The physics of particle acceleration at the heliospheric termination shock

Cosmic rays are ubiquitous in space, and the essential similarity of their energy spectra in many different regions places significant general constraints on the mechanisms for their acceleration and confinement. Diffusive shock acceleration is at present the most successful acceleration mechanism proposed, and, together with transport in Kolmogorov turbulence, can account for the universal specta. A unique laboratory for studying the acceleration and transport of charged particles is the outer heliosphere, including the solar wind termination shock and heliosheath.

A widely accepted paradigm for the transport and acceleration of energetic particles in the heliosphere has evolved over the last few decades. This picture has successfully explained many features of the modulation of galactic cosmic rays and the transport and acceleration of anomalous cosmic rays at the solar-wind termination shock. Recent Voyager observations near and beyond the termination shock have revealed new, and in some cases, unexpected phenomena which have led to questions concerning the established paradigm. The physical interpretation of the observations requires a blunt termination shock, rapid inward motion of the shock and temporal variations over time scales ranging from hours to 22 years. Incorporation of these into the physics has promise of explaining most, if not, all of the observed phenomena while retaining the advantages of the termination shock paradigm for both galactic and anomalous cosmic rays.     

Acceleration of Pick-up Ions at the Solar Wind Termination Shock

It is generally accepted that pick-up ions act as a seed population for anomalous cosmic rays originating at the solar wind termination shock. We believe that the ion pre-acceleration process operating in the heliosphere up to the termination shock can be very important to inject the ions into the shock acceleration process. The pick-up ions pre-accelerated by solar wind turbulences have already a pronounced high energy tail when they reach the shock. Some fraction of these ions can experience further acceleration up to energies of anomalous cosmic rays by means of shock drift and diffusive acceleration. In the present paper the shock drift acceleration of pick-up ions suffering multiple reflection due to abrupt changes in both the strength and direction of the magnetic field through the shock is considered. The reflection process operates for high velocity particles different from the reflection by the electric cross-shock potential. During the first reflection the mean kinetic energy of pick-up ions increases by approximately a factor of 10. Reflected particles have highly anisotropic velocity distribution. Subsequent excursion of the particles in the turbulent upstream flow leads to diffusion in pitch-angle space and, as a result, the particles can return to the shock again suffering, thus, multiple encounters. In order to describe the motion of particles in the upstream and down streamparts of the flow we solve the Fokker-Plank transport equation for anisotropic velocity distribution function. This revised version was published online in July 2006 with corrections to the Cover Date.     

Acceleration of anomalous cosmic rays at the heliospheric termination shock

Astronomy Letters - The acceleration of anomalous cosmic rays (ACRs) at the heliospheric termination shock and their influence on the shock structure and location are analyzed in terms of a...     

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.     

The Origin of Cosmic Rays from Supernova Remnants

The origin of cosmic rays is one of the key questions in high-energy astrophysics. Supernovae have been always considered as the dominant sources of cosmic rays below the energy spectrum knee. Multi-wavelength observations indeed show that supernova remnants are capable for accelerating particles into sub-PeV (10${}^{15}$ eV) energies. Diffusive shock acceleration is considered as one of the most efficient acceleration mechanisms of astrophysical high-energy particles, which may just operate effectively in the large-scale shocks of supernova remnants. Recently, a series of high-precision ground and space experiments have greatly promoted the study of cosmic rays and supernova remnants. New observational features challenge the classical acceleration model by diffusive shock and the application to the scenario of supernova remnants for the origin of Galactic cosmic rays, and have deepened our understanding to the cosmic high-energy phenomena. In combination with the time evolution of radiation energy spectrum of supernova remnants, a time-dependent particle acceleration model is established, which can not only explain the anomalies in cosmic-ray distributions around 200 GV, but also naturally form the cosmic-ray spectrum knee, even extend the contribution of supernova particle acceleration to cosmic ray flux up to the spectrum ankle. This model predicts that the high-energy particle transport behavior is dominated by the turbulent convection, which needs to be verified by future observations and plasma numerical simulations relevant to the particle transport.     

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.     

Physics and Gasdynamics of the Heliospheric Interface

During 30 years, a big theoretical effort to understand the physical processes in the heliospheric interface has followed the pioneer papers by Parker (1961) and Baranov et al. (1971). The heliospheric interface is a shell formed by the solar wind interaction with the ionized component of the circumsolar local interstellar medium (LISM). For fully ionized supersonic interstellar plasma two-shocks (the termination shock and the bow shock) and a contact discontinuity (the heliopause) are formed in the solar wind/LISM interaction. However, LISM consists of at least of three components additional to plasma: H-atoms, galactic cosmic rays and magnetic field. The interstellar atoms that penetrate into the solar wind, are ionized there and form pickup ions. A part of the pickup ions is accelerated to high energies of anomalous cosmic rays (ACRs). ACRs may modify the plasma flow upstream the termination shock and in the heliosheath. In this short review I summarize current understanding of the physical and gasdynamical processes in the heliospheric interface, outline unresolved problems and future perspectives. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the energy spectrum of galactic primary cosmic rays: Results from the transport equation

The spectrum of galactic primary cosmic rays at relativistic monenta is calculated. The primaries are assumed to be accelerated continuously from the thermal galactic background medium by first- and second-order Fermi acceleration. We show that the observed spectrum is readily obtained from the transport equation conventionally invoked to discuss propagation and loss of cosmic rays in our Galaxy from a distribution of sources. We have previously (Lerche and Schlickeiser, 1985) shown that the observed secondary to primary ratio is satisfactorily explained by a similar use of the transport equation, allowing for secondary production from the primaries. Accordingly, when the results of this paper are added to those concerning the secondary/primary ratio behaviour, it would seem that continuous Fermi acceleration accounts, in a quantitative fashion, for the spectral behaviours observed at Earth.     

Non-Linear Amplification of a Magnetic Field Driven by Cosmic Ray Streaming

One dimensional numerical results of the non-linear interaction between cosmic rays and a magnetic field are presented. These show that cosmic ray streaming drives large amplitude Alfvénic waves. The cosmic ray streaming energy is very efficiently transfered to the perturbed magnetic field of the Alfvén waves. Thus a magnetic field of interstellar values, assumed in models of supernova remnant blast wave acceleration, would not be appropriate in the region of the shock. The increased magnetic field reduces the acceleration time and so increases the maximum cosmic ray energy, which may provide a simple and elegant resolution to the highest energy galactic cosmic ray problem were the cosmic rays themselves provide the fields necessary for their acceleration. This revised version was published online in July 2006 with corrections to the Cover Date.     

On possible 'cosmic ray cocoons' of relativistic jets

We consider effects on an (ultra)relativistic jet and its ambient medium caused by high-energy cosmic rays accelerated at the jet side boundary. As illustrated by simple models, during the acceleration process a flat cosmic ray distribution can be created, with gyro-radii for the highest particle energies reaching scales comparable to the jet radius or energy density comparable to the pressure of the ambient medium . In the case of efficient radiative losses, a high-energy bump in the spectrum can dominate the cosmic ray pressure. In extreme cases, the cosmic rays are able to push the ambient medium off, providing a 'cosmic ray cocoon' separating the jet from the surrounding medium. The considered cosmic rays provide an additional jet braking force and lead to a number of consequences for the jet structure and its radiative output. In particular, the dynamic and acceleration time-scales involved are in the range observed in variable active galactic nuclei.     

Relationship between high-energy physical phenomena on the sun and in astrophysics

High energy phenomena on the surface of the Sun are manifestations of part of the solar dynamo cycle. Convection and magnetic field give rise to unstable, twisted flux loops that become solar flares when the resistive tearing mode proceeds to the nonlinear limit. If such twisted flux loops did not dissipate rapidly due to an enhanced resistivity, then the dynamo would not work. The act of dissipation leads to intense heating and acceleration leading to X-rays and accelerated particles. The particles in turn give rise to hard X-rays, gamma rays, neutrons, and solar cosmic rays. In high-energy astrophysics such phenomena occur in accretion disks around compact objects like black holes in quasars and SS433. The resulting acceleration may explain the observed extremely high-energy cosmic rays of up to 10²⁰ eV and the high-energy gamma rays of 10¹² to 10¹⁵ eV. These high energies are more readily explained by acceleration E parallel to B as opposed to stochastic shock acceleration. The anisotropy and localization of gamma rays from solar flares potentially may indicate which mechanism is prevalent.     

Cosmic Ray Nonlinear Processes in Space Plasma: Applications to the Dynamic Heliosphere

Influence of cosmic ray pressure and kinetic stream instability on space plasma dynamics and magnetic structure are considered. It is shown that in the outer Heliosphere are important dynamics effects of galactic cosmic ray pressure on solar wind and interplanetary shock wave propagation as well as on the formation of terminal shock wave of the Heliosphere and subsonic region between Heliosphere and interstellar medium. Kinetic stream instability effects are important on distances more than 40–60 AU from the Sun: formation of great anisotropy of galactic cosmic rays in about spiral interplanetary magnetic field leads to the Alfven turbulence generation by non isotropic cosmic ray fluxes. Generated Alfven turbulence influences on cosmic ray propagation, increases the cosmic ray modulation, decreases the cosmic ray anisotropy and increases the cosmic ray pressure gradient in the outer Heliosphere (the later is also important for terminal shock wave formation). This revised version was published online in July 2006 with corrections to the Cover Date.     

Energetic particles from the sun

This paper discusses solar cosmic ray phenomena and related topics from the solar physical point of view. Basic physics of the solar atmosphere and solar flare phenomena are, therefore, considered in some detail. Since solar cosmic rays are usually produced by solar flares, we must first understand the processes and mechanism of solar flares, especially the so-called proton flares, in order to understand the acceleration mechanism of solar cosmic rays and their behaviour in both the solar atmosphere and interplanetary space. For this reason, detailed discussion is given on various phenomena associated with solar flares, proton flare characteristics, and the mechanism of solar flares.Since the discovery of solar cosmic rays by Forbush, the interplanetary space has been thought of as medium in which solar cosmic rays propagate. In this paper, the propagation of solar cosmic rays in this space is, therefore, discussed briefly by referring to the observed magnetic properties of this space. Finally, some problems related to the physics of galactic cosmic rays are discussed.Astrophysics and Space Science Review Paper.     

Ballistic and diffusive components in the dynamic spectra of ultrahigh energy cosmic rays from nearby transient sources

Ultrahigh energy cosmic rays (UHECRs, E > 10¹⁸ eV) from extragalactic sources deviate in the galactic and intergalactic magnetic fields, which explains the diffusive character of their propagation, the isotropization of their total flux, and the absence of UHECR clusters associated with individual sources. Extremely high energy cosmic rays (E > 10^19.7 eV) are scattered mainly in localized magnetized structures, such as galaxy clusters, filaments, etc., with a mean free path of tens of megaparsecs; therefore, in the case of nearby transient sources, a substantial contribution to the observed flux is expected from unscattered and weakly scattered particles, which may be a decisive factor in the identification of these sources. We propose a method for calculating the time evolution of the UHECR energy spectra based on analytical solutions of the transport equation with the explicit determination of the contributions from scattered and unscattered particles. As examples, we consider the cases of transient activity of the nearest active galactic nucleus, Centaurus A, and the acceleration of UHECRs by a young millisecond pulsar.     

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.     

On the escape of particles from cosmic ray modified shocks

Stationary solutions to the problem of particle acceleration at shock waves in the non-linear regime, when the dynamical reaction of the accelerated particles on the shock cannot be neglected, are known to show a prominent energy flux escaping from the shock towards upstream infinity. On physical grounds, the escape of particles from the upstream region of a shock has to be expected in all those situations in which the maximum momentum of accelerated particles,   p _max  , decreases with time, as is the case for the Sedov–Taylor phase of expansion of a shell supernova remnant, when both the shock velocity and the cosmic ray induced magnetization decrease. In this situation, at each time t , particles with momenta larger than   p _max( t )  leave the system from upstream, carrying away a large fraction of the energy if the shock is strongly modified by the presence of cosmic rays. This phenomenon is of crucial importance for explaining the cosmic ray spectrum detected at the Earth. In this paper, we discuss how this escape flux appears in the different approaches to non-linear diffusive shock acceleration, and especially in the quasi-stationary semi-analytical kinetic ones. We apply our calculations to the Sedov–Taylor phase of a typical supernova remnant, including in a self-consistent way particle acceleration, magnetic field amplification and the dynamical reaction on the shock structure of both particles and fields. Within this framework, we calculate the temporal evolution of the maximum energy reached by the accelerated particles and of the escape flux towards upstream infinity. The latter quantity is directly related to the cosmic ray spectrum detected at the Earth.     

Intensity of galactic cosmic rays in the early sun epoch

The process of heliospheric modulation of intensity of galactic cosmic rays is investigated by solving the transport equation. The spatial-energetic distribution of cosmic rays in the present epoch and in the past is analyzed. It is demonstrated that the particle density and the energy density of cosmic rays in the Solar System in the distant past were much lower than the corresponding current values. The cosmic ray intensity modulation in the early heliosphere was especially strong in the case of low-energy particles.     

Statistical acceleration and spatial diffusion of cosmic rays in turbulent medium

Statistical acceleration of cosmic rays in a turbulent medium is considered. Charged particles are assumed to acquire energy in a bounded region of space and leave the acceleration region due to spatial diffusion caused by the scattering of cosmic rays in turbulent magnetic fields. Analytical solutions of the cosmic ray transport equation are obtained and equilibrium space-energy distributions of high-energy particles are studied in the acceleration region and beyond.     

Cosmic ray acceleration in hypernova remnants expanding in wind bubbles of Wolf-Rayet progenitor stars

The determination of the origin of cosmic rays with observed energies in excess of 10¹⁷ eV that exceed the expected energies of cosmic rays accelerated by supernova remnants in the galaxy is a pressing problem in modern astrophysics. Hypernova remnants are one of the possible galactic sources of cosmic rays with energies of up to 10¹⁹ eV. Hypernovae constitute a class of extremely powerful supernova explosions, whose supposed progenitors are massive Wolf-Rayet stars. We analyze the special aspects of acceleration of cosmic rays in hypernova remnants that expand in wind bubbles of Wolf-Rayet progenitor stars. We show that these cosmic rays may attain maximum energies of 10¹⁸ eV even with a relatively conservative choice of acceleration parameters and account for tens of percent of the total cosmic ray flux observed in the vicinity of the earth in the energy range of 10¹⁶–10¹⁸ eV if the galactic hypernova explosion rate in the modern epoch reaches ? _S ～ 10^?4 year^?1.     

Spectrum and anisotropy of cosmic rays at TeV–PeV-energies and contribution of nearby sources

The role of nearby galactic sources, the supernova remnants, in formation of observed energy spectrum and large-scale anisotropy of high-energy cosmic rays is studied. The list of these sources is made up based on radio, X-ray and gamma-ray catalogues. The distant sources are treated statistically as ensemble of sources with random positions and ages. The source spectra are defined based on the modern theory of cosmic ray acceleration in supernova remnants while the propagation of cosmic rays in the interstellar medium is described in the frameworks of galactic diffusion model. Calculations of dipole component of anisotropy are made to reproduce the experimental procedure of “two-dimensional” anisotropy measurements. The energy dependence of particle escape time in the process of acceleration in supernova remnants and the arm structure of sources defining the significant features of anisotropy are also taken into account. The essential new trait of the model is a decreasing number of core collapse SNRs being able to accelerate cosmic rays up to the given energy, that leads to steeper total cosmic ray source spectrum in comparison with the individual source spectrum. We explained simultaneously the new cosmic ray data on the fine structure of all particle spectrum around the knee and the amplitude and direction of the dipole component of anisotropy in the wide energy range 1 TeV–1 EeV. Suggested assumptions do not look exotic, and they confirm the modern understanding of cosmic ray origin.