Time characteristics of electron, muon, and Cherenkov photon fronts in giant air showers

Abstract

Calculations of the space-time structure of giant air showers in the energy range ${10}^{17}--{10}^{21} \mathrm{eV}$ carried out in the framework of the quark-gluon string model show the existence of three separate disks (or better lenses) of muons, Cherenkov photons, and electrons which follow each other. In a shower with an energy of ${10}^{19} \mathrm{eV}$ time delays at 1000 m from the shower core can be as large as 420, 450, and 1120 ns for muons, Cherenkov photons, and electrons, respectively, while the disk thickness for these three components can reach the values of 500, 680, and 1160 ns, respectively. At larger core distances the time delay and disk thickness may exceed a few $\ensuremath{\mu}\mathrm{s}$ and should be taken into account both in designing the new array electronics and interpreting the experimental data. Highly inclined showers which consist mainly of muons display a much flatter front: time delay decreases down to about 110 ns at a distance of 1000 m from the shower core. Approximations of the time parameters dependence on the primary energy and core distance are presented. The measurements of electron, muon, and Cherenkov photon time pulses are suggested to improve the estimations of the arrival direction and the energy of the showers and also to study the primary particle composition and parameters of hadron interactions at energies above ${10}^{19} \mathrm{eV}.$