Similarity of extensive air showers with respect to the shower age

Abstract

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.

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

“…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]). …”

“…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.…”

“…The angular distribution G e θ (θ; s, h) (per unit angle θ) can be calculated from the known angular distributions of electrons with fixed energies, g θ (θ; E) (per unit solid angle) [9], and the energy spectrum of all electrons at level s, f (E; s) [8,10],…”

“…This effect has been first aknowledged and allowed for by the Fly's Eye Collaboration [4]. Later some other methods to take it into account have been proposed [9][10][11]. In these papers, however, it was only the total number of Ch photons emitted from consecutive shower track elements that were taken into consideration.…”

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

“…Studies have shown that two extra parameters are needed for the full description of the general profiles, but there can be strong correlations between them [6,7]. A widely use, successful parametrization is the GaisserHillas profile [8], which can be written in terms of the new variables, X , N , as follows:…”