Turbulence, Magnetic Reconnection in Turbulent Fluids and Energetic Particle Acceleration

Turbulence is ubiquitous in astrophysics. It radically changes many astrophysical phenomena, in particular, the propagation and acceleration of cosmic rays. We present the modern understanding of compressible magnetohydrodynamic (MHD) turbulence, in particular its decomposition into Alfvén, slow and fast modes, discuss the density structure of turbulent subsonic and supersonic media, as well as other relevant regimes of astrophysical turbulence. All this information is essential for understanding the energetic particle acceleration that we discuss further in the review. For instance, we show how fast and slow modes accelerate energetic particles through the second order Fermi acceleration, while density fluctuations generate magnetic fields in pre-shock regions enabling the first order Fermi acceleration of high energy cosmic rays. Very importantly, however, the first order Fermi cosmic ray acceleration is also possible in sites of magnetic reconnection. In the presence of turbulence this reconnection gets fast and we present numerical evidence supporting the predictions of the Lazarian and Vishniac (Astrophys. J. 517:700–718, 1999) model of fast reconnection. The efficiency of this process suggests that magnetic reconnection can release substantial amounts of energy in short periods of time. As the particle tracing numerical simulations show that the particles can be efficiently accelerated during the reconnection, we argue that the process of magnetic reconnection may be much more important for particle acceleration than it is currently accepted. In particular, we discuss the acceleration arising from reconnection as a possible origin of the anomalous cosmic rays measured by Voyagers as well as the origin cosmic ray excess in the direction of Heliotail.     

Cosmic-Ray Energy Spectra and Time Variations in the Local Interstellar Medium: Constraints and Uncertainties

The spectra of galactic cosmic rays that are observed inside the heliosphere result from the interaction of the spectra present in the local interstellar medium with the structured but turbulent magnetic field carried by the solar wind. Observational tests of solar modulation theory depend on comparisons between spectra inside and outside the heliosphere. Our knowledge of the local interstellar spectra are indirect, using extrapolations of interplanetary spectra measured at high energies where solar modulation effects are minimal and modeling of the physical processes that occur during particle acceleration and transport in the interstellar medium. The resulting estimates of the interstellar spectra can also be checked against observations of the effects that cosmic rays have on the chemistry of the interstellar medium and on the production of the diffuse galactic gamma-ray background. I review the present understanding of the local galactic cosmic-ray spectra, emphasizing the constraints set by observations and the uncertainties that remain.     

Shock Acceleration of Ions in the Heliosphere

Energetic particles constitute an important component of the heliospheric plasma environment. They range from solar energetic particles in the inner heliosphere to the anomalous cosmic rays accelerated at the interface of the heliosphere with the local interstellar medium. Although stochastic acceleration by fluctuating electric fields and processes associated with magnetic reconnection may account for some of the particle populations, the majority are accelerated by the variety of shock waves present in the solar wind. This review focuses on “gradual” solar energetic particle (SEP) events including their energetic storm particle (ESP) phase, which is observed if and when an associated shock wave passes Earth. Gradual SEP events are the intense long-duration events responsible for most space weather disturbances of Earth’s magnetosphere and upper atmosphere. The major characteristics of gradual SEP events are first described including their association with shocks and coronal mass ejections (CMEs), their ion composition, and their energy spectra. In the context of acceleration mechanisms in general, the acceleration mechanism responsible for SEP events, diffusive shock acceleration, is then described in some detail including its predictions for a planar stationary shock, shock modification by the energetic particles, and wave excitation by the accelerating ions. Finally, some complexities of shock acceleration are addressed, which affect the predictive ability of the theory. These include the role of temporal and spatial variations, the distinction between the plasma and wave compression ratios at the shock, the injection of thermal plasma at the shock into the process of shock acceleration, and the nonlinear evolution of ion-excited waves in the vicinity of the shock.     

Particle Acceleration in Relativistic Outflows

In this review we confront the current theoretical understanding of particle acceleration at relativistic outflows with recent observational results on various source classes thought to involve such outflows, e.g. gamma-ray bursts, active galactic nuclei, and pulsar wind nebulae. We highlight the possible contributions of these sources to ultra-high-energy cosmic rays.     

Cosmic Rays in Galactic and Extragalactic Magnetic Fields

We briefly review sources of cosmic rays, their composition and spectra as well as their propagation in the galactic and extragalactic magnetic fields, both regular and fluctuating. A special attention is paid to the recent results of the X-ray and gamma-ray observations that shed light on the origin of the galactic cosmic rays and the challenging results of Pierre Auger Observatory on the ultra high energy cosmic rays. The perspectives of both high energy astrophysics and cosmic-ray astronomy to identify the sources of ultra high energy cosmic rays, the mechanisms of particle acceleration, to measure the intergalactic radiation fields and to reveal the structure of magnetic fields of very different scales are outlined.     

Diffusive Shock Acceleration and Magnetic Field Amplification

Diffusive shock acceleration is the theory of particle acceleration through multiple shock crossings. In order for this process to proceed at a rate that can be reconciled with observations of high-energy electrons in the vicinity of the shock, and for cosmic rays protons to be accelerated to energies up to observed galactic values, significant magnetic field amplification is required. In this review we will discuss various theories on how magnetic field amplification can proceed in the presence of a cosmic ray population. On both short and long length scales, cosmic ray streaming can induce instabilities that act to amplify the magnetic field. Developments in this area that have occurred over the past decade are the main focus of this paper.     

Particle Acceleration in the Heliosphere: Implications for Astrophysics

There has been a remarkable discovery concerning particles that are accelerated in the solar wind. At low energies, in the region where the particles are being accelerated, the spectrum of the accelerated particles is always the same: when expressed as a distribution function, the spectrum is a power law in particle speed with a spectral index of ?5, and a rollover at higher particle speeds that can often be described as exponential. This common spectral shape cannot be accounted for by any conventional acceleration mechanism, such as diffusive shock acceleration or traditional stochastic acceleration. It has thus been necessary to invent a new acceleration mechanism to account for these observations, a pump mechanism in which particles are pumped up in energy through a series of adiabatic compressions and expansions. The conditions under which the pump acceleration is the dominant acceleration mechanism are quite general and are likely to occur in other astrophysical plasmas. In this paper, the most compelling observations of the ?5 spectra are reviewed; the governing equation of the pump acceleration mechanism is derived in detail; the pump acceleration mechanism is applied to acceleration at shocks; and, as an illustration of the potential applicability of the pump acceleration mechanism to other astrophysical plasmas, the pump mechanism is applied to the acceleration of galactic cosmic rays in the interstellar medium.     

The Energy Spectra and Anisotropies of Cosmic Rays

The existing paradigm of the origin of Galactic cosmic rays places strong supernovae shocks as the acceleration site for this material. However, although the EGRET gamma-ray telescope has reported evidence for GeV gamma rays from some supernovae, it is still unclear if the signal is produced by locally intense cosmic rays. Although non-thermal X-ray emissions have been detected from supernova remnants and interpreted as synchrotron emission from locally intense electrons at energies up to 100 TeV, the inferred source energy spectral slopes seem much steeper than the electron source spectrum observed through direct measurements. It remains the case that simple energetics provide the most convincing argument that supernovae power the bulk of cosmic rays. Two characteristics which can be used to investigate this issue at high energy are the source energy spectra and the source composition derived from direct measurements.     

Electron-Ion Temperature Equilibration in Collisionless Shocks: The Supernova Remnant-Solar Wind Connection

Collisionless shocks are loosely defined as shocks where the transition between pre-and post-shock states happens on a length scale much shorter than the collisional mean free path. In the absence of collision to enforce thermal equilibrium post-shock, electrons and ions need not have the same temperatures. While the acceleration of electrons for injection into shock acceleration processes to produce cosmic rays has received considerable attention, the related problem of the shock heating of quasi-thermal electrons has been relatively neglected. In this paper we review the state of our knowledge of electron heating in astrophysical shocks, mainly associated with supernova remnants (SNRs), shocks in the solar wind associated with the terrestrial and Saturnian bowshocks, and galaxy cluster shocks. The solar wind and SNR samples indicate that the ratio of electron temperature, (T _e ) to ion temperature (T _p ) declining with increasing shock speed or Alfvén Mach number. We discuss the extent to which such behavior can be understood on the basis of waves generated by cosmic rays in a shock precursor, which then subsequently damp by heating electrons, and speculate that a similar explanation may work for both solar wind and SNR shocks.     

GeV Particle Acceleration in Solar Flares and Ground Level Enhancement (GLE) Events

Ground Level Enhancement (GLE) events represent the most energetic class of solar energetic particle (SEP) events, requiring acceleration processes to boost ?1?GeV ions in order to produce showers of secondary particles in the Earth’s atmosphere with sufficient intensity to be detected by ground-level neutron monitors, above the background of cosmic rays. Although the association of GLE events with both solar flares and coronal mass ejections (CMEs) is undisputed, the question arises about the location of the responsible acceleration site: coronal flare reconnection sites, coronal CME shocks, or interplanetary shocks? To investigate the first possibility we explore the timing of GLE events with respect to hard X-ray production in solar flares, considering the height and magnetic topology of flares, the role of extended acceleration, and particle trapping. We find that 50% (6 out of 12) of recent (non-occulted) GLE events are accelerated during the impulsive flare phase, while the remaining half are accelerated significantly later. It appears that the prompt GLE component, which is observed in virtually all GLE events according to a recent study by Vashenyuk et al. (Astrophys. Space Sci. Trans. 7(4):459–463, 2011), is consistent with a flare origin in the lower corona, while the delayed gradual GLE component can be produced by both, either by extended acceleration and/or trapping in flare sites, or by particles accelerated in coronal and interplanetary shocks.     

A Hitch-hiker’s Guide to Stochastic Differential Equations

In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via “toy models”. Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Aspects covered are the solar modulation of cosmic rays, diffusive shock acceleration, galactic cosmic ray propagation and solar energetic particle transport. We believe that the SDE method, due to its simplicity and computational efficiency on modern computer architectures, will be of significant relevance in energetic particle studies in the years to come.     

Optical and UV Diagnostics of Supernova Remnant Shocks

The relatively faint optical and UV emission from non-radiative shock waves provides diagnostics for processes related to cosmic ray acceleration in collisionless shocks. Emission line profiles and intensities can be used to determine the efficiencies of electron-ion and ion-ion thermal equilibration, which influence the population of fast particles injected into the acceleration process. It is found that T _e/T _p declines with shock speed and that T _i is roughly proportional to mass in fast shocks. Important information about cosmic ray precursors may be available, but the interpretation is still somewhat ambiguous. The compression ratios in shocks which efficiently accelerate cosmic rays are predicted to be substantially larger than the factor of 4 expected for a strong shock in a = 5/3 perfect gas, and some limits may be available from observations.     

Solar cosmic rays

The first observations of solar cosmic rays were made simultaneously by many investigators at worldwide cosmic-ray stations in the periods of powerful chromospheric flares on February 28 and March 7, 1942. The discovery of these and the investigation of cosmic-ray solar-daily variations with maximum time near noon led some authors (Richtmyer and Teller, 1948; Alfvén, 1949, 1950) to a model of apparent cosmic-ray solar origin. We present here the results of the properties of solar cosmic rays from ground events (experimental and theoretical investigations). We also discuss important information from solar experimental data relating to these ground events observed in September and October 1989 and May 1990. Some experimental evidence of acceleration processes in associated phenomena with flares and long-term (solar cycle) variation of the average flux of solar cosmic rays is discussed as also cornal and interplanetary propagation, and that in the terrestrial magnetosphere. Note that the energy spectrum of solar cosmic rays varied very strongly from one flare to another. What are the causes of these phenomena? What is the nature of chemical and isotopic contents of solar cosmic rays? How can its changes occur in the energy spectrum and chemical contents of solar cosmic rays in the process of propagation? Is it possible to recalculate these parameters to the source? What makes solar cosmic rays rich in heavy nucleus and³He? The important data about electrons, positrons, gamma-quanta and neutrons from flares will be discussed in a subsequent paper (Dorman and Venkatesan, 1992). The question is: What main acceleration mechanism of solar flare and associated phenomena are reliable? These problems are connected with the more general problem on solar flare origin and its energetics. In Dorman and Venkatesan (1993) we will consider these problems as well as the problem of prediction of radiation hazard from solar cosmic rays (not only in space, but also in the Earth's atmosphere too).     

Cosmic-Ray Transport and Interaction with Shocks

This paper reviews selected topics in cosmic-ray transport in the heliosphere, as well as recent insights on the interaction of cosmic rays with shocks. Topics include: (a) recent observations suggesting very long inferred scattering mean-free paths of cosmic rays, (b) recent insights into the diffusion of cosmic rays normal to a magnetic field, (c) the physics of super-diffusion and sub-diffusion, and (e) the interaction of cosmic rays with shocks moving through large-scale irregular magnetic fields.     

Cosmic Rays in the Heliosphere: Requirements for Future Observations

Since the publication of Cosmic Rays in the Heliosphere in 1998 there has been great progress in understanding how and why cosmic rays vary in space and time. This paper discusses measurements that are needed to continue advances in relating cosmic ray variations to changes in solar and interplanetary activity and variations in the local interstellar environment. Cosmic ray acceleration and transport is an important discipline in space physics and astrophysics, but it also plays a critical role in defining the radiation environment for humans and hardware in space, and is critical to efforts to unravel the history of solar activity. Cosmic rays are measured directly by balloon-borne and space instruments, and indirectly by ground-based neutron, muon and neutrino detectors, and by measurements of cosmogenic isotopes in ice cores, tree-rings, sediments, and meteorites. The topics covered here include: what we can learn from the deep 2008–2009 solar minimum, when cosmic rays reached the highest intensities of the space era; the implications of ¹⁰Be and ¹⁴C isotope archives for past and future solar activity; the effects of variations in the size of the heliosphere; opportunities provided by the Voyagers for discovering the origin of anomalous cosmic rays and measuring cosmic-ray spectra in interstellar space; and future space missions that can continue the exciting exploration of the heliosphere that has occurred over the past 50 years.     

The acceleration of pickup ions

The well-established association of pickup ions with anomalous cosmic rays shows that acceleration of pickup ions to energies above 1 GeV occurs. At present, diffusive shock acceleration of the pickup ions at the termination shock of the solar wind seems to be the best candidate for acceleration to the high energies of anomalous cosmic rays, accounting well for many of their observed properties. However, it is shown that acceleration of pickup ions from their initial energies by this process appears to be difficult at very strong, nearly perpendicular shocks such as the termination shock. This injection problem remains without a clear solution. A number of alternatives have been proposed for the initial acceleration of pickup ions to the point where diffusive acceleration at the termination shock can take over, but none of these processes has yet emerged as a clear favorite.     

Energetic particle observations at high heliographic latitudes

Energetic particles, accelerated in shocks which were associated with recurrent fast solar wind streams, were observed in high heliographic latitudes; fifteen such steams were included in the present study. Intensity variations ranged up to four orders of magnitude. Energy spectra were typically steeper near forward shocks than near reverse shocks. Electrons were observed only lated to the reverse shocks. Composition ratios in accelerated streams resembled those observed in fast CIR's. In periods between the recurrent acceleration regions elemental abundance ratios were similar to those of the anomalous cosmic rays (ACR). The intensity of the accelerated particles declined as the latitude of ULYSSES increased, probably due to the weakening of the shocks.     

The origin of cosmic rays in spiral galaxies

The problem of the origin and distribution of cosmic rays in the Galaxy is introduced by summarizing the literature on the radio and -ray studies of the Galaxy, discussing the propagation of cosmic rays in the interstellar medium, and listing the observed properties of cosmic rays. The localization of cosmic-ray electrons to their parent galaxies is an indicator that processes leading to cosmic-ray production may be common to galaxies like our own. The studies of external galaxies are therefore relevant to our own and have the advantage of better perspective.Studies of cosmic rays in exsternal galaxies are limited to the electron component which radiates synchrotron emission at radio frequencies. Multi-colour photometry of galaxies allows the separation of stellar populations that harbour particular classes of cosmic-ray sources. Statistical studies aimed at correlating integrated radio and optical properties of galaxies have reached conflicting conclusions. Although a correlation of cosmic rays with the older stellar population is proposed by some authors, others argue that the young stellar population harbours cosmic ray sources.Morphological studies of resolved galaxies provide information on the distributions of cosmic-ray electrons in galaxies. Studies in which the resolution of the radio images is much lower than in the optical are limited and have also produced contradictory results. Radio imaging at optical resolution is required for a direct comparison of cosmic-ray distributions with stellar distributions. Such studies are reviewed and the constraints they impose on cosmic-ray propagation and distribution of cosmic-ray sources is discussed.Theoretical cosmic-ray acceleration mechanisms are surveyed and an attempt is made to determine likely contributors. Mechanisms associated with shock waves in a variety of astrophysical settings are reviewed. Acceleration mechanisms not involving shocks, are also discussed. Finally, the status of the field is summarized along with some speculation on the future directions the field may take.     

Cosmic Ray Production in Supernovae

We give a brief review of the origin and acceleration of cosmic rays (CRs), emphasizing the production of CRs at different stages of supernova evolution by the first-order Fermi shock acceleration mechanism. We suggest that supernovae with trans-relativistic outflows, despite being rather rare, may accelerate CRs to energies above \(10^{18}\mbox{ eV}\) over the first year of their evolution. Supernovae in young compact clusters of massive stars, and interaction powered superluminous supernovae, may accelerate CRs well above the PeV regime. We discuss the acceleration of the bulk of the galactic CRs in isolated supernova remnants and re-acceleration of escaped CRs by the multiple shocks present in superbubbles produced by associations of OB stars. The effects of magnetic field amplification by CR driven instabilities, as well as superdiffusive CR transport, are discussed for nonthermal radiation produced by nonlinear shocks of all speeds including trans-relativistic ones.