The extensive air shower muon number spectrum beyond the knee in the cosmic-ray energy spectrum

The extensive air shower (EAS) muon number spectrum is obtained with increased statistics using the central muon detector of the EAS MSU array, which records muons with energies above 10 GeV. The dependence of the mass composition of primary cosmic rays on the energy is considered. The conclusion is confirmed that for energies from 3 × 10¹⁵ eV (the primary energy spectrum knee) up to 10¹⁷ eV a change in the composition associated with an increase in the proportion of heavy nuclei occurs; however, after the energy of 10¹⁷ eV, the proportion of heavy nuclei begins to decrease and the composition becomes lighter. A comparison with similar data from other experiments is conducted. The existence of an additional component of cosmic rays is confirmed; earlier an indication of its presence was derived from data on the EAS electron number spectrum.     

Dependence of the energy spectrum of UHE cosmic rays on the latitude of an extensive air shower array

Several energy spectra of cosmic rays with energies E ₀ ≥ 10¹⁷ eV measured at the Yakutsk EAS, AGASA, Haverah Park, HiRes, Auger, and SUGAR arrays are considered. It is shown that the fairly good mutual agreement of the spectrum shapes can be achieved if the energy of each spectrum is multiplied by a factor K specific for each spectrum. These factors exhibit a pronounced dependence on the latitude of the above-mentioned arrays.     

Ultrahigh-energy cosmic rays: Possible origin and spectrum

The complicated shape of the cosmic ray spectrum recorded by giant arrays in the energy range 10¹⁷–10²⁰ eV is analyzed. It is shown that in the energy region ∼10¹⁸–10¹⁹ eV the spectrum probably coincides with the injection spectrum whose exponent is equal approximately to 3.2–3.3. The flatter component in the energy region (3.2–5.0)×10¹⁹ eV is due to braking of extragalactic protons on primordial photons (the cosmic background radiation). At energies exceeding 3.2×10¹⁹ eV the spectrum does not have a blackbody cutoff. The possibility of determining the distances at which cosmic rays originate and investigating the evolution of their sources on the basis of ultrahigh-energy cosmic ray data is discussed. Zh. éksp. Teor. Fiz. 113, 12–20 (January 1998)     

Cosmic ray spectrum obtained from the energy scattered by the particles of extensive air showers in the atmosphere and the galactic model

The differential energy spectrum of cosmic rays that is obtained on the basis of the measurements of Cherenkov radiation from extensive air showers in an energy range of 10¹⁵–10²⁰ eV is compared with the model of the propagation of primary particles in the interstellar medium with fractal properties. It is found that the shape of the experimental spectrum is in good agreement with the shape of the calculated spectrum of “all particles” at 10¹⁵–10¹⁸ eV. The average mass composition of cosmic rays that is calculated on the basis of five components does not contradict the average mass composition obtained from the experimental data for several parameters in this energy range.     

Cosmic ray energy spectrum from measurements of air showers

This review focuses on high-energy cosmic rays in the PeV energy range and above. Of particular interest is the knee of the spectrum around 3 PeV and the transition from cosmic rays of Galactic origin to particles from extra-galactic sources. Our goal is to establish a baseline spectrum from 1014 to 10^20 eV by combining the results of many measurements at different energies. In combination with measurements of the nuclear composition of the primaries, the shape of the energy spectrum places constraints on the number and spectra of sources that may contribute to the observed spectrum.     

What should be the spectrum of galactic cosmic rays?

Numerous experimental data on cosmic rays sensitive to the spectrum of primary cosmic rays were analyzed in the energy range E>1 TeV. They proved to be incompatible with the pure power-law spectrum of primary particles. The spectral index of the proton spectrum is derived from the data considered. It was found to be 0.4±0.1 greater than for the nuclei with Z≥2. Therefore, the flux of galactic cosmic rays consisting of protons and nuclei with Z≥2 cannot be described by a unified power law in the energy range 0.1–10³ TeV.     

Energy spectrum and mass composition of primary cosmic rays at energies 10<Superscript>15</Superscript>–10<Superscript>18</Superscript> eV

Data on muon and electron components of extensive air showers (EAS) (obtained with the EAS MSU array) were used to derive the primary cosmic ray (PCR) mass composition. It is shown that for energies beyond the knee at energy 3 × 10¹⁵ eV the abundance of heavy nuclei increases with energy. But at energies above 10¹⁷ eV the abundance of light nuclei starts to grow. The primary cosmic ray spectrum in the range 10¹⁵–10¹⁸ eV is analyzed. It is shown that at energies above 10¹⁷ eV the additional component appears and it differs from the bulk of Galactic cosmic rays generated by shocks in SN remnants.     

The energy spectrum of neutrons produced by cosmic ray muons in LVD

The energy spectrum of neutrons produced by cosmic ray muons in the underground detector LVD (3650 m.w.e.) is obtained for the energy range of 30–450 MeV. The spectrum is derived using the energy release spectrum of neutron interaction products in 1.5 m³ scintillation counters.     

Cosmic ray spectrum obtained from the energy scattered by the particles of extensive air showers in the atmosphere and the galactic model

The differential energy spectrum of cosmic rays that is obtained on the basis of the measurements of Cherenkov radiation from extensive air showers in an energy range of 10¹⁵–10²⁰ eV is compared with the model of the propagation of primary particles in the interstellar medium with fractal properties. It is found that the shape of the experimental spectrum is in good agreement with the shape of the calculated spectrum of “all particles” at 10¹⁵–10¹⁸ eV. The average mass composition of cosmic rays that is calculated on the basis of five components does not contradict the average mass composition obtained from the experimental data for several parameters in this energy range. Original Russian Text ? S.P. Knurenko, A.A. Ivanov, A.V. Saburov, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 10, pp. 709–712.     

Cosmic rays of energies in the range 103–105 TeV and higher

Over a period of more than 30 years, the knee in the spectrum of extensive air showers (EAS) generated by cosmic radiation has been explained in two ways: as a consequence of a cusp in the energy spectrum of primary cosmic rays or as a consequence of a change undergone by the process of multiparticle hadron production in the interactions of primary protons with nuclei of air atoms. Investigations at the Tien Shan EAS array confirm a change in the properties of showers generated by protons near the upper boundary of the atmosphere and evince the invariability of the energy spectrum of protons in the energy range 10³–10⁵ TeV.     

High-energy cosmic ray muons in the Earth’s atmosphere

We present the calculations of the atmospheric muon fluxes at energies 10–10⁷ GeV based on a numerical-analytical method for solving the hadron-nucleus cascade equations. It allows the non-power-law behavior of the primary cosmic ray (PCR) spectrum, the violation of Feynman scaling, and the growth of the total inelastic cross sections for hadron-nucleus collisions with increasing energy to be taken into account. The calculations have been performed for a wide class of hadron-nucleus interaction models using directly the PCR measurements made in the ATIC-2 and GAMMA experiments and the parameterizations of the primary spectrum based on a set of experiments. We study the dependence of atmospheric muon flux characteristics on the hadronic interaction model and the influence of uncertainties in the PCR spectrum and composition on the muon flux at sea level. Comparison of the calculated muon energy spectra at sea level with the data from a large number of experiments shows that the cross sections for hadron-nucleus interactions introduce the greatest uncertainty in the energy region that does not include the knee in the primary spectrum.     

High-energy cosmic rays: Puzzles,models, and giga-ton neutrino telescopes

The existence of cosmic rays of energies exceeding 10²⁰ eV is one of the mysteries of high-energy astrophysics. The spectrum and the high energy to which it extends rule out almost all suggested source models. The challenges posed by observations to models for the origin of high-energy cosmic rays are reviewed, and the implications of recent new experimental results are discussed. Large area high-energy cosmic ray detectors and large volume high-energy neutrino detectors currently under construction may resolve the high-energy cosmic ray puzzle, and shed light on the identity and physics of the most powerful accelerators in the Universe.     

Meson cascade in the atmosphere,uncertainties in calculating the fluxes of high-energy muons,and data of direct measurements

A new calculation of the atmospheric fluxes of cosmic-ray hadrons and muons in the energy range 10–10⁴ GeV is performed on the basis of the method for solving nuclear-cascade equations with allowance for a nonscaling behavior of inclusive hadron-production cross sections, the growth of cross sections for inelastic hadron-nucleus collisions with increasing energy, and a non-power-law character of the primary spectrum. The fluxes of secondary cosmic rays at various levels in the atmosphere are calculated for three models of the spectrum and composition of primary cosmic rays. The effect of uncertainties in the spectrumand composition of primary cosmic rays on the flux of atmosphericmuons and their charge ratio at sea level is investigated. The calculated energy spectra of muons at sea level are compared with the results of previous experiments and the results of recent measurements performed by means of the L3 + Cosmic and CosmoALEPH spectrometers, as well as with the results of other calculations.     

Energy spectrum of primary cosmic rays at energies of 2 × 10<Superscript>13</Superscript> to 5 × 10<Superscript>17</Superscript> eV,according to Tien Shan data

The primary cosmic ray energy spectrum at energies of 10¹⁵ to 5 × 10¹⁷ eV is presented using the results from observations by the Tien Shan HADRON array. The spectrum was obtained from the spectrum of showers according to the number of electrons using a new way of determining the parameter of spatial distribution function S of electrons. The energy spectrum can be extended to low energies up to 2 × 10¹³ eV using data from separate experiments at the former Tien Shan array. Conclusions are drawn regarding changes in the form of the spectrum and its chemical composition at energies over 10¹⁶ eV. The spectrum is compared to the results from the TUNKA installation.     

The GZK horizon and constraints on the cosmic ray source spectrum from observations in the GZK regime

We discuss the GZK horizon of protons and present a method to constrain the injection spectrum of ultrahigh energy cosmic rays (UHECRs) from supposedly identified extragalactic sources. This method can be applied even when only one or two events per source are observed and is based on the analysis of the probability for a given source to populate different energy bins, depending on the actual cosmic ray injection spectral index. In particular, we show that for a typical source density of 4 × 10⁻⁵ Mpc⁻³, a data set of 100 events above 6 × 10¹⁹ eV allows one in 97% of all cases to distinguish a source spectrum dN/dE ∝ E ^−1.1 from one with E ^–2.7 at 95% confidence level. The article is published in the original.     

On the composition of cosmic rays with E 0 ≥ 1017 eV according to the Yakutsk EAS array data

The energy spectrum and anisotropy of primary cosmic rays, as well as the lateral distribution functions of electrons and muons in extensive air showers (EASs) with E ₀ ≥ 10¹⁷ eV, are presented according to the Yakutsk EAS array data. It has been shown that the spectrum and lateral distribution functions in some energy ranges have different shapes for the particles that arrive from the disc of the Supergalaxy (Local Supercluster of galaxies) and from the other part of the celestial sphere. This is interpreted as the manifestation of the interaction of extragalactic primary cosmic rays with the gas of the Supergalaxy that possibly leads to the production of new ultra-high-energy particles.     

Rising Inelastic Cross Section and its Contribution to Steepening of the Cosmic Ray Energy Spectrum

Calculations have been carried out to investigate the contribution of an increasing total cross section to steepening of the cosmic ray energy spectrum at very high energies (E ? 10¹² eV). Our results suggest that increasing total cross section contributes only a part to the steepening of primary energy spectrum at very high energies even if the composition is pure primary iron flux.     

Effect of the near-Earth electric field on the intensity of the soft component of cosmic rays

The transformation of the energy spectrum of the electron-positron component of cosmic rays in the energy range 10–100 MeV in the near-Earth electric field of thunderstorm atmosphere has been estimated analytically by solving the kinetic equation for secondary cosmic rays in the one-dimensional case. The solution obtained adequately describes the observed variations in the soft component in moderate electric fields (±7 kV m^?1).