Universality of electron distributions in high-energy air showers—Description of Cherenkov light production

Abstract

The shower simulation code CORSIKA has been used to investigate the electron energy and angular distributions in high-energy showers. Based on the universality of both distributions, we develop an analytical description of Cherenkov light emission in extensive air showers, which provides the total number and angular distribution of photons. The parameterisation can be used e.g. to calculate the contribution of direct and scattered Cherenkov light to shower profiles measured with the air fluorescence technique.

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]). …”

“…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.…”

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.…”

“…1c. The Cherenkov light production is calculated following [67] and for the fluorescence-light emission along the shower we use the precise laboratory measurements of the fluorescence yield from [70,71].…”