc…
Recently, ground-based Imaging Atmospheric Cherenkov Telescopes have reported the detection of very-high-energy (VHE) gamma-rays from some gamma-ray bursts (GRBs). One of them, GRB~190829A, was triggered by the Swift satellite, and about 20000 s after the burst onset the VHE gamma-ray emission was detected by H.E.S.S. with ~ 5 sigma significance. This event had unusual features of having much smaller isotropic equivalent gamma-ray energy than typical long GRBs and achromatic peaks in X-ray and optical afterglow at about 1400 s. Here we propose an off-axis jet scenario that explains these obser…
Gamma-ray burst (GRB) jets are narrow, and thus typically point away from us. They are initially ultra-relativistic, causing their prompt $γ$-ray and early afterglow emission to be beamed away from us. However, as the jet gradually decelerates its beaming cone widens and eventually reaches our line of sight and the afterglow emission may be detected. Such orphan afterglows were not clearly detected so far. Nevertheless, they should be detected in upcoming optical or radio surveys, and it would be challenging to clearly distinguish between them and other types of transients. Therefore, we perfo…
We model the possible afterglow of the Fermi GBM event associated with LIGO detection GW150914, under the assumption that the gamma-ray are produced by a short GRB-like relativistic outflow. We model GW150914-GBM as both a weak, on-axis short GRB and normal short GRB seen far off axis. Given the large uncertainty in the position of GW150914, we determine that the best chance of finding the afterglow is with ASKAP or possibly the MWA, with the flux from an off-axis short GRB reaching 0.2 - 4 mJy (0.12 - 16 mJy) at 150 MHz (863.5 MHz) by 1 - 12 months after the initial event. At low frequencies,…
As we further our studies on Gamma-ray bursts (GRBs), both on theoretical models and observational tools, more and more options begin to open for exploration of its physical properties. As transient events primarily dominated by synchrotron radiation, it is expected that the synchrotron photons emitted by GRBs should present some degree of polarization throughout the evolution of the burst. Whereas observing this polarization can still be challenging due to the constraints on observational tools, especially for short GRBs, it is paramount that the groundwork is laid for the day we have abundan…
We investigate the optical/near-infrared light curve of the afterglow of GRB 080710 in the context of rising afterglows. Optical and near-infrared photometry was performed using the seven channel imager GROND and the Tautenburg Schmidt telescope. X-ray data were provided by the X-ray Telescope onboard the Swift satellite. The optical/NIR light curve of the afterglow of GRB 080710 is dominated by an initial increase in brightness, which smoothly turns over into a shallow power law decay. The initially rising achromatic light curve of the afterglow of GRB 080710 can be accounted for with a model…
Energy injection into the external shock system that generates the afterglow to a gamma-ray burst (GRB) can result in a re-brightening of the emission. Here we investigate the off-axis view of a re-brightened refreshed shock afterglow. We find that the afterglow light-curve, when viewed from outside of the jet opening angle, could be characterised by a slow rise, or long-plateau, with a maximum flux determined by the total system energy. Using the broadband afterglow data for GRB170817A, associated with the gravitational wave detected binary neutron star merger GW170817, we show that a refresh…
Electromagnetic observations of the first binary Neutron Star (BNS) merger GW170817 has established that relativistic jets can be successfully launched in BNS mergers. Typically, such jets produce emission in two phases: $γ$-ray prompt emission and multi-wavelength afterglow. Due to relativistic de-boosting, the detectability of both these counterparts is dependent on the angle ($θ_v$) between the observer's line of sight and the jet axis. We compare the detectability of prompt and afterglow emission from off-axis jets, assuming standard detector thresholds. We find that for top-hat jets, afte…
The recent radio observations (Mooley et al, 2018) of a superluminal radio afterglow following GRB 170817A are interpreted in terms of a jet impacting a baryonic cloak, which is presumably the material caught at the front of the jet as the latter emerges from a denser ejected material. Assuming that we the observers are located {\bf at a viewing angle of $\sim 0.2$ radians from the emitting material (perhaps slightly more from jet axis)}, we suggest that the Lorentz factor of the jet is $\lesssim 20$ at the time of the prompt emission, and that, as suggested previously, it is accelerated to mu…
A relativistic electron-positron ($e^{+}e^{-}$) pair wind from a rapidly rotating, strongly magnetized neutron star (NS) would interact with a gamma-ray burst (GRB) external shock and reshapes afterglow emission signatures. Assuming that the merger remnant of GW170817 is a long-lived NS, we show that a relativistic $e^{+}e^{-}$ pair wind model with a simple top-hat jet viewed off-axis can reproduce multi-wavelength afterglow lightcurves and superluminal motion of GRB 170817A. The Markov chain Monte Carlo (MCMC) method is adopted to obtain the best-fitting parameters, which give the jet half-op…
Gravitational-wave detected neutron star mergers provide an opportunity to investigate short gamma-ray burst (GRB) jet afterglows without the GRB trigger. Here we show that the post-peak afterglow decline can distinguish between an initially ultra-relativistic jet viewed off-axis and a mildly relativistic wide-angle outflow. Post-peak the afterglow flux will decline as $F_ν\propto t^{-α}$. The steepest decline for a jet afterglow is $α>3p/4$ or $> (3p+1)/4$, for an observation frequency below and above the cooling frequency, respectively, where $p$ is the power-law index of the electron energy…
The ultra-relativistic outflows powering gamma-ray bursts (GRBs) acquire angular structure through their interaction with external material. They are often characterized by a compact, nearly uniform narrow core (with half-opening angle $θ_{c,\{ε,Γ\}}$) surrounded by material with energy per unit solid angle ($ε=ε_cΘ_ε^{-a}$, where $Θ_{\{ε,Γ\}}=[1+θ^2/θ_{c,\{ε,Γ\}}^2]^{1/2}$) and initial specific kinetic energy ($Γ_0-1=[Γ_c-1]Θ_Γ^{-b}$) declining as power laws. Multi-wavelength afterglow lightcurves of off-axis jets (with viewing angle $θ_{\rm obs} > θ_c$) offer robust ways to constrain $a$, $b…
We systematically investigate the outflow structure of GW170817 in comparison with a sample of 27 cosmological short GRBs by modelling their afterglow light curves. We find that cosmological short GRBs share the same outflow structures with GW170817, relativistic structured jets. The jet opening angle of GW170817 is $6.3^{+1.1}_{-0.6}{}^{\circ}$, which is consistent with that of cosmological short GRBs ($θ_0 = 6.9^\circ \pm 2.3^{\circ}$). Our analysis indicates that GW170817 is viewed off-axis ($θ_{\rm obs} = 30^{+7}_{-4}{}^{\circ}$), while cosmological short GRBs are viewed on-axis ($θ_{\rm o…
The peculiar short gamma-ray burst GRB 170817A has been firmly associated to the gravitational wave event GW170817, which has been unaninmously interpreted as due to the coalescence of a double neutron star binary. The unprecedented behaviour of the non-thermal afterglow led to a debate about its nature, which was eventually settled by high-resolution VLBI observations, which strongly support the off-axis structured jet scenario. Using information on the jet structure derived from multi-wavelength fitting of the afterglow emission and of the apparent VLBI image centroid motion, we compute the …
Assuming neutron star (NS) or neutron star/stellar-mass black hole (BH) mergers as progenitors of the short gamma ray bursts, we derive and demonstrate a simple analysis tool for modelling the efficiency of recovering on-axis optical afterglows triggered by a candidate gravitational wave event detected by the Advanced LIGO and Virgo network. The coincident detection efficiency has been evaluated for different classes of operating telescopes using observations of gamma ray bursts. We show how the efficiency depends on the luminosity distribution of the optical afterglows, the telescope features…
Starting as highly relativistic collimated jets, gamma-ray burst outflows gradually decelerate and become non-relativistic spherical blast waves. Although detailed analytical solutions describing the afterglow emission received by an on-axis observer during both the early and late phases of the outflow evolution exist, a calculation of the received flux during the intermediate phase and for an off-axis observer requires either a more simplified analytical model or direct numerical simulations of the outflow dynamics. In this paper we present light curves for off-axis observers covering the lon…
Long-duration gamma-ray bursts (GRBs) are almost unequivocally associated with very energetic, broad-lined supernovae (SNe) of Type Ic-BL. While the gamma-ray emission is emitted in narrow jets, the SN emits radiation isotropically. Therefore, some SN Ic-BL not associated with GRBs have been hypothesized to arise from events with inner engines such as off-axis GRBs or choked jets. Here we present observations of the nearby ($d = 120$ Mpc) SN 2020bvc (ASAS-SN 20bs) which support this scenario. \textit{Swift} UVOT observations reveal an early decline (up to two days after explosion) while optica…
An extremely bright slow-rising afterglow from an off-axis jet in GRB 260310A
University of Rome “Tor Vergata”（罗马第二大学）；INAF - Istituto di Radioastronomia（意大利国家天体物理研究所射电天文台）；The Hong Kong Institute for Astronomy and Astrophysics, The University of Hong Kong（香港大学香港天文及天体物理研究所）；Department of Physics, The University of Hong Kong（香港大学物理系）；Instituto de Astrofísica de Andalucía (IAA-CSIC)（安达卢西亚天体物理学研究所（西班牙高等科学研究委员会））；McWilliams Center for Cosmology and Astrophysics, Department of Physics, Carnegie Mellon University（卡内基梅隆大学麦威廉斯宇宙学与天体物理学中心物理系）
In light of the most recent observations of late afterglows produced by the merger of compact objects or by the core-collapse of massive dying stars, we research the evolution of the afterglow produced by an off-axis top-hat jet and its interaction with a surrounding medium. The medium is parametrized by a power law distribution of the form $n(r)\propto r^{-k}$ is the stratification parameter and contains the development when the surrounding density is constant ($k=0$) or wind-like ($k=2$). We develop an analytical synchrotron forward-shock model when the outflow is viewed off-axis, and it is …
Constraining gamma-ray burst viewing angles with Swift/XRT afterglow light curves
Qufu Normal University（曲阜师范大学）；Huazhong University of Science and Technology（华中科技大学）；Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；University of Science and Technology of China（中国科学技术大学）；Nanjing University（南京大学）
We report on a VLA survey for late-time radio emission from 59 supernovae (SNe) of Type I b/c, which have been associated with long-duration gamma-ray bursts (GRBs). An "off-axis" GRB burst (i.e. whose relativistic jet points away from us) is expected to have late-time radio emission even in the absence of significant prompt gamma-ray emission. From our sample, we detected only SN 2003gk with an 8.4-GHz flux density of $2260 \pm 130 \,μ$Jy. Our subsequent VLBI observations of SN 2003gk, at an age of $\sim$8 yr, allowed us to determine its radius to be $(2.4 \pm 0.4) \times 10^{17}$ cm, or $94 …
Numerical jet simulations serve a valuable role in calculating gamma-ray burst afterglow emission beyond analytical approximations. Here we present the results of high resolution 2D simulations of decelerating relativistic jets performed using the RAM adaptive mesh refinement relativistic hydrodynamics code. We have applied a separate synchrotron radiation code to the simulation results in order to calculate light curves at frequencies varying from radio to X-ray for observers at various angles from the jet axis. We provide a confirmation from radio light curves from simulations rather than fr…
We present full-time-domain, moving-mesh, relativistic hydrodynamic simulations of jets launched from the center of a massive progenitor star and compute the resulting synchrotron light curves for observers at a range of viewing angles. We follow jet evolution from ignition inside the stellar center, propagation in the stellar envelope and breakout from the stellar surface, then through the coasting and deceleration phases. The jet compresses into a thin shell, sweeps up the circumstellar medium, and eventually enters the Newtonian phase. The jets naturally develop angular and radial structure…
A binary neutron star (BNS) merger has been widely argued to be one of the progenitors of a short gamma-ray burst (SGRB). This central engine can be verified if its gravitational-wave (GW) event is detected simultaneously. Once confirmed, this kind of association will be a landmark in multi-messenger astronomy and will greatly enhance our understanding of the BNS merger processes. Due to the limited detection horizon of BNS mergers for the advanced LIGO/Virgo GW observatories, we are inclined to local SGRBs within few hundreds of mega-parsecs. Since normal SGRBs rarely fall into such a close r…
Short Gamma-Ray Bursts (SGRBs) are expected to form from the coalescence of compact binaries, either of primordial origin or from dynamical interactions in globular clusters. In this paper, we investigate the possibility that the offset and afterglow brightness of a SGRB can help revealing the origin of its progenitor binary. We find that a SGRB is likely to result from the primordial channel if it is observed within 10 kpc from the center of a massive galaxy and shows a detectable afterglow. The same conclusion holds if it is 100 kpc away from a small, isolated galaxy and shows a weak aftergl…
The shock system that produces the afterglow to GRBs consists of a forward- and a reverse-shock. For short GRBs, observational evidence for a reverse-shock has been sparse, however, the afterglow to GRB 160821B requires a reverse-shock at early times to explain the radio observations. GRB 160821B is additionally accompanied by the best-sampled macronova without a gravitational-wave detection, and an interesting late-time X-ray afterglow behaviour indicative of a refreshed-shock. The presence of an observed reverse-shock in an on-axis short GRB means that the reverse-shock should be considered …
We show that observed properties of the low luminosity GRB171205A and its afterglow, like those of most other low-luminosity (LL) gamma ray bursts (GRBs) associate with a supernova (SN), indicate that it is an ordinary SN-GRB, which was produced by inverse Compton scattering of glory light by a highly relativistic narrowly collimated jet ejected in a supernova explosion and viewed from a far off-axis angle. As such, VLA/VLBI follow-up radio observations of a superluminal displacement of its bright radio afterglow from its parent supernova, will be able to test clearly whether it is an ordinary…
The afterglow emission of some gamma-ray bursts (GRBs) show a shallow decay (plateau) phase implying continuous injection of energy. The source of this energy is very commonly attributed to the spin-down power of a nascent millisecond magnetar. The magnetic dipole radiation torque is considered to be the mechanism causing the spin-down of the neutron star. This torque has a component working for the alignment of the angle between rotation and magnetic axis, i.e., inclination angle, which has been neglected in modelling GRB afterglow light curves. Here, we demonstrate the evolution of the incli…
GRB 170817A/GW 170817 is the first GRB clearly viewed far from the GRB jet's symmetry axis. Its afterglow was densely monitored over a wide range of frequencies and times. It has been modeled extensively, primarily numerically, and although this endeavour was very fruitful, many of the underlying model parameters remain undetermined. We provide analytic modelling of GRB afterglows observed off-axis, considering jets with a narrow core (of half-opening angle $θ_{\rm c}$) and power-law wings in energy per unit solid angle ($ε=ε_cΘ^{-a}$ where $Θ=[1+(θ/θ_{\rm c})^2]^{1/2}$) and initial specific k…
In the first work of this series, we adopt a GW170817-like, viewing-angle-dependent kilonova model and the standard afterglow model with the lightcurve distribution based on the properties of cosmological short gamma-ray bursts afterglows to simulate the luminosity functions and color evolution of both kilonovae and optical afterglow emissions from binary neutron star (BNS) mergers. {We find that $\sim10\%$ afterglows are brighter than the associated kilonovae at the peak time, most of which are on-axis or nearly-on-axis. These kilonovae would be significantly polluted by the associated afterg…
A number of gamma-ray bursts (GRBs) exhibit the late simultaneous bumps in their optical and Xray afterglows around the jet break. Its origin is unclear. Based on the following two facts, we suggest that this feature may sound a transition of circum-burst environment from a free-wind medium to a homogeneous medium. (I) The late bump followed by a steep decay is strongly reminiscent of the afterglows of GRB 170817A, which is attributed to an off-axis observed external-forward shock (eFS) propagating in an interstellar medium. (II) Observations seem to feature a long shallow decay before the lat…
We performed calculations of the late radio and X-ray afterglow of GRB/GW170817 in the cocoon-jet paradigm, predicting the appearance of a second peak in the afterglow light curve ~ one-three years after the explosion. The model assumes that the prompt emission and early afterglows originate from a cocoon generated during break-out of the delayed magnetically powered jet. As the jet breaks out from the torus-generated wind, a nearly isotropic mildly relativistic outflow is generated; at the same time the primary jet accelerates to high Lorentz factors and avoids detection. As the fast jet slow…
Gamma-ray bursts (GRBs) associated with gravitational wave events are, and will likely continue to be, viewed at a larger inclination than GRBs without gravitational wave detections. As demonstrated by the afterglow of GW170817, this requires an extension of the common GRB afterglow models which typically assume emission from an on-axis top hat jet. We present a characterization of the afterglows arising from structured jets, providing a framework covering both successful and choked jets. We compute new closure relations for structured jets and compare with the established relations for energy…
Swift captured for the first time a smoothly rising X-ray re-brightening of clear non-flaring origin after the steep decay in a long gamma-ray burst (GRB): GRB081028. A rising phase is likely present in all GRBs but is usually hidden by the prompt tail emission and constitutes the first manifestation of what is later to give rise to the shallow decay phase. Contemporaneous optical observations reveal a rapid evolution of the injection frequency of a fast cooling synchrotron spectrum through the optical band, which disfavours the afterglow onset (start of the forward shock emission along our li…
Jet precessions are widely involved in astrophysical phenomena from galaxies to X-ray binaries and gamma-ray bursts (GRBs). Polarization presents a unique probe of the magnetic fields in GRB jets. The precession of GRBs relativistic jets will change the geometry within the observable emitting region of the jet, which can potentially affect the polarization of the afterglow. In this paper, we take into account jet precession to study the polarization evolution and corresponding light curves in GRB early optical afterglows with ordered and random magnetic field geometries. We find that the jet p…
In the \swift era, two-component jet models were introduced to explain the complex temporal profiles and the diversity of early afterglows. In this paper, we concentrate on the two-component jet model; first component is the conventional afterglow and second is the emission due to the late internal dissipation such as the late-prompt emission. We suggest herein that the two-component jet model can be probed by the existence of two optical peaks for orphan GRB afterglows. Each peak is caused by its respective jet as its relativistic beaming cone widens to encompass the off-axis line of sight. T…
Early rebrightenings at a post-burst time of 10^2 - 10^4 s have been observed in the afterglows of some gamma-ray bursts (GRBs). Unlike X-ray flares, these rebrightenings usually last for a relatively long period. The continuous energy injection mechanism usually can only produce a plateau in the afterglow light curve, but not a rebrightening. Also, a sudden energy injection can give birth to a rebrightening, but the rebrightening is a bit too rapid. Here we argued that the early rebrightenings can be produced by the ring-shaped jet model. In this scenario, the GRB outflow is not a full cone, …
