Relativistic Turbulence Research Articles

Radiation Process in Relativistic MHD Waves: The Case of Circularly Polarized Alfvén Waves

Turbulence in highly magnetized plasma can be relativistic and induce an electric field comparable to the background magnetic field. Such a strong electric field can affect the emission process of nonthermal electrons. As the first step toward elucidating the emission process in relativistic turbulence, we study the radiation process of electrons in relativistic circularly polarized Alfvén waves. While the induced electric field boosts the average energy of low-energy electrons with a Larmor radius smaller than the wavelength, the emissivity for such electrons is suppressed because of the elongated gyromotion trajectory. The trajectory of high-energy electrons is shaken by the small-scale electric field, which enhances the emissivity. Since the effective Lorentz factor of E × B drift is ≃2 in the circularly polarized Alfvén waves, the deviation from the standard synchrotron emission is not so prominent. However, a power-law energy injection in the waves can produce a concave photon spectrum, which is similar to the GeV extra component seen in GRB spectra. If the turbulence electric field is responsible for the GeV extra component in GRBs, the estimates of the typical electron energy and magnetic field should be largely altered.

Intermittency and Dissipative Structures Arising from Relativistic Magnetized Turbulence

Kinetic simulations of relativistic turbulence have significantly advanced our understanding of turbulent particle acceleration. Recent progress has highlighted the need for an updated acceleration theory that can account for particle acceleration within the plasma’s coherent structures. Here, we investigate how intermittency modeling connects statistical fluctuations in turbulence to regions of high-energy dissipation. This connection is established by employing a generalized She–Leveque model to characterize the exponents ζ p for the structure functions Sp∝lζp . The fitting of the scaling exponents provides us with a measure of the codimension of the dissipative structures, for which we subsequently determine the filling fraction. We perform our analysis for a range of magnetizations σ and relative fluctuation amplitudes δ B 0/B 0. We find that increasing values of σ and δ B 0/B 0 allow the turbulent cascade to break sheetlike structures into smaller regions of dissipation that resemble chains of flux ropes. However, as their dissipation measure increases, the dissipative regions become less volume filling. With this work, we aim to inform future turbulent acceleration theories that incorporate particle energization from interactions with coherent structures within relativistic turbulence.

A complete analysis of the link uncertainty budget for pulsed laser time transfer on China space station

High-precision Time-Frequency Rack (HTFR) mission, a part of experiment module II of the China Space Station (CSS), was equipped with a Sr optical clock, H-maser, and laser-cooled microwave clock. To compare time and frequency across widely separated clocks, a microwave link, and a pulsed laser link were both established, which probably enables new possibilities for fundamental science, geodesy, and metrology. Based on the existing relativistic theory for time and frequency transfer, we derive a relativistic model of satellite-ground laser time transfer on CSS (CLT), which can be of direct use in CLT data processing. In addition to first and second-order Sagnac effects, it also includes relativistic rate shifts, atmospheric refraction, and turbulence, laser retroreflector array (LRA) range correction, and position correction between detector and reflector, satisfying the stability evaluation of CSS atomic clocks with fractional frequency stability of 3 × 10−17/10000 s. Additionally, we numerically investigate the link error magnitude and use Monte Carlo simulations to assess the impact of correcting for link errors on the stability of the CLT, taking into account the CSS orbit and attitude determinations as well as the CLT payload calibration parameters. It is shown that the CLT link can be considered to reach a TDEV of approximately 0.1 ps/300 s while meeting the CSS design objectives. The primary factors that influence the stability of the CLT are the position correction between detector and reflector, LRA range correction, and the coupling relation of these two error distributions.

Gamma-ray Emission and Variability Processes in High-Energy-Peaked BL Lacertae Objects

BL Lac objects are active galactic nuclei notable for a beamed nonthermal radiation, which is generated in one of the relativistic jets forming a small angle to the observer’s line-of-sight. The broadband spectra of BL Lacs show a two-component spectral energy distribution (SED). High-energy-peaked BL Lacs (HBLs) exhibit their lower-energy (synchrotron) peaks at UV to X-ray frequencies. The origin of the higher-energy SED component, representing the γ-ray range in HBLs, is still controversial and different emission scenarios (one- and multi-zone synchrotron self-Compton, hadronic etc.) are proposed. In γ-rays, HBLs show a complex flaring behavior with rapid and large-amplitude TeV-band variations on timescales down to a few minutes. This review presents a detailed characterization of the hypothetical emission mechanisms which could contribute to the γ-ray emission, their application to the nearby TeV-detected HBLs, successes in the broadband SED modeling and difficulties in the interpretation of the observational data. I also overview the unstable processes to be responsible for the observed γ-ray variability and particle energization up to millions of Lorentz factors (relativistic shocks, magnetic reconnection, turbulence and jet-star interaction). Finally, the future prospects for solving the persisting problems by means of the dedicated gamma-ray observations and sophisticated simulations are also addressed.

Spatial Intermittency of Particle Distribution in Relativistic Plasma Turbulence

Relativistic magnetically dominated turbulence is an efficient engine for particle acceleration in a collisionless plasma. Ultrarelativistic particles accelerated by interactions with turbulent fluctuations form nonthermal power-law distribution functions in the momentum (or energy) space, f(γ)d γ ∝ γ −α d γ, where γ is the Lorenz factor. We argue that in addition to exhibiting non-Gaussian distributions over energies, particles energized by relativistic turbulence also become highly intermittent in space. Based on particle-in-cell numerical simulations and phenomenological modeling, we propose that the bulk plasma density has lognormal statistics, while the density of the accelerated particles, n, has a power-law distribution function, . We argue that the scaling exponents are related as β ≈ α + 1, which is broadly consistent with numerical simulations. Non-space-filling, intermittent distributions of plasma density and energy fluctuations may have implications for plasma heating and for radiation produced by relativistic turbulence.

Blazar Jets as Possible Sources of Ultra-High Energy Photons: A Short Review

In this paper, I present a qualitative discussion on the prospect of production of ultra-high photons in blazars. The sources are a subclass of active galactic nuclei which host supermassive black holes and fire relativistic jets into the intergalactic medium. The kpc-scale jets are believed to be dominated by Poynting flux and constitute one of the most efficient cosmic particle accelerators, that potentially are capable of accelerating the particles up to EeV energies. Recent IceCube detection of astrophysical neutrino emissions, in coincidence with the enhanced gamma-ray from Tev blazar TXS 0506 + 056, further supports hadronic models of blazar emissions in which particle acceleration processes, such as relativistic shocks, magnetic re-connection, and relativistic turbulence, could energize hadrons, e.g., protons, up to energies equivalent to billions of Lorentz factors. The ensuing photo-pionic processes may then result in gamma-rays accompanied by neutrino flux. Furthermore, the fact that blazars are the dominant source of observed TeV emission encourages search for signatures of acceleration scenarios that would lead to the creation of ultra-high-energy photons.

Runko: Modern multiphysics toolbox for plasma simulations

runko is a new open-source plasma simulation framework implemented in C++ and Python. It is designed to function as an easy-to-extend general toolbox for simulating astrophysical plasmas with different theoretical and numerical models. Computationally intensive low-level kernels are written in modern C++ taking advantage of polymorphic classes, multiple inheritance, and template metaprogramming. High-level functionality is operated with Python scripts. The hybrid program design ensures good code performance together with ease of use. The framework has a modular object-oriented design that allows the user to easily add new numerical algorithms to the system. The code can be run on various computing platforms ranging from laptops (shared-memory systems) to massively parallel supercomputer architectures (distributed-memory systems). The framework supports heterogeneous multiphysics simulations in which different physical solvers can be combined and run simultaneously. Here, we showcase the framework’s relativistic particle-in-cell (PIC) module by presenting (i) 1D simulations of relativistic Weibel instability, (ii) 2D simulations of relativistic kinetic turbulence in a suddenly stirred magnetically-dominated pair plasma, and (iii) 3D simulations of collisionless shocks in an unmagnetized medium.

Non-thermal particle acceleration from maximum entropy in collisionless plasmas

Dissipative processes cause collisionless plasmas in many systems to develop non-thermal particle distributions with broad power-law tails. The prevalence of power-law energy distributions in space/astrophysical observations and kinetic simulations of systems with a variety of acceleration and trapping (or escape) mechanisms poses a deep mystery. We consider the possibility that such distributions can be modelled from maximum-entropy principles, when accounting for generalizations beyond the Boltzmann–Gibbs entropy. Using a dimensional representation of entropy (related to the Renyi and Tsallis entropies), we derive generalized maximum-entropy distributions with a power-law tail determined by the characteristic energy scale at which irreversible dissipation occurs. By assuming that particles are typically energized by an amount comparable to the free energy (per particle) before equilibrating, we derive a formula for the power-law index as a function of plasma parameters for magnetic dissipation in systems with sufficiently complex topologies. The model reproduces several results from kinetic simulations of relativistic turbulence and magnetic reconnection.

Balancing turbulent heating with radiative cooling in blazars

ABSTRACT Recently, particle-in-cell (PIC) simulations have shown that relativistic turbulence in collisionless plasmas can result in an equilibrium particle distribution function where turbulent heating is balanced by radiative cooling of electrons. Strongly magnetized plasmas are characterized by higher energy peaks and broader particle distributions. In relativistically moving astrophysical jets, it is believed that the flow is launched Poynting flux dominated and that the resulting magnetic instabilities may create a turbulent environment inside the jet, i.e. the regime of relativistic turbulence. In this paper, we extend previous PIC simulation results to larger values of plasma magnetization by linearly extrapolating the diffusion and advection coefficients relevant for the turbulent plasmas under consideration. We use these results to build a single-zone turbulent jet model that is based on the global parameters of the blazar emission region, and consistently calculate the particle distribution and the resulting emission spectra. We then test our model by comparing its predictions with the broad-band quiescent emission spectra of a dozen blazars. Our results show good agreement with observations of low synchrotron peaked (LSP) sources and find that LSPs are moderately Poynting flux dominated with magnetization 1 ≲ σ ≲ 5, have bulk Lorentz factor Γj ∼ 10–30, and that the turbulent region is located at the edge, or just beyond the broad-line region (BLR). The turbulence is found to be driven at an area comparable to the jet cross-section.

Effect of the Nuclear Equation of State and Relativistic Turbulence on Core-Collapse Supernovae

The nuclear Equation of State (EoS) is an important component in the evolution and subsequent explosion of core collapse supernovae. We make a survey of various equations of state that can be found in the literature and analyze their effect on the explosion. To simulate the supernovae, we use the general relativistic spherically-symmetric code GR1D, modified to take into account the effects of three-dimensional turbulence through a new mixing length theory approach (STIR). We show that the viability of the explosion is quite EoS dependent and that the strength of explosions correlate best with the central entropy density right after bounce and the onset of turbulent mixing in the proto-neutron star.

Dynamic Alignment and Plasmoid Formation in Relativistic Magnetohydrodynamic Turbulence

Abstract We present high-resolution 2D and 3D simulations of magnetized decaying turbulence in relativistic, resistive magnetohydrodynamics. The simulations show dynamic formation of large-scale intermittent long-lived current sheets being disrupted into plasmoid chains by the tearing instability. These current sheets are locations of enhanced magnetic-field dissipation and heating of the plasma. We find magnetic energy spectra ∝k −3/2, together with strongly pronounced dynamic alignment of Elsässer fields and of velocity and magnetic fields, for strong guide-field turbulence, whereas we retrieve spectra ∝k −5/3 for the case of a weak guide-field.

Particle Energization in Relativistic Plasma Turbulence: Solenoidal versus Compressive Driving

Abstract Many high-energy astrophysical systems contain magnetized collisionless plasmas with relativistic particles, in which turbulence can be driven by an arbitrary mixture of solenoidal and compressive motions. For example, turbulence in hot accretion flows may be driven solenoidally by the magnetorotational instability or compressively by spiral shock waves. It is important to understand the role of the driving mechanism on kinetic turbulence and the associated particle energization. In this work, we compare particle-in-cell simulations of solenoidally driven turbulence with similar simulations of compressively driven turbulence. We focus on plasma that has an initial beta of unity, relativistically hot electrons, and varying ion temperature. Apart from strong large-scale density fluctuations in the compressive case, the turbulence statistics are similar for both drives, and the bulk plasma is described reasonably well by an isothermal equation of state. We find that nonthermal particle acceleration is more efficient when turbulence is driven compressively. In the case of relativistically hot ions, both driving mechanisms ultimately lead to similar power-law particle energy distributions, but over a different duration. In the case of nonrelativistic ions, there is significant nonthermal particle acceleration only for compressive driving. Additionally, we find that the electron-to-ion heating ratio is less than unity for both drives, but takes a smaller value for compressive driving. We demonstrate that this additional ion energization is associated with the collisionless damping of large-scale compressive modes via perpendicular electric fields.

Fully developed relativistic turbulence

We use a simple model consisting of energy-momentum tensor conservation and a Maxwell-Cattaneo equation for its viscous part to study nonlinear phenomena in a real relativistic fluid. We focus on new types of behavior without nonrelativistic equivalents, such as an entropy cascade driven by fluctuations in the tensor degrees of freedom of the theory. We write down the von K\'arm\'an-Howarth equations for this kind of turbulence, and consider the correlations corresponding to fully developed turbulence.

Production and Persistence of Extreme Two-temperature Plasmas in Radiative Relativistic Turbulence

Abstract Turbulence is a predominant process for energizing electrons and ions in collisionless astrophysical plasmas, and thus is responsible for shaping their radiative signatures (luminosity, spectra, and variability). To better understand the kinetic properties of a collisionless radiative plasma subject to externally driven turbulence, we investigate particle-in-cell simulations of relativistic plasma turbulence with external inverse Compton cooling acting on the electrons. We find that ions continuously heat up while electrons gradually cool down (due to the net effect of radiation), and hence the ion-to-electron temperature ratio T i /T e grows in time. We show that T i /T e is limited only by the size and duration of the simulations (reaching ), indicating that there are no efficient collisionless mechanisms of electron–ion thermal coupling. This result has implications for models of radiatively inefficient accretion flows, such as observed in the Galactic center and in M87, for which so-called two-temperature plasmas with have been invoked to explain their low luminosity. Additionally, we find that electrons acquire a quasi-thermal distribution (dictated by the competition of turbulent particle energization and radiative cooling), while ions undergo efficient nonthermal acceleration (acquiring a harder distribution than in equivalent nonradiative simulations). There is a modest nonthermal population of high-energy electrons that are beamed intermittently in space, time, and direction; these beamed electrons may explain rapid flares in certain high-energy astrophysical systems (e.g., in the Galactic center). These numerical results demonstrate that extreme two-temperature plasmas can be produced and maintained by relativistic radiative turbulence.

A global model of particle acceleration at pulsar wind termination shocks

Context. Pulsar wind nebulae are efficient particle accelerators, and yet the processes at work remain elusive. Self-generated, microturbulence is too weak in relativistic magnetized shocks to accelerate particles over a wide energy range, suggesting that the global dynamics of the nebula may be involved in the acceleration process instead. Aims. In this work, we study the role played by the large-scale anisotropy of the transverse magnetic field profile on the shock dynamics. Methods. We performed large two-dimensional particle-in-cell simulations for a wide range of upstream plasma magnetizations, from weakly magnetized to strongly magnetized pulsar winds. Results. The magnetic field anisotropy leads to a dramatically different structure of the shock front and downstream flow. A large-scale velocity shear and current sheets form in the equatorial regions and at the poles, where they drive strong plasma turbulence via Kelvin-Helmholtz vortices and kinks. The mixing of current sheets in the downstream flow leads to efficient nonthermal particle acceleration. The power-law spectrum hardens with increasing magnetization, akin to those found in relativistic reconnection and kinetic turbulence studies. The high end of the spectrum is composed of particles surfing on the wake produced by elongated spearhead-shaped cavities forming at the shock front and piercing through the upstream flow. These particles are efficiently accelerated via the shear-flow acceleration mechanism near the Bohm limit. Conclusions. Magnetized relativistic shocks are very efficient particle accelerators. Capturing the global dynamics of the downstream flow is crucial to understanding them, and therefore local plane parallel studies may not be appropriate for pulsar wind nebulae and possibly other astrophysical relativistic magnetized shocks. A natural outcome of such shocks is a variable and Doppler-boosted synchrotron emission at the high end of the spectrum originating from the shock-front cavities, reminiscent of the mysterious Crab Nebula gamma-ray flares.

Particle acceleration in relativistic turbulence: A theoretical appraisal

The authors provide a comprehensive study, both analytical and numerical, of cosmic ray acceleration in relativistic magnetohydrodynamic (MHD) turbulence. Effects beyond the magnetostatic quasi-linear theory, such as resonance broadening due to large-scale turbulence modes, as well as a non-MHD effect, are incorporated.

First-principles Demonstration of Diffusive-advective Particle Acceleration in Kinetic Simulations of Relativistic Plasma Turbulence

Abstract Nonthermal relativistic plasmas are ubiquitous in astrophysical systems like pulsar wind nebulae and active galactic nuclei, as inferred from their emission spectra. The underlying nonthermal particle acceleration (NTPA) processes have traditionally been modeled with a Fokker–Planck (FP) diffusion-advection equation in momentum space. In this Letter, we directly test the FP framework in ab initio kinetic simulations of driven magnetized turbulence in relativistic pair plasma. By statistically analyzing the motion of tracked particles, we demonstrate the diffusive nature of NTPA and measure the FP energy diffusion (D) and advection (A) coefficients as functions of particle energy . We find that scales as in the high-energy nonthermal tail, in line with second-order Fermi acceleration theory, but has a much weaker scaling at lower energies. We also find that A is not negligible and reduces NTPA by tending to pull particles toward the peak of the particle energy distribution. This study provides strong support for the FP picture of turbulent NTPA, thereby enhancing our understanding of space and astrophysical plasmas.

A Nonthermal Bomb Explains the Near-infrared Superflare of Sgr A*

Abstract The Galactic center supermassive black hole, Sgr A*, has experienced a strong, unprecedented flare in 2019 May when its near-infrared luminosity reached much brighter levels than ever measured. We argue that an explosive event of particle acceleration to nonthermal energies in the innermost parts of the accretion flow—a nonthermal bomb—explains the near-infrared light curve. We discuss potential mechanisms that could explain this event such as magnetic reconnection and relativistic turbulence acceleration. Multiwavelength monitoring of such superflares in radio, infrared, and X-rays should allow a concrete test of the nonthermal bomb model and put better constraints on the mechanism that triggered the bomb.

Gamma-Ray Bursts Induced by Turbulent Reconnection

Abstract We revisit the Internal-Collision-induced MAgnetic Reconnection and Turbulence model of gamma-ray bursts (GRBs) in view of the advances made in understanding of both relativistic magnetic turbulence and relativistic turbulent magnetic reconnection. We identify the kink instability as the most natural way of changing the magnetic configuration to release the magnetic free energy through magnetic reconnection, as well as driving turbulence that enables fast turbulent reconnection. We show that this double role of the kink instability is important for explaining the prompt emission of GRBs. Our study confirms the critical role that turbulence plays in boosting reconnection efficiency in GRBs and suggests that the GRB phenomena can be modeled in the magnetohydrodynamics approximation. That is, the modeling is not constrained by reproducing the detailed microphysical properties of relativistic magnetized plasmas.

Generalized Fermi acceleration

In highly conducting astrophysical plasmas, charged particles are generically accelerated through Fermi-type processes involving repeated interactions with moving magnetized scattering centers. The present paper proposes a generalized description of these acceleration processes, by following the momentum of the particle through a continuous sequence of accelerated frames, defined in such a way that the electric field vanishes at each point along the particle trajectory. In each locally inertial frame, the Lorentz force affects the direction of motion of the particle, but the energy changes solely as a result of inertial corrections. This unified description of Fermi acceleration applies equally well in sub- and ultrarelativistic settings, in Cartesian or non-Cartesian geometries, flat or nonflat space-time. Known results are recovered in a variety of regimes -- shock, turbulent and shear acceleration -- and new results are derived in lieu of applications, e.g. nonresonant acceleration in relativistic turbulence, stochastic unipolar inductive acceleration and centrifugo-shear acceleration close to the horizon of a black hole.