G. F. Fedorova

Upper limit on the ultrahigh-energy photon flux from AGASA and Yakutsk data

We present the interpretation of the muon and scintillation signals of ultrahigh-energy air showers observed by AGASA and Yakutsk extensive air shower array experiments. We consider case-by-case ten highest-energy events with known muon content and conclude that at the 95% confidence level none of them was induced by a primary photon. Taking into account statistical fluctuations and differences in the energy estimation of proton and photon primaries, we derive an upper limit of 36% at a 95% confidence level on the fraction of primary photons in the cosmic-ray flux above 10{sup 20} eV. This result disfavors the Z-burst and superheavy dark-matter solutions to the Greisen-Zatsepin-Kuzmin-cutoff problem.

Test of Lorentz invariance through observation of the longitudinal development of ultrahigh-energy extensive air showers

An idea that Lorentz invariance can be violated was proposed by Coleman and Glashow to overcome the astrophysical problems of air showers of ultrahigh energies E>1020 eV. This statement can be tested by analyzing experimental data on these showers. The longitudinal development of showers and the distribution of the depths of shower maxima were calculated in the model of quark-gluon strings with allowance made for the Landau-Pomeranchuk-Migdal effect and the interactions of ultrahigh-energy neutral pions. Comparison of the calculations with available experimental data provides a new bound |cγ−cπ°| <0−20 for the possible difference between the speeds of photons and neutral pions. This bound becomes |cγ−cπ°|<10−22 when one takes the upper limiting value for the observed depth of maximum.

Estimation of the attenuation length of the charged particle density at 600 meters from the shower axis

Abstract The observations of the giant air showers with energies well in excess of 10 20 eV put forward a very dramatic puzzle to cosmic ray astrophysics. Billions of secondary particles produced in interactions with the atomic nuclei and decay processes in the atmosphere are spread out to distances of about a few kilometers from the shower axis at ground level. The density of charged particles at 600 m from the shower axis is used as a reliable estimator of the energy of individual showers. As giant showers are assumed to be isotropic, one needs the attenuation length of a signal in a standard scintillator at 600 m from the shower axis to recalculate the signal observed in a vertical direction. This attenuation length usually was estimated indirectly by taking cuts of constant intensity in signal spectra for showers detected at different zenith angles. The reliability of such a procedure for the total number of secondary particles was analyzed. As for the signal at 600 m this reliability is investigated in this paper. Besides, some new methods are also discussed. The first one is related to the longitudinal development of a signal and the second to calculations of signals both for vertical and inclined showers with the same energy. Calculations were carried out in terms of the quark-gluon string model for primary protons and an observation level of 1020xa0g/cm 2 for showers with various zenith angles. The Landau–Pomeranchuk–Migdal effect and neutral pions interactions are taken into account at high energies. The Monte Carlo method was used for primary protons while cascades from numerous charged pions were considered with the help of transport equations. Nearly 10 5 showers were simulated with various energies and zenith angles using a cluster of computers. Then signal spectra were calculated assuming the standard energy spectrum of the primary particles. Finally taking cuts of the signal spectra one can obtain the reconstructed development curve for a signal and estimate the attenuation length. The longitudinal development of a signal was calculated to estimate the attenuation length in the individual showers. The applicability of the second method is straightforward. As a result the value of 530±60xa0g/cm 2 was estimated for the attenuation length by the constant intensity cuts method which should be compared with 520±70xa0g/cm 2 found experimentally. The dependence of this calculated attenuation length on the primary particle energy agrees roughly with the experimental data excepting very inclined showers. The dependence on the zenith angle is also shown. The increase of the attenuation length with the zenith angle agrees with enlarging of the muon content of the charged particle density. The longitudinal development gives a very broad distribution of the attenuation length changing from ∼300 to 3000 g/cm 2 , while calculations for vertical and inclined showers lead to various attenuation lengths distributed mainly between 450÷ 550xa0g/cm 2 excepting nearly vertical showers for which the range of distributions is elongated above 3000 g/cm 2 . So the standard method of the constant intensity cuts may decrease (or increase) energy estimates of showers by a factor of 1.1–2.

Estimates of arrival directions of giant air showers

The arrival directions of giant air showers generated in the atmosphere by the primary cosmic ray particles with energies above ∼5 · 10 19 eV may be connected with possible extragalactic sources, because the Larmor radius of such particles is too large. Besides it was suggested that the primary particles with enormous energies may be neutrons. In this case it is possible to avoid the energy loss in interactions with the microwave background radiation and arrival directions will strongly point to sources. Thus it is of primary importance to decrease possible errors in the estimates of arrival directions of giant air showers. To estimate the arrival direction of a giant air shower one has to have any model of its space–time structure. The simplest model of the shower time front is a model of the flat front when all particles are located in this front plane. It was shown that possible errors in estimates of the zenith and azimuth angles which characterize the arrival directions may be as large as 5 ◦ or even more. The χ 2 method gives very large values of χ 2 . That means that this model is inconsistent with the data. A much more realistic model of a shower time front was suggested by Linsley. Calculations displayed that both the shower disk thickness and the average time delay depend on the energy of the primary particles. So the calculated time front of the shower for both electrons and muons may fit the data and thus provides better accuracy. The standard mathematical procedure to interpret data is the χ 2 method. This method leads to reasonable estimates of the zenith and azimuth angles with uncertainties of 2÷3 ◦ . In some cases the minimax procedure may be utilized to interpret data. It was shown that the possible error in estimates of the zenith and azimuth angles may be decreased up to 0.5 ◦ . At last the fuzzy uncertain variables and the possibility theory are suggested here to be used for interpreting the data. Calculations were carried out in terms of the quark-gluon string model for primary protons and an observation level of 1020 g/cm. The Landau–Pomeranchuk–Migdal effect and interactions of neutral pions with nuclei in the atmosphere at high energies are taken into account. The Monte Carlo method was used for primary protons while cascades from numerous charged pions were considered with the help of cascade equations. Though experimental statistics is very low no evidence is found to prefer any directions. Thus the isotropic distribution of the arrival directions of giant air showers with

Separation of muons in the giant air showers by the geomagnetic field

Abstract The observation of giant air showers with energies above ∼10 20 xa0eV is extremely interesting for elementary particle physics and astrophysics. The giant air shower is a cascade of secondary particles (mainly electrons and muons) generated in the atmosphere by an ultrahigh energy (>10 19 xa0eV) primary cosmic ray particle. The density of electrons and muons at a fixed distance from the shower axis (primary particle direction of motion) is usually used as shower energy estimator. The shower arrival direction is estimated with the help of the shower time front of the muons detected. Deflections of muons by the geomagnetic field are noticeable. These deflections perturb not only the energy estimator but also the time delays of the muons detected. Billions of muons diverging from the shower axis are deflected by the geomagnetic field. Because muons are produced at different depths in the atmosphere and with various energies and directions of motion it is a problem to simulate their trajectories. Calculations were carried out in terms of the quark–gluon string model for primary protons and an observation level of 1020xa0g/cm 2 for inclined showers. Interactions of neutral pions with nuclei in the atmosphere at ultrahigh energies were taken into account. The interactions of the primary particle with the nuclei in the atmosphere were simulated by the Monte Carlo method. The passing of secondary hadrons was treated with the help of the cascade equations. Muons were grouped into blocks with some differences in depth production, zenith and azimuth angles and energy. For every “block” of muons a relativistic equation of motion with ionization losses taken into account was solved as for a single muon with average energy, height production and zenith and azimuth angles in each bin (a method of “group” particle). The calculated lateral distribution of muons displays noticeable asymmetry at all distances from the shower axis and particularly the energy estimator changes by a factor ofxa01.5. Due to deflection in the geomagnetic field the arrival time of the detected muons increases by tens of ns disturbing the shower time front. Thus it is important to treat experimental data on giant air showers taking into account the geomagnetic field.

Pions in primary cosmic rays of ultrahigh energies

In the framework of the Coleman-Glashow hypothesis of an extremely weak violation of Lorentz invariance, neutral and charged pions can be stable for energies above 1019 eV and enter into the composition of primary cosmic rays of ultrahigh energies. The kinematic exclusion of reactions of pions with relic photons is particularly important, because it allows the Greisen-Zatsepin-Kuzmin paradox to be resolved. The parameters of extensive air showers induced by primary pions calculated within the model of quark-gluon strings with allowance for the Landau-Pomeranchuk-Migdal effect and interactions of neutral pions of ultrahigh energies are not contradictory to the available data of observations. It has been shown that observations of production heights of muons with energies above 10GeV will make it possible to distinguish between primary nuclei, protons, and pions; to verify Lorentz invariance for energies above 1020 eV; and to obtain a new limit on the difference between the maximum possible velocities of muons and pions (cµ−cπ)<4×10−26.

Methods for estimating the energy of extensive air showers

A multilevel scheme for calculating estimates of the energy of extensive air showers on the basis of signals in different detectors is considered. The numerical energy estimates at specified values of signals in scintillation detectors are smaller than the experimental ones by a factor of about 1.6. The results of the calculation confirmed that the total flux of Cherenkov light is proportional to the shower energy. The flux of fluorescent light generated within 100 m from the shower core is due to only 60% of the total energy.

Longitudinal development of giant air showers and problem of estimating the energy of primary-cosmic-ray particles

The attenuation length for the charged-particle density at a distance of 600 m from the shower axis may differ from that adopted in experimental investigations by 40–50%. This casts some doubt on experimental estimates previously obtained for the energy of primary-cosmic-ray particles in the region of ultrahigh energies.