Possible origin and spectrum of ultrahigh-energy cosmic rays

The complicated form of the cosmic-ray spectrum recorded in the energy range 10¹⁷–10²⁰ eV by giant detector arrays is analyzed. It is shown that the spectrum in the region 10¹⁸–10¹⁹ eV is apparently identical to the injection spectrum with power-law exponent approximately equal to 3.2–3.3. The flat component in the region (3.2–5)×10¹⁹ eV is due to the braking of extragalactic protons by relict photons. The spectrum apparently has no blackbody cutoff at energies above 3.2×10¹⁹ eV. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 10, 729–733 (25 May 1997)     

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 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.     

Search for anisotropy of ultrahigh-energy cosmic rays

It is shown that a statistically significant anisotropy exists in the arrival directions of cosmic rays with energies ∼1×10¹⁷ eV and 4×10¹⁸ eV. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 5, 289–292 (10 September 1997)     

Changes in the chemical composition of primary cosmic radiation at ultrahigh energies

The signals from particles of extensive air showers in the energy region of 10¹⁷–10²⁰ eV in both the surface and underground scintillation detectors of the Yakutsk array are calculated using the CORSIKA 6.616 and GEANT4 software packages and compared with experimental data. It is shown that a transition from a heavy primary composition to proton primaries at energies (1–2.6) × 10¹⁸ eV and from primary protons again to heavy primaries at energies above 1.3 × 10¹⁹ eV might be observed.     

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.     

Identification of extragalactic cosmic-ray sources using data from various detection facilities

Showers with energies E>3.2×10¹⁹ eV and E≥10²⁰ eV detected at the AGASA (Akeno, Japan), Haverah Park, and Yakutsk arrays are investigated. The question of how the identification of sources depends on the error in determining the shower arrival directions is analyzed. Confirmation is obtained for the conclusion in the author’s earlier work, that the principal sources of shower-driven particles are Seyfert galaxies with red shifts z≤0.0092, which are weak emitters in the x-ray and radio ranges. Zh. éksp. Teor. Fiz. 116, 1121–1130 (October 1999)     

Determining the primary cosmic ray energy from the total flux of Cherenkov light measured at the Yakutsk EAS array

We present a method for determining the energy of the primary particle that generates an extensive air shower (EAS) of comic rays based on measuring the total flux of Cherenkov light from the shower. Applying this method to Cherenkov light measurements at the Yakutsk EAS array has allowed us to construct the cosmic ray energy spectrum in the range 10¹⁵ ? 3 × 10¹⁹ eV.     

Nonlinear Thomson scattering of an ultrashort laser pulse

The nonlinear scattering of an ultrashort laser pulse by free electrons is considered. The pulse is described in the “Mexican hat” wavelet basis. The equation of motion for a charged particle in the field of a plane electromagnetic wave has an exact solution allowing, together with the instant spectrum approximation, the calculation of the intensity of nonlinear Thomson scattering for a high-intensity laser pulse. The spectral distribution of scattered radiation for the entire pulse duration is found by integrating with respect to time. The maximum of the emission spectrum of a free electron calculated in 10¹⁹–10²¹ W/cm² fields lies in the UV spectral region between 3 and 12 eV. A part of the continuous spectrum achieves high photon energies. One percent of the scattered energy for the field intensity 10²⁰ W/cm² is concentrated in the range ħω > 2.7 × 10² eV, for a field intensity of 10²¹ W/cm² in the range ħΩ > 7.9 × 10² eV, and for an intensity of 10²² W/cm² in the range ħΩ > 2.45 × 10⁵ eV. These results allow us to estimate nonlinear scattering as a source of hard X-rays.     

Peculiarities of the anisotropy of cosmic rays with E0 ≥ 1019 eV from Yakutsk EAS array data

The arrival directions of primary cosmic ray particles with energies E ₀ ≥ 10¹⁹ eV and zenith angles θ ≤ 60° recorded on the Yakutsk array over the period 1974–2009 are analyzed. These events separated by different time intervals are shown to have different global anisotropies.     

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.     

Energetic neutrons and gamma rays measured on the Aryabhata satellite

An experiment to measure energetic neutrons and gamma rays in space was launched in the first Indian scientific satellite,Aryobhata, on April 19, 1975. From this experiment, the first measurements in space of the Earth’s albedo fiux of neutrons of energy between 20 and 500 MeV have been made; the values obtained for two mean geomagnetic vertical cut-off rigidities of 5.6 and 17.0 GV are (6.3±0.4)×10⁻² and (1.4±0.3)×10⁻² neutrons cm⁻² sec⁻¹ respectively. These measurements confirm that protons arising from cosmic ray albedo neutron decay, can adequately account for the protons in the inner radiation belt. Observations on gamma rays of energy between 0.2 and 24 MeV have enabled the determination of the total background gamma ray flux in space as a function of latitude. This in turn has permitted useful information on the diffuse cosmic gamma rays. We have also observed four events that showed sudden increases in the gamma ray counting rates between 0.2 and 4.0 MeV. Observational details of these events are given.     

Local anisotropy of cosmic rays with <Emphasis Type="Italic">E</Emphasis><Subscript>0</Subscript> ≥ 10<Superscript>17</Superscript> eV from Yakutsk EAS array data

The arrival directions of primary cosmic ray particles with energies E ₀ ≥ 10¹⁷ eV and zenith angles θ ≤ 60° recorded on the Yakutsk array over the period 1974–2009 are analyzed. These events are shown to have different anisotropies in different energy ranges.     

Origin of cosmic rays

Cosmic rays were discovered in 1911 but it is only now that some ideas are beginning to emerge as to their origin. This paper will examine the present evidence concerning the origin question over the whole energy range, from 10⁹ eV to 10²⁰ eV. At the lowest energies, (10⁹–10¹⁰ eV), the new subject of gamma ray astronomy plays a crucial role and a galactic origin is favoured. At higher energies (10¹²–10¹⁷ eV) recent measurements of the anisotropies in arrival directions also suggest a galactic origin, although the evidence is not as strong. At the very highest energies it seems likely that some, at least, of the particles come from outside the galaxy although the non-existence of the cut-off at about 6 × 10¹⁹ eV arising from interactions with the cosmological relict radiation provides a paradox. The likely future areas of advance in this fascinating subject will be indicated. Based on the B. B. Roy memorial lectures delivered at Calcutta University, February 1–3, 1978.     

Generation of 1015–1017 eV photons by ultrahigh-energy cosmic rays in the Galactic magnetic field

It is shown that the expected dip in the diffuse photon spectrum above the threshold of e ⁺ e ⁻ pair production, i.e., at energies 10¹⁵–10¹⁷ eV, may be absent due to the synchrotron radiation by the electron component of the extragalactic ultrahigh-energy cosmic rays (UHE CRs) in the Galactic magnetic field. The mechanism we propose requires small (<2×10⁻¹² G) extragalactic magnetic fields and a large photon fraction in the UHE CRs. For a typical photon flux expected in top-down scenarios of UHE CRs, the predicted flux in the region of the dip is close to the existing experimental limit. The sensitivity of our mechanism to the extragalactic magnetic field may be used to improve existing bounds on the latter by two orders of magnitude. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 8, 487–492 (25 October 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Significance of the second dip in the ultra-high energy cosmic ray spectrum

A new feature in the spectrum of ultra high energy cosmic rays (UHECR) has been announced in the paper by Berezinsky, Gazizov and Kachelrieβ. The ratio of the solution of the exact transport equation to its solution in the continuous energy loss limit shows intriguing features which, according to the Authors, are related to the very nature of the energy loss processes of UHECR: the very sharp second dip predicted at 6.3 × 10¹⁹ eV can be used as an energy calibration point and also as the UHECR mass indicator for big future cosmic ray experiments. In the present paper we would like to advocate that this statement is an overinterpretation. The second dip is a result of an inappropriate approximation used, and thus it cannot help to understand the nature of UHECR in any way.      

Ultrahigh-energy cosmic rays, superheavy long-lived particles, and matter creation after inflation

Cosmic rays of the highest energy, above the Greisen-Zatsepin-Kuzmin (GZK) cutoff of the spectrum, may originate in decays of superheavy long-lived particles. We conjecture that these particles may be produced naturally in the early Universe from vacuum fluctuations during inflation and may constitute a considerable fraction of cold dark matter. We predict a new cutoff in the ultrahigh-energy cosmic ray spectrum E _cutoff<m _inflaton≈10¹³ GeV, the exact position of the cutoff and the shape of the cosmic ray spectrum beyond the GZK cutoff being determined by the QCD quark/gluon fragmentation. The Pierre Auger Project installation may in principle observe this phenomenon. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 4, 255–259 (25 August 1998)     

Atmospheric gamma rays in the energy region 40–1000 GeV

A large stack of lead-emulsion sandwich detector assembly was flown over Hyderabad, India. High energy gamma rays at the float altitude were unambiguously identified from the cascades they induced, and their energies reliably determined by improved methods. From an analysis of 163 gamma rays of energy ≳ 30 GeV, it is found that the differential energy spectrum is represented by the power lawJ _r (E)= 129·4E ^{−2·62±0·12} photons m⁻² sr⁻¹sec⁻¹ GeV⁻¹ at an effective atmospheric depth of 14·3 g cm⁻²; this is the first reliable balloon measurement of atmospheric gamma rays in the energy range 40–1000 GeV. After correcting for the gamma rays radiated by the primary cosmic ray electrons, the production spectrum of gamma rays, resulting from the collisions of cosmic ray nuclei with air nuclei, at the top of the atmosphere isP _r (E, 0)=8·2 × 10⁻⁴ E^2.60±0.09 photons g⁻¹sr⁻¹sec⁻¹ GeV⁻¹. The atmospheric propagation of the electromagnetic component due to the cascade process is also derived from the gamma ray production spectrum.     

Model of cosmic ray generation

It is shown that the two bends observed in the cosmic ray energy spectrum can be well approximated by equations derived by assuming that cosmic rays can be generated and accelerated in plasma pinches. Zh. éksp. Teor. Fiz. 111, 385–403 (February 1997)     

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)