We survey the theory and experimental tests for the propagation of cosmic rays in the Galaxy up to energies of 10 15 eV. A guide to the previous reviews and essential literature is given, followed by an exposition of basic principles. The basic ideas of cosmic-ray propagation are described, and the physical origin of its processes is explained. The various techniques for computing the observational consequences of the theory are described and contrasted. These include analytical and numerical techniques. We present the comparison of models with data, including direct and indirect—especially γ-ray—observations, and indicate what we can learn about cosmic-ray propagation. Some important topics, including electron and antiparticle propagation, are chosen for discussion.

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Cosmic-Ray Propagation and Interactions in the Galaxy

One century ago Viktor Hess carried out several balloon flights that led him to conclude that the penetrating radiation responsible for the discharge of electroscopes was of extraterrestrial origin. One century from the discovery of this phenomenon seems to be a good time to stop and think about what we have understood about Cosmic Rays. The aim of this review is to illustrate the ideas that have been and are being explored in order to account for the observable quantities related to cosmic rays and to summarize the numerous new pieces of observation that are becoming available. In fact, despite the possible impression that development in this field is somewhat slow, the rate of new discoveries in the last decade or so has been impressive, and mainly driven by beautiful pieces of observation. At the same time scientists in this field have been able to propose new, fascinating ways to investigate particle acceleration inside the sources, making use of multifrequency observations that range from the radio, to the optical, to X-rays and gamma rays. These ideas can now be confronted with data.

The origin of galactic cosmic rays

Cosmic-ray astrophysics has advanced rapidly in recent years, and its impact on other astronomical disciplines has broadened. Many new experiments measuring these particles, both directly in the atmosphere or space and indirectly via γ rays and synchrotron radiation, have widened the range and quality of the information available on their origin, propagation, and interactions. The impact of low-energy cosmic rays on interstellar chemistry is a fast-developing topic, including the propagation of these particles into the clouds in which the chemistry occurs. Cosmic rays, via their γ-ray production, also provide a powerful way to probe the gas content of the interstellar medium. Substantial advances have been made in the observations and modelling of the interplay between cosmic rays and the interstellar medium. Focusing on energies up to 1 TeV, these interrelating aspects are covered at various levels of detail, giving a guide to the state of the subject.

http://publications.lib.chalmers.se/records/fulltext/222464/local_222464.pdf

The Nine Lives of Cosmic Rays in Galaxies

One century ago Viktor Hess carried out several balloon flights that led him to conclude that the penetrating radiation responsible for the discharge of electroscopes was of extraterrestrial origin. One century from the discovery of this phenomenon seems to be a good time to stop and think about what we have understood about Cosmic Rays. The aim of this review is to illustrate the ideas that have been and are being explored in order to account for the observable quantities related to cosmic rays and to summarize the numerous new pieces of observation that are becoming available. In fact, despite the possible impression that development in this field is somewhat slow, the rate of new discoveries in the last decade or so has been impressive, and mainly driven by beautiful pieces of observation. At the same time scientists in this field have been able to propose new, fascinating ways to investigate particle acceleration inside the sources, making use of multifrequency observations that range from the radio, to the optical, to X-rays and gamma rays. These ideas can now be confronted with data. I will mostly focus on supernova remnants as the most plausible sources of Galactic cosmic rays, and I will review the main aspects of the modern theory of diffusive particle acceleration at supernova remnant shocks, with special attention for the dynamical reaction of accelerated particles on the shock and the phenomenon of magnetic field amplification at the shock. Cosmic ray escape from the sources is discussed as a necessary step to determine the spectrum of cosmic rays at the Earth. In the end of this review I will also discuss the phenomenon of cosmic ray acceleration at shocks propagating in partially ionized media and the implications of this phenomenon in terms of width of the Balmer line emission.

The Origin of Galactic Cosmic Rays

In this paper we investigate the effect of stochasticity in the spatial and temporal distribution of supernova remnants on the spectrum and chemical composition of cosmic rays observed at Earth. The calculations are carried out for different choices of the diffusion coefficient D(E) experienced by cosmic rays during propagation in the Galaxy. In particular, at high energies we assume that D(E)Eδ, with δ = 1/3 and δ = 0.6 being the reference scenarios. The large scale distribution of supernova remnants in the Galaxy is modeled following the distribution of pulsars, with and without accounting for the spiral structure of the Galaxy. We find that the stochastic fluctuations induced by the spatial and temporal distribution of supernovae, together with the effect of spallation of nuclei, lead to mild but sensible violations of the simple, leaky-box-inspired rule that the spectrum observed at Earth is N(E)E−α with α = γ+δ, where γ is the slope of the cosmic ray injection spectrum at the sources. Spallation of nuclei, even with the small rates appropriate for He, may account for small differences in spectral slopes between different nuclei, possibly providing an explanation for the recent CREAM observations. For δ = 1/3 we find that the slope of the proton and helium spectra are ~ 2.67 and ~ 2.6 respectively (with fluctuations depending on the realization of source distribution) at energies around ~ 1 TeV (to be compared with the measured values of 2.66±0.02 and 2.58±0.02). For δ = 0.6 the hardening of the He spectra is not observed. The stochastic effects discussed above cannot be found in ordinary propagation calculations, such as GALPROP, where these effects and the point like nature of the sources are not taken into account. We also comment on the effect of time dependence of the escape of cosmic rays from supernova remnants, and of a possible clustering of the sources in superbubbles. In a second paper we will discuss the implications of these different scenarios for the anisotropy of cosmic rays.

https://iopscience.iop.org/article/10.1088/1475-7516/2012/01/010/pdf

Diffusive propagation of cosmic rays from supernova remnants in the Galaxy. I: spectrum and chemical composition

We have studied the impact of cosmic-ray (CR) acceleration in supernova remnants on the spectra of CR nuclei in the Galaxy using a series expansion of the propagation equation, which allows us to use analytical solutions for part of the problem and to perform an efficient numerical treatment of the remaining equations and thus accurately describes the cosmic-ray propagation on small scales around their sources in three spatial dimensions and time. We found strong variations of the cosmic-ray nuclei flux by typically 20%, with occasional spikes of much higher amplitude, but only minor changes in the spectral distribution. The locally measured spectra of primary cosmic rays fit well into the obtained range of possible spectra. We furthermore showed that the spectra of the secondary element boron show almost no variations, so that the above findings also imply significant fluctuations of the boron-to-carbon ratio. Therefore, the commonly used method of determining CR propagation parameters by fitting secondary-to-primary ratios appears flawed on account of the variations that these ratios would show throughout the Galaxy.

https://iopscience.iop.org/article/10.1086/426537/pdf

Cosmic-Ray Propagation Properties for an Origin in Supernova Remnants

Perpendicular diffusion coefficients and mean free paths of cosmic particles are computed for an anisotropic Alfvenic turbulence spectrum corresponding to the Goldreich-Sridhar model by employing an enhanced nonlinear guiding center theory. The calculations are important for understanding cosmic ray propagation in the Galaxy and in the solar system. In addition, the knowledge of diffusion coefficients is also useful for modeling charged particles which experience diffusive shock acceleration in supernova remnants and at interplanetary shock waves. To replace the parallel diffusion coefficient in our equation for the perpendicular diffusion coefficient, we employ different models such as quasilinear results and phenomenological models. The results are compared with those derived earlier. We demonstrate that the choice of the turbulence model as well as the choice of the model for the parallel diffusion coefficient has a strong influence on the perpendicular diffusion coefficient.

https://iopscience.iop.org/article/10.1088/0004-637X/725/2/2117/pdf

Perpendicular diffusion of cosmic rays for a goldreich-sridhar spectrum

The propagation of cosmic rays in the Galaxy is controlled by spatial diffusion coefficients. Since parallel scattering is the strongest scattering effect, it is believed that the diffusion coefficient along the mean magnetic field controls the confinement of charged cosmic particles in the Galaxy. In this paper, we combine a turbulence spectrum with dissipation range with a nonlinear particle diffusion theory to compute transport parameters. We find a decreasing parallel diffusion coefficient for increasing particle energy for particles having rigidities lower than 3 GeV. Our approach provides an explanation of the observed boron-to-carbon ratio at these particle energies without the need to introduce stochastic acceleration.

http://iopscience.iop.org/article/10.1088/0004-637X/725/2/2110/pdf

Influence of Turbulence Dissipation Effects on the Propagation of Low-energy Cosmic Rays in the Galaxy

Particle acceleration at supernova remnant (SNR) shock waves is regarded as the most probable mechanism for providing Galactic cosmic rays at energies below 10 15 eV. The Galactic cosmic ray hadron component would in this picture result from the injection of relativistic particles from many SNRs. It is well known that the superposition of individual power law source spectra with dispersion in the spectral index value, which behaviour is observed in the synchrotron radio spectra of shell SNR, displays a positive curvature in the total spectrum and in particular shows a hardening at higher energies. Recent observations made with the EGRET instrument on the Compton Gamma-Ray Observatory of the diffuse Galactic γ -ray emission reveal a spectrum which is incompatible with the assumption that the cosmic ray spectra measured locally hold throughout the Galaxy: the spectrum above 1 GeV, where the emission is supposedly dominated by $\pi^0$-decay, is harder than that derived from the local cosmic ray proton spectrum. We demonstrate that in case of a SNR origin of cosmic ray nucleons part of this γ -ray excess may be attributed to the dispersion of the spectral indices in these objects. In global averages, as are γ -ray line-of-sight integrals, this dispersion leads to a positive curvature in the composite spectrum, and hence to modified $\pi^0$-decay γ -ray spectra.

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Excess GeV radiation and cosmic ray origin

Recent EGRET observations of the diffuse Galactic gamma-ray emission reveal a spectrum which is incompatible with the assumption that the cosmic ray spectra measured locally hold throughout the Galaxy: the spectrum above 1 GeV, where the emission is supposedly dominated by pi^0-decay, is harder than that derived from the local cosmic ray proton spectrum. 
We demonstrate that in case of a SNR origin of cosmic ray nucleons part of this gamma-ray excess may be attributed to the dispersion of the spectral indices in these objects. In global averages, as are gamma-ray line-of-sight integrals, this dispersion leads to a positive curvature in the composite spectrum, and hence to modified pi^0-decay gamma-ray spectra.

/pdf/excess-gev-radiation-and-cosmic-ray-origin-4a6crzzbjg.pdf

I. Büsching

Papers

Cosmic-Ray Propagation Properties for an Origin in Supernova Remnants

Perpendicular diffusion of cosmic rays for a goldreich-sridhar spectrum

Influence of Turbulence Dissipation Effects on the Propagation of Low-energy Cosmic Rays in the Galaxy

Excess GeV radiation and cosmic ray origin

Excess GeV radiation and cosmic ray origin