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

Abstract

We show that the shape of the energy spectrum of electrons in an extensive air shower with an ultra-high energy (E ⩾ 1019 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., Fly's 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.

Depth of maximum of air-shower profiles at the Pierre Auger Observatory. I. Measurements at energies above1017.8 eV

“…The production yield of the former is proportional to the energy deposited by the shower particles within the volume under study, and the latter depends on the number of charged particles above the energy threshold for Cherenkov emission. Due to the universality of the energy spectra of electrons and positrons in air showers [65][66][67][68], the energy deposit and the number of particles are proportional, and therefore an exact solution for the reconstruction of the longitudinal profile of either of these quantities exists [69]. An example of a profile of the reconstructed energy deposit can be seen in Fig.…”

Influence of the scattered Cherenkov light on the width of shower images as measured in the EAS fluorescence experiments

“…We show here that due to the similarity of high energy showers [8,9,14] it is possible to calculate the lateral distribution of ChL (LDCh) without time-consuming shower simulations, but in an analytical way (with numerical calculations of integrals), using the various earlier determined electron distributions which are universal.…”

“…on the age parameter s [8]; it does not depend on primary particle mass or energy (the same conclusion was obtained by Nerling et al [10]), -the angular distribution of electrons with a fixed energy depends on this energy only -it is the same anywhere in the shower [9]; from the two statements above it follows that the angular distribution of all electrons (with any energy) depends on the shower age only, -the lateral distribution of electrons, if distances are expressed in the Molière unit r M at the level in consideration, depends on the shower age only [14] (the same holds for electrons with a fixed energy [19]). …”

“…The problem is that some fraction of shower particles (∼0.36 [8]) also emit Cherenkov light (ChL). Its direction is almost the same as that of the emitting particle velocity, so one might think that this light will not add to the fluorescence flux detected by a telescope situated at a large distance (more than a few km) from the shower.…”

Mass composition and cross-section from the shape of cosmic ray shower longitudinal profiles

“…The longitudinal profile of extensive air showers is mostly determined by the maximum number of particles reached (N max ) and the corresponding depth (X max ) and have a characteristic "universal" shape after translation to X = X − X max and normalization N = N/N max [5]. In figure 1, these transformations are exemplified for simulated samples of different primaries and energies.…”