We examine with a particle-in-cell (PIC) simulation the collision of two equally dense clouds of cold pair plasma. The clouds interpenetrate until instabilities set in, which heat up the plasma and trigger the formation of a pair of shocks. The fastest-growing waves at the collision speed c/5 and low temperature are the electrostatic two-stream mode and the quasi-electrostatic oblique mode. Both waves grow and saturate via the formation of phase space vortices. The strong electric fields of these nonlinear plasma structures provide an efficient means of heating up and compressing the inflowing upstream leptons. The interaction of the hot leptons, which leak back into the upstream region, with the inflowing cool upstream leptons continuously drives electrostatic waves that mediate the shock. These waves heat up the inflowing upstream leptons primarily along the shock normal, which results in an anisotropic velocity distribution in the post-shock region. This distribution gives rise to the Weibel instability. Our simulation shows that even if the shock is mediated by quasi-electrostatic waves, strong magnetowaves will still develop in its downstream region.
We report here on a fast current-driven instability at relativistic collisionless shocks, triggered by the perpendicular current carried by the supra-thermal particles as they gyrate around the background magnetic field in the shock precursor. We show that this instability grows faster than any other instability studied so far in this context, and we argue that it is likely to shape the physics of the shock and of particle acceleration in a broad parameter range.
Mildly relativistic shocks in magnetized electron-ion plasmas are investigated with 2D kinetic particle-in-cell simulations of unprecedentedly high resolution and large scale for conditions that may be found at internal shocks in blazar cores. Ion-scale effects cause corrugations along the shock surface whose properties somewhat depend on the configuration of the mean perpendicular magnetic field, that is either in or out of the simulation plane. We show that the synchrotron maser instability persists to operate in mildly relativistic shocks in agreement with theoretical predictions and produc…
The non-thermal acceleration of electrons and ions at an oblique, non-relativistic shock is studied using large scale particle-in-cell (PIC) simulations in one spatial dimension. Physical parameters are selected to highlight the role of electron pre-heating in injection and subsequent acceleration of particles at high Mach number shocks. Simulation results show evidence for the early onset of the diffusive shock acceleration process for both electrons and ions at a highly oblique subluminal shock. Ion acceleration efficiencies of $\lesssim 5\%$ are measured at late times, though this is not th…
Relativistic collisionless shocks are believed to be efficient particle accelerators. Nonlinear outcome of the interaction of accelerated particles that run ahead of the shock, the so-called "precursor", with the unperturbed plasma of the shock upstream, is thought to facilitate additional acceleration of these particles and to possibly modify the hydrodynamic structure of the shock. We explore here the linear growth of kinetic modes appearing in the precursor-upstream interaction in relativistic shocks propagating in non and weakly magnetized plasmas: electrostatic two-stream parallel mode an…
The growth rate of long wavelength kinetic instabilities arising due to the interaction of a collimated beam of relativistic particles and a cold unmagnetized plasma are calculated in the ultra relativistic limit. For sufficiently culminated beams, all long wave-length modes are shown to be Weibel-unstable, and a simple analytic expression for their growth rate is derived. For large transverse velocity spreads, these modes become stable. An analytic condition for stability is given. These analytic results, which generalize earlier ones given in the literature, are shown to be in agreement with…
We develop a comprehensive theoretical model of relativistic collisionless pair shocks mediated by the current filamentation instability. We notably characterize the noninertial frame in which this instability is of a mostly magnetic nature, and describe at a microscopic level the deceleration and heating of the incoming background plasma through its collisionless interaction with the electromagnetic turbulence. Our model compares well to large-scale 2D3V PIC simulations, and provides an important touchstone for the phenomenology of such plasma systems.
We assess the impact of non-thermally shock-accelerated particles on the magnetohydrodynamic (MHD) jump conditions of relativistic shocks. The adiabatic constant is calculated directly from first principle particle-in-cell simulation data, enabling a semi-kinetic approach to improve the standard fluid model and allowing for an identification of the key parameters that define the shock structure. We find that the evolving upstream parameters have a stronger impact than the corrections due to non-thermal particles. We find that the decrease of the upstream bulk speed yields deviations from the s…
Particle acceleration and heating at mildly relativistic magnetized shocks in electron-ion plasma are investigated with unprecedentedly high-resolution two-dimensional particle-in-cell simulations that include ion-scale shock rippling. Electrons are super-adiabatically heated at the shock, and most of the energy transfer from protons to electrons takes place at or downstream of the shock. We are the first to demonstrate that shock rippling is crucial for the energization of electrons at the shock. They remain well below equipartition with the protons. The downstream electron spectra are approx…
We investigated the efficiency of coherent upstream large-amplitude electromagnetic wave emission via synchrotron maser instability at relativistic magnetized shocks by using two-dimensional particle-in-cell simulations. We considered the purely perpendicular shock in an electron-positron plasma. The coherent wave emission efficiency was measured as a function of the magnetization parameter σ, which is defined by the ratio of the Poynting flux to the kinetic energy flux. The wave amplitude was systematically smaller than that observed in one-dimensional simulations. However, it continued to pe…
Relativistic magnetized shocks are a natural source of coherent emission, offering a plausible radiative mechanism for Fast Radio Bursts (FRBs). We present first-principles 3D simulations that provide essential information for the FRB models based on shocks: the emission efficiency, spectrum, and polarization. The simulated shock propagates in an $e^\pm$ plasma with magnetization $σ>1$. The measured fraction of shock energy converted to coherent radiation is $\simeq 10^{-3} \, σ^{-1}$, and the energy-carrying wavenumber of the wave spectrum is $\simeq 4 \,ω_{\rm c}/c$, where $ω_{\rm c}$ is the…
Energetic electromagnetic emissions by astrophysical jets like those that are launched during the collapse of a massive star and trigger gamma-ray bursts (GRBs) are partially attributed to relativistic internal shocks. The shocks are mediated in the collisionless plasma of such jets by the filamentation instability of counterstreaming particle beams. The filamentation instability grows fastest only if the beams move at a relativistic relative speed. We model here with a particle-in-cell (PIC) simulation the collision of two cold pair clouds at the speed c/2 (c: speed of light). We demonstrate …
The course of non-thermal electron ejection in relativistic unmagnetized electron-ion shocks is investigated by performing self-consistent particle-in-cell simulations. The shocks are excited through the injection of relativistic jet into ambient plasma, leading to two distinct shocks (named as the trailing shock and leading shock) and a contact discontinuity. The Weibel-like instabilities heat the electrons up to approximately half of ion kinetic energy. The double layers formed in the trailing and leading edges then accelerated the electrons by the ion kinetic energy. The electron distributi…
Expansion of non-spherical relativistic blast waves is considered in the Kompaneets (the thin shell) approximation. We find that the relativistic motion effectively "freezes out" the lateral dynamics of the shock front: only extremely strongly collimated shocks, with the opening angles $Δθ\leq 1/Γ^2$, show appreciable modification of profiles due to sideways expansion. For less collimated profiles the propagation is nearly ballistic; the sideways expansion of relativistic shock becomes important only when they become mildly relativistic.
As a shock front interacts with turbulence, it develops corrugation which induces outgoing wave modes in the downstream plasma. For a fast shock wave, the incoming wave modes can either be fast magnetosonic waves originating from downstream, outrunning the shock, or eigenmodes of the upstream plasma drifting through the shock. Using linear perturbation theory in relativistic MHD, this paper provides a general analysis of the corrugation of relativistic magnetized fast shock waves resulting from their interaction with small amplitude disturbances. Transfer functions characterizing the linear re…
We examine limits to the energy to which cosmic rays can be accelerated by relativistic shocks, showing that acceleration of light ions as high as 100 EeV is unlikely. The implication of our estimates is that if ultra-high energy cosmic rays are accelerated by shocks, then those shocks are probably not relativistic.
This paper summarizes recent progresses in our theoretical understanding of particle acceleration at relativistic shock waves and it discusses two salient consequences: (1) the maximal energy of accelerated particles; (2) the impact of the shock-generated micro-turbulence on the multi-wavelength light curves of gamma-ray burst afterglows.
We analyze the main features of radiation-mediated shocks at arbitrary shock velocities, both non-relativistic and relativistic. We describe two mechanisms, which may lead to formation of a sharp viscous subshock within otherwise smooth velocity profile at the shock front, even if the radiation pressure in the upstream is overwhelmingly large. These mechanisms are specific to sub-relativistic and relativistic radiation-mediated shocks and set high-velocity shocks apart from their non-relativistic counterparts, which do not develop a subshock if the radiation pressure is high enough. We briefly…
We are demonstrating in what way slowing down ultrarelativistic shocks are creating GRB lags. The reflection process produces positive lags and Cracow acceleration process negative lags. We present a way the seed particles are injected into relativistic jets.
We present in this paper both a linear study and numerical relativistic MHD simulations of the non-resonant streaming instability occurring in the precursor of relativistic shocks. In the shock front restframe, we perform a linear analysis of this instability in a likely configuration for ultra-relativistic shock precursors. This considers magneto-acoustic waves having a wave vector perpendicular to the shock front and the large scale magnetic field. Our linear analysis is achieved without any assumption on the shock velocity and is thus valid for all velocity regimes. In order to check our ca…
Astrophysical explosions are accompanied by the propagation of a shock wave through an ambient medium. Depending on the mass and energy involved in the explosion, the shock velocity $V$ can be non-relativistic ($V \ll c$, where $c$ is the speed of light), ultra-relativistic ($V \simeq c$), or moderately relativistic ($V \sim few\times 0.1c$). While self-similar, energy-conserving solutions to the fluid equations that describe the shock propagation are known in the non-relativistic (the Sedov-Taylor blastwave) and ultra-relativistic (the Blandford-McKee blastwave) regimes, the finite speed of l…
Relativistic sources, e.g. gamma-ray bursts, pulsar wind nebulae and powerful active galactic nuclei produce relativistic outflows that lead to the formation of collisionless shock waves, where particle acceleration is thought to take place. Our understanding of relativistic shock acceleration has improved in the past decade, thanks to the combination of analytical studies and high level numerical simulations. In ultra-relativistic shocks, particle acceleration is made difficult by the generically transverse magnetic field and large advection speed of the shocked plasma. Fast growing microturb…
Collisionless relativistic shocks have been the focus of intense theoretical and numerical investigations in recent years. The acceleration of particles, the generation of electromagnetic microturbulence and the building up of a shock front are three interrelated essential ingredients of a relativistic collisionless shock wave. In this paper we investigate two issues of importance in this context: (1) the transport of suprathermal particles in the excited microturbulence upstream of the shock and its consequences regarding particle acceleration; (2) the preheating of incoming background electr…
We investigate shock structure and particle acceleration in relativistic magnetized collisionless electron-ion shocks by means of 2.5D particle-in-cell simulations with ion-to-electron mass ratios (m_i/m_e) ranging from 16 to 1000. We explore a range of inclination angles between the pre-shock magnetic field and the shock normal. In "subluminal" shocks, where relativistic particles can escape ahead of the shock along the magnetic field lines, ions are efficiently accelerated via a Fermi-like mechanism. The downstream ion spectrum consists of a relativistic Maxwellian and a high-energy power-la…
We explore the possibility that a single relativistic shock, where the gas dynamics is coupled with radiation, can fit the light curves of long GRBs. For this we numerically solve the one dimensional relativistic radiation hydrodynamics equations with a single initial shock. We calculate light curves due to the evolution of this shock in terms of the velocity of the shock, the opacity of the gas, mass density and density of radiated energy. We explore how the variation of each of these parameters provides different features in the light curves. As examples we include the fitting of two long GR…
Diffusive shock acceleration (DSA) at relativistic shocks is expected to be an important acceleration mechanism in a variety of astrophysical objects including extragalactic jets in active galactic nuclei and gamma ray bursts. These sources remain good candidate sites for the generation of ultra-high energy cosmic rays. In this paper, key predictions of DSA at relativistic shocks that are germane to production of relativistic electrons and ions are outlined. The technique employed to identify these characteristics is a Monte Carlo simulation of such diffusive acceleration in test-particle, rel…
We present results from a Monte Carlo simulation of a parallel collisionless shock undergoing particle acceleration. Our simulation, which contains parameterized scattering and a particular thermal leakage injection model, calculates the feedback between accelerated particles ahead of the shock, which influence the shock precursor and "smooth" the shock, and thermal particle injection. We show that there is a transition between nonrelativistic shocks, where the acceleration efficiency can be extremely high and the nonlinear compression ratio can be substantially greater than the Rankine-Hugoni…
For an expanding spherical relativistic shock, we derive relations between the parameters of downstream emitting zone and the quantities measured by a distant observer. These relations are formulated in terms of dimensionless effective coefficients combined with self-evident dimensional estimates. Our calculations take into account evolution of the shock's Lorentz factor, geometrical delay due to the shock's front curvature, and angular dependence of Lorentz boost for frequency and brightness. The relations are designed primarily for application in Gamma-Ray Burst afterglow studies, although t…
The interactions between a relativistic magnetized collisionless shock and dense clumps have been expected to play a crucial role on the magnetic field amplification and cosmic-ray acceleration. We investigate this process by two-dimensional Particle-In-Cell (PIC) simulations for the first time, where the clump size is much larger than the gyroradius of downstream particles. We also perform relativistic magnetohydrodynamic (MHD) simulations for the same condition to see the kinetic effects. We find that particles escape from the shocked clump along magnetic field lines in the PIC simulations, …
Relativistic magnetohydrodynamic shocks are efficient particle accelerators, often invoked in the models of gamma-ray bursts (GRBs) and shock-powered fast radio bursts (FRBs). Most theoretical studies assume a perpendicular shock with an ordered magnetic field perpendicular to the shock normal. However, the degree of magnetization $σ$ and the magnetic field geometry in shock-powered GRB/FRB scenarios are still poorly constrained by observations. Analogous to the magnetization $σ$ associated with the total field strength, we define a tangential magnetization $σ_\perp$ associated with the tangen…
The physics of instabilities in the precursor of relativistic collisionless shocks is of broad importance in high energy astrophysics, because these instabilities build up the shock, control the particle acceleration process and generate the magnetic fields in which the accelerated particles radiate. Two crucial parameters control the micro-physics of these shocks: the magnetization of the ambient medium and the Lorentz factor of the shock front; as of today, much of this parameter space remains to be explored. In the present paper, we report on a new instability upstream of electron-positron …
We use kinetic hybrid simulations (kinetic ions - fluid electrons) to characterize the fraction of ions that are accelerated to non-thermal energies at non-relativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasi-parallel shocks) reform quasi-periodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. This is a necessary condition for being injected, but it is not sufficient. Also by following the traject…
We study diffusive shock acceleration (DSA) of electrons in non-relativistic quasi-perpendicular shocks using self-consistent one-dimensional particle-in-cell (PIC) simulations. By exploring the parameter space of sonic and Alfvénic Mach numbers we find that high Mach number quasi-perpendicular shocks can efficiently accelerate electrons to power-law downstream spectra with slopes consistent with DSA prediction. Electrons are reflected by magnetic mirroring at the shock and drive non-resonant waves in the upstream. Reflected electrons are trapped between the shock front and upstream waves and …
An extreme case of electron shock drift acceleration in low Mach number collisionless shocks is investigated as a plausible mechanism of initial acceleration of relativistic electrons in large-scale shocks in galaxy clusters where upstream plasma temperature is of the order of 10 keV and a degree of magnetization is not too small. One-dimensional electromagnetic full particle simulations reveal that, even though a shock is rather moderate, a part of thermal incoming electrons are accelerated and reflected through relativistic shock drift acceleration and form a local nonthermal population just…
It is proposed that the prompt emission observed in bursts that exhibit a thermal component originates from relativistic radiation mediated shocks that form below the photosphere of the GRB outflow. It is argue that such shocks are expected to form in luminous bursts via collisions of shells that propagate with moderate Lorentz factors $Γ\lesssim 500$. Faster shells will collide above the photosphere to form collisionless shocks. We demonstrate that in events like GRB 090902B a substantial fraction of the explosion energy is dissipated below the photosphere, in a region of moderate optical dep…
Fast shocks that form in optically thick media are mediated by Compton scattering and, if relativistic, pair creation. Since the radiation force acts primarily on electrons and positrons, the question arises of how the force is mediated to the ions which are the dominant carriers of the shock energy. It has been widely thought that a small charge separation induced by the radiation force generates electric field inside the shock that decelerates the ions. In this paper we argue that, while this is true in sub-relativistic shocks which are devoid of positrons, in relativistic radiation mediated…
Radiation mediated shocks (RMS) play a key role in shaping the early emission observed in many transients. In most cases, e.g., shock breakout in supernovae, llGRBs and neutron star mergers, the upstream plasma is devoid of radiation, and the photons that ultimately reach the observer are generated predominantly inside and downstream of the shock. Predicting the observed spectrum requires detailed calculations of the shock structure and thermodynamic state that account properly for the shock microphysics. We present results of self-consistent Monte-Carlo simulations of photon-starved RMS, that…
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 < Γ< 10). It also reproduces approximate a…
We study the dynamic and radiative efficiency of conversion of kinetic-to-thermal/magnetic energy by internal shocks in relativistic magnetized outflows. A parameter study of a large number of collisions of cylindrical shells is performed. We explore how, while keeping the total flow luminosity constant, the variable fluid magnetization influences the efficiency and find that the interaction of shells in a mildly magnetized jet yields higher dynamic, but lower radiative efficiency than in a non-magnetized flow. A multi-wavelength radiative signature of different shell magnetization is computed…
The maximum energy to which cosmic rays can be accelerated at weakly-magnetised ultra-relativistic shocks is investigated. We demonstrate that for such shocks, in which the scattering of energetic particles is mediated exclusively by ion skin-depth scale structures, as might be expected for a Weibel-mediated shock, there is an intrinsic limit on the maximum energy to which particles can be accelerated. This maximum energy is determined from the requirement that particles must be isotropised in the downstream plasma frame before the mean field transports them far downstream, and falls considera…
Using the modified internal shock wave model we fit the gamma ray burst (GRB) light and spectral curves of 30 GRBs observed with BATSE. From the best fitting we obtain basic parameters of the relativistic shells which are in good agreement with predictions given earlier. We compare measured GRB parameters with those obtained from the model and discuss connections between them in the frame of the physical processes laying behind GRB events.
Relativistic shocks are usually thought to occur in violent astrophysical explosions. These collisionless shocks are mediated by a plasma kinetic streaming instability, often loosely referred to as the Weibel instability, which generates strong magnetic fields "from scratch" very efficiently. In this review paper we discuss the shock micro-physics and present a recent model of "pre-conditioning" of an initially unmagnetized upstream region via the cosmic-ray-driven Weibel-type instability.
We present the global solutions of low angular momentum, inviscid, advective accretion flow around Kerr-Taub-NUT (KTN) black hole in presence and absence of shock waves. These solutions are obtained by solving the governing equations that describe the relativistic accretion flow in KTN spacetime which is characterized by the Kerr parameter ($a_{\rm k}$) and NUT parameter ($n$). During accretion, rotating flow experiences centrifugal barrier that eventually triggers the discontinuous shock transition provided the relativistic shock conditions are satisfied. In reality, the viability of shocked …
We use fully kinetic particle-in-cell simulations with unprecedentedly large transverse box sizes to study particle acceleration in weakly-magnetized mildly relativistic shocks traveling at a velocity $\approx 0.75c$ and a Mach number of 15. We examine both subluminal (quasi-parallel) and superluminal (quasi-perpendicular) magnetic field orientations. We find that quasi-parallel shocks are mediated by a filamentary non-resonant (Bell) instability driven by non-thermal ions, producing magnetic fluctuations on scales comparable to the ion gyro-radius. In quasi-parallel shocks, both electrons and…
