Gamma-ray bursts (GRB's), short and intense pulses of low-energy $\ensuremath{\gamma}$ rays, have fascinated astronomers and astrophysicists since their unexpected discovery in the late sixties. During the last decade, several space missions---BATSE (Burst and Transient Source Experiment) on the Compton Gamma-Ray Observatory, BeppoSAX and now HETE II (High-Energy Transient Explorer)---together with ground-based optical, infrared, and radio observatories have revolutionized our understanding of GRB's, showing that they are cosmological, that they are accompanied by long-lasting afterglows, and that they are associated with core-collapse supernovae. At the same time a theoretical understanding has emerged in the form of the fireball internal-external shocks model. According to this model GRB's are produced when the kinetic energy of an ultrarelativistic flow is dissipated in internal collisions. The afterglow arises when the flow is slowed down by shocks with the surrounding circumburst matter. This model has had numerous successful predictions, like the predictions of the afterglow itself, of jet breaks in the afterglow light curve, and of the optical flash that accompanies the GRB's. This review focuses on the current theoretical understanding of the physical processes believed to take place in GRB's.

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The physics of gamma-ray bursts

Gamma-ray bursts are the most luminous explosions in the Universe, and their origin and mechanism are the focus of intense research and debate. More than three decades after their discovery, and after pioneering breakthroughs from space and ground experiments, their study is entering a new phase with the recently launched Swift satellite. The interplay between these observations and theoretical models of the prompt gamma-ray burst and its afterglow is reviewed.

https://iopscience.iop.org/article/10.1088/0034-4885/69/8/R01/pdf

Gamma-ray bursts

We present evidence that relativistic shocks propagating in unmagnetized plasmas can self-consistently accelerate particles. We use long-term two-dimensional particle-in-cell simulations to study the well-developed shock structure in unmagnetized pair plasma. The particle spectrum downstream of such a shock consists of two components: a relativistic Maxwellian, with a characteristic temperature set by the upstream kinetic energy of the flow, and a high-energy tail, extending to energies >100 times that of the thermal peak. This high-energy tail is best fitted as a power law in energy with index –2.4 ± 0.1, modified by an exponential cutoff. The cutoff moves to higher energies with time of the simulation, leaving a larger power-law range. The number of particles in the tail is ~1% of the downstream population, and they carry ~10% of the kinetic energy in the downstream region. Investigating the trajectories of particles in the tail, we find that the energy gains occur as particles bounce between the upstream and downstream regions in the magnetic fields generated by the Weibel instability. We compare this mechanism to the first-order Fermi acceleration and set a lower limit on the efficiency of the shock acceleration process.

Particle acceleration in relativistic collisionless shocks: Fermi process at last?

Relativistic collisionless shocks in electron-ion plasmas are thought to occur in the afterglow phase of gamma-ray bursts (GRBs) and in other environments where relativistic flows interact with the interstellar medium. A particular regime of shocks in an unmagnetized plasma has generated much interest for GRB applications. In this Letter, we present ab initio particle-in-cell simulations of unmagnetized relativistic electron-ion shocks. Using long-term 2.5-dimensional simulations with ion-electron mass ratios from 16 to 1000, we resolve the shock formation and reach a steady state shock structure beyond the initial transient. We find that even at high ion-electron mass ratios initially unmagnetized shocks can be effectively mediated by the ion Weibel instability with a typical shock thickness of ~20 ion skin depths. Upstream of the shock, the interaction with merging ion current filaments heats the electron component, so that the postshock flow achieves near-equipartition between the ions and electrons, with the electron temperature reaching 50% of the ion temperature. This energy exchange helps to explain the large electron energy fraction inferred from GRB afterglow observations.

https://iopscience.iop.org/article/10.1086/527374/pdf

On the Structure of Relativistic Collisionless Shocks in Electron-Ion Plasmas

This article presents a comprehensive overview of numerical hydrodynamics and magneto-hydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003), most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do) overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable, an effort has been made to focus on multidimensional studies, directing the interested reader to earlier versions of the review for discussions on one-dimensional works.

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Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity

We present results from three-dimensional particle simulations of collisionless shock formation, with relativistic counterstreaming ion-electron plasmas. Particles are followed over many skin depths downstream of the shock. Open boundaries allow the experiments to be continued for several particle crossing times. The experiments confirm the generation of strong magnetic and electric fields by a Weibel-like kinetic streaming instability and demonstrate that the electromagnetic fields propagate far downstream of the shock. The magnetic fields are predominantly transversal and are associated with merging ion current channels. The total magnetic energy grows as the ion channels merge and as the magnetic field patterns propagate downstream. The electron populations are quickly thermalized, while the ion populations retain distinct bulk speeds in shielded ion channels and thermalize much more slowly. The results help reveal processes of importance in collisionless shocks and may help to explain the origin of the magnetic fields responsible for afterglow synchrotron/jitter radiation from gamma-ray bursts.

https://iopscience.iop.org/article/10.1086/421262/pdf

Magnetic Field Generation in Collisionless Shocks: Pattern Growth and Transport

We present results from three-dimensional particle simulations of collisionless shocks with relativistic counter-streaming ion-electron plasmas. Particles are followed over many skin depths downstream of the shock. Open boundaries allow the experiments to be continued for several particle crossing times. The experiments confirm the generation of strong magnetic and electric fields by a Weibel-like kinetic streaming instability, and demonstrate that the electromagnetic fields propagate far downstream of the shock. The magnetic fields are predominantly transversal, and are associated with merging ion current channels. The total magnetic energy grows as the ion channels merge, and as the magnetic field patterns propagate down stream. The electron populations are quickly thermalized, while the ion populations retain distinct bulk speeds in shielded ion channels and thermalize much more slowly. These results may help explain the origin of the magnetic fields responsible for afterglow synchrotron/jitter radiation from Gamma-Ray Bursts.

https://arxiv.org/pdf/astro-ph/0308104.pdf

Magnetic Field Generation in Collisionless Shocks; Pattern Growth and Transport

Collisionless plasma shock theory, which applies, for example, to the afterglow of gamma-ray bursts, still contains key issues that are poorly understood. In this Letter, we study charged particle dynamics in a highly relativistic collisionless shock numerically using ~109 particles. We find a power-law distribution of accelerated electrons, which upon detailed investigation turns out to originate from an acceleration mechanism that is decidedly different from Fermi acceleration. Electrons are accelerated by strong filamentation instabilities in the shocked interpenetrating plasmas and coincide spatially with the power-law-distributed current filamentary structures. These structures are an inevitable consequence of the now well-established Weibel-like two-stream instability that operates in relativistic collisionless shocks. The electrons are accelerated and decelerated instantaneously and locally: a scenery that differs qualitatively from recursive acceleration mechanisms such as Fermi acceleration. The slopes of the electron distribution power laws are in concordance with the particle power-law spectra inferred from observed afterglow synchrotron radiation in gamma-ray bursts, and the mechanism can possibly explain more generally the origin of nonthermal radiation from shocked interstellar and circumstellar regions and from relativistic jets.

http://iopscience.iop.org/article/10.1086/427387/pdf

Non-Fermi Power-Law Acceleration in Astrophysical Plasma Shocks

Collisionless plasma shock theory, which applies for example to the afterglow of gamma ray bursts, still contains key issues that are poorly understood. In this paper we study charged particle dynamics in a highly relativistic collisionless shock numerically using ~10^9 particles. We find a power law distribution of accelerated electrons, which upon detailed investigation turns out to originate from an acceleration mechanism that is decidedly different from Fermi acceleration. 
Electrons are accelerated by strong filamentation instabilities in the shocked interpenetrating plasmas and coincide spatially with the power law distributed current filamentary structures. These structures are an inevitable consequence of the now well established Weibel-like two-stream instability that operates in relativistic collisionless shocks. 
The electrons are accelerated and decelerated instantaneously and locally; a scenery that differs qualitatively from recursive acceleration mechanisms such as Fermi acceleration. 
The slopes of the electron distribution power laws are in concordance with the particle power law spectra inferred from observed afterglow synchrotron radiation in gamma ray bursts, and the mechanism can possibly explain more generally the origin of non-thermal radiation from shocked inter- and circum-stellar regions and from relativistic jets.

http://arxiv.org/pdf/astro-ph/0408558.pdf

Non-Fermi Power law Acceleration in Astrophysical Plasma Shocks

We present a numerical study of Gamma-Ray Burst - Circumburst Medium interaction and plasma preconditioning via Compton scattering. The simulation tool employed is a unique hybrid model; it combines a highly parallelized (Vlasov) particle-in-cell approach with continuous weighting of particles and a sub-Debye Monte-Carlo binary particle interaction framework. These first results from 3D simulations with this new simulation tool, the PhotonPlasma code, suggests that magnetic fields and plasma density filaments are created in the wakefield of prompt gamma-ray bursts, and that the photon flux density gradient has a significant impact on particle acceleration in the burst head and wakefield. We discuss some possible implications of the circumburst medium preconditioning for the trailing afterglow, and also discuss which additional processes will be needed to improve future studies within this unique and powerful simulation framework.

J. Trier Frederiksen

Papers

Magnetic Field Generation in Collisionless Shocks: Pattern Growth and Transport

Magnetic Field Generation in Collisionless Shocks; Pattern Growth and Transport

Non-Fermi Power-Law Acceleration in Astrophysical Plasma Shocks

Non-Fermi Power law Acceleration in Astrophysical Plasma Shocks

Stochastically Induced Gamma-Ray Burst Wakefield Processes