Gamma-ray burst afterglow scaling coefficients for general density profiles

Gamma-ray burst (GRB) afterglows are well described by synchrotron emission originating from the interaction between a relativistic blast wave and the external medium surrounding the GRB progenitor. We introduce a code to reconstruct spectra and light curves from arbitrary fluid configurations, making it especially suited to study the effects of fluid flows beyond those that can be described using analytical approximations. As a check and first application of our code, we use it to fit the scaling coefficients of theoretical models of afterglow spectra. We extend earlier results of other authors to general circumburst density profiles. We rederive the physical parameters of GRB 970508 and compare with other authors.     

Gamma暴余辉的相对论流体动力学演化和光变曲线

本文首先对Gamma暴的观测特性和物理过程作了简要的介绍 ,而后 ,对火球模型的相对论流体动力学机制和同步加速辐射机制作了论述。主要工作是 :具体研究火球所抛出壳层的相对论流体动力学演化 ,应用同步加速辐射机制 ,通过由共动坐标系到实验室坐标系的相对论变换 ,得到Gamma暴余辉的光变曲线。对于火球壳层的不同的动力学演化规律 ,各向同性或各向异性的壳层抛出形式 ,以及不同的外部介质环境 ,所得到的光变曲线都各不相同。通过对这些不同的光变曲线的比较 ,明确了Gamma暴余辉的整体的物理演化图象以及各种物理过程在Gamma暴余辉演化过程中所起的作用 ,并从余辉演化的方面进一步理解了Gamma暴的物理本质     

A systematic description of shocks in gamma-ray bursts – II. Simulation

In Paper I, we presented a detailed formulation of the relativistic shocks and synchrotron emission in the context of gamma-ray burst (GRB) physics. To see how well this model reproduces the observed characteristics of the GRBs and their afterglows, here we present the results of some simulations based on this model. They are meant to reproduce the prompt and afterglow emissions in some intervals of time during a burst. We show that this goal is achieved for both short and long GRBs and their afterglows, at least for part of the parameter space. Moreover, these results are evidence of the physical relevance of the two phenomenological models we have suggested in Paper I for the evolution of the active region – synchrotron emitting region in a shock. The dynamical active region model seems to reproduce the observed characteristics of prompt emissions and late afterglow better than the quasi-steady model which is more suitable for the onset of afterglows. Therefore, these simulations confirm the arguments presented in Paper I about the behaviour of these models based on their physical properties.     

Synchrotron emission in the fast cooling regime: which spectra can be explained?

We consider the synchrotron emission from relativistic shocks assuming that the radiating electrons cool rapidly (either through synchrotron or any other radiation mechanism). It is shown that the theory of synchrotron emission in the fast cooling regime can account for a wide range of spectral shapes. In particular, the magnetic field, which decays behind the shock front, brings enough flexibility to the theory to explain the majority of gamma-ray burst spectra even in the parameter-free fast cooling regime. Also, we discuss whether location of the peak in observed spectral energy distributions of gamma-ray bursts and active galactic nuclei can be made consistent with predictions of diffusive shock acceleration theory, and find that the answer is negative. This result is a strong indication that a particle injection mechanism, other than the standard shock acceleration, works in relativistic shocks.     

Radiative losses and cut-offs of energetic particles at relativistic shocks

We investigate the acceleration and simultaneous radiative losses of electrons in the vicinity of relativistic shocks. Particles undergo pitch angle diffusion, gaining energy as they cross the shock by the Fermi mechanism and also emitting synchrotron radiation in the ambient magnetic field. A semi-analytic approach is developed which allows us to consider the behaviour of the shape of the spectral cut-off and the variation of that cut-off with the particle pitch angle. The implications for the synchrotron emission of relativistic jets, such as those in gamma-ray burst sources and blazars, are discussed.     

High-energy afterglow emission from gamma-ray bursts

We calculate the very high-energy (sub-GeV to TeV) inverse Compton emission of GRB afterglows. We argue that this emission provides a powerful test of the currently accepted afterglow model. We focus on two processes: synchrotron self-Compton emission within the afterglow blast wave, and external inverse Compton emission which occurs when flare photons (produced by an internal process) pass through the blast wave. We show that if our current interpretations of the Swift X-ray telescope (XRT) data are correct, there should be a canonical high-energy afterglow emission light curve. Our predictions can be tested with high-energy observatories such as GLAST , Whipple, HESS and MAGIC. Under favourable conditions we expect afterglow detections in all these detectors.     

Hard electron energy distribution in the relativistic shocks of gamma-ray burst afterglows

Particle acceleration in relativistic shocks is not a very well understood subject. Owing to that difficulty, radiation spectra from relativistic shocks, such as those in gamma-ray burst (GRB) afterglows, have been often modelled by making assumptions about the underlying electron distribution. One such assumption is a relatively soft distribution of the particle energy, which need not be true always, as is obvious from observations of several GRB afterglows. In this paper, we describe modifications to the afterglow standard model to accommodate energy spectra which are 'hard'. We calculate the overall evolution of the synchrotron and Compton flux arising from such a distribution. We also model two afterglows, GRB010222 and GRB020813, under this assumption and estimate the physical parameters.     

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.     

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.     

A complete reference of the analytical synchrotron external shock models of gamma-ray bursts

Gamma-ray bursts are most luminous explosions in the universe. Their ejecta are believed to move towards Earth with a relativistic speed. The interaction between this “relativistic jet” and a circumburst medium drives a pair of (forward and reverse) shocks. The electrons accelerated in these shocks radiate synchrotron emission to power the broad-band afterglow of GRBs. The external shock theory is an elegant theory, since it invokes a limit number of model parameters, and has well predicted spectral and temporal properties. On the other hand, depending on many factors (e.g. the energy content, ambient density profile, collimation of the ejecta, forward vs. reverse shock dynamics, and synchrotron spectral regimes), there is a wide variety of the models. These models have distinct predictions on the afterglow decaying indices, the spectral indices, and the relations between them (the so-called “closure relations”), which have been widely used to interpret the rich multi-wavelength afterglow observations. This review article provides a complete reference of all the analytical synchrotron external shock afterglow models by deriving the temporal and spectral indices of all the models in all spectral regimes, including some regimes that have not been published before. The review article is designated to serve as a useful tool for afterglow observers to quickly identify relevant models to interpret their data. The limitations of the analytical models are reviewed, with a list of situations summarized when numerical treatments are needed.     

GRB 080319B: evidence for relativistic turbulence, not internal shocks

We show that the excellent optical and gamma-ray data available for GRB 080319B rule out the internal shock model for the prompt emission. The data instead point to a model in which the observed radiation was produced close to the deceleration radius  (∼10¹⁷ cm)  by a turbulent source with random Lorentz factors of ∼10 in the comoving frame. The optical radiation was produced by synchrotron emission from relativistic electrons, and the gamma-rays by inverse-Compton scattering of the synchrotron photons. The gamma-ray emission originated both in eddies and in an inter-eddy medium, whereas the optical radiation was mostly from the latter. Therefore, the gamma-ray emission was highly variable whereas the optical was much less variable. The model explains all the observed features in the prompt optical and gamma-ray data of GRB 080319B. We are unable to determine with confidence whether the energy of the explosion was carried outwards primarily by particles (kinetic energy) or magnetic fields. Consequently, we cannot tell whether the turbulent medium was located in the reverse shock (we can rule out the forward shock) or in a Poynting-dominated jet.     

Early afterglows of short gamma-ray bursts

In the relativistic fireball model, the afterglow of a gamma-ray burst (GRB) is produced by synchrotron radiation of the electrons accelerated in the external shock that emerges as the relativistic flow moves. According to this model, the afterglow peaks on a time scale of ～10 s when observed in the soft gamma-ray band. The peak flux can be high enough to be detected by modern all-sky monitors. We investigate the emission from short (ΔT<1 s) GRBs on a time scale t≈10 s using BATSE/CGRO data. A significant flux is recorded for ～20% of the events. In most cases, the observed persistent emission can be explained in terms of the model as an early burst afterglow. No early afterglows of most short GRBs are observed. The model parameters for these bursts are constrained.     

A Study on the Light Curves of GRBs

It is generally believed that the complexity and variability of the light curves of gamma-ray bursts (GRBs) are caused by the internal shocks, which would occur when a rapid shell catches up a slower one and collides with it. The electrons in the shock layer are heated by the shocks and radiate via the mechanisms of synchrotron radiation and inverse Compton scattering. Based on relativistic kinematics, a relation between the photon number of the emission from the rapidly moving shock layer and the number of the photons received by an observer is derived. Then, employing the angular spreading of the internal shock emission, the curve equation and profile of a single pulse are obtained, and the shape is typically in the shape of a fast rise and exponential decline. Furthermore, by using the model of the successive collisions of multiple shells under the condition of reasonable parameters, the observed light curves are fitted with a rather good effect. Therefore, by this means, more different types of light curves of GRBs can be explained.     

The precession of eccentric discs in close binaries

If the emission of gamma-ray bursts were as a result of the synchrotron process in the standard internal shock scenario, then the typical observed spectrum should have a slope F _ν ∝ ν ^−1/2, which strongly conflicts with the much harder spectra observed. This directly follows from the cooling time being much shorter than the dynamical time. Particle re-acceleration, deviations from equipartition, quickly changing magnetic fields and adiabatic losses are found to be inadequate to account for this discrepancy. We also find that in the internal shock scenario the relativistic inverse Compton scattering is always as important as the synchrotron process, and faces the same problems. This indicates that the burst emission is not produced by relativistic electrons emitting synchrotron and inverse Compton radiation.     

Electron surfing acceleration in oblique magnetic fields

Initially, inhomogeneous plasma jets, ejected by active galactic nuclei and associated with gamma-ray bursts, are thermalized by the formation of internal shocks. Jet subpopulations can hereby collide at Lorentz factors of a few. As the resulting relativistic shock expands into the upstream plasma, a significant fraction of the upstream ions is reflected. These ions, together with downstream ions that leak through the shock, form relativistic beams of ions that outrun the shock. The thermalization of these beams via the two-stream instability is thought to contribute significantly to plasma heating and particle acceleration by the shock. Here, the capability of a two-stream instability to generate relativistic field-aligned and cross-field electron flow, is examined for a magnetized plasma by means of a particle-in-cell (PIC) simulation. The electrons interact with the developing quasi-electrostatic waves and oblique magnetic fields. The simulation results bring forward evidence that such waves, by their non-linear interactions with the plasma, produce a highly relativistic field-aligned electron flow and electron energies, which could contribute to the radio synchrotron emissions from astrophysical jets, to ultrarelativistic leptonic subpopulations propagating with the jet and to the halo particles surrounding the accretion disc of the black hole.     

Gamma-ray bursts from internal shocks in a relativistic wind: temporal and spectral properties

We construct models for gamma-ray bursts in which the emission comes from internal shocks in a relativistic wind with a highly non-uniform distribution of the Lorentz factor. We follow the evolution of the wind using a very simplified approach in which a large number of layers interact by direct collisions but all pressure waves have been suppressed. We suppose that the magnetic field and the electron Lorentz factor reach large equipartition values in the shocks. Synchrotron photons emitted by the relativistic electrons have a typical energy in the gamma-ray range in the observer frame. Synthetic bursts are constructed as the sum of the contributions from all the internal elementary shocks, and their temporal and spectral properties are compared with the observations. We reproduce the diversity of burst profiles, the 'FRED' shape of individual pulses and the short time-scale variability. Synthetic bursts also satisfy the duration–hardness relation and individual pulses are found to be narrower at high energy, in agreement with the observations. These results suggest that internal shocks in a relativistic wind may indeed be at the origin of gamma-ray bursts. A potential problem, however, is the relatively low efficiency of the dissipation process. If the relativistic wind is powered by accretion from a disc to a stellar mass black hole, it implies that a substantial fraction of the available energy is injected into the wind.     

High-energy afterglow emission from giant flares of soft gamma-ray repeaters: the case of the 2004 December 27 event from SGR 1806–20

We discuss the high-energy afterglow emission (including high-energy photons, neutrinos and cosmic rays) following the 2004 December 27 giant flare from the soft gamma-ray repeater (SGR) 1806−20. If the initial outflow is relativistic with a bulk Lorentz factor  Γ₀∼  tens, the high-energy tail of the synchrotron emission from electrons in the forward shock region gives rise to a prominent sub-GeV emission, if the electron spectrum is hard enough and if the initial Lorentz factor is high enough. This signal could serve as a diagnosis of the initial Lorentz factor of the giant flare outflow. This component is potentially detectable by the Gamma-Ray Large Area Telescope ( GLAST ) if a similar giant flare occurs in the GLAST era. With the available 10-MeV data, we constrain that  Γ₀ < 50  if the electron distribution is a single power law. For a broken power-law distribution of electrons, a higher Γ₀ is allowed. At energies higher than 1 GeV, the flux is lower because of a high-energy cut-off of the synchrotron emission component. The synchrotron self-Compton emission component and the inverse Compton scattering component off the photons in the giant flare oscillation tail are also considered, but they are found not significant given a moderate Γ₀ (e.g. ≤ 10). The forward shock also accelerates cosmic rays to the maximum energy 10¹⁷ eV, and generates neutrinos with a typical energy 10¹⁴ eV through photomeson interaction with the X-ray tail photons. However, they are too weak to be detectable.     

Quantum relativistic theory of the synchrotron/cyclotron radiation in a strongly-magnetized plasma: The case of longitudinal propagation

Full quantum relativistic treatment of the cyclotron/synchrotron emission and absorption in tenuous plasmas with superstrong magnetic field is developed for the case when the radiation wave-vector is parallel to the magnetic field. The emissivities and absorption coefficients for a plasma with arbitrary distribution function of particles are presented in terms of simple sums over the Landau levels. On the basis of these expressions, the negative absorption (maser amplification) is shown to be impossible for the longitudinal propagation in a tenuous plasma. The summation over the Landau levels is performed analytically, and the quantum effects are analysed in detail, for the thermal distribution of plasma particles. A new type of quantum relativistic oscillations is predicted in the emission and absorption spectra for a plasma with anisotropic temperature. The results obtained are useful for an interpretation of the X-ray and gamma-ray observations of the objects associated with strongly magnetized neutron stars (particularly of the gamma-ray bursters).     

Non-pulsed Emission from the Binary System B1259-63

PSR B1259-63 is the only known binary system with a radio pulsar from which the non-pulsed radio and X-ray emission was detected. The companion star in this system is a Be star SS 2883. A rapidly rotating radio pulsar is expected to produce a wind of relativistic particles. Be stars are known to produce highly asymmetric mass loss. Due to the interaction of the pulsar wind and the Be star wind the system of two shocks between the pulsar and the Be star forms. In this paper we show that the observed non-pulsed radio emission from the system is a result of the synchrotron emission of the relativistic particles in the outflow beyond the shock wave and that the non-pulsed X-ray emission is due to the inverse Compton scattering of the Be star photons on this particles. This revised version was published online in July 2006 with corrections to the Cover Date.     

3-D Rpic Simulations of Relativistic Jets: Particle Acceleration, Magnetic Field Generation, and Emission

We have applied numerical simulations and modeling to the particle acceleration, magnetic field generation, and emission from relativistic shocks. We investigate the nonlinear stage of theWeibel instability and compare our simulations with the observed gamma-ray burst emission. In collisionless shocks, plasma waves and their associated instabilities (e.g., the Weibel, Buneman and other two-stream instabilities) are responsible for particle (electron, positron, and ion) acceleration and magnetic field generation. 3-D relativistic electromagnetic particle (REMP) simulations with three different electron-positron jet velocity distributions and also with an electron-ion plasma have been performed and show shock processes including spatial and temporal evolution of shocks in unmagnetized ambient plasmas. The growth time and nonlinear saturation levels depend on the initial jet parallel velocity distributions. Simulations show that the Weibel instability created in the collisionless shocks accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The nonlinear fluctuation amplitude of densities, currents, electric, and magnetic fields in the electron-positron shocks are larger for smaller jet Lorentz factor. This comes from the fact that the growth time of the Weibel instability is proportional to the square of the jet Lorentz factor. We have performed simulations with broad Lorentz factor distribution of jet electrons and positrons, which is assumed to be created by photon annihilation. Simulation results with this broad distribution show that the Weibel instability is excited continuously by the wide-range of jet Lorentz factor from lower to higher values. In all simulations the Weibel instability is responsible for generating and amplifying magnetic fields perpendicular to the jet propagation direction, and contributes to the electron’s (positron’s) transverse deflection behind the jet head. This small scale magnetic field structure contributes to the generation of “jitter” radiation from deflected electrons (positrons), which is different from synchrotron radiation in uniform magnetic fields. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks. The detailed studies of shock microscopic process evolution may provide some insights into early and later GRB afterglows.