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 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.     

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.     

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.     

Efficiency of the production of γ families with halos and the fraction of protons at an energy of 10<Superscript>16</Superscript> eV

γ Families with halos detected in the “Pamir” experiment have been analyzed. Comparison of the experimental data with the results of calculation within the quark-gluon string model (MC0 code) made it possible to determine the efficiency of halo formation by protons, α particles, and heavy nuclei, as well as the fraction of protons in the mass composition of primary cosmic rays at an energy of 10¹⁶ eV. It is shown that halos are formed predominantly by protons. The fraction of protons in the mass composition of primary cosmic rays at an energy of 10¹⁶ eV is 20%.     

About the character of the “Knee” at E⋍3×1015 eV in the energy spectrum and the mass composition of primary cosmic rays in the energy range 1015–1017 eV

The method of rescaling from the muon-multiplicity spectrum to the extensive-air-shower spectrum as a function of the total muon number n _μ is presented. The method allows a direct comparison of data obtained in different experiments with muon groups. A direct comparison of data at n _μ>1800 and n _μ=76–660 has been performed. The data in the region n _μ=75–3500 agree better with the assumption that the slope change in the energy spectrum of primary cosmic rays occurs approximately at the same energy per nucleus, E _c=3×10¹⁵ eV, and the mass composition in the energy range 10¹⁵–10¹⁷ eV is close to that observed at 10¹⁴ eV.     

Study of the energy spectrum and mass composition of primary cosmic rays in the energy range of 10<Superscript>18</Superscript>–10<Superscript>20</Superscript> eV using a balloon setup in antarctica (SPHERE-antarctica project)

An Antarctic balloon experiment for measuring the energy spectrum and elemental composition of cosmic rays in the ultrahigh-energy range (10¹⁸–10²⁰) eV is proposed. Scientific equipment will measure fluorescence caused by an extensive air shower formed in the atmosphere by an ultrahigh energy particle and Cherenkov light of this shower reflected from a snow surface. It is assumed that the balloon will fly in the circumpolar orbit in Antarctica at a height of ~25 km for (2–3) winter (in the Southern Hemisphere)months. For this time, ~3000 events caused by particles with energies above 10¹⁸ eV and (200–300) events caused by particles with energies above 10¹⁹ eV will be detected.     

Composition of cosmic rays accelerated in supernova remnants

The kinetic theory of regular acceleration of cosmic rays in supernova remnants is used to investigate the expected chemical composition of the rays. It is shown that the shapes of the calculated profiles of the chemical elements making up the cosmic rays are consistent with experiment wherever the results of measurements are available. The acceleration process is accompanied by relative enrichment of the cosmic rays with heavy elements. If the analogous property of the mechanism underlying the injection of superthermal particles into the acceleration regime is taken into account, such enrichment supports the formation of the required composition of cosmic rays in the energy range up to 10¹⁴–10¹⁵ eV. Zh. éksp. Teor. Fiz. 116, 737–759 (September 1999)     

Hybrid method for detecting cascades produced by ultrahigh-energy cosmic particles using a circumlunar satellite

A hybrid method for detecting cosmic rays and neutrino cascades using the radio method and the conventional method for detecting cascade particles was proposed. Cascades produced in the lunar soil near the surface by ultrahigh-energy cosmic rays and neutrinos in the energy range of 1 GeV–100 TeV, coming from above at different angles, were calculated. The calculated energy and angular distributions were extrapolated to the energy region of 10²⁰ eV. Using these results, the detection threshold was estimated as 10²⁰ eV which is approximately identical to the threshold for the radio detector previously considered by the authors.     

Mass content of ultrahigh-energy cosmic rays within different time periods

Estimates obtained for the average atomic number 〈lnA〉 of nuclei of primary particles with energies in the region of E ₀ ? 10¹⁵ eV over the past 36 years at the Yakutsk array and other arrays worldwide for studying extensive air showers are presented. It is shown that these estimates are markedly different with in different time periods. Earlier than 1996, the composition of cosmic rays in the energy range of 5 × 10¹⁵–10¹⁸ eV was markedly lighter than in later years. After 2008, there appeared a trend toward a decrease in 〈lnA〉. This is likely to be a manifestation of some explosive process in the Milky Way Galaxy after 1996.     

Description of gamma-hadron families on the basis of the quasiscaling model for a normal nuclear composition of primary cosmic rays

The nuclear composition of primary cosmic rays is investigated in the energy range 10¹⁵–10¹⁶ eV. These investigations are performed by comparing the properties of the gamma-hadron families observed by the Pamir and the Pamir-Chacaltaya collaborations with the properties of families generated on the basis of the MC0 quasiscaling model for various nuclear compositions. It is shown that all properties of experimental families are in good agreement with the predictions of the MC0 model for a normal nuclear composition, but that these experimental results are at odds with the results of the calculations that assume a nuclear composition enriched in heavy nuclei.     

Investigation of the properties of the flux and interaction of ultrahigh-energy cosmic rays by the method of local-muon-density spectra

A new method for studying extensive air showers is considered. The method is based on the phenomenology of the localmuon density. It is shown that measurement ofmuon-density spectra at various zenith angles makes it possible to obtain information about the energy spectrum, mass composition, and interaction of cosmic rays over a broad range of energies (10¹⁵–10¹⁸ eV) by using a single array of comparatively small size. The results obtained from a comparison of experimental data on muon bundles from the DECOR coordinate detector with the results of simulation performed under various assumptions on the properties of the primary flux and for various hadron-interaction models are presented, and possible versions of the interpretation of these results are discussed.     

Modernization of the Carpet-2 array of the Baksan Neutrino Observatory

The state of the art and the project of modernization of the extensive-air-shower array Carpet-2 of the Baksan Neutrino Observatory of the Institute for Nuclear Research, Russian Academy of Sciences are described. The modernized array will allow the performance of detailed study of variations in the cosmic ray intensity, the energy spectra and composition of primary cosmic rays in the energy range 10¹³–10¹⁶ eV, and the anisotropy of primary cosmic rays with energies above 10¹³ eV.     

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.     

Fraction of protons in primary cosmic rays according to data from the PAMIR experiment in consideration of the response of X-ray emulsion chambers

Adjusted data on the fraction of protons in the mass composition of primary cosmic rays (PCRs) in the energy range of 10¹⁵–10¹⁷ eV are presented. Adjustments are made according to detailed calculations of the response of the X-ray emulsion chamber in the PAMIR experiment. It is demonstrated that the fraction of protons in a PCR is 16–18% for E ₀ ≈ 10¹⁵–10¹⁶ eV and does not change within the error for E ₀ ≈ 10¹⁶–10¹⁷ eV.     

The surfatron acceleration of cosmic rays in the galactic plasma

The optimum conditions for a prolonged holding of charged particles resonantly trapped from the galactic plasma by nonlinear waves and for the acceleration of these particles to high energies by the surfatron mechanism are established. The density of particles trapped by the plasma waves of large amplitude and by the quasitransverse magnetosonic shock waves is estimated. Various reasons leading to possible breakage of the process of surfatron acceleration of cosmic rays in the Galaxy are considered. Within the framework of the surfatron acceleration mechanism, galactic cosmic rays originate predominantly from the interstellar plasma and their energy spectrum is formed in two stages. In the first stage, some of the galactic plasma particles are accelerated from thermal energies to 10¹⁵ eV/nucleon; in the second stage, the cosmic rays may continue gaining energy up to 10¹⁹ eV/nucleon and above.     

Modeling Source Spectra and Composition of Ultrahigh Energy Cosmic Rays

The inverse problem of cosmic ray transport of ultra-high energy cosmic rays is considered. The source spectrum and composition are derived based on the recent Auger data on energy spectrum, energy dependence of mean logarithm of atomic mass number and its variance. The dependence of results on the extrapolation of observable spectrum beyond energies 10²⁰ eV is investigated.

     

Cosmic rays from the knee to the highest energies

This review summarizes recent developments in the understanding of high-energy cosmic rays. It focuses on galactic and presumably extragalactic particles in the energy range from the knee (10¹⁵ eV ) up to the highest energies observed (>10²⁰ eV). Emphasis is put on observational results, their interpretation, and the global picture of cosmic rays that has emerged during the last decade.