Characteristics of air showers produced by extremely high energy gamma-rays

Abstract

The technique of adjoint cascade equations has been applied to calculate the properties of air showers produced by extremely high energy (EHE) γ-rays in the energy range 1018–1022 eV. The high intrinsic accuracy, combined with very modest (compared with the traditional Monte Carlo codes) computational time requirements, make this method as an effective tool for the detailed study of development of EHE showers in the Earth's atmosphere. In this paper a wide range of parameters of γ-ray-induced showers are analysed taking into account two independent effects which become crucial for the cascade development in the EHE regime—the Landau–Pomeranchuk–Migdal (LPM) effect and the interaction of primary γ-rays with the geomagnetic field (GMF). Although the LPM effect leads to dramatic modifications of shower characteristics, especially at primary energies exceeding 1019 eV, the GMF effect, which starts to ‘work’ at approximately the same energies, prevents, to a large extent, the LPM effect by converting the primary γ-ray into a bunch of synchrotron γ-ray photons with energies effectively below the threshold of the LPM effect. This bunch of secondary photons hits the atmosphere and creates a large number of simultaneous showers. The superposition of these independent showers mimics a single shower with energy E = ∑Ei ≃ E0, but without the signatures of the LPM effect. This makes the longitudinal profile of such a composite electromagnetic shower quite similar to the longitudinal profile of hadronic showers. At the same time, the number of muons as well as their lateral distribution differ significantly from the corresponding parameters of proton-induced showers. In the ‘gamma-ray bunch’ regime, the total number of muons is less, by a factor of 5–10, than the number of muons in hadronic showers. Also, compared with the hadronic showers, the electromagnetic showers are characterized by a significantly narrower lateral distribution of muons. Even so, for inclined EHE γ-ray showers the density of muon flux at large distances from the shower core (≥1000 m) can exceed the electron density.