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 similar to5 (.) 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 5degrees or even more. The chi(2) method gives very large values of chi(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 chi(2) method. This method leads to reasonable estimates of the zenith and azimuth angles with uncertainties of 2divided by3degrees. 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 0.5degrees. 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 energies above 10(19) eV seems to fit the data. (C) 2002 Elsevier Science B.V. All rights reserved.