Contribution of nuclei accelerated by gamma-ray pulsars to cosmic rays in the Galaxy

We consider the galactic population of gamma-ray pulsars as possible sources of cosmic rays at and just above the “knee” in the observed cosmic ray spectrum at 10¹⁵–10¹⁶ eV. We suggest that iron nuclei may be accelerated in the outer gaps of pulsars, and then suffer partial photo-disintegration in the non-thermal radiation fields of the outer gaps. As a result, protons, neutrons, and surviving heavier nuclei are injected into the expanding supernova remnant. We compute the spectra of nuclei escaping from supernova remnants into the interstellar medium, taking into account the observed population of radio pulsars.

Our calculations, which include a realistic model for acceleration and propagation of nuclei in pulsar magnetospheres and supernova remnants, predict that heavy nuclei accelerated directly by gamma-ray pulsars could contribute about 20% of the observed cosmic rays in the knee region. Such a contribution of heavy nuclei to the cosmic ray spectrum at the knee can significantly increase the average value of lnA with increasing energy as is suggested by recent observations.     

Extragalactic UHE proton spectrum and prediction for iron-nuclei flux at 10–10 GeV

We investigate the problem of transition from galactic cosmic rays to extragalactic ultra-high energy cosmic rays. Using the model for extragalactic ultra-high energy cosmic rays and observed all-particle cosmic ray spectrum, we calculate the galactic spectrum of iron nuclei in the energy range 10⁸–10⁹ GeV. The flux and spectrum predicted at lower energies agree well with the KASCADE data. The transition from galactic to extragalactic cosmic rays is distinctly seen in spectra of protons and iron nuclei, when they are measured separately. The shape of the predicted iron spectrum agrees with the Hall diffusion.     

Implications of particle acceleration in active galactic nuclei for cosmic rays and high energy neutrino astronomy

We consider the production of high energy neutrinos and cosmic rays in radio-quiet active galactic nuclei (AGN) or in the central regions of radio-loud AGN. We use a model in which acceleration of protons takes place at a shock in an accretion flow onto a supermassive black hole, and follow the cascade that results from interactions of the accelerated protons in the AGN environment. We use our results to estimate the diffuse high energy neutrino intensity and cosmic ray intensity due to AGN. We discuss our results in the context of high energy neutrino telescopes under construction, and measurements of the cosmic ray composition in the region of the “knee” in the energy spectrum at 10⁷ GeV.     

On origin of ultra high energy cosmic rays

Propagation of UHE protons through CMB radiation leaves the imprint on energy spectrum in the form of Greisen–Zatsepin–Kuzmin (GZK) cutoff, bump (pile-up protons) and dip. The dip is a feature in energy range 1×10¹⁸–4×10¹⁹ eV, caused by electron-positron pair production on CMB photons. Calculated for power-law generation spectrum with index γ _g =2.7, the shape of the dip is confirmed with high accuracy by data of Akeno—AGASA, HiRes, Yakutsk and Fly’s Eye detectors. The predicted shape of the dip is robust: it is valid for the rectilinear and diffusive propagation, for different discretenesses in the source distribution, for local source overdensity and deficit etc. This property of the dip allows us to use it for energy calibration of the detectors. The energy shift λ for each detector is determined by minimum χ ² in comparison of observed and calculated dip. After this energy calibration the absolute fluxes, measured by AGASA, HiRes and Yakutsk detectors remarkably coincide in energy region 1×10¹⁸–1×10²⁰ eV. Below the characteristic energy E _c ≈1×10¹⁸ eV the spectrum of the dip flattens for both diffusive and rectilinear propagation, and more steep galactic spectrum becomes dominant at E<E _c . The energy of transition E _tr<E _c approximately coincides with the position of the second knee E _2kn , observed in the cosmic ray spectrum. The dip-induced transition from galactic to extragalactic cosmic rays at the second knee is compared with traditional model of transition at ankle, the feature observed at energy ∼1×10¹⁹ eV.      

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.     

Ultra-high energy cosmic rays in the galactic corona

On the basis of recent new information on regular and chaotic magnetic fields in coronae of spiral galaxies, we discuss propagation of ultra-high energy cosmic rays of energies exceeding 10¹⁷ eV in the galactic corona. It is shown that the expected regular magnetic field is able to confine to the corona protons of energies up to 3×10¹⁹ eV. Chaotic magnetic fields of the corona play an important role in dynamics of cosmic-ray protons of energy up to 7×10¹⁸ eV.     

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.     

Cosmic ray propagation in a closed galaxy

A simple model of cosmic ray propagation is proposed from which the major experimental results can be derived: The model reproduces the observed nuclear abundances and accounts for the observed changes of nuclear composition with energy, the high degree of isotropy of cosmic ray flux at all energies, and the high degree of its constancy throughout the history of the Solar System. It is consistent with the observed size distribution of extensive airshowers, the intensity and energy distribution of the electron component, and the diffuse emission of γ-rays and radio waves. The model is characterized by the two basic assumptions: (1) that cosmic rays have been injected at an unchanging rate by sources located in the galactic spiral arms and (2) that a large-scale magnetic field retains all particles in our galaxy, where they interact with interstellar gas, so that all complex nuclei are finally fragmented and their energy dissipated in meson production and electro-magnetic interactions.     

Pulsars and the origin of cosmic rays

The capabilities and limitations of pulsars as sources of cosmic rays are reviewed in the light of experimental observations. Pulsars can supply the cosmic ray power if they have rotational velocities in excess of 700 rad s^?1 at birth. Though this is theoretically possible, there is no experimental proof for the same. Pulsars can accelerate particles to the highest energies of 10²⁰ eV, but in general, the spectra on simple considerations, turn out to be flatter than the observed cosmic ray spectrum. At the highest energies, absorption processes due to fragmentation and photodisintegration dominate for heavy nuclei. The existence of a steady flux of cosmic rays of energy greater than 10¹⁷ eV demands acceleration of particles to last over fifty years, the time interval between supernovae outbursts, whereas the expected period of activity is less than a few years. Finally, the problem of anisotropy with relevance to pulsars as sources and the possibility of observing pulsar accelerated particles from galactic clusters is considered.     

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.     

Propagation of galactic cosmic rays in the outer heliosphere

The propagation of galactic cosmic rays in heliospheric magnetic fields is studied. An approximate solution to the cosmic ray transport equation has been derived on the basis of a method that takes into account the small value of anisotropy of particle angular distribution. The spatial and energy distributions of the cosmic ray intensity and anisotropy have been investigated, and estimates of cosmic ray energy flux have been carried out.     

Decaying nuclei and the age of cosmic rays in the galaxy

The propagation of radioactive nuclei of cosmic rays in a flat diffusion galactic model (sources and the main gaseous mass are concentrated in the galactic disc) is considered. The corresponding results are not reducible to the results of a simple homogeneous model. It is shown that the recent data on the Be¹⁰ nuclei abundance in cosmic rays do not contradict the occurrence of a large cosmic ray halo.     

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.     

Ultrahigh energy cosmic ray acceleration in Seyfert galactic nuclei

We propose a model for the particle acceleration to energy E≈10²¹ eV in Seyfert galactic nuclei. The model is based on the theory of active galactic nuclei by Vilkoviskij et al. (1999). The acceleration takes place in hot spots of relativistic jets, which decay in a dense stellar kernel at a distance of 1–3 pc from the center. The maximum energy and chemical composition of the accelerated particles depend on the jet magnetic-field strength. Fe nuclei acquire the largest energy, E≈8×10²⁰ eV, if the jet field strength is B≈16 G. At a field strength B～5–40 G, the nuclei with Z≥10 acquire energy E≥2×10²⁰ eV; the lighter nuclei are accelerated to E≤10²⁰ eV. In a field B～1000 G, only the particles with Z≥23 gain energy E≤10²⁰ eV. The protons are accelerated to E<4×10¹⁹ eV, and they do not fall within the energy range concerned at any field strength B. Interactions with infrared photons do not affect the accelerated-particle escape from the sources if the galactic luminosity L≤10⁴⁶ erg s^?1 and if the angle between the normal to the galactic plane and the line of sight is sufficiently small, i.e., if the galactic-disk axial ratio is comparatively large. The particles do not lose their energy through magnetodrift radiation if their deflection from the jet axis does not exceed 0.03–0.04 pc at a distance R≈40–50 pc from the center. The synchrotron losses are small, because the magnetic field frozen in the galactic wind at R≤40–50 pc is directed (as in the jet) predominantly along the motion. If this model is correct, then the detected protons are nuclear fragments or are accelerated in other sources. The jet magnetic fields can be estimated by using the cosmic-ray energy spectrum and chemical composition.     

Spiral arms as cosmic ray source distributions

The Milky Way is a spiral galaxy with (or without) a bar-like central structure. There is evidence that the distribution of suspected cosmic ray sources, such as supernova remnants, are associated with the spiral arm structure of galaxies. It is yet not clearly understood what effect such a cosmic ray source distribution has on the particle transport in our Galaxy. We investigate and measure how the propagation of Galactic cosmic rays is affected by a cosmic ray source distribution associated with spiral arm structures.We use the PICARD code to perform high-resolution 3D simulations of electrons and protons in galactic propagation scenarios that include four-arm and two-arm logarithmic spiral cosmic ray source distributions with and without a central bar structure as well as the spiral arm configuration of the NE2001 model for the distribution of free electrons in the Milky Way. Results of these simulation are compared to an axisymmetric radial source distribution. Also, effects on the cosmic ray flux and spectra due to different positions of the Earth relative to the spiral structure are studied.We find that high energy electrons are strongly confined to their sources and the obtained spectra largely depend on the Earth’s position relative to the spiral arms. Similar finding have been obtained for low energy protons and electrons albeit at smaller magnitude. We find that even fractional contributions of a spiral arm component to the total cosmic ray source distribution influences the spectra on the Earth. This is apparent when compared to an axisymmetric radial source distribution as well as with respect to the Earth’s position relative to the spiral arm structure. We demonstrate that the presence of a Galactic bar manifests itself as an overall excess of low energy electrons at the Earth.Using a spiral arm geometry as a cosmic ray source distributions offers a genuine new quality of modeling and is used to explain features in cosmic ray spectra at the Earth that are else-wise attributed to other propagation effects. We show that realistic cosmic ray propagation scenarios have to acknowledge non-axisymmetric source distributions.     

Gamma rays from molecular clouds

It is believed that the observed diffuse gamma-ray emission from the galactic plane is the result of interactions between cosmic rays and the interstellar gas. Such emission can be amplified if cosmic rays penetrate into dense molecular clouds. The propagation of cosmic rays inside a molecular cloud has been studied assuming an arbitrary energy and space dependent diffusion coefficient. If the diffusion coefficient inside the cloud is significantly smaller compared to the average one derived for the galactic disk, the observed gamma-ray spectrum appears harder than the cosmic ray spectrum, mainly due to the slower penetration of the low energy particles towards the core of the cloud. This may produce a great variety of gamma-ray spectra.     

Analytic calculations of the spectra of ultra high energy cosmic ray nuclei. II. The general case of background radiation

We discuss the problem of ultra high energy nuclei propagation in extragalactic background radiations. The present paper is the continuation of the accompanying paper I where we have presented three new analytic methods to calculate the fluxes and spectra of ultra high energy cosmic ray nuclei, both primary and secondary, and secondary protons. The computation scheme in this paper is based on the analytic solution of coupled kinetic equations, which takes into account the continuous energy losses due to the expansion of the universe and pair-production, together with photo-disintegration of nuclei. This method includes in the most natural way the production of secondary nuclei in the process of photo-disintegration of the primary nuclei during their propagation through extragalactic background radiations. In paper I, in order to present the suggested analytical schemes of calculations, we have considered only the case of the cosmic microwave background radiation, in the present paper we generalize this computation to all relevant background radiations, including infra-red and visible/ultra-violet radiations, collectively referred to as extragalactic background light. The analytic solutions allow transparent physical interpretation of the obtained spectra. Extragalactic background light plays an important role at intermediate energies of ultra high energy cosmic ray nuclei. The most noticeable effect of the extragalactic background light is the low-energy tail in the spectrum of secondary nuclei.     

Production of neutrons, neutrinos and gamma-rays by a very fast pulsar in the Galactic Centre region

We consider the possibility that the excess of cosmic rays near ∼10¹⁸ eV, reported by the AGASA and SUGAR groups from the direction of the Galactic Centre, is caused by a young, very fast pulsar in the high-density medium. The pulsar accelerates iron nuclei to energies ∼10²⁰ eV, as postulated by the Galactic models for the origin of the highest-energy cosmic rays. The iron nuclei, about 1 yr after pulsar formation, leave the supernova envelope without energy losses and diffuse through the dense central region of the Galaxy. Some of them collide with the background matter creating neutrons (from disintegration of Fe), neutrinos and gamma-rays (in inelastic collisions). We suggest that neutrons produced at a specific time after the pulsar formation are responsible for the observed excess of cosmic rays at ∼10¹⁸ eV. From normalization of the calculated neutron flux to the one observed in the cosmic ray excess, we predict the neutrino and gamma-ray fluxes. It has been found that the 1 km² neutrino detector of the IceCube type should detect from a few up to several events per year from the Galactic Centre, depending on the parameters of the considered model. Moreover, future systems of Cherenkov telescopes (CANGAROO III, HESS, VERITAS) should be able to observe  1–10 TeV  gamma-rays from the Galactic Centre if the pulsar was created inside a huge molecular cloud about  3–10×10³ yr  ago.     

A machine learning method to separate cosmic ray electrons from protons from 10 to 100 GeV using DAMPE data

DArk Matter Particle Explorer(DAMPE) is a general purpose high energy cosmic ray and gamma ray observatory, aiming to detect high energy electrons and gammas in the energy range 5 Ge V to 10 Te V and hundreds of Te V for nuclei. This paper provides a method using machine learning to identify electrons and separate them from gammas, protons, helium and heavy nuclei with the DAMPE data acquired from 2016 January 1 to 2017 June 30, in the energy range from 10 to 100 Ge V.