G. Wieczorek

Energy spectra of electrons in the extensive air showers of ultra-high energy

We show that the shape of the energy spectrum of electrons in an extensive air shower with an ultra-high energy (E ≥ 10 19 eV) at a given level in the atmosphere depends only on the shower age at this level. It depends practically neither on the primary particle mass nor on its energy. This fact considerably simplifies interpretation of data from the experiments (e.g., Flys Eye, HiRes and Auger) determining cascade curves of single showers by the fluorescence technique. In particular, the contribution of the scattered Cherenkov light to the total flux produced by a shower can be easily taken into account. Our conclusion has been drawn by analysing results of Monte Carlo simulations of showers with the CORSIKA (Heck et al 1998 Report FZKA 6019) program, using the QGSJet interaction model.

Similarity of extensive air showers with respect to the shower age

Using CORSIKA simulations of the highest energy extensive air showers we show that all showers are similar when described by the shower age parameter: the angular and energy spectra of electrons at a given level in the atmosphere depend only on the shower age at this level. Moreover, electrons with a given energy have the same angular distributions at any level (age) of the shower. We have calculated these distributions and found analytical functions describing them quite well. The total number of particles can also be described in a simple way as a function of age by two halves of a Gaussian function with the widths, however, fluctuating from one shower to another. The description of large showers in terms of age (instead of depth in the atmosphere) is very useful in interpreting data from experiments observing fluorescence light, with admixture of Cherenkov, induced by the showers in the air.

EXTENSIVE AIR SHOWER CHARACTERISTICS AS FUNCTIONS OF SHOWER AGE

We show that extensive air showers (EAS) are all very similar when described by shower age and Moliere length unit. This allows to analyze fluorescence and Cherenkov light emitted by showers in a unified and simple way.

On possibilities of the fluorescence detector to measure the shower light curve

A method to determine the primary energy of very rare big extensive air showers is to measure the fluorescence light flashes induced by them in the atmosphere. From a shower fluorescence image (and its time dependence) it is, in principle, possible to reconstruct the shower cascade curve. The Pierre Auger experiment (in construction) has been using this method (together with measuring the shower charged particles as well) to determine the highest energy part of the cosmic ray spectrum (E J 10 19 eV) and particle arrival directions. Here we analyse which shower parameters affect its image, and, if not taken into account in the reconstruction procedure, may lead to systematic errors in determining its light (cascade) curve, and in consequence, the energy and/or mass of the primary particle. In particular, we analyse the lateral distribution of particles, the thickness and curvature of the shower disk, together with the spherical aberration of the collecting mirror. We show that a non-negligible part of the light flux for showers closer than � 15 km to the detector may be hidden in the non-triggered pixels of the camera. For more distant showers this effect is small, but then the atmospheric attenuation has to be known better. We also derive an analytical solution for a spherical mirror focal plane position and the minimal size of the image (spot size) of a parallel light beam. � 2002 Elsevier Science B.V. All rights reserved.

An extended universality of electron distributions in cosmic ray showers of high energies and its application

Abstract It is shown that the shape of any electron distribution in a high energy air shower is the same in all such showers, if taken at the same age, independently of the primary energy, mass and thus, of the interaction model. A universal behaviour has been also found within a single shower, such that the lateral distributions of electrons with fixed energies, at various shower ages, can be described by a single function of only one variable. The angular distributions of electrons with a fixed energy can be represented, at a given lateral distance, by a function of the product θ · E α only, which is explained by a model of small angle electron scattering with simplified energy losses. These results have been obtained by Monte Carlo simulations of the extensive air showers. The electron universality can be used as a method for determining the longitudinal profile of any single shower from its optical images measured by the fluorescence light technique, which is particularly useful with showers observed with large fraction of the Cherenkov light.