Fermi acceleration in astrophysical jets

We consider the acceleration of energetic particles by Fermi processes (i.e., diffusive shock acceleration, second order Fermi acceleration, and gradual shear acceleration) in relativistic astrophysical jets, with particular attention given to recent progress in the field of viscous shear acceleration. We analyze the associated acceleration timescales and the resulting particle distributions, and discuss the relevance of these processes for the acceleration of charged particles in the jets of AGN, GRBs and microquasars, showing that multi-component powerlaw-type particle distributions are likely to occur.     

Cosmic rays in central regions of active galaxies

We consider the acceleration of charged particles by the Fermi mechanism on magnetic field irregularities in active galactic regions. The relativistic particles are shown to be accelerated most efficiently, while the acceleration of nonrelativistic particles by this mechanism is possible only in highly nonuniform galactic nuclei, that is, in nuclei with strong turbulization. The conditions for the acceleration of charged particles in active galactic nuclei at various stages of their evolution are investigated.     

Acceleration of pickup interstellar protons by shock waves in corotating solar wind regions

It follows from numerous measurements of the differential fluxes of energetic charged particles in corotating interaction regions between solar wind streams with different speeds that the spectra of particles accelerated by reverse shocks are harder than those of particles accelerated by forward shocks. The measurements cannot be explained in terms of the theory of diffusive acceleration (first-order Fermi acceleration). We show that the measurements can be easily explained in terms of the theory of drift acceleration of charged particles by shock waves with allowance made for their multiple scattering from the front.     

Fast magnetic reconnection and energetic particle acceleration

Our numerical simulations show that the reconnection of magnetic field becomes fast in the presence of weak turbulence in the way consistent with the Lazarian and Vishniac (1999) model of fast reconnection. We trace particles within our numerical simulations and show that the particles can be efficiently accelerated via the first order Fermi acceleration. We discuss the acceleration arising from reconnection as a possible origin of the anomalous cosmic rays measured by Voyagers.     

Statistical acceleration of cosmic rays in anisotropic turbulent medium

Acceleration of cosmic rays interacting with the anisotropic magnetohydrodynamic turbulent medium is studied. Particle acceleration is caused by a large-scale electric field arising in a turbulent medium due to the α-effect. A comparison is made of equilibrium spectra of cosmic rays, characteristic of the specific acceleration mechanism, with the energy distribution of particles corresponding to the statistical Fermi acceleration.     

The fermi mechanism and the source spectrum of cosmic ray nuclei

It is shown that the velocity term, occurring in the expression for the rate of energy gain by the Fermi mechanism of acceleration, is to be taken into account in case of acceleration of non-relativistic particles. A spectral form of accelerated particles is derived on this basis and is called the ‘Fermi Spectrum’. At non-relativistic energies this spectral form is significantly different from the currently used forms of power law in total energy per nucleon and in rigidity, and lies about midway between them. It is shown that using this form of source spectrum of cosmic ray nuclei, satisfactory agreement can be obtained between the calculated values and the observed ones of the ratios of H²/He⁴ and He³/He⁴, and the energy spectra of protons and helium nuclei near the Earth.     

Cosmic-ray diffusive acceleration at shock waves with finite upstream and downstream escape boundaries

In the present paper we discuss the modifications introduced into the first-order Fermi shock acceleration process due to a finite extent of diffusive regions near the shock or due to boundary conditions leading to an increased particle escape upstream and/or downstream of the shock. In the simple example of the planar shock wave considered we idealize the escape phenomenon by imposing a particle escape boundary at some distance from the shock. The presence of such a boundary (or boundaries) leads to coupled steepening of the accelerated particle spectrum and decreasing of the acceleration time scale. It allows for a semi-quantitative evaluation and, in some specific cases, also for modelling of the observed steep particle spectra as a result of the first-order Fermi shock acceleration. We also note that the particles close to the upper energy cut-off are younger than the estimate based on the respective acceleration time scale. In Appendix A we present a new time-dependent solution for infinite diffusive regions near the shock allowing for different constant diffusion coefficients upstream and downstream of the shock.     

Comparison of the Fermi and betatron acceleration efficiencies in collapsing magnetic traps

The acceleration of charged particles in the solar corona during flares is investigated in terms of a model in which the electrons and ions preaccelerated in the magnetic reconnection region are injected into a collapsing magnetic trap. Here, the particle energy increases rapidly simultaneously through the Fermi and betatron mechanisms. Comparison of the efficiencies of the two mechanisms shows that the accelerated electrons in such a trap produce more intense hard X-ray (HXR) bursts than those in a trap where only the Fermi acceleration mechanism would be at work. This effect explains the Yohkoh and RHESSI satellite observations in which HXR sources more intense than the HXR emission from the chromosphere were detected in the corona.     

Particle acceleration by ultrarelativistic shocks: theory and simulations

We consider the acceleration of charged particles near ultrarelativistic shocks, with Lorentz factor     . We present simulations of the acceleration process and compare these with results from semi-analytical calculations. We show that the spectrum that results from acceleration near ultrarelativistic shocks is a power law,     , with a nearly universal value     for the slope of this power law.
We confirm that the ultrarelativistic equivalent of the Fermi acceleration at a shock differs from its non-relativistic counterpart by the occurrence of large anisotropies in the distribution of the accelerated particles near the shock. In the rest frame of the upstream fluid, particles can only outrun the shock when their direction of motion lies within a small loss cone of opening angle     around the shock normal.
We also show that all physically plausible deflection or scattering mechanisms can change the upstream flight direction of relativistic particles originating from downstream by only a small amount:     . This limits the energy change per shock crossing cycle to     , except for the first cycle where particles originate upstream. In that case the upstream energy is boosted by a factor     for those particles that are scattered back across the shock into the upstream region.     

Change of solar flare proton to alpha ratios during an energetic storm particle event

Observations of the temporal behavior of energetic storm protons and alpha particles are presented for the event associated with the storm sudden commencement observed on Earth on March 8, 1970. The data are obtained on board the low altitude polar orbiting satellite GRS-A/AZUR by means of two particle telescopes. Large changes in the proton to alpha ratios for particles of equal energy and for particles of equal energy per nucleon are observed, whereas no significant change in the equal energy per charge ratio is observed. Electric fields, Fermi acceleration and cyclotron resonance are discussed as possible modulation mechanisms.     

On the role of injection in kinetic approaches to non-linear particle acceleration at non-relativistic shock waves

The dynamical reaction of the particles accelerated at a shock front by the first-order Fermi process can be determined within kinetic models that account for both the hydrodynamics of the shocked fluid and the transport of the accelerated particles. These models predict the appearance of multiple solutions, all physically allowed. We discuss here the role of injection in selecting the real solution, in the framework of a simple phenomenological recipe, which is a variation of what is sometimes referred to as thermal leakage. In this context we show that multiple solutions basically disappear and when they are present they are limited to rather peculiar values of the parameters. We also provide a quantitative calculation of the efficiency of particle acceleration at cosmic ray modified shocks and we identify the fraction of energy which is advected downstream and that of particles escaping the system from upstream infinity at the maximum momentum. The consequences of efficient particle acceleration for shock heating are also discussed.     

Critical Self-Organization of Astrophysical Shocks

There are two distinct regimes of the first-order Fermi acceleration of shocks. The first is a linear (test-particle) regime in which most of the shock energy goes into thermal and bulk motions of the plasma. The second is an efficient regime in which the shock energy goes into accelerated particles. Although the transition region between them is narrow, we identify the factors that drive the system toward a self-organized critical state between those two regimes. Using an analytic solution, we determine this critical state and calculate the spectra and maximum energy of accelerated particles.     

A model of particle acceleration to high energies by multiple supernova explosions in OB associations

The possibility of cosmic-ray (CR) acceleration to energies above 10⁹ GeV per nucleus in extended Galactic OB associations is analyzed. A two-stage acceleration mechanism is justified: at the first stage, the acceleration by separate shock fronts from spatially and temporally correlated supernovae explosions takes place, and, at the second stage, the Fermi acceleration by supersonic turbulence in an extended, strongly perturbed region near the OB association takes place. We calculate the CR energy spectrum, the change in CR chemical composition with energy, and the energy dependence of the mean logarithm of atomic mass, ?lnA?, for the accelerated particles. The calculated values are compared with those observed near the break in the energy spectrum. We estimate the turbulence parameters, which allow the observed features of the energy spectrum and the CR enrichment with heavy elements to be explained.     

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.     

Diffusion in momentum space as a picture of second-order Fermi acceleration

Energetic particles in a turbulent medium can be subject to second-order Fermi acceleration due to scattering on moving plasma waves. This mechanism leads to growing particle momentum dispersion and, at the same time, increases the mean particle energy. In the most frequently met situations both processes can be represented by a single momentum diffusion term in the particle kinetic equation. In the present paper we discuss the conditions allowing the additional term for regular acceleration to arise. For forward-backward asymmetric scattering centres, besides the diffusive term one should explicitly consider the regular acceleration term in momentum space, which can consist of the first-order (∝ V), as well as the second-order (∝ V²) part in the wave velocity V. We derive the condition for the scattering probability in the wave rest frame requied for vanishing the regular acceleration term and provide a simple mechanical example illustrating the theoretical concepts. Finally, we address its possible role in cosmic ray acceleration processes.     

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.     

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.     

Interaction of fast particles with magneto-hydrodynamical turbulence

The acceleration of fast particles by Alfvén and magnetic sound waves of small amplitude is considered. The waves exist against the background of a strong, uniform magnetic field. We take into accunnt the contributions to acceleration from a large scale random field (harmonics withk<R ^–1, whereR is the Larmor radius), as well as from a small scale field (k>R ^–1). The small scale field was considered by perturbation theory, while large scale random field-in an adiabatic approximation. The energy dependence of the diffusion coefficient in momentum space, and the time of acceleration are estimated. The possible anisotropy of angular distribution is taken into account.If the Alfvén waves have spectral power index >2 and wave amplitude is small enough, then the energy dependance of the diffusion coefficient is stronger than in the case of the Fermi acceleration. For magnetic sound waves with 2 the energy dependance of the diffusion coefficient is the same as for the Fermi acceleration, but for <2 this dependance is less.The space diffusion coefficient of particles across the regular magnetic field is estimated. It is shown that this diffusion is due mainly to the large scale random field.     

A plasmon model for the knots of M 87

A plasmon model for the optical-radio knots of M87 is discussed with reference to their observed characteristics and physical conditions. The spectral evolution is investigated under the joint dissipation through expansion, Fermi acceleration and synchrotron radiation. A Fermi acceleration coefficient of 10⁻⁹ s⁻¹ was obtained, and it was also shown that a spectral break should occur at 5 × 10¹⁴Hz and that this frequency should vary very slowly in time, in agreement with observations.