Non-thermal Power-law Tail Research Articles

Turbulence and Particle Acceleration in a Relativistic Plasma

Abstract In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a nonthermal power-law tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameter σ ≫ 1) quickly evolves into a state with ultrarelativistic plasma temperature but mildly relativistic turbulent fluctuations. We present a phenomenological and numerical study suggesting that in this case, the exponent α in the power-law particle-energy distribution function, f(γ)d γ ∝ γ −α d γ, depends on magnetic compressibility of turbulence. Our analytic prediction for the scaling exponent α is in good agreement with the numerical results.

Nonthermal ion acceleration by the kink instability in nonrelativistic jets

We investigate the self-consistent particle acceleration physics associated with the development of the kink instability (KI) in nonrelativistic, electron-ion plasma jets. Using 3D fully kinetic particle-in-cell simulations, we show that the KI efficiently converts the initial toroidal magnetic field energy into energetic ions. The accelerated ions form a nonthermal power-law tail in the energy spectrum, containing ≃10% of the initial magnetic field energy, with the maximum ion energy extending to the confinement energy of the jet. We find that the ions are efficiently accelerated by the concerted action of the motional electric field and the highly tangled magnetic field that develop in the nonlinear phase of the KI: fast curvature drift motions of ions across magnetic field lines enable their acceleration along the electric field. We further investigate the role of Coulomb collisions in the ion acceleration efficiency and identify the collisional threshold above which nonthermal ion acceleration is suppressed. Our results reveal how energetic ions may result from unstable nonrelativistic plasma jets in space and astrophysics and provide constraints on the plasma conditions required to reproduce this acceleration mechanism in laboratory experiments.

Explosive X-point collapse in relativistic magnetically dominated plasma

The extreme properties of the gamma-ray flares in the Crab nebula present a clear challenge to our ideas on the nature of particle acceleration in relativistic astrophysical plasma. It seems highly unlikely that standard mechanisms of stochastic type are at work here and hence the attention of theorists has switched to linear acceleration in magnetic reconnection events. In this series of papers, we attempt to develop a theory of explosive magnetic reconnection in highly magnetized relativistic plasma which can explain the extreme parameters of the Crab flares. In the first paper, we focus on the properties of the X-point collapse. Using analytical and numerical methods (fluid and particle-in-cell simulations) we extend Syrovatsky’s classical model of such collapse to the relativistic regime. We find that the collapse can lead to the reconnection rate approaching the speed of light on macroscopic scales. During the collapse, the plasma particles are accelerated by charge-starved electric fields, which can reach (and even exceed) values of the local magnetic field. The explosive stage of reconnection produces non-thermal power-law tails with slopes that depend on the average magnetization $\unicode[STIX]{x1D70E}$. For sufficiently high magnetizations and vanishing guide field, the non-thermal particle spectrum consists of two components: a low-energy population with soft spectrum that dominates the number census; and a high-energy population with hard spectrum that possesses all the properties needed to explain the Crab flares.

Particle acceleration in relativistic magnetic flux-merging events

Using analytical and numerical methods (fluid and particle-in-cell simulations) we study a number of model problems involving merger of magnetic flux tubes in relativistic magnetically dominated plasma. Mergers of current-carrying flux tubes (exemplified by the two-dimensional ‘ABC’ structures) and zero-total-current magnetic flux tubes are considered. In all cases regimes of spontaneous and driven evolution are investigated. We identify two stages of particle acceleration during flux mergers: (i) fast explosive prompt X-point collapse and (ii) ensuing island merger. The fastest acceleration occurs during the initial catastrophic X-point collapse, with the reconnection electric field of the order of the magnetic field. During the X-point collapse, particles are accelerated by charge-starved electric fields, which can reach (and even exceed) values of the local magnetic field. The explosive stage of reconnection produces non-thermal power-law tails with slopes that depend on the average magnetization $\unicode[STIX]{x1D70E}$. For plasma magnetization $\unicode[STIX]{x1D70E}\leqslant 10^{2}$ the spectrum power-law index is $p>2$; in this case the maximal energy depends linearly on the size of the reconnecting islands. For higher magnetization, $\unicode[STIX]{x1D70E}\geqslant 10^{2}$, the spectra are hard, $p<2$, yet the maximal energy $\unicode[STIX]{x1D6FE}_{\text{max}}$ can still exceed the average magnetic energy per particle, ${\sim}\unicode[STIX]{x1D70E}$, by orders of magnitude (if $p$ is not too close to unity). The X-point collapse stage is followed by magnetic island merger that dissipates a large fraction of the initial magnetic energy in a regime of forced magnetic reconnection, further accelerating the particles, but proceeds at a slower reconnection rate.

Erratum: Reconnection and particle acceleration in interacting flux ropes – II. 3D effects on test particles in magnetically dominated plasmas

We analyze particle acceleration in explosive reconnection events in magnetically dominated proton-electron plasmas. Reconnection is driven by large-scale magnetic stresses in interacting current-carrying flux tubes. Our model relies on development of current-driven instabilities on macroscopic scales. These tilt-kink instabilities develop in an initially force-free equilibrium of repelling current channels. Using MHD methods we study a 3D model of repelling and interacting flux tubes in which we simultaneously evolve test particles, guided by electromagnetic fields obtained from MHD. We identify two stages of particle acceleration; Initially particles accelerate in the current channels, after which the flux ropes start tilting and kinking and particles accelerate due to reconnection processes in the plasma. The explosive stage of reconnection produces non-thermal energy distributions with slopes that depend on plasma resistivity and the initial particle velocity. We also discuss the influence of the length of the flux ropes on particle acceleration and energy distributions. This study extends previous 2.5D results to 3D setups, providing all ingredients needed to model realistic scenarios like solar flares, black hole flares and particle acceleration in pulsar wind nebulae: formation of strong resistive electric fields, explosive reconnection and non-thermal particle distributions. By assuming initial energy equipartition between electrons and protons, applying low resistivity in accordance with solar corona conditions and limiting the flux rope length to a fraction of a solar radius we obtain realistic energy distributions for solar flares with non-thermal power law tails and maximum electron energies up to 11 MeV and maximum proton energies up to 1 GeV.

Reconnection and particle acceleration in interacting flux ropes – II. 3D effects on test particles in magnetically dominated plasmas

We analyze particle acceleration in explosive reconnection events in magnetically dominated proton-electron plasmas. Reconnection is driven by large-scale magnetic stresses in interacting current-carrying flux tubes. Our model relies on development of current-driven instabilities on macroscopic scales. These tilt-kink instabilities develop in an initially force-free equilibrium of repelling current channels. Using MHD methods we study a 3D model of repelling and interacting flux tubes in which we simultaneously evolve test particles, guided by electromagnetic fields obtained from MHD. We identify two stages of particle acceleration; Initially particles accelerate in the current channels, after which the flux ropes start tilting and kinking and particles accelerate due to reconnection processes in the plasma. The explosive stage of reconnection produces non-thermal energy distributions with slopes that depend on plasma resistivity and the initial particle velocity. We also discuss the influence of the length of the flux ropes on particle acceleration and energy distributions. This study extends previous 2.5D results to 3D setups, providing all ingredients needed to model realistic scenarios like solar flares, black hole flares and particle acceleration in pulsar wind nebulae: formation of strong resistive electric fields, explosive reconnection and non-thermal particle distributions. By assuming initial energy equipartition between electrons and protons, applying low resistivity in accordance with solar corona conditions and limiting the flux rope length to a fraction of a solar radius we obtain realistic energy distributions for solar flares with non-thermal power law tails and maximum electron energies up to 11 MeV and maximum proton energies up to 1 GeV.

COLLISIONLESS ELECTRON–ION SHOCKS IN RELATIVISTIC UNMAGNETIZED JET–AMBIENT INTERACTIONS: NON-THERMAL ELECTRON INJECTION BY DOUBLE LAYER

ABSTRACT 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 a relativistic jet into ambient plasma, leading to two distinct shocks (referred to as the trailing shock and leading shock) and a contact discontinuity. The Weibel-like instabilities heat the electrons up to approximately half of the ion kinetic energy. The double layers formed in the trailing and leading edges then accelerate the electrons up to the ion kinetic energy. The electron distribution function in the leading edge shows a clear, non-thermal power-law tail which contains ∼1% of electrons and ∼8% of the electron energy. Its power-law index is −2.6. The acceleration efficiency is ∼23% by number and ∼50% by energy, and the power-law index is −1.8 for the electron distribution function in the trailing edge. The effect of the dimensionality is examined by comparing the results of three-dimensional simulations with those of two-dimensional simulations. The comparison demonstrates that electron acceleration is more efficient in two dimensions.

NON-THERMAL ELECTRON ACCELERATION IN LOW MACH NUMBER COLLISIONLESS SHOCKS. I. PARTICLE ENERGY SPECTRA AND ACCELERATION MECHANISM

Electron acceleration to non-thermal energies in low Mach number (M<5) shocks is revealed by radio and X-ray observations of galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Diffusive shock acceleration, also known as first-order Fermi acceleration, cannot be directly invoked to explain the acceleration of electrons. Rather, an additional mechanism is required to pre-accelerate the electrons from thermal to supra-thermal energies, so they can then participate in the Fermi process. In this work, we use two- and three-dimensional particle-in-cell plasma simulations to study electron acceleration in low Mach number shocks. We focus on the particle energy spectra and the acceleration mechanism in a reference run with M=3 and a quasi-perpendicular pre-shock magnetic field. We find that about 15 percent of the electrons can be efficiently accelerated, forming a non-thermal power-law tail in the energy spectrum with a slope of p~2.4. Initially, thermal electrons are energized at the shock front via shock drift acceleration. The accelerated electrons are then reflected back upstream, where their interaction with the incoming flow generates magnetic waves. In turn, the waves scatter the electrons propagating upstream back toward the shock, for further energization via shock drift acceleration. In summary, the self-generated waves allow for repeated cycles of shock drift acceleration, similarly to a sustained Fermi-like process. This mechanism offers a natural solution to the conflict between the bright radio synchrotron emission observed from the outskirts of galaxy clusters and the low electron acceleration efficiency usually expected in low Mach number shocks.

THE EFFICIENCY OF SECOND-ORDER FERMI ACCELERATION BY WEAKLY COMPRESSIBLE MAGNETOHYDRODYNAMIC TURBULENCE

We investigate the effects of pitch-angle scattering on the efficiency of particle heating and acceleration by MHD turbulence using phenomenological estimates and simulations of non-relativistic test particles interacting with strong, subsonic MHD turbulence. We include an imposed pitch-angle scattering rate, which is meant to approximate the effects of high frequency plasma waves and/or velocity space instabilities. We focus on plasma parameters similar to those found in the near-Earth solar wind, though most of our results are more broadly applicable. An important control parameter is the size of the particle mean free path lambda_{mfp} relative to the scale of the turbulent fluctuations L. For small scattering rates, particles interact quasi-resonantly with turbulent fluctuations in magnetic field strength. Scattering increases the long-term efficiency of this resonant heating by factors of a few-10, but the distribution function does not develop a significant non-thermal power-law tail. For higher scattering rates, the interaction between particles and turbulent fluctuations becomes non-resonant, governed by particles heating and cooling adiabatically as they encounter turbulent density fluctuations. Rapid pitch-angle scattering can produce a power-law tail in the proton distribution function but this requires fine-tuning of parameters. Moreover, in the near-Earth solar wind, a significant power-law tail cannot develop by this mechanism because the particle acceleration timescales are longer than the adiabatic cooling timescale set by the expansion of the solar wind. Our results thus imply that MHD-scale turbulent fluctuations are unlikely to be the origin of the v^{-5} tail in the proton distribution function observed in the solar wind.

The AGILE monitoring of Cygnus X-3: transient gamma-ray emission and spectral constraints

We present the AGILE-GRID monitoring of Cygnus X-3, during the period between November 2007 and July 2009. We report here the whole AGILE-GRID monitoring of Cygnus X-3 in the AGILE "pointing" mode data-taking, to confirm that the gamma-ray activity coincides with the same repetitive pattern of multiwavelength emission and to analyze in depth the overall gamma-ray spectrum by assuming both leptonic and hadronic scenarios. Seven intense gamma-ray events were detected in this period, with a typical event lasting one or two days. These durations are longer than the likely cooling times of the gamma-ray emitting particles, implying we see continuous acceleration rather than the result of an impulsive event such as the ejection of a single plasmoid which then cools as it propagates outwards. Cross-correlating the AGILE-GRID light curve with X-ray and radio monitoring data, we find that the main events of gamma-ray activity have been detected while the system was in soft spectral X-ray states (RXTE/ASM count rate > 3 counts/s), that coincide with local and often sharp minima of the hard X-ray flux (Swift/BAT count rate < 0.02 counts/cm^2/s), a few days before intense radio outbursts. [...] These gamma-ray events may thus reflect a sharp transition in the structure of the accretion disk and its corona, which leads to a rebirth of the microquasar jet and subsequent enhanced radio activity. [...] Finally, we examine leptonic and hadronic emission models for the gamma-ray events and find that both scenarios are valid. In the leptonic model - based on inverse Compton scatterings of mildly relativistic electrons on soft photons from the Wolf-Rayet companion star and from the accretion disk - the emitting particles may also contribute to the overall hard X-ray spectrum, possibly explaining the hard non-thermal power-law tail sometimes seen during special soft X-ray states in Cygnus X-3.

A multi-wavelength investigation of the non-thermal radio emitting O-star 9 Sgr

We report the results of a multi-wavelength investigation of the O4 V star 9 Sgr (= HD 164794). Our data include observations in the X-ray domain withXMM-Newton, in the radio domain with the VLA as well as optical spectroscopy. 9 Sgr is one of a few presumably single OB stars that display non-thermal radio emission. This phenomenon is attributed to synchrotron emission by relativistic electrons accelerated in strong hydrodynamic shocks in the stellar wind. Given the enormous supply of photospheric UV photons in the wind of 9 Sgr, inverse Compton scattering by these relativistic electrons is a priori expected to generate a non-thermal power law tail in the X-ray spectrum. Our EPIC and RGS spectra of 9 Sgr reveal a more complex situation than expected from this simple theoretical picture. While the bulk of the thermal X-ray emission from 9 Sgr arises most probably in a plasma at temperature3 10 6 K distributed throughout the wind, the nature of the hard emission in the X-ray spectrum is less clear. Assuming a non-thermal origin, our best fitting model yields a photon index of2: 9f or the power law component which would imply a low compression ratio of1:79 for the shocks responsible for the electron acceleration. However, the hard emission can also be explained by a thermal plasma at a temperature2 10 7 K. Our VLA data indicate that the radio emission of 9 Sgr was clearly non-thermal at the time of the XMM-Newton observation. Again, we derive a low compression ratio (1.7) for the shocks that accelerate the electrons responsible for the synchrotron radio emission. Finally, our optical spectra reveal long-term radial velocity variations suggesting that 9 Sgr could be a long-period spectroscopic binary.

Synchrotron emission and gamma-ray bursts

The parameter space within which synchrotron emission models for gamma-ray burst spectra are valid is evaluated in the cases of thermal and power-law particle distributions. The spectra emitted by noncooling and cooling thermal and power-law particle distributions are modeled numerically over relativistic and nonrelativistic regimes. The structure of the radiation is defined near the fundamental and the continuum up to the 1000th harmonic. Comparisons are made with burst event data collected during the Apollo 16, Venera, SMM, Pioneer Venus Orbiter and Hackucho missions. A two-component synchrotron model is proposed for gamma-ray burst events. The electron-positron distribution is projected to have a thermal component and a nonthermal power-law tail.

Low-Energy Charged Particle Environment at Jupiter: A First Look

The low-energy charged particle instrument on Voyager was designed to measure the hot plasma (electron and ion energies greater, similar 15 and greater, similar 30 kiloelectron volts, respectively) component of the Jovian magnetosphere. Protons, heavier ions, and electrons at these energies were detected nearly a third of an astronomical unit before encounter with the planet. The hot plasma near the magnetosphere boundary is predominantly composed of protons, oxygen, and sulfur in comparable proportions and a nonthermal power-law tail; its temperature is about 3 x 10(8) K, density about 5 x 10(-3) per cubic centimeter, and energy density comparable to that of the magnetic field. The plasma appears to be corotating throughout the magnetosphere; no hot plasma outflow, as suggested by planetary wind theories, is observed. The main constituents of the energetic particle population ( greater, similar200 kiloelectron volts per nucleon) are protons, helium, oxygen, sulfur, and some sodium observed throughout the outer magnetosphere; it is probable that the sulfur, sodium, and possibly oxygen originate at 1o. Fluxes in the outbound trajectory appear to be enhancedfrom approximately 90 degrees to approximately 130 degrees longitude (System III). Consistent low-energy particle flux periodicities were not observed on the inbound trajectory; both 5-and 10-hour periodicities were observed on the outbound trajectory. Partial absorption of > 10 million electron volts electrons is observed in the vicinity of the Io flux tube.