3-D Rpic Simulations of Relativistic Jets: Particle Acceleration, Magnetic Field Generation, and Emission

We have applied numerical simulations and modeling to the particle acceleration, magnetic field generation, and emission from relativistic shocks. We investigate the nonlinear stage of theWeibel instability and compare our simulations with the observed gamma-ray burst emission. In collisionless shocks, plasma waves and their associated instabilities (e.g., the Weibel, Buneman and other two-stream instabilities) are responsible for particle (electron, positron, and ion) acceleration and magnetic field generation. 3-D relativistic electromagnetic particle (REMP) simulations with three different electron-positron jet velocity distributions and also with an electron-ion plasma have been performed and show shock processes including spatial and temporal evolution of shocks in unmagnetized ambient plasmas. The growth time and nonlinear saturation levels depend on the initial jet parallel velocity distributions. Simulations show that the Weibel instability created in the collisionless shocks accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The nonlinear fluctuation amplitude of densities, currents, electric, and magnetic fields in the electron-positron shocks are larger for smaller jet Lorentz factor. This comes from the fact that the growth time of the Weibel instability is proportional to the square of the jet Lorentz factor. We have performed simulations with broad Lorentz factor distribution of jet electrons and positrons, which is assumed to be created by photon annihilation. Simulation results with this broad distribution show that the Weibel instability is excited continuously by the wide-range of jet Lorentz factor from lower to higher values. In all simulations the Weibel instability is responsible for generating and amplifying magnetic fields perpendicular to the jet propagation direction, and contributes to the electron’s (positron’s) transverse deflection behind the jet head. This small scale magnetic field structure contributes to the generation of “jitter” radiation from deflected electrons (positrons), which is different from synchrotron radiation in uniform magnetic fields. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks. The detailed studies of shock microscopic process evolution may provide some insights into early and later GRB afterglows.     

Relativistic anisotropic pair plasmas

The properties of waves able to propagate in a relativistic pair plasma are at the basis of the interpretation of several astrophysical observations. For instance, they are invoked in relation to radio emission processes in pulsar magnetospheres and to radiation mechanisms for relativistic radio jets. In such physical environments, pair plasma particles probably have relativistic, or even ultrarelativistic, temperatures. Besides, the presence of an extremely strong magnetic field in the emission region constrains the particles to one-dimensional motion: all the charged particles strictly move along magnetic field lines.
We take anisotropic effects and relativistic effects into account by choosing one-dimensional relativistic Jűttner–Synge distribution functions to characterize the distribution of electrons and/or positrons in a relativistic, anisotropic pair plasma. The dielectric tensor, from which the dispersion relation associated with plane wave perturbations of such a pair plasma is derived, involves specific coefficients that depend on the distribution function of particles. A precise determination of these coefficients, using the relativistic one-dimensional Jűttner–Synge distribution function, allows us to obtain the appropriate dispersion relation. The properties of waves able to propagate in anisotropic relativistic pair plasmas are deduced from this dispersion relation. The conditions in which a beam and a plasma, both ultrarelativistic, may interact and trigger off a two-stream instability are obtained from this same dispersion relation. Two astrophysical applications are discussed.     

On the theory of cyclotron lines in the spectra of magnetic white dwarfs

The radiation transfer at the gyrofrequency in the coronae of magnetic white dwarfs is considered. The electron distribution over Landau levels, taking both radiative and collisional transitions into account, is obtained. The emissivity and absorption coefficients of extraordinary radiation at the gyrofrequency are calculated. The ranges of parameters where cyclotron lines are observed in emission or absorption are found. The upper limit on coronal plasma density (2×10¹¹ cm^–3) for isolated magnetic white dwarfs with absorption lines in the spectrum is specified.     

Relativistic ejection from compact stars with a strong magnetic field

The electron cyclotron resonance leads to a large enhancement of radiative force and may result in the ejection from magnetized compact stars (Papers I and II). On this ground, the acceleration of charged particles by radiation in a strong magnetic field is considered. Different regimes of ejection, the dependence on intensity, spectrum, angular distribution and polarization of accelerating radiation, and the influence of the opacity of ejecting plasma are analyzed. The energy of ejected plasma is shown to increase up to relativistic values, in many cases the gamma-factor appears to be 1. A possible connection of relativistic ejection with the origin of gamma-ray bursts and other astrophysical consequences are discussed.     

Precessing jets interacting with interstellar material as the origin for the light curves of gamma-ray bursts

We present an internal shock model with external characteristics for explaining the complicated light curves of gamma-ray bursts. Shocks produce gamma-rays in the interaction between a precessing beam of relativistic particles and the interstellar medium. Each time the particle beam passes the same line of sight with the observer the interstellar medium is pushed outward. Subsequent interactions between the medium and the beam are delayed by the extra distance to be travelled for the particles before the shock can form. This results in a natural retardation and leads to an intrinsic asymmetry in the light curves produced for gamma-ray bursts. In addition, we account for the cooling of the electron–proton plasma in the shocked region, which gives rise to an exponential decay in the gamma-ray flux. The combination of these effects and the precessing jet of ultrarelativistic particles produces light curves that can be directly compared with observed gamma-ray burst light curves. We illustrate the model by fitting a number of observed gamma-ray bursts that are difficult to explain with only a precessing jet. We develop a genetic algorithm to fit several observed gamma-ray bursts with remarkable accuracy. We find that for different bursts the observed fluence, assuming isotropic emission, easily varies over four orders of magnitude from the energy generated intrinsically.     

A revised calculation of the bremsstrahlung cross-section in the high magnetic field of pulsars

It has been postulated that electron bremsstrahlung in a strong external magnetic field is the dominant radiation mechanism within the accretion plasma near the magnetic polar regions of binary X-ray sources. Earlier works on the cross section for such a process proved to be unsatisfactory.The present work uses the simple structure of the propagator obtained in a previous calculation for mildly relativistic electrons occupying no more than the first few Landau levels. Particular emphasis is put on the integration over the possible range of momentum transfer during a single collision with the ion. Typical behaviour for two linear polarization modes is illustrated for forward and backward electron scattering. It is found that the previously predicted behaviour at low frequencies for the two modes is only correct in the limit of weak field and large momentum transfer. At higher frequencies resonances are present irrespective of the polarization of the emitted radiation.     

The Lifshitz-Kosevich-Shoenberg theory of relativistic electronic gas in neutron stars

Similar to the de Haas-van Alphen magnetic oscillatory in some normal metals when the Landau quantization is predominant, the magnetic oscillation can also occur in highly degenerate and relativistic electron gas in neutron stars. At large Landau quantum number (Landau quantum number r≥2), we generalize the Lifshitz-Kosevich-Shoenberg theory in non-relativistic electron gas to relativistic gas. At small Landau quantum number (r<2), we expand the grand potential into Fourier series and get similar harmonic oscillatory formula of magnetization. These results indicate that magnetic phase transition similar as Condon transition observed in metals can appear in neutron stars when the differential susceptibility exceeds 1/4π.     

Plasma instability in relativistic jets

Based on the Maxwel-Vlasov equations, we consider the possible generation mechanisms of hard emission through the growth of plasma instabilities in a relativistic jet composed of electrons and protons. The accelerated material of the jet moves by inertia. When a small difference arises between the electron and proton velocities (which may result from the interaction of jet material with background plasma or from the acceleration mechanism) plasma instabilities can grow. The particle distribution functions, which were initially delta functions both in angle and in energy, transform into complex angular and energy dependences. In this case, the probability of collisions between high-energy particles in the jet increases, resulting in hard gamma-ray emission.     

Unified classical and quantum radiation mechanism for ultrarelativistic electrons in curved and inhomogeneous magnetic fields

We analyse the general radiation emission mechanism from a charged particle moving in a curved inhomogeneous magnetic field. The consideration of the gradient makes the vacuum magnetic field compatible with the Maxwell equations, and adds a non-trivial term to the transverse drift velocity, and, consequently, to the general radiation spectrum. To obtain the radiation spectrum in the classical domain a general expression for the spectral distribution and characteristic frequency of an electron in arbitrary motion is derived, by using Schwinger's method. The radiation patterns of the ultrarelativistic electron are represented in terms of the acceleration of the particle. The same results can be obtained by considering that the motion of the electron can be formally described as an evolution caused by magnetic and electric forces. By defining an effective electromagnetic field, which combines the magnetic field with the fictitious electric field associated to the curvature and drift motion, one can obtain all the physical characteristics of the radiation by replacing the constant magnetic field with the effective field. The power, angular distribution and spectral distribution of all three components (synchrotron, curvature and gradient) of the radiation are considered, in both the classical and the quantum domain, within the framework of this unified formalism. In the quantum domain the proposed approach allows the study of the effects of the inhomogeneities and curvature of the magnetic field on the radiative transition rates of electrons between low-lying Landau levels and the ground state.     

Gamma-ray bursts from internal shocks in a relativistic wind: temporal and spectral properties

We construct models for gamma-ray bursts in which the emission comes from internal shocks in a relativistic wind with a highly non-uniform distribution of the Lorentz factor. We follow the evolution of the wind using a very simplified approach in which a large number of layers interact by direct collisions but all pressure waves have been suppressed. We suppose that the magnetic field and the electron Lorentz factor reach large equipartition values in the shocks. Synchrotron photons emitted by the relativistic electrons have a typical energy in the gamma-ray range in the observer frame. Synthetic bursts are constructed as the sum of the contributions from all the internal elementary shocks, and their temporal and spectral properties are compared with the observations. We reproduce the diversity of burst profiles, the 'FRED' shape of individual pulses and the short time-scale variability. Synthetic bursts also satisfy the duration–hardness relation and individual pulses are found to be narrower at high energy, in agreement with the observations. These results suggest that internal shocks in a relativistic wind may indeed be at the origin of gamma-ray bursts. A potential problem, however, is the relatively low efficiency of the dissipation process. If the relativistic wind is powered by accretion from a disc to a stellar mass black hole, it implies that a substantial fraction of the available energy is injected into the wind.     

Relativistic blast waves and synchrotron emission

Relativistic shocks can accelerate particles by the first-order Fermi mechanism; the particles then emit synchrotron emission in the post-shock gas. This process is of particular interest in the models used for the afterglow of gamma-ray bursts. In this paper we use recent results in the theory of particle acceleration at highly relativistic shocks to model the synchrotron emission in an evolving, inhomogeneous and highly relativistic flow. We have developed a numerical code that integrates the relativistic Euler equations for fluid dynamics with a general equation of state, together with a simple transport equation for the accelerated particles. We present tests of this code and, in addition, we use it to study the gamma-ray burst afterglow predicted by the fireball model, along with the hydrodynamics of a spherically-symmetric relativistic blast wave.
We find that, while broadly speaking the behaviour of the emission is similar to that already predicted with semi-analytic approaches, the detailed behaviour is somewhat different. The 'breaks' in the synchrotron spectrum behave differently with time, and the spectrum above the final break is harder than had previously been expected. These effects are due to the incorporation of the geometry of the (spherical) blast wave, along with relativistic beaming and adiabatic cooling of the energetic particles leading to a mix, in the observed spectrum, between recently injected 'uncooled' particles and the older 'cooled' population in different parts of the evolving, inhomogeneous flow.     

Radiative losses and cut-offs of energetic particles at relativistic shocks

We investigate the acceleration and simultaneous radiative losses of electrons in the vicinity of relativistic shocks. Particles undergo pitch angle diffusion, gaining energy as they cross the shock by the Fermi mechanism and also emitting synchrotron radiation in the ambient magnetic field. A semi-analytic approach is developed which allows us to consider the behaviour of the shape of the spectral cut-off and the variation of that cut-off with the particle pitch angle. The implications for the synchrotron emission of relativistic jets, such as those in gamma-ray burst sources and blazars, are discussed.     

Acceleration of charged particles in the magnetosphere of a collapsing star and their nonthermal electromagnetic radiation

We investigate a transformation of a magnetic field and plasma in nonhomogeneous magnetospheres of collapsing stars with a dipole initial magnetic field and certain initial energy distributions of particles in the magnetosphere as the power low, relativistic Maxwell and Boltzmann. The betatron mechanism of the charged particles acceleration in a collapsing star’s magnetosphere is considered. When a magnetized star is compressed in the stage of the gravitational collapse, the magnetic field increases strongly. This variable magnetic field generates a vortical electric field. Our calculations show that this electric field will accelerate charged particles up to relativistic velocities. Thus, collapsing stars may be sources of high energy cosmic rays in our galaxy as in others. The acceleration of particles during the collapse happens mostly in polar regions of the magnetosphere that leads to polar relativistic streams (jets) formation. When moving in a magnetic field, these particles will generate nonthermal electromagnetic radiation in a broad electromagnetic wavelength band from radioto gamma rays. Thus, in the stage of the gravitational collapse, relativistic jets are formed in stellar magnetospheres. These jets are powerful sources of the nonthermal electromagnetic radiation.     

Synchrotron emission in the fast cooling regime: which spectra can be explained?

We consider the synchrotron emission from relativistic shocks assuming that the radiating electrons cool rapidly (either through synchrotron or any other radiation mechanism). It is shown that the theory of synchrotron emission in the fast cooling regime can account for a wide range of spectral shapes. In particular, the magnetic field, which decays behind the shock front, brings enough flexibility to the theory to explain the majority of gamma-ray burst spectra even in the parameter-free fast cooling regime. Also, we discuss whether location of the peak in observed spectral energy distributions of gamma-ray bursts and active galactic nuclei can be made consistent with predictions of diffusive shock acceleration theory, and find that the answer is negative. This result is a strong indication that a particle injection mechanism, other than the standard shock acceleration, works in relativistic shocks.     

Landau damping of longitudinal oscillation in ultra-relativistic plasmas by analytic function of nonextensive distribution

The analytic function of relativistic nonextensive distribution is given, and employed to solve the Landau damping of longitudinal oscillation in ultra-relativistic plasmas. The unified expression of Landau damping which reduces to the result in relativistic Maxwellian distributed plasmas in the extensive limit is obtained, and find that Landau damping is relevant to both the number and energy of resonant particles, which described by temperature and nonextensive parameters in relativistic nonextensive distribution.     

A magnetically driven origin for the low luminosity GRB 170817A associated with GW170817

The gamma-ray burst GR170817 A associated with GW170817 is subluminous and subenergetic compared with other typical short gamma-ray bursts. It may be due to a relativistic jet viewed off-axis, or a structured jet or cocoon emission. Giant flares from magnetars may possibly be ruled out.However, the luminosity and energetics of GRB 170817 A are coincident with those of magnetar giant flares. After the coalescence of a binary neutron star, a hypermassive neutron star may be formed. The hypermassive neutron star may have a magnetar-strength magnetic field. During the collapse of this hypermassive neutron star, magnetic field energy will also be released. This giant-flare-like event may explain the luminosity and energetics of GRB 170817 A. Bursts with similar luminosity and energetics are expected in future neutron star-neutron star or neutron star-black hole mergers.     

GRB 080319B: evidence for relativistic turbulence, not internal shocks

We show that the excellent optical and gamma-ray data available for GRB 080319B rule out the internal shock model for the prompt emission. The data instead point to a model in which the observed radiation was produced close to the deceleration radius  (∼10¹⁷ cm)  by a turbulent source with random Lorentz factors of ∼10 in the comoving frame. The optical radiation was produced by synchrotron emission from relativistic electrons, and the gamma-rays by inverse-Compton scattering of the synchrotron photons. The gamma-ray emission originated both in eddies and in an inter-eddy medium, whereas the optical radiation was mostly from the latter. Therefore, the gamma-ray emission was highly variable whereas the optical was much less variable. The model explains all the observed features in the prompt optical and gamma-ray data of GRB 080319B. We are unable to determine with confidence whether the energy of the explosion was carried outwards primarily by particles (kinetic energy) or magnetic fields. Consequently, we cannot tell whether the turbulent medium was located in the reverse shock (we can rule out the forward shock) or in a Poynting-dominated jet.     

Two-photon positron–electron annihilation in a strong magnetic field

We consider the two-photon positron and electron annihilation in flight, it means the annihilating particles exhibit the middly relativistic momenta in a super strong magnetic field. Such particles are present in the corona of pulsars and magnetars. The paper presents how the total emission rate for the two-photon process is affected not only by magnetic field but also by the relativistic momentum of the annihilating particles. We found that the momenta influence significantly the total emission rate and the directions of the emitted photons. Additionally, the total emission for the two-photon process is comparable to that for the one-photon process at the momentum of annihilating particles of about m₀, where m₀ is the electron mass, and the magnetic field close to the critical Schwinger value of 4.41 × 10¹³ G. The latter is reported as a main annihilation channel in a super strong magnetic field. We calculated also the energetic spectra of annihilating photons emitted, which are also affected by the magnetic field and the momenta of the annihilating particles.     

Formation of “lightnings” in a neutron star magnetosphere and the nature of RRATs

The connection between the radio emission from “lightnings” produced by the absorption of high-energy photons from the cosmic gamma-ray background in a neutron star magnetosphere and radio bursts from rotating ratio transients (RRATs) is investigated. The lightning length reaches 1000 km; the lightning radius is 100 m and is comparable to the polar cap radius. If a closed magnetosphere is filled with a dense plasma, then lightnings are efficiently formed only in the region of open magnetic field lines. For the radio emission from a separate lightning to be observed, the polar cap of the neutron star must be directed toward the observer and, at the same time, the lightning must be formed. The maximum burst rate is related to the time of the plasma outflow from the polar cap region. The typical interval between two consecutive bursts is ∼100 s. The width of a single radio burst can be determined both by the width of the emission cone formed by the lightning emitting regions at some height above the neutron star surface and by a finite lightning lifetime. The width of the phase distribution for radio bursts from RRATs, along with the integrated pulse width, is determined by the width of the bundle of open magnetic field lines at the formation height of the radio emission. The results obtained are consistent with the currently available data and are indicative of a close connection between RRATs, intermittent pulsars, and extreme nullers.