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.     

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.     

Non-linear particle acceleration at non-relativistic shock waves in the presence of self-generated turbulence

Particle acceleration at astrophysical shocks may be very efficient if magnetic scattering is self-generated by the same particles. This non-linear process adds to the non-linear modification of the shock due to the dynamical reaction of the accelerated particles on the shock. Building on a previous general solution of the problem of particle acceleration with arbitrary diffusion coefficients, we present here the first semi-analytical calculation of particle acceleration with both effects taken into account at the same time; charged particles are accelerated in the background of Alfvén waves that they generate due to the streaming instability, and modify the dynamics of the plasma in the shock vicinity.     

Acceleration time-scale in an ultrarelativistic shock

The acceleration mechanism in ultrarelativistic shocks is investigated using Monte Carlo simulations. We apply a method of discrete small-amplitude particle momentum scattering to reproduce highly anisotropic conditions at the shock and describe the acceleration mechanism carefully. The obtained acceleration time equals 1.0 r _g c if the spectral index reaches the value of 2.2, independent of physical conditions in the shock. Some other parameters of the acceleration process are also provided.     

Efficiency of cosmic ray reflections from an ultrarelativistic shock wave

The process of cosmic ray acceleration up to energies in excess of 10²⁰ eV at relativistic shock waves with large Lorentz factors, Γ≫1, requires ∼Γ² particle energy gains at single reflections from the shock (cf. Gallant & Achterberg). In the present Letter , by applying numerical simulations we address an efficiency problem arising for such models. The actual efficiency of the acceleration process is expected to be substantially lower than the estimates of previous authors.     

Cosmic ray acceleration to very high energy through the non-linear amplification by cosmic rays of the seed magnetic field

The maximum energy for cosmic ray acceleration at supernova shock fronts is usually thought to be limited to around 10¹⁴–10¹⁵ eV by the size of the shock and the time for which it propagates at high velocity. We show that the magnetic field can be amplified non-linearly by the cosmic rays to many times the pre-shock value, thus increasing the acceleration rate and facilitating acceleration to energies well above 10¹⁵ eV. A supernova remnant expanding into a uniform circumstellar medium may accelerate protons to 10¹⁷ eV and heavy ions, with charge Ze , to Z ×10¹⁷ eV. Expansion into a pre-existing stellar wind may increase the maximum cosmic ray energy by a further factor of 10.     

Diffusive propagation of fast particles in the presence of a moving shock wave

Based on an analytical model, we determined the temporal dynamics of the spectral shape and spatial distribution of the particles that were impulsively (in time) injected with a specified spectrum in the vicinity of a moving plane shock front. We obtained a condition to determine the influence of the shock front on the particle propagation, where the spatial diffusion coefficient of the particles plays a major role. Diffusive shock acceleration is shown to strongly affect low-energy particles (the intensity maximum coincides spatially with the shock front; hard and soft spectral regions are formed in the spectrum) and weakly affect high-energy particles (the time at which the intensity reaches its maximum is well ahead of the shock arrival time; the spectral shape does not change). In events accompanied by a significant increase in the turbulence level, the influence of the shock front on high-energy particles can change from weak to strong. This change shows up in the spatial distribution and spectral shape of the particles. The dynamics of the particle intensity, calculated with the diffusion coefficients that were determined in accordance with the quasi-linear theory for measured turbulence levels, qualitatively corresponds to the observed solar energetic-particle intensity.     

Intergalactic shock acceleration and the cosmic gamma-ray background

We investigate numerically the contribution to the cosmic gamma-ray background from cosmic-ray ions and electrons accelerated at intergalactic shocks associated with cosmological structure formation. We show that the kinetic energy of accretion flows in the low-redshift intergalactic medium is thermalized primarily through moderately strong shocks, which allow for an efficient conversion of shock ram pressure into cosmic-ray pressure. Cosmic rays accelerated at these shocks produce a diffuse gamma-ray flux which is dominated by inverse Compton emission from electrons scattering off cosmic microwave background photons. Decay of neutral π mesons generated in p–p inelastic collisions of the ionic cosmic-ray component with the thermal gas contribute about 30 per cent of the computed emission. Based on experimental upper limits on the photon flux above 100 MeV from nearby clusters we constrain the efficiency of conversion of shock ram pressure into relativistic CR electrons to  ≲1 per cent  . Thus, we find that cosmic rays of cosmological origin can generate an overall significant fraction of order 20 per cent and no more than 30 per cent of the measured gamma-ray background.     

宇宙线的超新星遗迹起源

宇宙线的起源是高能天体物理的核心问题之一.一直以来,超新星爆发被认为是能谱膝区以下宇宙线的主要来源.多波段观测表明,超新星遗迹有能力加速带电粒子至亚PeV (10~(15)eV)能量.扩散激波加速被认为是最有效的天体高能粒子加速机制之一,而超新星遗迹的大尺度激波正好为这一机制提供平台.近年来,一系列较高精度的地面和空间实验极大地推动了对宇宙线以及超新星遗迹的研究.新的观测事实挑战着传统的扩散激波加速模型以及其在银河系宇宙线超新星遗迹起源学说上的应用,深化了人们对宇宙高能现象的认识.结合超新星遗迹辐射能谱的时间演化特性,构建的时间依赖的超新星遗迹粒子加速模型,不仅能够解释200 GV附近宇宙线的能谱反常,还自然地形成能谱膝区,甚至可以将超新星遗迹粒子加速对宇宙线能谱的贡献延伸至踝区.该模型预期超新星遗迹中粒子的输运行为表现为湍流扩散,这需要未来的观测以及与粒子输运相关的等离子体数值模拟工作来进一步验证.     

High-energy particle acceleration and production of ultra-high-energy cosmic rays in the giant lobes of Centaurus A

The nearby radio galaxy Centaurus A is poorly studied at high frequencies with conventional radio telescopes because of its very large angular size, but is one of a very few extragalactic objects to be detected and resolved by the Wilkinson Microwave Anisotropy Probe ( WMAP ). We have used the five-year WMAP data for Cen A to constrain the high-frequency radio spectra of the 10° giant lobes and to search for spectral changes as a function of position along the lobes. We show that the high-frequency radio spectra of the northern and southern giant lobes are significantly different: the spectrum of the southern lobe steepens monotonically (and is steeper further from the active nucleus) whereas the spectrum of the northern lobe remains consistent with a power law. The inferred differences in the northern and southern giant lobes may be the result of real differences in their high-energy particle acceleration histories, perhaps due to the influence of the northern middle lobe, an intermediate-scale feature which has no detectable southern counterpart. In light of these results, we discuss the prospects for Fermi Gamma-ray Space Telescope detections of inverse-Compton emission from the giant lobes and the lobes' possible role in the production of the ultra-high-energy cosmic rays (UHECR) detected by the Pierre Auger Observatory. We show that the possibility of a Fermi detection depends sensitively on the physical conditions in the giant lobes, with the northern lobe more likely to be detected, and that any emission observed by Fermi is likely to be dominated by photons at the soft end of the Fermi energy band. On the other hand, we argue that the estimated conditions in the giant lobes imply that UHECRs can be accelerated there, with a potentially detectable γ-ray signature at TeV energies.     

Using X‐ray observations to identify the particle acceleration mechanisms in VHE SNRs and “dark” VHE sources

Very high energy (VHE) γ‐ray observations have proven to be very successful in localizing Galactic acceleration sites of VHE particles. Observations of shell‐type supernova remnants have confirmed that particles are accelerated to VHE energies in supernova blast waves; the interpretation of the γ‐ray data in terms of hadronic or leptonic particle components in these objects relies nevertheless strongly on input from X‐ray observations. The largest identified Galactic VHE source class consists of pulsar wind nebulae, as detected in X‐rays. Many of the remaining VHE sources remain however unidentified until now. With X‐ray observations of these enigmatic “dark” objects one hopes to solve the following questions: What is the astrophysical nature of these sources? Are they predominantly electron or hadron accelerators? And what is their contribution to the overall cosmic ray energy budget? The paper aims to provide an overview over the identification status of the Galactic VHE source population. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)