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.     

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 particles in the vicinity of a massive black hole

Recent results of the gamma-ray Cherenkov astronomy definitely prove the existence of fast variability in the very high energy (V.H.E.) gamma-ray flux of some active galactic nuclei. The BL Lac PKS 2155-304 for instance showed variations down to a few minutes time scale. From standard light travel time argument, these variations put extremely strong constraints on the size of the TeV emitting zone, which has to be of the order of a few Schwarzschild radius, even for high values of the relativistic Doppler factor of the emitting jets. Such discovery is a challenge for particle acceleration scenarios, which have to imagine efficient acceleration processes at work in a very compact zone. Eventually, the immediate vicinity of the central black hole appears as the most conservative choice for the location of the TeV emission region of active galactic nuclei. In this paper, we propose a two-step mechanism for charged particle acceleration in the magnetosphere of a massive black hole surrounded by an accretion disk. Particles first gain energy by a stochastic process during the accretion phase. It is shown that effective proton acceleration up to energies 10¹⁷–10¹⁹ eV is possible in a low-luminosity magnetized accretion disk with 2D turbulent motion. The distribution function of energetic protons over energies is a power law function with typical index ≃−1. Here electrons are not very efficiently accelerated because of their drastic losses by synchrotron radiation. In a second time, part of the fast particles escape from the disk and are then entrained by the magnetic structure above the disk, in the rotating black hole magnetosphere. They thus gain additional energy by direct centrifugal mechanism, up to about 10²⁰ eV for the protons and to 10–100 TeV for the electrons when they cross the light cylinder surface. Such energetic particles can further radiate in the TeV spectral range observed by Cherenkov experiments as HESS, MAGIC and VERITAS. Energetic protons can produce γ-radiation in the energy band 1 GeV–100 TeV and above mainly by nuclei collisions with the disk matter, clouds, or ambient low energy photons. Energetic electrons can also reach the required spectral range by inverse Compton emission. However their acceleration is less efficient due to heavy radiation losses, and only gained by centrifugal process during the second phase of the whole mechanism we describe. Our present analysis would therefore favor hadronic scenarios for TeV emission of active galactic nuclei. It is tempting to relate long term variability over years of TeV active galactic nuclei to the first stochastic acceleration phase, which also provides the needed power law particle distributions, while short term variability over minutes is more likely due to perturbations of the second fast direct acceleration phase.     

Incoherent radiation from relativistic electrons with power energetic spectrum

It is shown that an incoherent high-frequency radiation from an ensemble of relativistic particles with the power energy distribution is described by a certain general expression which covers practically all the cases of particle radiation in random electromagnetic fields of cosmic radiation sources.     

Active galactic nuclei and pulsars as cosmic ray sources

Relativistic e^± particles and cosmic rays are accelerated in the magnetospheres of supermassive black holes and neutron stars. The possibility of synchrotron radiation with extremely high intensity inside the deepest regions of magnetospheres is investigated. Very high brightness temperatures are expected for such radiation by relativistic protons, which can be made even higher in the presence of non-stationary conditions, Doppler boosting and coherent processes. The main parameters for models of such high-brightness-temperature radiation are determined. Two types of active galactic nuclei (AGNs) are expected. One type is associated with the acceleration and ejection of relativistic e^± particles only (probably non-IDV sources and FR-I radio galaxies). The second type of AGN is also associated with e^± acceleration, but is dominated by the contribution of relativistic protons (probably IDV sources and FR-II radio galaxies). Analogous objects for pulsars are plerion and shell supernova remnants with neutron stars or pulsars without synchrotron nebulae, respectively.     

The cosmic rays of superhigh energies

The paper considers the generation mechanism of the relativistic particles of superhigh energies (10¹⁸ eV) in a plasma where the supersonic turbulence and the hydrodynamic shock waves occur. It is found that the conditions necessary for the formation of this turbulence are realized in supernovae shells during the period of the outburst. The estimations of the energy gain rate of the charged particles and comparison with their energy loss rate conditioned by synchrotron radiation and collisions with photons and nuclei show that in the actually determined conditions of shells in Crab and Cassiopeia nebulae, at the early stages of their expansion, acceleration surpasses deceleration. And finally, the estimations of the total number of superhigh energy particles generated during the flare are in agreement with the observed data.     

Scale transformations, tree-level perturbation theory and the cosmological matter bispectrum

Soon after the discovery of radio pulsars in 1967, the pulsars are identified as strongly magnetic (typically 10¹² G) rapidly rotating (∼10²− 0.1 Hz) neutron stars. However, the mechanism of particle acceleration in the pulsar magnetosphere has been a longstanding problem. The central problem is why the rotation power manifests itself in both gamma-ray beams and a highly relativistic wind of electron–positron plasmas, which excites surrounding nebulae observed in X-ray. Here we show with a three-dimensional particle simulation for the global axisymmetric magnetosphere that a steady outflow of electron–positron pairs is formed with associated pair sources, which are the gamma-ray emitting regions within the light cylinder. The magnetic field is assumed to be a dipole, and to be consistent, the pair creation rate is taken to be small, so that the model might be applicable to old pulsars such as Geminga. The pair sources are charge-deficient regions around the null surface, and we identify them as the outer gap. The wind mechanism is the electromagnetic induction which brings about fast azimuthal motion and eventually trans-field drift by radiation drag in the close vicinity of the light cylinder and beyond. The wind causes loss of particles from the system. This maintains charge deficiency in the outer gap and pair creation. The model is thus in a steady state, balancing loss and supply of particles. Our simulation implies how the wind coexists with the gamma-ray emitting regions in the pulsar magnetosphere.     

On the origin of highest energy cosmic rays

In this paper we show that the conventional diffusive shock acceleration mechanism for cosmic rays associated with relativistic astrophysical shocks in active galactic nuclei (AGNs) has severe difficulties to explain the highest energy cosmic ray events. We show that protons above around 2 x 10²⁰ eV could have marginally been produced by this mechanism in an AGN or a rich galaxy cluster not further away than around 100 Mpc. However, for the highest energy Fly's Eye and Yakutsk events this is inconsistent with the observed arrival directions. Galactic and intergalactic magnetic fields appear unable to alter the direction of such energetic particles by more than a few degrees. We also discuss some other options for these events associated with relativistic particles including pulsar acceleration of high Z nuclei. At the present stage of knowledge the concept of topological defects left over from the early universe as the source for such events appears to be a promising option. Such sources are discussed and possible tests of this hypothesis are proposed.     

Particle-acceleration time-scales in TeV blazar flares

Observations of minute-scale flares in TeV Blazars place constraints on particle-acceleration mechanisms in those objects. The implications for a variety of radiation mechanisms have been addressed in the literature; in this paper, we compare four different acceleration mechanisms: diffusive shock acceleration, second-order Fermi, shear acceleration and the converter mechanism. When the acceleration time-scales and radiative losses are taken into account, we can exclude shear acceleration and the neutron-based converted mechanism as possible acceleration processes in these systems. The first-order Fermi process and the converter mechanism working via synchrotron self-Compton (SSC) photons are still practically instantaneous, however, provided sufficient turbulence is generated on the time-scale of seconds. We propose stochastic acceleration as a promising candidate for the energy-dependent time delays in recent gamma-ray flares of Markarian 501.     

On proton and electron acceleration by shock waves during large solar flares

The data on optical, X-ray and gamma emission from proton flares, as well as direct observations of flare-associated phenomena, show energetic proton acceleration in the corona rather than in the flare region. In the present paper, the acceleration of protons and accompanying relativistic electrons is accounted for by a shock wave arising during the development of a large flare. We deal with a regular acceleration mechanism due to multiple reflection of resonance protons and fast electrons from a collisionless shock wave front which serves as a moving mirror. The height of the most effective acceleration in the solar corona is determined. The accelerated particle energy and density are estimated. It is shown in particular that a transverse collisionless shock wave may produce the required flux of protons with energy of 10 MeV and of relativistic electrons of 1–10 MeV.The proposed scheme may also serve as an injection mechanism when the protons are accelerated up to relativistic energies by other methods.     

High energy processes in pulsar wind nebulae

Young pulsars produce relativistic winds which interact with matter ejected during the supernova explosion and the surrounding interstellar gas. Particles are accelerated to very high energies somewhere in the pulsar winds or at the shocks produced in collisions of the winds with the surrounding medium. As a result of the interactions of relativistic leptons with the magnetic field and low energy radiation (of synchrotron origin, thermal, or microwave background), non-thermal radiation is produced from the lowest possible energies up to ～100 TeV. The high energy (TeV) γ-ray emission has been originally observed from the Crab Nebula and recently from several other objects. Recent observations by the HESS Cherenkov telescopes allow to study for the first time the morphology of the sources of high energy emission, showing unexpected spectral features. They might be also interpreted as due to acceleration of hadrons. However, theory of particle acceleration in the PWNe and models for production of radiation are still at their early stage of development since it becomes clear that realistic modeling of these objects should include their time evolution and three-dimensional geometry. In this paper we concentrate on the attempts to create a model for the high energy processes inside the PWNe which includes existence of not only relativistic leptons but also of hadrons inside the nebula. Such model should also take into account evolution of the nebula in time. Possible high energy expectations based on such a model are discussed in the context of new observations.     

Acceleration of relativistic charged particles by supersonic hydromagnetic turbulence

The acceleration of relativistic particles is considered during their intersection with hydromagnetic shock fronts in the presence of randomly distributed large-scale magnetic fields. In a series of astronomical objects, the Larmor radius of the relativistic particles exceeds the width of the shock front. In this case there is a change in the adiabatic invariant which results in an increase in the energy of the particle when it crosses the front in any direction. We have proved that the adiabatic part of the energy change will be partially or completely compensated by its reverse change in the weaker regions of the magnetic field. The acceleration mechanism considered is found to be more effective than the Fermi mechanism.If the mean free path of the particles is much less than the distance between the shock fronts, magnetic small-scale fluctuations cause further scattering of the particles. In this case the particles following and crossing the front will return to it. After reversed crossing, a fraction of the particles-defined by the ratio of the front speed to the particle velocity or of the distance between the fronts to the free path — will not return to the front. It is proved that for both large and small free paths the rates at which the particle gains energy are nearly the same.     

Gamma-ray detectors (>10MeV)

Photons in the energy region above 10 MeV can provide unique information about the highest energy particles produced in solar flares. Measurements of the energy spectra, temporal behavior and anisotropies of the incident photons, can give valuable insights into the particle acceleration process. In this paper we review the detection techniques used at these energies, typical instruments which use these techniques, and future solar missions both actual and potential.     

On the production of hard X-rays in solar flares

The problem of producing the hard X-ray burst at the onset of solar flares may be thought of in terms of the problem of producing the non-thermal electrons which emit the X-rays via bremsstrahlung. Electron acceleration to relativistic energies without similar ion acceleration is difficult to achieve, even in an ad hoc theoretical model. Yet from global energetic considerations, it is not feasible to accelerate the electrons as a minor constituent of the total energetic particle population. Therefore, it is necessary to invoke a more sophisticated process for the electron acceleration. In this paper we describe a mechanism for achieving this via an initial acceleration of a neutralized ion beam. When such a beam impacts the chromosphere, the electrons start to scatter while the ions continue downwards, rapidly setting up an electric field which is either cancelled by the inflow of background chromospheric electrons or results in the runaway acceleration of beam electrons. In the former case the result is simply heating, whereas in the latter case much of the ion kinetic energy is transferred into electron kinetic energy. The final electron energy may be similar to the typical energy of the ions. The electrons that are accelerated are those in the neutral beam that experience an electric field greater than the critical Dreicer field. Thus there will be a low-energy cut-off to the electron spectrum which overcomes the well-known energetics problem at low energies with certain other spectral forms.     

The emission and propagation of ∼ 40keV solar flare electrons

Observations of prompt 40 keV solar flare electron events by the IMP series of satellites in the period August, 1966 to December, 1967 are tabulated along with prompt energetic solar proton events in the period 1964–1967. The interrelationship of the various types of energetic particle emission by the sun, including relativistic energy electrons reported by Cline and McDonald (1968) are investigated. Relativistic energy electron emission is found to occur only during proton events. The solar optical, radio and X-ray emission associated with these various energetic particle emissions as well as the propagation characteristics of each particle species are examined in order to study the particle acceleration and emission mechanisms in a solar flare. Evidence is presented for two separate particle acceleration and/or emission mechanisms, one of which produces 40 keV electrons and the other of which produces solar proton and possibly relativistic energy electrons. It is found that solar flares can be divided into three categories depending on their energetic particle emission: (1) small flares with no accompanying energetic phenomena either in particles, radio or X-ray emission; (2) small flares which produce low energy electrons and which are accompanied by type III and microwave radio bursts and energetic ( 20 keV) X-ray bursts; and (3) major solar flare eruptions characterized by energetic solar proton production and type II and IV radio bursts and accompanied by intense microwave and X-ray emission and relativistic energy electrons.     

High energy radiation from the center of the local supercluster

Evidence in X-rays, gamma rays and ultra high energy cosmic rays (UHCR) suggests the existence of active centers in extragalactic space which eject high energy particles and quanta. A concentration of these highest energy sources in the direction of the Local Supercluster indicates that the brightest apparent magnitude AGN's such as 3C274 (M87), 3C273, 3C279 and Markarian 421 are the only candidate sources for this radiation. A theoretical model of mass creation in the Local Supercluster based on a Machian theory of gravitation is described as a possible mechanism for production of the high energy while at the same time allowing the AGN's to be at the relatively close distance of the Supercluster. The fact that infrared photons fill intergalactic space limits the distance to the UHCR sources at a little over twice the distance to the center of the Local Supercluster strongly localizing the highest energy radiation to this relatively close distance.     

Particle acceleration at multiple internal relativistic shocks

Relativistic shocks provide an efficient method for high-energy particle acceleration in many astrophysical sources. Multiple shock systems are even more effective and of importance, for example, in the internal shock model of gamma-ray bursts. We investigate the reacceleration of pre-existing energetic particles at such relativistic internal shocks by the first order Fermi process of pitch angle scattering. We use a well established eigenfunction method to calculate the resulting spectra for infinitely thin shocks. Implications for GRBs and relativistic jets are discussed. Paul Dempsey would like to thank IRCSET for their financial support.     

Pulsar radiation belts and transient radio emission

It is proposed that radiation belts similar to the ones in the planetary magnetosphere can exist for a pulsar with a relatively long period and a strong magnetic field. In the belts located in the closed field line region near the light cylinder relativistic pairs are trapped and maintained at a density substantially higher than the local Goldreich–Julian corotation density. The trapped plasma can be supplied and replenished by either direct injection of relativistic pairs from acceleration of externally supplied particles in a dormant outer gap or in situ ionization of the accreted neutral material in the trapping region. The radiation belts can be disrupted by waves that are excited in the region as the result of plasma instabilities or emitted from the surface due to starquakes or stellar oscillations. The disruption can cause an intermittent particle precipitation towards the star producing radio bursts. It is suggested that such bursts may be seen as rotating radio transients.     

Magnetostatic structures in collisionless plasma and their synchrotron radiation

The properties of the magnetostatic structures in a collisionless relativistic plasma found by exactly solving the nonlinear self-consistent kinetic and Maxwell equations using the method of invariants of particle motion are analyzed. These structures include individual neutral current sheets and cylindrically symmetric filaments as well as their ensembles, admitting a wide variety of types of particle energy distribution functions. Relationships are established between the possible parameters of the current sheets and filaments—their sizes, currents and magnetic fields, and the degree of anisotropy of the particle momentum distribution. The extent to which these parameters are conditioned by the properties of the Weibel instability that can produce these structure is also discussed. The spectral peculiarities of the synchrotron radiation from the particles that form the current sheets and filaments are investigated in the special case of power-law energy distribution functions.     

A nonlinear theory of stellar wind with allowance for the influence of relativistic particles

We solve the nonlinear problem of the dynamics of a steady-state, spherically symmetric stellar wind by taking into account particle acceleration to relativistic energies near the shock front. The particles are assumed to be accelerated through the Fermi mechanism, interacting with stellar-wind turbulence and crossing many times the shock front that separates the supersonic and subsonic stellar-wind regions. We take into account the influence of the accelerated particles on hydrodynamic plasma-flow parameters. Our method allows all hydrodynamic parameters of the shock front and plasma in the supersonic region to be determined in a self-consistent way and the accelerated-particle energy spectrum to be calculated. Our numerical and analytic calculations show that the plasma compression ratio at the shock front increases compared to the case where there are no relativistic particles and that the velocity profile in the supersonic region acquires a characteristic kink. The shape of the energy spectrum for the accelerated particles and their pressure near the front are essentially determined by the presumed dependence of the diffusion coefficient on particle energy, which, in turn, depends on the scale distribution of turbulent pulsations and other stellar-wind inhomogeneities.