The cosmic ray energy spectrum between 10 and 10 eV

The energy spectrum of cosmic rays with primary energies between 10¹⁴ eV and 10¹⁶ eV has been studied with the CASA-MIA air shower array. The measured differential energy spectrum is a power law (dj/dE ∝ E^−y) with spectral indices γ of 2.66±0.02 below approximately 10¹⁵ eV and 3.00±0.05 above. A new method is used for measuring primary energy derived from ground-based data in a compositionally insensitive way. In contrast with some previous reports, the “knee” of the energy spectrum does not appear sharp, but rather a smooth transition over energies from 10¹⁵ eV to 3.0 × 10¹⁵ eV.     

Ultra high energy cosmic rays and the Galactic halo

An analysis has been made of the fraction of ultra high energy cosmic rays (above 10¹⁸ eV) which could be due to processes involved in two possible ‘Models’. The first is the Giant Magnetic Halo Model and the second is the Dark Matter Halo Model. We find that the former, in which heavy nuclei are trapped in a giant halo, fails for energies above about 3 × 10¹⁹ eV. For the Dark Matter Halo Model, in which relic particles follow the “conventional” dark matter and whose decays give ultra high energy cosmic rays, the predicted anisotropies are much higher than those observed. The lack of observation of a finite flux from the Andromeda Galaxy means that the conclusion is insensitive to the spatial scale size of the assumed halo distribution. It is concluded that less than 10% of the ultra high energy cosmic rays come from relic particles in the Galactic halo.     

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.     

Separation of gamma and hadron initiated air showers with energies between 20 and 500 TeV

The discrimination between air showers initiated by γ rays and by hadrons is one of the fundamental problems in experimental cosmic-ray physics. The physics of this ‘γ/hadron separation’ is discussed in this paper. We restrict ourselves to the energy range from about 20 to 500 TeV, and take only the information contained in the lateral Čerenkov light distribution and the number of electrons at the detector level into consideration. An understanding of the differences between air showers generated by γ rays and those due to hadrons leads us to formulate suitable observables for the separation process. Angle integrating Čerenkov arrays (AICA) offer a promising new approach to ground-based γ-ray astronomy in the energy region from about 20 to 500 TeV. In order to establish this technique, an efficient suppression of the overwhelming hadronic background radiation is required. As an example for our general discussion, we present one method for γ/hadron separation in AICAs called ‘LES’. It is based on the simultaneous determination of the shower size and some characteristic parameters of the lateral distribution of the Čerenkov light. The potential inherent within this technique is demonstrated in quantitative detail for the existing ‘AIROBICC’ AICA. We also propose an objective measure of the intrinsic sensitivity of a detection scheme in ground-based γ-ray astronomy, the ‘reduced quality factor’. It is shown that AICAs may reach a sensitivity to γ-ray point sources in the high VHE range similar to that of the Čerenkov-telescope imaging technique in the low VHE region.     

Chemical composition of primary cosmic rays with energies from 10 to 10 eV

The chemical composition of primary cosmic rays with energies from 10¹⁵ to 10^16.5 eV, so called “knee” region, is examined. We have observed the time structures of air Čerenkov light associated with air showers at Mt. Chacaltaya, Bolivia, since 1995. The distribution of a parameter that characterizes the observed time structures is compared with that calculated with a Monte Carlo technique for various chemical compositions. Then the energy dependence of the average logarithmic mass numbers ln A of the primary cosmic rays is determined. The present result at 10^15.3 eV is almost consistent with the result of JACEE (A12) and shows gradual increase in ln A as a function of the primary energy (A24 at 10¹⁶ eV). Form the comparison of the observational results with several theoretical models, we conclude that the supernova explosion of massive stars is a plausible candidate for the origin of cosmic rays around the “knee” region.     

On the contribution of nearby sources to the observed cosmic ray nuclei

The presence of nearby discrete cosmic ray (CR) sources can lead to many interesting effects on the observed properties of CRs. In this paper, we study about the possible effects on the CR primary and secondary spectra and also the subsequent effects on the CR secondary-to-primary ratios. For the study, we assume that CRs undergo diffusive propagation in the Galaxy and we neglect the effect of convection, energy losses and reacceleration. In our model, we assume that there exists a uniform and continuous distribution of CR sources in the Galaxy generating a stationary CR background at the Earth. In addition, we also consider the existence of some nearby sources which inject CRs in a discrete space–time model. Assuming a constant CR source power throughout the Galaxy, our study has found that the presence of nearby supernova remnants (SNRs) produces noticeable variations in the primary fluxes mainly above ∼100 GeV n⁻¹, if CRs are assumed to be released instantaneously after the supernova explosion. The variation reaches a value of ∼45 per cent at around 10⁵ GeV n⁻¹. Respect to earlier studies, the variation in the case of the secondaries is found to be almost negligible. We also discuss about the possible effects of the different particle release times from the SNRs. For the particle release time of ∼10⁵ yr, predicted by the diffusive shock acceleration theories in SNRs, we have found that the presence of the nearby SNRs hardly produces any significant effects on the CRs at the Earth.     

Impact of cosmic rays on Population III star formation

We explore the implications of a possible cosmic-ray (CR) background generated during the first supernova explosions that end the brief lives of massive Population III stars. We show that such a CR background could have significantly influenced the cooling and collapse of primordial gas clouds in minihaloes around redshifts of   z ∼ 15–20  , provided the CR flux was sufficient to yield an ionization rate greater than about 10⁻¹⁹ s⁻¹ near the centre of the minihalo. The presence of CRs with energies  ≲10⁷  eV would indirectly enhance the molecular cooling in these regions, and we estimate that the resulting lower temperatures in these minihaloes would yield a characteristic stellar mass as low as  ∼10 M_⊙  . CRs have a less-pronounced effect on the cooling and collapse of primordial gas clouds inside more massive dark matter haloes with virial masses  ≳10⁸ M_⊙  at the later stages of cosmological structure formation around   z ∼ 10–15  . In these clouds, even without CR flux the molecular abundance is already sufficient to allow cooling to the floor set by the temperature of the cosmic microwave background.     

Simulations of a giant hybrid air shower detector

We have used Monte Carlo simulations to investigate the capabilities of a giant air shower observatory designed to detect showers initiated by cosmic rays with energies exceeding 10¹⁹ eV. The observatory is to consist of an array of detectors that will characterise the air shower at ground level, and optical detectors to measure the fluorescence light emitted by the shower in the atmosphere. Using these detectors together in a ‘hybrid’ configuration, we find that precise geometrical reconstruction of the shower axis is possible, leading to excellent resolution in energy. The technique is also shown to provide very good reconstruction below 10¹⁹ eV, at energies where the ground array is not fully efficient.     

Angular correlation of ultra-high energy cosmic rays with compact radio-loud quasars

Angular correlations of ultra-high energy cosmic rays with cosmologically distant sources may provide clues to these mysterious events. We compare cosmic ray tracks with energies above 10²⁰ eV to a compilation of radio-loud compact QSO positions. The statistical method emphasizes invariant quantities and a test of statistical independence of track and source distributions. Statistical independence is ruled out by several independent statistics at confidence levels of orders 97–99%, indicating that track directions and QSO source positions are correlated at a significant level.     

The anisotropy of cosmic ray arrival directions around 10 eV

Anisotropy in the arrival directions of cosmic rays with energies above 10¹⁷ eV is studied using data from the Akeno 20 km² array and the Akeno Giant Air Shower Array (AGASA), using a total of about 114 000 showers observed over 11 years. In the first harmonic analysis, we have found a strong anisotropy of 4% around 10¹⁸ eV, corresponding to a chance probability of 0.2% after taking the number of independent trials into account. with two-dimensional analysis in right ascension and declination, this anisotropy is interpreted as an excess of showers near the directions of the Galactic Center and the Cygnus region.     

A possible universal origin of hadronic cosmic rays from ultrarelativistic ejecta of bipolar supernovae

Based on the “cannonball model” for gamma-ray bursts of Dar and De Rújula, it is proposed that masses of baryonic plasma (“cannonballs”), ejected in bipolar supernova explosions in our Galaxy are the sources of hadronic Galactic cosmic rays (CRs) at all energies. The propagation of the cannonballs in the Galactic disk and halo is studied. Two mechanisms for the acceleration of the observed CRs are proposed. The first is based on ultrarelativistic shocks in the interstellar medium and could accelerate the bulk of CRs up to the “knee” energy of 4×10¹⁵ eV. The second operates with second-order Fermi acceleration within the cannonball. If the total initial energy of the ejected plasmoids in a SN explosion is 10⁵³ erg or higher, this second mechanism may explain the CR spectrum above the knee up to the highest observed energies. It is shown that together with plausible assumptions about CR propagation in the Galactic confinement volume, the observed spectral indices of the CR spectrum can be theoretically understood to first order. The model allows a natural understanding of various basic CR observations like the absence of the Greisen–Zatsepin cutoff, the anisotropy of arrival directions as function of energy and the small Galactocentric gradient of the CR density.     

The cosmic ray primary composition in the “knee” region through the EAS electromagnetic and muon measurements at EAS-TOP

The evolution of the cosmic ray primary composition in the energy range 10⁶–10⁷ GeV (i.e. the “knee” region) is studied by means of the e.m. and muon data of the Extensive Air Shower EAS-TOP array (Campo Imperatore, National Gran Sasso Laboratories). The measurement is performed through: (a) the correlated muon number (N_μ) and shower size (N_e) spectra, and (b) the evolution of the average muon numbers and their distributions as a function of the shower size. From analysis (a) the dominance of helium primaries at the knee, and therefore the possibility that the knee itself is due to a break in their energy spectrum (at E_k^He=(3.5±0.3)×10⁶ GeV) are deduced. Concerning analysis (b), the measurement accuracies allow the classification in terms of three mass groups: light (p,He), intermediate (CNO), and heavy (Fe). At primary energies E₀≈10⁶ GeV the results are consistent with the extrapolations of the data from direct experiments. In the knee region the obtained evolution of the energy spectra leads to: (i) an average steep spectrum of the light mass group (γ_p,He>3.1), (ii) a spectrum of the intermediate mass group harder than the one of the light component (γ_CNO2.75, possibly bending at E_k^CNO≈(6–7)×10⁶ GeV), (iii) a constant slope for the spectrum of the heavy primaries (γ_Fe2.3–2.7) consistent with the direct measurements. In the investigated energy range, the average primary mass increases from lnA=1.6–1.9 at E₀1.5×10⁶ GeV to lnA=2.8–3.1 at E₀1.5×10⁷ GeV. The result supports the standard acceleration and propagation models of galactic cosmic rays that predict rigidity dependent cut-offs for the primary spectra of the different nuclei. The uncertainties connected to the hadronic interaction model (QGSJET in CORSIKA) used for the interpretation are discussed.     

Changes of the cosmic-ray mass composition in the 10–10 eV energy range

Data taken with ten Cosmic Ray Tracking (CRT) detectors and the HEGRA air-shower array on La Palma, Canary Islands, have been analysed to investigate changes of the cosmic ay mass composition at the ‘knee’ of the cosmic-ray flux spectrum near 10¹⁵ eV energy. The analysis is based on the angular distributions of particles in air showers. HEGRA data provided the shower size, direction, and core position and CRT data the particle track information. It is shown that the angular distribution of muons in air showers is sensitive to the composition over a wide range of shower sizes and, thus, primary cosmic-ray energies with little systematic uncertainties. Results can be easily expressed in terms of ln A of primary cosmic rays. In the lower part of the energy range covered, we have considerable overlap with direct composition measurements by the JACEE collaboration and find compatible results in the observed rise of ln A. Above about 10¹⁵ eV energy we find no or at most a slow further rise of ln A. Simple cosmic-ray composition models are presented which are fully consistent with our results as well as the JACEE flux and composition measurements and the flux measurements of the Tibet ASγ collaboration. Minimal three-parameter composition models defined by the same power-law slope of all elements below the knee and a common change in slope at a fixed rigidity are inconsistent with these data.     

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.     

Power spectra of cosmic ray intensity variations at the ground and atmospheric pressure oscillations

Power spectrum estimates are computed for cosmic ray and pressure variations in the frequency range of 1.6 × 10⁻⁶ to 4.15 × 10⁻³ c/sec for three data sets each of 27 days length (2 min interval) recorded at Chacaltaya (Bolivia) during 1965–1966. The general trend of these spectra showy ƒ⁻ fit having exponent values from −1.5 to −1.9 for L.F. side. From the semi-diurnal peaks both in cosmic rays and pressure, the average value of pressure coefficient is found to be 0.3 per cent/mm of Hg. For the same three sets of data, a detailed analysis of cross-spectrum, coherence and phase relationship between cosmic rays and pressure is carried out in the frequency range of 1–12 c/day. Besides semi-diurnal peak, variations of 3, 4, 7 and 8 c/day are found to be common both in cosmic rays and pressure. The value of pressure coefficient and residual amplitude of cosmic rays for these particular frequencies are calculated.     

Constraining the power spectrum using clusters

We analyze an extended redshift sample of Abell/ACO clusters and compare the results with those coming from numerical simulations of the cluster distribution, based on the truncated Zel'dovich approximation (TZA), for a list of eleven dark matter (DM) models. For each model we run several realizations, so that we generate a set of 48 independent mock Abell/ACO cluster samples per model, on which we estimate cosmic variance effects. Other than the standard CDM model, we consider (a) Ω₀ = 1 CDM models based on lowering the Hubble parameter and/or on tilting the primordial spectrum; (b) Ω₀ = 1 Cold + Hot DM models with 0.1 ≤Ω_ν ≤0.5; (c) low-density flat ΛCDM models with 0.3 ≤Ω₀ ≤0.5. We compare real and simulated cluster distributions by analysing correlation statistics, the probability density function, and supercluster properties from percolation analysis. We introduce a generalized definition of the spectrum shape parameter Γ in terms of σ₂₅/σ₈, where σ_ris the rms fluctuation amplitude within a sphere of radius r. As a general result, we find that the distribution of galaxy clusters provides a constraint only on the shape of the power spectrum, but not on its amplitude: a shape parameter 0.18 Γ 0.25 and an effective spectral index at the 20 h⁻¹ Mpc scale −1.1 n_eff −0.9 are required by the Abell/ACO data. In order to obtain complementary constraints on the spectrum amplitude, we consider the cluster abundance as estimated using the Press-Schechter approach, whose reliability is explicitly tested against N-body simulations. By combining results from the analysis of the distribution and the abundance of clusters we conclude that, of the cosmological models considered here, the only viable models are either Cold + Hot DM ones with 0.2 Ω_ν 0.3, better if shared between two massive ν species, and ΛCDM ones with 0.3 Ω₀0.5.     

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.     

Ground level enhancements of cosmic rays in solar cycle 24

Using data from ground-based observations of cosmic rays (CRs) on the worldwide network of stations and spacecraft, we have investigated the proton spectra and the CR anisotropy during the ground level enhancements of CRs on May 17, 2012 (GLE71) and January 6, 2014 (GLE72) occurred in solar cycle 24 by the spectrographic global survey method. We provide the CR rigidity spectra and the relative changes in the intensity of CRs with a rigidity of 2 GV in the solar–ecliptic geocentric coordinate system in specific periods of these events. We show that the proton acceleration during GLE71 and GLE72 occurred up to rigidities R ~ 2.3?2.5 GV, while the differential rigidity spectra of solar CRs are described neither by a power nor by an exponential function of particle rigidity. At the times of the events considered the Earth was in a loop-like structure of the interplanetary magnetic field.     

A prediction for three neutrino masses and mixings and similarity between quark and lepton mixings

If neutrinos have mass, we give reasons for a possible pattern of three (squaed) mass eigenvalues: m₁² (2.8−5.8) (eV)², m₂² 0.01 (eV)², m₃² (1.5−1) × 10⁻⁴ (eV)². The flavor states ν_μ and ν_e are mixtures of the eigenstates with m₂ and m₃ with a significant mixing, corresponding to an effective mixing angle of about 0.45. The ν_τ is nearly the state with m₁; the other two effective mixing angles are about an order of magnitude smaller than 0.45. There is a marked similarity to mixing in the quark sector.     

Measurement of the cosmic ray composition at the knee with the SPASE-2/AMANDA-B10 detectors

The mass composition of high-energy cosmic rays at energies above 10¹⁵ eV can provide crucial information for the understanding of their origin. Air showers were measured simultaneously with the SPASE-2 air shower array and the AMANDA-B10 Cherenkov telescope at the South Pole. This combination has the advantage to sample almost all high-energy shower muons and is thus a new approach to the determination of the cosmic ray composition. The change in the cosmic ray mass composition was measured versus existing data from direct measurements at low energies. Our data show an increase of the mean log atomic mass lnA by about 0.8 between 500 TeV and 5 PeV. This trend of an increasing mass through the “knee” region is robust against a variety of systematic effects.