Relativistic Shock Acceleration Research Articles

Particle Acceleration and Magnetic Field Amplification by Relativistic Shocks in Inhomogeneous Media

Particle acceleration and magnetic field amplification in relativistic shocks propagating in inhomogeneous media are investigated by three-dimensional magnetohydrodynamical (MHD) simulations and test-particle simulations. The MHD simulations show that the interaction between the relativistic shock and dense clumps amplifies the downstream magnetic field to the value expected from observations of the gamma-ray burst. The test-particle simulations in the electromagnetic field given by the MHD simulation show that particles are accelerated by the downstream turbulence and the relativistic shock. We provide the injection energy to the shock acceleration in this system. If the amplitude of upstream density fluctuations is sufficiently large, low-energy particles are initially accelerated to the injection energy by the downstream turbulence and then rapidly accelerated to higher energies by the relativistic shock. Therefore, the density fluctuation significantly affects particle acceleration in the relativistic shock.

Shock Corrugation to the Rescue of the Internal Shock Model in Microquasars: The Single-scale Magnetohydrodynamic View

Questions regarding the energy dissipation in astrophysical jets remain open to date, despite numerous attempts to limit the diversity of the models. Some of the most popular models assume that energy is transferred to particles via internal shocks, which develop as a consequence of the nonuniform velocity of the jet matter. In this context, we study the structure and energy deposition of colliding plasma shells, focusing our attention on the case of initially inhomogeneous shells. This leads to the formation of distorted (corrugated) shock fronts—a setup that has recently been shown to revive particle acceleration in relativistic magnetized perpendicular shocks. Our study shows that the radiative power of the far downstream of nonrelativistic magnetized perpendicular shocks is moderately enhanced with respect to the flat-shock cases. Based on the decay rate of the downstream magnetic field, we make predictions for multiwavelength polarization properties.

Magnetic Field Amplification by a Plasma Cavitation Instability in Relativistic Shock Precursors

Abstract Plasma streaming instabilities play an important role in magnetic field amplification and particle acceleration in relativistic shocks and their environments. However, in the far shock precursor region where accelerated particles constitute a highly relativistic and dilute beam, streaming instabilities typically become inefficient and operate at very small scales when compared to the gyroradii of the beam particles. We report on a plasma cavitation instability that is driven by dilute relativistic beams and can increase both the magnetic field strength and coherence scale by orders of magnitude to reach near-equipartition values with the beam energy density. This instability grows after the development of the Weibel instability and is associated with the asymmetric response of background leptons and ions to the beam current. The resulting net inductive electric field drives a strong energy asymmetry between positively and negatively charged beam species. Large-scale particle-in-cell simulations are used to verify analytical predictions for the growth and saturation level of the instability and indicate that it is robust over a wide range of conditions, including those associated with pair-loaded plasmas. These results can have important implications for the magnetization and structure of shocks in gamma-ray bursts, and more generally for magnetic field amplification and asymmetric scattering of relativistic charged particles in plasma astrophysical environments.

Fermi acceleration in relativistic collisionless plasma shocks correlates with anisotropic energy gains

Collisionless shocks generated by two colliding relativistic electron-positron plasma shells are studied using particle-in-cell simulations. Shocks are mediated by the Weibel instability (WI), and the kinetic energy of the fastest accelerated particles is found to be anisotropically modified by WI-induced electric fields. Specifically, we show that all particles interacting with the shock bifurcate into two groups based on their final relativistic Lorentz factor γ: slow (γ<γbf) and fast (γ>γbf), where γbf is the bifurcation Lorentz factor that was found to be approximately twice the initial (upstream) Lorentz factor γ0. We have found that the kinetic energies of the slow particles are equally affected by the longitudinal and transverse components of the shock electric field, whereas the fast particles are primarily accelerated by the transverse field component.

Diffusive acceleration in relativistic shocks: particle feedback

ABSTRACT The spectral index s of high-energy particles diffusively accelerated in a non-magnetized relativistic shock, such as in a γ-ray burst afterglow, depends on the unknown angular diffusion function $\mathcal {D}$, which itself depends on the particle distribution function f if acceleration is efficient. We develop a relaxation code to compute s and f for an arbitrary functional $\mathcal {D}$ that depends on f. A local $\mathcal {D}(f)$ dependence is motivated and shown, when rising (falling) upstream, to soften (harden) s with respect to the isotropic case, shift the angular distribution towards upstream (downstream) directions, and strengthen (weaken) the particle confinement to the shock; an opposite effect on s is found downstream. However, variations in s remain modest even when $\mathcal {D}$ is a strong function of f, so the standard, isotropic-diffusion results remain approximately applicable unless $\mathcal {D}$ is both highly anisotropic and not a local function of f. A mild, ∼0.1 softening of s, in both 2D and 3D, when $\mathcal {D}(f)$ rises sufficiently fast, may be realized in ab initio simulations.

On the injection of relativistic electrons in the jet of 3C 279

ABSTRACTThe acceleration of electrons in 3C 279 is investigated through analysing the injected electron energy distribution (EED) in a time-dependent synchrotron self-Compton+external Compton emission model. In this model, it is assumed that relativistic electrons are continuously injected into the emission region, and the injected EED [$Q_{\rm e}^\prime (\gamma ^\prime)$] follows a single power-law form with low- and high-energy cut-offs $\rm \gamma _{min}^{\prime }$ and $\rm \gamma _{max}^{\prime }$, respectively, and the spectral index n, i.e. $Q_{\rm e}^\prime (\gamma ^\prime)\propto \gamma ^{\prime -n}$. This model is applied to 14 quasi-simultaneous spectral energy distributions of 3C 279. The Markov Chain Monte Carlo (MCMC)-fitting technique is performed to obtain the best-fitting parameters and the uncertainties on the parameters. The results show that the injected EED is well constrained in each state. The value of n is in the range of 2.5–3.8, which is larger than that expected by the classic non-relativistic shock acceleration. However, the large value of n can be explained by the relativistic oblique shock acceleration. The flaring activity seems to be related to an increased acceleration efficiency, reflected in an increased $\gamma ^{\prime }_{\rm min}$ and electron injection power.

Precursor Wave Emission Enhanced by Weibel Instability in Relativistic Shocks

Abstract We investigated the precursor wave emission efficiency in magnetized purely perpendicular relativistic shocks in pair plasmas. We extended our previous study to include the dependence of upstream magnetic field orientations. We performed two-dimensional particle-in-cell simulations and focused on two magnetic field orientations: the magnetic field in the simulation plane (i.e., in-plane configuration) and that perpendicular to the simulation plane (i.e., out-of-plane configuration). Our simulations in the in-plane configuration demonstrated that not only extraordinary but also ordinary mode waves are excited. We quantified the emission efficiency as a function of the magnetization parameter σ e and found that the large-amplitude precursor waves are emitted for a wide range of σ e . We found that especially at low σ e , the magnetic field generated by Weibel instability amplifies the ordinary mode wave power. The amplitude is large enough to perturb the upstream plasma, and transverse density filaments are generated as in the case of the out-of-plane configuration investigated in the previous study. We confirmed that our previous conclusion holds regardless of upstream magnetic field orientations with respect to the two-dimensional simulation plane. We discuss the precursor wave emission in three dimensions and the feasibility of wakefield acceleration in relativistic shocks based on our results.

On the origin of ultra-high rigidity cosmic rays

This paper argues in a first part that the observation of anisotropies at energies close to the GZK cut-off strongly argues in favor of the existence of protons at these energies. It then discusses the possible source of such protons, providing first general bounds on the luminosity of the source and on the amount of energy to be released in the ultra-high energy range. The necessary conditions point towards relativistic shock acceleration as an acceleration agent. Then, it discusses the physics of relativistic shock acceleration from a more microphysical point of view.

Analytic study of 1D diffusive relativistic shock acceleration

Diffusive shock acceleration (DSA) by relativistic shocks is thought to generate the dN/dE∝ E−p spectra of charged particles in various astronomical relativistic flows. We show that for test particles in one dimension (1D), p−1=1− ln [γd(1+βd)]/ ln [γu(1+βu)], where βu (βd) is the upstream (downstream) normalized velocity, and γ is the respective Lorentz factor. This analytically captures the main properties of relativistic DSA in higher dimensions, with no assumptions on the diffusion mechanism. Unlike 2D and 3D, here the spectrum is sensitive to the equation of state even in the ultra-relativistic limit, and (for a J{üttner-Synge equation of state) noticeably hardens with increasing 1<γu<57, before logarithmically converging back to p(γu→∞)=2. The 1D spectrum is sensitive to drifts, but only in the downstream, and not in the ultra-relativistic limit.

Towards Understanding the Physics of Collisionless Relativistic Shocks

Relativistic astrophysical collisionless shocks represent outstanding dissipation agents of the huge power of relativistic outflows produced by accreting black holes, core collapsed supernovae and other objects into multi-messenger radiation (cosmic rays, neutrinos, electromagnetic radiation). This article provides a theoretical discussion of the fundamental physical ingredients of these extreme phenomena. In the context of weakly magnetized shocks, in particular, it is shown how the filamentation type instabilities, which develop in the precursor of pair dominated or electron-ion shocks, provide the seeds for the scattering of high energy particles as well as the agent which preheats and slows down the incoming precursor plasma. This analytical discussion is completed with a mesoscopic, non-linear model of particle acceleration in relativistic shocks based on Monte Carlo techniques. This Monte Carlo model uses a semi-phenomenological description of particle scattering which allows it to calculate the back-reaction of accelerated particles on the shock structure on length and momentum scales which are currently beyond the range of microscopic particle-in-cell (PIC) simulations.

Constraining Relativistic Bow Shock Properties in Rotation-powered Millisecond Pulsar Binaries

Multiwavelength followup of unidentified Fermi sources has vastly expanded the number of known galactic-field "black widow" and "redback" millisecond pulsar binaries. Focusing on their rotation-powered state, we interpret the radio to X-ray phenomenology in a consistent framework. We advocate the existence of two distinct modes differing in their intrabinary shock orientation, distinguished by the phase-centering of the double-peaked X-ray orbital modulation originating from mildly-relativistic Doppler boosting. By constructing a geometric model for radio eclipses, we constrain the shock geometry as functions of binary inclination and shock stand-off R0. We develop synthetic X-ray synchrotron orbital light curves and explore the model parameter space allowed by radio eclipse constraints applied on archetypal systems B1957+20 and J1023+0038. For B1957+20, from radio eclipses the stand-off is R0 ~ 0.15-0.3 fraction of binary separation from the companion center, depending on the orbit inclination. Constructed X-ray light curves for B1957+20 using these values are qualitatively consistent with those observed, and we find occultation of the shock by the companion as a minor influence, demanding significant Doppler factors to yield double peaks. For J1023+0038, radio eclipses imply R0 ≲ 0.4 while X-ray light curves suggest 0.1 ≲ R0 ≲ 0.3 (from the pulsar). Degeneracies in the model parameter space encourage further development to include transport considerations. Generically, the spatial variation along the shock of the underlying electron power-law index should yield energy-dependence in the shape of light curves motivating future X-ray phase-resolved spectroscopic studies to probe the unknown physics of pulsar winds and relativistic shock acceleration therein.

Particle acceleration, magnetization and radiation in relativistic shocks

What are the mechanisms of particle acceleration and radiation, as well as magnetic field build up and decay in relativistic shocks are open questions with important implications to various phenomena in high energy astrophysics. While the Weibel instability is possibly responsible for magnetic field build up and diffusive shock acceleration is a model for acceleration, both have problems and current PIC simulation show that particles are accelerated only under special conditions and the magnetic field decays on a short length scale. We present here a novel model for the structure and the emission of highly relativistic collisionless shocks. The model takes into account (and is based on) non-local energy and momentum transport across the shock front via emission and absorption of high-energy photons. This leads to a pre-acceleration of the fluid and pre-amplificaiton of the magnetic fields in the upstream region. Both have drastic implications on the shock structure. The model explains the persistence of the shock generated magnetic field at large distances from the shock front. The dissipation of this magnetic field results in a continuous particle acceleration within the downstream region. The model suggests two non-uniform emission zones (the downstream and the upstream), that give rise to three emission components with different spectral and temporal properties. A unique feature of the model is the existence of an "attractor", toward which any shock will evolve. This enables us to estimate from first principles the synchrotron and inverse Compton spectrum of the downstream emission. The model is applicable to any relativistic shock, but its distinctive features show up only for large compactness. We demonstrate that prompt and afterglow Gamma-Ray Bursts' shocks satisfy the relevant conditions and compare their observations with the predictions.

Recent Highlights from VERITAS

VERITAS is a ground-based gamma-ray observatory consisting of an array of four atmospheric Cherenkov telescopes located in southern Arizona, USA. VERITAS carries out an extensive observation program of the gamma-ray sky at energies above 0.1 TeV. Observations of Galactic and extragalactic sources in the TeV band are sensitive probes of the highly energetic processes occurring in these objects. Observations by VERITAS of the Galactic center and nearby dwarf spheroidal galaxies provide constraints on particle dark matter with masses above a few hundred GeV. VERITAS observations also provide constraints on fundamental physics and cosmology, such as probing the history of galaxy formation and studying Lorentz invariance violation (LIV). The majority of the sources detected by VERITAS are active galactic nuclei (AGN), with gamma-ray emission originating in their relativistic jets. TeV observations of AGN help us constrain models of particle acceleration and energy dissipation in relativistic jets, and the size and location of the gamma-ray emission region. Galactic sources at TeV energies include supernova remnants, pulsar wind nebulae, and binary systems, and TeV emission is a key diagnostic of the highly energetic particles in these objects. VERITAS observations provide important clues on the origin of cosmic rays and on particle acceleration in supernova blast shocks and relativistic pulsar wind-termination shocks. In this article I will present some highlights of particle-astrophysics measurements made with VERITAS.

4.5 YEARS OF MULTI-WAVELENGTH OBSERVATIONS OF MRK 421 DURING THE ARGO-YBJ AND FERMI COMMON OPERATION TIME

ABSTRACT We report on the extensive multi-wavelength observations of the blazar Markarian 421 (Mrk 421) covering radio to γ-rays, during the 4.5 year period of ARGO-YBJ and Fermi common operation time, from 2008 August to 2013 February. These long-term observations, extending over an energy range of 18 orders of magnitude, provide a unique chance to study the variable emission of Mrk 421. In particular, due to the ARGO-YBJ and Fermi data, the entire energy range from 100 MeV to 10 TeV is covered without any gap. In the observation period, Mrk 421 showed both low- and high-activity states at all wavebands. The correlations among flux variations in different wavebands were analyzed. The X-ray flux is clearly correlated with the TeV γ-ray flux, while the GeV γ-rays only show a partial correlation with the TeV γ-rays. Radio and UV fluxes seem to be weakly or not correlated with the X-ray and γ-ray fluxes. Seven large flares, including five X-ray flares and two GeV γ-ray flares with variable durations (3–58 days), and one X-ray outburst phase were identified and used to investigate the variation of the spectral energy distribution with respect to a relative quiescent phase. During the outburst phase and the seven flaring episodes, the peak energy in X-rays is observed to increase from sub-keV to a few keV. The TeV γ-ray flux increases up to 0.9–7.2 times the flux of the Crab Nebula. The behavior of GeV γ-rays is found to vary depending on the flare, a feature that leads us to classify flares into three groups according to the GeV flux variation. Finally, the one-zone synchrotron self-Compton model was adopted to describe the emission spectra. Two out of three groups can be satisfactorily described using injected electrons with a power-law spectral index around 2.2, as expected from relativistic diffuse shock acceleration, whereas the remaining group requires a harder injected spectrum. The underlying physical mechanisms responsible for different groups may be related to the acceleration process or to the environment properties.

Particle spectra and efficiency in nonlinear relativistic shock acceleration – survey of scattering models

We include a general form for the scattering mean free path in a nonlinear Monte Carlo model of relativistic shock formation and Fermi acceleration. Particle-in-cell (PIC) simulations, as well as analytic work, suggest that relativistic shocks tend to produce short-scale, self-generated magnetic turbulence that leads to a scattering mean free path (mfp) with a stronger momentum dependence than the mfp ~ p dependence for Bohm diffusion. In unmagnetized shocks, this turbulence is strong enough to dominate the background magnetic field so the shock can be treated as parallel regardless of the initial magnetic field orientation, making application to gamma-ray bursts (GRBs), pulsar winds, Type Ibc supernovae, and extra-galactic radio sources more straightforward and realistic. In addition to changing the scale of the shock precursor, we show that, when nonlinear effects from efficient Fermi acceleration are taken into account, the momentum dependence of the mfp has an important influence on the efficiency of cosmic-ray production as well as the accelerated particle spectral shape. These effects are absent in nonrelativistic shocks and do not appear in relativistic shock models unless nonlinear effects are self-consistently described. We show, for limited examples, how the changes in Fermi acceleration translate to changes in the intensity and spectral shape of gamma-ray emission from proton-proton interactions and pion-decay radiation.

Relativistic Shocks: Particle Acceleration and Magnetization

We review the physics of relativistic shocks, which are often invoked as the sources of non-thermal particles in pulsar wind nebulae (PWNe), gamma-ray bursts (GRBs), and active galactic nuclei (AGN) jets, and as possible sources of ultra-high energy cosmic-rays. We focus on particle acceleration and magnetic field generation, and describe the recent progress in the field driven by theory advances and by the rapid development of particle-in-cell (PIC) simulations. In weakly magnetized or quasi parallel-shocks (where the magnetic field is nearly aligned with the flow), particle acceleration is efficient. The accelerated particles stream ahead of the shock, where they generate strong magnetic waves which in turn scatter the particles back and forth across the shock, mediating their acceleration. In contrast, in strongly magnetized quasi-perpendicular shocks, the efficiencies of both particle acceleration and magnetic field generation are suppressed. Particle acceleration, when efficient, modifies the turbulence around the shock on a long time scale, and the accelerated particles have a characteristic energy spectral index of ~ 2.2 in the ultra-relativistic limit. We discuss how this novel understanding of particle acceleration and magnetic field generation in relativistic shocks can be applied to high-energy astrophysical phenomena, with an emphasis on PWNe and GRB afterglows.

Electron and ion acceleration in relativistic shocks with applications to GRB afterglows

We have modeled the simultaneous first-order Fermi shock acceleration of protons, electrons, and helium nuclei by relativistic shocks. By parameterizing the particle diffusion, our steady-state Monte Carlo simulation allows us to follow particles from particle injection at nonthermal thermal energies to above PeV energies, including the nonlinear smoothing of the shock structure due to cosmic-ray (CR) backpressure. We observe the mass-to-charge (A/Z) enhancement effect believed to occur in efficient Fermi acceleration in non-relativistic shocks and we parameterize the transfer of ion energy to electrons seen in particle-in-cell (PIC) simulations. For a given set of environmental and model parameters, the Monte Carlo simulation determines the absolute normalization of the particle distributions and the resulting synchrotron, inverse-Compton, and pion-decay emission in a largely self-consistent manner. The simulation is flexible and can be readily used with a wide range of parameters typical of gamma-ray burst (GRB) afterglows. We describe some preliminary results for photon emission from shocks of different Lorentz factors and outline how the Monte Carlo simulation can be generalized and coupled to hydrodynamic simulations of GRB blast waves. We assume Bohm diffusion for simplicity but emphasize that the nonlinear effects we describe stem mainly from an extended shock precursor where higher energy particles diffuse further upstream. Quantitative differences will occur with different diffusion models, particularly for the maximum CR energy and photon emission, but these nonlinear effects should be qualitatively similar as long as the scattering mean free path is an increasing function of momentum.

Active Galactic Nuclei: Jets as the Source of Hadrons and Neutrinos

Active galactic nuclei are extragalactic sources, and their relativistic hot-plasma jets are believed to be the main candidates of the cosmic-ray origin, above the so-called knee region of the cosmic-ray spectrum. Relativistic shocks, either single or multiple, have been observed or been theorized to be forming within relativistic jet channels in almost all active galactic nuclei sources. The acceleration of non-thermal particles (e.g. electrons, protons) via the shock Fermi acceleration mechanism, is believed to be mainly responsible for the power-law energy distribution of the observed cosmic-rays, which in very high energies can consequently radiate high energy gamma-rays and neutrinos, through related radiation channels. Here, we will focus on the primary particle (hadronic) shock acceleration mechanism, and we will present a comparative simulation study of the properties of single and multiple relativistic shocks, which occur in AGN jets. We will show that the role of relativistic (quasi-parallel either quasi-perpendicular) shocks, is quite important since it can dramatically alter the primary CR spectral indices and acceleration eciencies. These properties being carried onto gamma-ray and neutrino radiation characteristics, makes the combination of them a quite appealing theme for relativistic plasma and shock acceleration physics, as well as observational cosmic-ray, gamma-ray and neutrino astronomy.

A new time-dependent finite-difference method for relativistic shock acceleration

We present a new approach to calculate the particle distribution function about relativistic shocks including synchrotron losses using the method of lines with an explicit finite difference scheme. A steady, continuous, one dimensional plasma flow is considered to model thick (modified) shocks, leading to a calculation in three dimensions plus time, the former three being momentum, pitch angle and position. The method accurately reproduces the expected power law behaviour in momentum at the shock for upstream flow speeds ranging from 0.1c to 0.995c (1 < \Gamma < 10). It also reproduces approximate analytical results for the synchrotron cutoff shape for a non-relativistic shock, demonstrating that the loss process is accurately represented. The algorithm has been implemented as a hybrid OpenMP--MPI parallel algorithm to make efficient use of SMP cluster architectures and scales well up to many hundreds of CPUs.

Diffusive and Shock-Drift Acceleration in Relativistic Shocks

It is accepted that the shock acceleration mechanism can explain the non-thermal cosmic rays in supernova remnants, active galactic nuclei and gamma ray bursts. Especially, the importance of relativistic shock acceleration of cosmic rays in extragalactic sources is an important subject of study. In this work we will discuss the shock acceleration mechanism and will review the properties of non-relativistic and relativistic shocks, particularly focusing on relativistic Monte Carlo simulation studies.