Shock surfing acceleration

Analytical and numerical analysis identify shock surfing acceleration as an ideal pre-energization mechanism for the slow pick-up ions at quasiperpendicular shocks. After gaining sufficient energy by shock surfing, pick-up ions undergo diffusive acceleration to reach their observed energies. Energetic ions upstream of the cometary bow shock, acceleration of solar energetic particles by magnetosonic waves in corona, ion enhancement in interplanetary shocks, generation of anomalous cosmic rays from interstellar pick-up ions at the termination shock are some of the cases where shock surfing acceleration apply. Inclusion of the lower-hybrid wave turbulence into the laminar model of shock surfing can explain the preferential acceleration of heavier particles as observed by Voyager at the termination shock. At relativistic energies, unlimited acceleration of ions is theoretically possible; because for sufficiently strong shocks main limitation of the mechanism, caused by the escape of accelerated particles downstream of the shock during acceleration no longer exists.     

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.     

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.     

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.     

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.     

Electron surfing acceleration in oblique magnetic fields

Initially, inhomogeneous plasma jets, ejected by active galactic nuclei and associated with gamma-ray bursts, are thermalized by the formation of internal shocks. Jet subpopulations can hereby collide at Lorentz factors of a few. As the resulting relativistic shock expands into the upstream plasma, a significant fraction of the upstream ions is reflected. These ions, together with downstream ions that leak through the shock, form relativistic beams of ions that outrun the shock. The thermalization of these beams via the two-stream instability is thought to contribute significantly to plasma heating and particle acceleration by the shock. Here, the capability of a two-stream instability to generate relativistic field-aligned and cross-field electron flow, is examined for a magnetized plasma by means of a particle-in-cell (PIC) simulation. The electrons interact with the developing quasi-electrostatic waves and oblique magnetic fields. The simulation results bring forward evidence that such waves, by their non-linear interactions with the plasma, produce a highly relativistic field-aligned electron flow and electron energies, which could contribute to the radio synchrotron emissions from astrophysical jets, to ultrarelativistic leptonic subpopulations propagating with the jet and to the halo particles surrounding the accretion disc of the black hole.     

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.     

Fundamentals of collisionless shocks for astrophysical application, 2. Relativistic shocks

In this concise review of the recent developments in relativistic shock theory in the Universe we restrict ourselves to shocks that do not exhibit quantum effects. On the other hand, emphasis is given to the formation of shocks under both non-magnetised and magnetised conditions. We only briefly discuss particle acceleration in relativistic shocks where much of the results are still preliminary. Analytical theory is rather limited in predicting the real shock structure. Kinetic instability theory is briefed including its predictions and limitations. A recent self-similar relativistic shock theory is described which predicts the average long-term shock behaviour to be magnetised and to cause reasonable power-law distributions for energetic particles. The main focus in this review is on numerical experiments on highly relativistic shocks in (i) pair and (ii) electron-nucleon plasmas and their limitations. These simulations do not validate all predictions of analytic and self-similar theory and so far they do not solve the injection problem and the self-modification by self-generated cosmic rays. The main results of the numerical experiments discussed in this review are: (i) a confirmation of shock evolution in non-magnetised relativistic plasma in 3D due to either the lepton-Weibel instability (in pair plasmas) or to the ion-Weibel instability; (ii) the sensitive dependence of shock formation on upstream magnetisation which causes suppression of Weibel modes for large upstream magnetisation ratios σ>10⁻³; (iii) the sensitive dependence of particle dynamics on the upstream magnetic inclination angle θ _Bn , where particles of θ _Bn >34° cannot escape upstream, leading to the distinction between ‘subluminal’ and ‘superluminal’ shocks; (iv) particles in ultra-relativistic shocks can hardly overturn the shock and escape to upstream; they may oscillate around the shock ramp for a long time, so to speak ‘surfing it’ and thereby becoming accelerated by a kind of SDA; (v) these particles form a power-law tail on the downstream distribution; their limitations are pointed out; (vi) recently developed methods permit the calculation of the radiation spectra emitted by the downstream high-energy particles; (vii) the Weibel-generated downstream magnetic fields form large-amplitude vortices which could be advected by the downstream flow to large distances from the shock and possibly contribute to an extended strong field region; (viii) if cosmic rays are included, Bell-like modes can generate upstream magnetic turbulence at short and, by diffusive re-coupling, also long wavelengths in nearly parallel magnetic field shocks; (ix) advection of such large-amplitude waves should cause periodic reformation of the quasi-parallel shock and eject large-amplitude magnetic field vortices downstream where they contribute to turbulence and to maintaining an extended region of large magnetic fields.     

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.     

A One-Dimensional Relativistic Shock Model for the Light Curve of Gamma-ray Bursts

We investigate the forming of gamma-ray burst pulses with a simple one-dimensional relativistic shock model. The mechanism is that a "central engine" drives forward the nearby plasma inside the fireball to generate a series of pressure waves. We give a relativistic geometric recurrence formula that connects the time when the pressure waves are produced and the time when the corresponding shocks occurred. This relation enables us to relate the pulse magnitude with the observation time. Our analysis shows that the evolution of the pressure waves leads to a fast rise and an exponential decay pulses. In determining the width of the pulses, the acceleration time is more important than that of the deceleration.     

Computation of X-Ray Blazar Light Curves Using RHD Simulations

We present the results of a two-dimensional relativistic hydrodynamic simulation of collisions of dense shells of matter moving within a uniform jet. The non-thermal synchrotron radiation produced by the relativistic electrons injected at shocks is computed following their temporal and spatial evolution. We test different parameterizations of the shock acceleration process and compute the corresponding X-ray light curves. A time lag between hard and soft X-ray radiation is found. The collision has an efficiency of few times 10^?3 in converting kinetic energy into radiation.     

Limit shocks of relativistic magnetohydrodynamics

In this paper we show that switch-on and switch-off shocks are allowed by the shock equations of relativistic MHD and have similar properties to their Newtonian counterparts. Just like in Newtonian MHD they are limits of fast and slow shock solutions and as such they may be classified as weakly evolutionary shocks.     

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.     

Radio Relics in Cosmological Simulations

Radio relics have been discovered in many galaxy clusters. They are believed to trace shock fronts induced by cluster mergers. Cosmological simulations allow us to study merger shocks in detail since the intra-cluster medium is heated by shock dissipation. Using high resolution cosmological simulations, identifying shock fronts and applying a parametric model for the radio emission allows us to simulate the formation of radio relics. We analyze a simulated shock front in detail. We find a rather broad Mach number distribution. The Mach number affects strongly the number density of relativistic electrons in the downstream area, hence, the radio luminosity varies significantly across the shock surface. The abundance of radio relics can be modeled with the help of the radio power probability distribution which aims at predicting radio relic number counts. Since the actual electron acceleration efficiency is not known, predictions for the number counts need to be normalized by the observed number of radio relics. For the characteristics of upcoming low frequency surveys we find that about thousand relics are awaiting discovery.     

High Energetic Electrons Accelerated by a Coronal Shock Wave

Combined SOHO (Solar and Helisopheric Observatory) and ground based radio observations show evidently signatures of electrons accelerated by a shock wave during the event on July 9, 1996. A solar type II radio burst has been received as a signature of a coronal shock wave at 300 MHz on 9:10:54 UT. It was accompanied with electron beams appearing as type III radio bursts below 80 MHz. Simultaneously, the COSTEP (Comprehensive Suprathermal and Energetic Particle Analyzer) instrument aboard SOHO has measured enhanced electron fluxes in the range 30 keV – 3 MeV. This indicates that a coronal shock wave was able to produce high energetic electrons. A mechanism of electron acceleration up to relativistic velocities is presented and compared with the observations. The electron acceleration takes place at substructures of quasi-parallel collisionless shocks. This revised version was published online in July 2006 with corrections to the Cover Date.     

Radio signature of cosmological structure formation shocks

In the course of the formation of cosmological structures, large shock waves are generated in the intracluster medium (ICM). In analogy to processes in supernova remnants, these shock waves may generate a significant population of relativistic electrons which, in turn, produce observable synchrotron emission. The extended radio relics found at the periphery of several clusters and possibly also a fraction of radio halo emission may have this origin. Here, we derive an analytic expression for (i) the total radio power in the downstream region of a cosmological shock wave, and (ii) the width of the radio-emitting region. These expressions predict a spectral slope close to −1 for strong shocks. Moderate shocks, such as those produced in mergers between clusters of galaxies, lead to a somewhat steeper spectrum. Moreover, we predict an upper limit for the radio power of cosmological shocks. Comparing our results to the radio relics in Abell 115, 2256 and 3667, we conclude that the magnetic field in these relics is typically at a level of 0.1 μG. Magnetic fields in the ICM are presumably generated by the shocks themselves; this allows us to calculate the radio emission as a function of the cluster temperature. The resulting emissions agree very well with the radio power–temperature relation found for cluster haloes. Finally, we show that cosmic accretion shocks generate less radio emission than merger shock waves. The latter may, however, be detected with upcoming radio telescopes.     

黑洞吸积理论的新进展(II):含激波的吸积理论

着重评述了含激波吸积理论的发展历史和研究现状, 介绍了在伪牛顿势以及严格广义相对论框架下, 对等温和绝热两种不同的流体模型中可能发生的Ｒ－ Ｈ 激波、等温激波等各种不同激波的解析和数值模拟研究, 包括激波发生的参数空间、不同流体参数（ 比能量和比角动量） 下激波发生的位置、强度以及耗散的能量。这些研究结果表明, 在理想流体近似下, 黑洞吸积流中必定会产生激波。此外, 还介绍了含激波吸积理论在活动星系核方面的应用。对黑洞吸积理论简单讨论, 评述了含激波吸积理论与ＡＤＡＦ 吸积理论的关系, 着重评述了目前对于ＡＤＡＦ 中是否会发生激波这一存在很大争议的问题。     

General relativistic self-similar solutions in cosmology

We present general relativistic solutions for self-similar spherical perturbations in an expanding cosmological background of cold pressure-less gas. We focus on solutions having shock discontinuities propagating in the surrounding cold gas. The pressure, p , and energy density, μ, in the shock-heated matter are assumed to obey   p = w μ  , where w is a positive constant. Consistent solutions are found for shocks propagating from the symmetry centre of a region of a positive density excess over the background. In these solutions, shocks exist outside the radius marking the event horizon of the black hole which would be present in a shock-less collapse. For large jumps in the energy density at the shock, a black hole is avoided altogether and the solutions are regular at the centre. The shock-heated gas does not contain any sonic points, provided the motion of the cold gas ahead of the shock deviates significantly from the Hubble flow. For shocks propagating in the uniform background, sonic points always appear for small jumps in the energy density. We also discuss self-similar solutions without shocks in fluids with   w < −1/3  .     

Relativistic shock waves in double radio sources

Using a model of relativistic collision between two media and based on the theory of shock waves in an ideal relativistic fluid, we calculate in detail, the main parameters at the Initial stage of the formation of radio component sources, including the separation velocity and the travelling speed of the shock. The evolution of the hot spot as it moved from within the galaxy to a quasi-steady state in the intergalactic space is discussed qualitatively. Lastly, the parameters in the quasi-steady state are approximately evaluated using the formulae for strong shocks. The results obtained are in overall agreement with observations.     

Astrophysical boosters

Constraints are derived on the acceleration of charges in shocks to highly relativistic energies. When applied to the extended extragalactic radio sources and to the cosmic rays, they cast doubt on the mechanism of ‘in-situ acceleration’, both for energy, entropy and statistical mechanics reasons.