Recent particle-in-cell simulations suggest that a large fraction of the energy dissipated in a relativistic shock is deposited into a Maxwellian distribution of electrons that is connected to the high-energy power-law tail. Here, we explore the observational implications of such a mixed thermal-nonthermal particle distribution for the afterglow and prompt emission of gamma-ray bursts. When the Maxwellian component dominates the energy budget, the afterglow lightcurves show a very steep decline phase followed by a more shallow decay when the characteristic synchrotron frequency crosses the observed band. The steep decay appears in the X-rays at ~100 sec after the burst and is accompanied by a characteristic hard-soft-hard spectral evolution that has been observed in a large number of early afterglows. If internal shocks produce a similar mixed electron distribution, a bump is expected at the synchrotron peak of the nu*f_nu spectrum.
Optically thick energy dominated plasma created in the source of Gamma-Ray Bursts (GRBs) expands radially with acceleration and forms a shell with constant width measured in the laboratory frame. When strong Lorentz factor gradients are present within the shell it is supposed to spread at sufficiently large radii. There are two possible mechanisms of spreading: hydrodynamical and thermal ones. We consider both mechanisms evaluating the amount of spreading that occurs during expansion up to the moment when the expanding shell becomes transparent for photons. We compute the hydrodynamical spread…
Fermi Gamma ray Space Telescope measurements of spectra, variability time scale, and maximum photon energy give lower limits to the apparent jet powers and, through gammagamma opacity arguments, the bulk Lorentz factors of relativistic jets. The maximum cosmic-ray particle energy is limited by these two quantities in Fermi acceleration scenarios. Recent data are used to constrain the maximum energies of cosmic-ray protons and Fe nuclei accelerated in colliding shells of GRBs and blazars. The Fermi results indicate that Fe rather than protons are more likely to be accelerated to ultra-high ener…
We focus on understanding the beaming of gravitational radiation from gamma ray bursts (GRBs) by approximating GRBs as linearly accelerated point masses. For accelerated point masses, it is known that gravitational radiation is beamed isotropicly at high speeds, and beamed along the polar axis at low speeds. Aside from this knowledge, there has been very little work done on beaming of gravitational radiation from GRBs, and the impact beaming could have on gravitational wave (GW) detection. We determine the following: (1) the observation angle at which the most power is emitted as a function of…
Bimodal spectral energy distributions (SEDs) of gamma-ray burst (GRB) afterglow of GRBs 190114C, 130427A and 180720B confirm that they are originated from the synchrotron emission (Syn) and synchrotron self-Compton Scattering process (SSC) of electrons accelerated in the jets. The radiation mechanism and the physics of the observed spectrum-luminosity/energy relations of GRBs remain as open questions. By extracting the Syn component through fitting their early afterglow SEDs with the Syn+SSC model, we find that their luminosity ($L_{\rm syn}$), peak energy ($E_{\rm p,syn,z}$), and the Lorentz …
Shear Particle Acceleration in Structured Gamma-Ray Burst Jets: I. Physical Origin of the Band Function and Application to GRBs 090926A, 131108A, and 160509A
Low-luminosity gamma-ray bursts (GRBs) with luminosity . 10^49erg/s probably consititute a distinct population from the classic high-luminosity GRBs. They are the most luminous objects detected so far within ~ 100 Mpc, the horizon distance of ultra-high energy cosmic rays (UHECRs), so they are considered to be candidate sources of UHECRs. It was recently argued that the energy production rate in UHECRs is much larger than that in gamma-ray photons of long GRBs measured by the Fermi satellite, which, if true, would challenge the view that GRBs can be the sources of UHECRs. We here suggest that …
Long-lived >100 MeV emission has been a common feature of most Fermi-LAT detected gamma-ray bursts (GRBs), e.g., detected up to ~10^3s in long GRBs 080916C and 090902B and ~10^2s in short GRB 090510. This emission is consistent with being produced by synchrotron emission of electrons accelerated to high energy by the relativistic collisionless shock propagating into the weakly magnetized medium. Here we show that this high-energy afterglow emission constrains the preshock magnetic field to satisfy 1(n/1cc)^{9/8} mG<B<10^2(n/1cc)^{3/8}mG, where n is the preshock density, more stringent than the…
Relativistic jets are universal in long-duration gamma-ray burst (GRB) models. Before breaking out, they must propagate in the progenitor envelope along with a forward shock and a reverse shock forming at the jet head. Both electrons and protons will be accelerated by the shocks. High energy neutrinos could be produced by these protons interacting with stellar materials and electron-radiating photons. The jet will probably be collimated, which may have a strong effect on the final neutrino flux. Under the assumption of a power-law stellar-envelope density profile $ρ\propto r^{-α}$ with an inde…
Prompt extra power-law (PL) spectral component is discovered in some bright gamma-ray bursts (GRBs), which usually dominates the spectral energy distribution below tens of keV or above about 10 MeV. However, its origin is still unclear. In this paper, we present a systematic analysis 13 Fermi short GRBs as of August 2020, with the contemporaneous keV-MeV and GeV detections at the prompt emission phase. We find that the extra PL component is a ubiquitous spectral feature for short GRBs, showing up in all 13 analyzed GRBs. The PL indices are mostly harder than -2.0, which may be well reproduced …
The Fermi satellite has been reporting the detailed temporal properties of gamma-ray bursts (GRBs) in an extremely broad spectral range, 8 keV - 300 GeV, in particular, the unexpected delays of the GeV emission onsets behind the MeV emission of some GRBs. We focus on GRB 080916C, one of the Fermi-LAT GRBs for which the data of the delayed high-energy emission are quite extensive, and we show that the behavior of the high-energy emission of this burst can be explained by a model in which the prompt emission consists of two components: one is the MeV component due to the synchrotron-self-Compton…
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…
The acceleration site for ultra-high energy cosmic rays (UHECR) is still an open question despite extended research. In this paper, we reconsider the prompt phase of gamma-ray bursts (GRBs) as a possible candidate for this acceleration and constrain the maximum proton energy in optically thin synchrotron and photospheric models, using properties of the prompt photon spectra. We find that neither of the models favour acceleration of protons to $10^{20}$ eV in high-luminosity bursts. We repeat the calculations for low-luminosity GRBs (llGRBs) considering both protons and completely stripped iron…
The high-energy (> 100MeV) emission observed by Fermi-LAT during the prompt phase of some luminous gamma-ray bursts (GRBs) could arise from the cascade induced by interactions between accelerated protons and the radiation field of GRBs. The photomeson process, which is usually suggested to operate in such a hadronic explanation, requires a rather high proton energy (> 10^17eV) for an efficient interaction. However, whether GRBs can accelerate protons to such a high energy is far from guaranteed, although they have been suggested as the candidate source for ultrahigh-energy cosmic rays. In this…
The origin of ultra-high-energy cosmic rays (UHECRs) remains elusive. Gamma-ray bursts (GRBs) are among the best candidates able to meet the stringent energy requirements needed for particle acceleration to such high energies. If UHECRs were accelerated by the central engine of GRB 221009A, it might be possible to detect secondary photons and neutrinos as the UHECRs travel from the source to the Earth. Here we attempt to interpret some of the early publicly available data connected to this burst. If the reported early GeV-TeV detection was produced by secondary emission from UHECRs it probably…
In this work, we have modeled the hydrodynamic evolution of the GRBs fireball in violent interaction with the external medium (the ISM) surrounding the burst source by assuming a power law distribution of the accelerated relativistic electrons. For this purpose, a computer code based only on the contribution of the predominant synchrotron radiation mechanism was developed. Light curves for the afterglow emissions following several GRBs over the X-ray and the visible R frequency bands were calculated. Their comparison to observed data by the XRT/Swift satellite and Earth telescopes, respectivel…
Extended emission (EE) is a high-energy, early time rebrightening sometimes seen in the light curves of short gamma-ray bursts (GRBs). We present the first contiguous fits to the EE tail and the later X-ray plateau, unified within a single model. Our central engine is a magnetar surrounded by a fall-back accretion disc, formed by either the merger of two compact objects or the accretion-induced collapse of a white dwarf. During the EE phase, material is accelerated to super-Keplarian velocities and ejected from the system by the rapidly rotating ($P \approx 1 - 10$ ms) and very strong ($10^{15…
Here we test different models of dark energy beyond the standard cosmological constant scenario. We start considering the CPL parameterization of the equation of state (EOS), then we consider a dark energy scalar field (Quintessense). Finally we consider models with dark energy at early times (EDE). Our analysis is based on the Union2 type Ia supernovae data set, a Gamma Ray Bursts (GRBs) Hubble diagram, a set of 28 independent measurements of the Hubble parameter, some baryon acoustic oscillations (BAO) measurements. We performed a statistical analysis and explore the probability distribution…
We propose a two-component jet model consistent with the observations of several gamma ray bursts (GRBs) and active galactic nuclei (AGNs). The jet consists of inner and outer components, and they are supposed to be driven by the Blandford-Znajek (BZ) and Blandford-Payne (BP) processes, respectively. The baryons in the BP jet is accelerated centrifugally via the magnetic field anchored in the accretion disk. The BZ jet is assumed to be entrained a fraction of accreting matter leaving the inner edge of the accretion disk, and the baryons are accelerated in the conversion from electromagnetic en…
We reexamine the general synchrotron model for GRBs' prompt emission and determine the regime in the parameter phase space in which it is viable. We characterize a typical GRB pulse in terms of its peak energy, peak flux and duration and use the latest Fermi observations to constrain the high energy part of the spectrum. We solve for the intrinsic parameters at the emission region and find the possible parameter phase space for synchrotron emission. Our approach is general and it does not depend on a specific energy dissipation mechanism. Reasonable synchrotron solutions are found with energy …
The dominant component of the (100 MeV - 50 GeV) GRB emission detected by LAT starts with a delay relative to the prompt soft (sub-MeV) gamma-rays and lasts long after the soft component fades. This has lead to the intriguing suggestion that this high energy emission is generated via synchrotron emission of relativistic electrons accelerated by the external shock. Moreover, the limits on the MeV afterglow emission lead to the suggestion that, at least in bright GeV bursts the field is not amplified beyond compression in the shock. We show here that considerations of confinement (within the dec…
The afterglow of GRBs is believed to originate from the synchrotron emission of shock-accelerated electrons produced by the interaction between the outflow and the external medium. The accelerated electrons are usually assumed to follow a power law energy distribution with an index of $p$. Observationally, although most GRB afterglows have a $p$ larger than 2, there are still a few GRBs suggestive of a hard ($p<2$) electron spectrum. GRB 091127, with well-sampled broad-band afterglow data, shows evidence of a hard electron spectrum and strong spectral evolution, with a spectral break moving fr…
A recent research shows that particles with a spectrum of a relativistic Maxwellian plus a high-energy tail can be accelerated by relativistic collisionless shocks. We investigate the possibility of the high-energy particles with this new spectrum injected in pulsar wind nebulae (PWNe) from the terminate shock based on the study of multiwavelength emission from PWNe.} {The dynamics of a supernova remnant (SNR) and multiband nonthermal emission from the PWN inside the remnant are investigated using a dynamical model with electrons/positrons injected with the new spectrum. In this model, the dyn…
We explore photospheric emissions from stratified two-component jets, wherein a highly relativistic spine outflow is surrounded by a wider and less relativistic sheath outflow. Thermal photons are injected in regions of high optical depth and propagated until they escape at the photosphere. Due to the presence of shear in velocity (Lorentz factor) at the boundary of the spine and sheath region, a fraction of the injected photons are accelerated via a Fermi-like acceleration mechanism such that a high energy power-law tail is formed in the resultant spectrum. We show, in particular, that if a v…
This paper introduces a kinetic code that simulates gamma-ray burst (GRB) afterglow emission from the external forward shock and presents examples of some of its applications. One interesting research topic discussed in the paper is the high-energy radiation produced by Compton scattering of the prompt GRB photons against the shock-accelerated electrons. The difference between the forward shock emission in a wind-type and a constant-density medium is also studied, and the emission due to Maxwellian electron injection is compared to the case with pure power-law electrons. The code calculates th…
The afterglow emission from gamma-ray bursts (GRBs) is usually interpreted as synchrotron radiation from electrons accelerated at the GRB external shock, that propagates with relativistic velocities into the magnetized interstellar medium. By means of multi-dimensional particle-in-cell simulations, we investigate the acceleration performance of weakly magnetized relativistic shocks, in the magnetization range 0<sigma<1e-1. The pre-shock magnetic field is orthogonal to the flow, as generically expected for relativistic shocks. We find that relativistic perpendicular shocks propagating in electr…
Late-time X-ray afterglows of GRBs: Implications for particle acceleration at relativistic shocks
SISSA（国际高等研究学院）；INAF - Osservatorio Astronomico di Brera（意大利国家天体物理研究所布雷拉天文台）；INFN - Sezione di Milano-Bicocca（意大利国家核物理研究所米兰-比科卡分部）；INFN - Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；IFPU - Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）
This paper examines the possibility that hadronic processes produce the >100 MeV photons in the prompt phase of gamma-ray bursts (GRBs) observed by the Fermi-LAT. We calculate analytically the radiation from protons and from secondary electron-positron pairs produced by high energy protons interacting with gamma-rays inside of the GRB jet. We consider both photo-pion and Bethe-Heitler pair production processes to create secondary electrons and positrons that then radiate via inverse Compton and synchrotron processes. We also consider synchrotron radiation from the protons themselves. We calcul…
Relativistic electrons accelerated by both the first-order and the second-order Fermi accelerations in some synchrotron sources have a hybrid shape of thermal and nonthermal energy distribution. This particle acceleration result is supported by some recent numerical simulations. We calculate the synchrotron polarization by applying this electron energy distribution. The polarization degrees in the cases of active galactic nucleus (AGN) jets and gamma-ray bursts (GRBs) are given as examples. The possible application for the polarization study of Sgr A* is also mentioned. We finally suggest high…
Radiation from GRBs in the prompt phase, flares and an afterglow is thought to be produced by accelerated electrons in magnetic fields. Such emission may be produced at collisionless shocks of baryonic outflows or at reconnection sites (at least for the prompt and flares) of the magnetically dominated (Poynting flux driven) outflows, where no shocks presumably form at all. An astonishing recent discovery is that during reconnection strong small-scale magnetic fields are produced via the Weibel instability, very much like they are produced at relativistic shocks. The relevant physics has been s…
The origin of the highest energy cosmic rays remains an enigma. They offer a window to new physics, including tests of physical laws relevant to their propagation and interactions, at energies unattainable by terrestrial accelerators. They must be accelerated locally, as otherwise background radiations would severely suppress the flux of protons and nuclei, at energies above the Greisen-Zatsepin-Kuzmin (GZK) limit. Nearby Gamma Ray Bursts (GRBs), Hypernovae, Active Galactic Nuclei (AGNs) and their flares, have all been suggested and debated as possible sources. A local sub-population of type I…
GRB 131231A was detected by the Large Area Telescope onboard Fermi Space Gamma-ray Telescope. The high energy gamma-ray ($> 100$ MeV) afterglow emission spectrum is $F_ν\propto ν^{-0.54\pm0.15}$ in the first $\sim 1300$ s after the trigger and the most energetic photon has an energy $\sim 62$ GeV arriving at $t\sim 520$ s. With reasonable parameters of the GRB outflow as well as the density of the circum-burst medium, the synchrotron radiation of electrons or protons accelerated at an external forward shock have difficulty accounting for the data. The synchrotron self-Compton radiation of the …
The physical origin of the >0.1 GeV emission detected from Gamma-Ray Bursts (GRBs) by the Fermi satellite has not yet been completely understood. In this work we consider the GeV light curves of ten GRBs with measured redshift detected by the Fermi-LAT. These light curves are characterised by a long-lived ($\gtrsim10^2$ seconds) emission, whose luminosity decays in time as a power-law. While the decay rate is similar for all GRBs (i.e. $L_{LAT}\propto t^{-1.2}$), the normalisation spans about two orders of magnitude in luminosity. However, after re-normalising the luminosities to the prompt en…
Cosmic Ray (CR) acceleration still challenges the researchers. Fast particles may be accelerated in astrophysical environments by a variety of processes. Acceleration in magnetic reconnection sites in particular, has lately attracted the attention of researchers not only for its potential importance in the solar system context, but also in other astrophysical environments, like compact stellar sources, AGNs and GRBs, and even in diffusive media like the ISM and the IGM, especially when the environment is magnetically dominated. In this talk we review this process and also present three-dimensi…
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…
Understanding the origin of the highest energy cosmic rays is a crucial step in probing new physics at energies unattainable by terrestrial accelerators. Their sources remain an enigma half a century after their discovery. They must be accelerated in the local universe as otherwise interaction with cosmic background radiations would severely deplete the flux of protons and nuclei at energies above the Greisen-Zatsepin-Kuzmin (GZK) limit. Hypernovae, nearby GRBs, AGNs and their flares have all been suggested and debated in the literature as possible sources. Type Ibc supernovae have a local sub…
We study high-energy gamma-ray afterglow emission from gamma-ray bursts (GRBs) in the prior emission model, which is proposed to explain the plateau phase of the X-ray afterglow. This model predicts the high-energy gamma-ray emission when the prompt GRB photons from the main flow are up-scattered by relativistic electrons accelerated at the external shock due to the prior flow. The expected spectrum has the peak of 10-100 GeV at around the end time of the plateau phase for typical GRBs, and high-energy gamma rays from nearby and/or energetic GRBs can be detected by current and future Cherenkov…
In recent work we suggested that photons of energy >100 MeV detected from GRBs by the Fermi Satellite are produced via synchrotron emission in the external forward shock with a weak magnetic field - consistent with shock compressed upstream magnetic field of a few tens of micro-Gauss. Here we investigate whether electrons can be accelerated to energies such that they radiate synchrotron photons with energy up to about 10 GeV in this particular scenario. We do this using two methods: (i) we check if these electrons can be confined to the shock front; and (ii) we calculate radiative losses while…
Synchrotron radiation mechanism, when electrons are accelerated in a relativistic shock, is known to have serious problems to explain the observed gamma-ray spectrum below the peak for most Gamma-Ray Bursts (GRBs); the synchrotron spectrum below the peak is much softer than observed spectra. Recently, the possibility that electrons responsible for the radiation cool via Inverse Compton, but in the Klein-Nishina regime, has been proposed as a solution to this problem. We provide an analytical study of this effect and show that it leads to a hardening of the low energy spectrum but not by enough…
We consider a sample of 107 Gamma Ray Bursts (GRBs) for which early UV emission was measured by Swift, and extrapolate the photon intensity to lower energies. Protons accelerated in the GRB jet may interact with such photons to produce charged pions and subsequently ultra high energy neutrinos $\varepsilon_ν\geq 10^{16}$ eV. We use simple energy conversion efficiency arguments to predict the maximal neutrino flux expected from each GRB. We estimate the neutrino detection rate at large area radio based neutrino detectors and conclude that the early afterglow neutrino emission is too weak to be …
Gamma ray bursts (GRBs) are thought to originate from highly relativistic jets. The fireball model predicts internal shocks in the jets, causing magnetic field to be amplified and particles to be accelerated. We model the effects of an asymmetric density configuration for an internal plasma collision in a quasi-parallel magnetic field. We measured electron acceleration and found that a tenuous population of electrons is accelerated to Lorentz factors of \sim 300 - close to energy equipartition with ions. We found that the filaments did not remain static, but were deflected by the Lorentz force…
Relativistic shocks that accompany supernovae (SNe) produce X-ray burst emissions as they break out in the dense circumstellar medium around the progenitors. This phenomenon is sometimes associated with peculiar low-luminosity gamma-ray bursts (LL GRBs). Here, we investigate the high energy neutrino and gamma-ray counterparts of such a class of SNe. Just beyond the shock breakout radius, particle acceleration in the collisionless shock starts to operate in the presence of breakout photons. We show that protons may be accelerated to sufficiently high energies and produce high energy neutrinos a…
The properties of solar flare plasma can be determined from the observation of optically thin lines. The emitting ion distribution determines the shape of the line, with an isothermal Maxwellian ion distribution producing a Gaussian profile. Non-Gaussian lines may indicate more complex ion distributions. We investigate the possibility of determining flare-accelerated non-thermal ion or plasma velocity distributions. We study EUV spectral lines during a flare SOL2013-05-15T01:45 using the Hinode EUV Imaging Spectrometer (EIS). The flare is located close to the eastern solar limb with an extende…
Balmer emission may be a powerful diagnostic tool to test the paradigm of cosmic ray (CR) acceleration in young supernova remnant (SNR) shocks. The width of the broad Balmer line is a direct indicator of the downstream plasma temperature. In case of efficient particle acceleration an appreciable fraction of the total kinetic energy of the plasma is channeled into CRs, therefore the downstream temperature decreases and so does the broad Balmer line width. This width also depends on the level of thermal equilibration between ions and neutral hydrogen atoms in the downstream. Since in general in …
We performed a time-resolved spectral analysis of 53 bright gamma-ray bursts (GRBs) observed by \textit{Fermi}/GBM. Our sample consists of 908 individual spectra extracted from the finest time slices in each GRB. We fitted them with the synchrotron radiation model by considering the electron distributions in five different cases: mono-energetic, single power-law, Maxwellian, traditional fast cooling, and broken power-law. Our results were further qualified through Bayesian Information Criterion (BIC) by comparing with the fit by empirical models, namely the so-called Band function and cut-off …
Electrons accelerated in relativistic collisionless shocks are usually assumed to follow a power-law energy distribution with an index of $p$. Observationally, although most gamma-ray bursts (GRBs) have afterglows that are consistent with $p>2$, there are still a few GRBs suggestive of a hard ($p<2$) electron energy spectrum. Our previous work showed that GRB 091127 gave strong evidence for a double power-law hard electron energy (DPLH) spectrum with $1<p_1<2$, $p_2>2$ and an "injection break" assumed as $γ_{\rm b}\propto γ^q$ in the highly relativistic regime, where $γ$ is the bulk Lorentz fa…
Even though the observed spectra for GRB prompt emission is well constrained, no single radiation mechanism can robustly explain its distinct non-thermal nature. Here we explore the radiation mechanism with the photospheric emission model using our Monte Carlo Radiative Transfer (MCRaT) code. We study the sub-photospheric Comptonization of fast cooled synchrotron photons while the Maxwellian electrons and mono-energetic protons are accelerated to relativistic energies by repeated dissipation events. Unlike previous simulations, we implement a realistic photon to electron number ratio $N_γ/N_{e…
The spectral shape of the prompt emissions of gamma-ray bursts (GRBs) is typically expressed by the Band function: smooth joining of two power-law functions for high-energy and low-energy regions. To reveal the origin of the Band function, we revisit the stochastic acceleration model, in which electrons are accelerated via scattering with turbulent waves in the GRB outflow. The balance between the acceleration and synchrotron cooling yields a narrow energy-distribution similar to the Maxwellian distribution. The synchrotron spectrum becomes consistent with the observed hard photon index for th…
Although the physical origin of gamma-ray burst (GRB) prompt emission is still controversial, synchrotron radiation from accelerated electrons is a promising mechanism. It is believed that electrons are accelerated continuously by ultra-relativistic shocks or magnetic reconnections. At the same time, these electrons will be cooled via several processes (mainly adiabatic expansion, synchrotron radiation and inverse Compton scattering (ICS)), which regulate the distribution of electrons. An extra high-energy spectrum component is expected to be induced by ICS. However, the gamma-gamma annihilati…
The origin of magnetic fields that permeate the blast waves of gamma-ray bursts (GRBs) is a long-standing problem. The present paper argues that in four GRBs revealing extended emission at >100 MeV, with follow-up in the radio, optical and X-ray domains at later times, this magnetization can be described as the partial decay of the micro-turbulence that is generated in the shock precursor. Assuming that the bulk of the extended emission >100 MeV can be interpreted as synchrotron emission of shock accelerated electrons, we model the multi-wavelength light curves of GRB 090902B, GRB 090323, GRB …
Electrons accelerated in relativistic collisionless shocks are usually assumed to follow a power-law energy distribution with an index of $p$. Observationally, although most gamma-ray bursts (GRBs) have afterglows that are consistent with $p>2$, there are still a few GRBs suggestive of a hard ($p<2$) electron energy spectrum. Our previous works found strong evidence for the exist of a double power-law hard electron energy (DPLH) spectrum with $1<p_1<2$, $p_2>2$ and an injection break assumed as $γ_{\rm b}\propto γ^{q}$ in the relativistic regime. Moreover, these works suggested a possibly univ…
